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` Track Stability Management Track Stability Management DOCUMENT CONTROL SHEET Document: Title: Track Stability Management: Development of Rail-Temperature Prediction Model and Software CRC for Rail Innovation Floor 23, HSBC Building Brisbane Qld 4000 Project Leader: Nirmal Mandal GPO Box 1422 Brisbane Qld 4001 Authors: Ying Min Wu Associate Professor Mohammad Rasul Professor Masud Khan Tel: +61 7 3221 2536 Fax: +61 7 3235 2987 Reviewers Professor Colin Cole (Program Leader, CQUniversity) John Powell (Project Chair), QR www.railcrc.net.au Project No: R3.112 Project Name: Track Stability Management Synopsis: The main goal of this study was to develop a model and software to accurately predict rail-track temperatures 24 hours in advance, in order to provide data that can be used in managing rail buckling. Three major tasks were undertaken to achieve this goal: designing field experimentation and procedures; developing a multivariate regression model of rail-track temperatures; and verifying the regression model against measured rail temperatures. The researchers concluded that Australian Bureau of Meteorology NWP ACCESS-A* data can be used to accurately predict rail temperatures 24 to 48 hours in advance, using a software code developed in MATLAB. Data produced in this way could give rail-industry operators at least one day’s advance notice of when rail temperatures may become critical. This has the potential to deliver substantial benefits to operators and their customers. * Numerical weather prediction Australian Community Climate and Earth-System Simulator REVISION/CHECKING HISTORY REVISION NUMBER 0 DATE ACADEMIC REVIEW (PROGRAM LEADER) INDUSTRY REVIEW (PROJECT CHAIR) APPROVAL (RESEARCH DIRECTOR) DISTRIBUTION REVISION DESTINATION 0 1 2 3 4 5 6 7 8 9 10 Industry Participant for Review CRC for Rail Innovation 9 August 2011 Page 1 Track Stability Management Established and supported under the Australian Government’s Cooperative Research Centres Programme Copyright © 2012 This work is copyright. Apart from any use permitted under the Copyright Act 1968, no part may be reproduced by any process, nor may any other exclusive right be exercised, without the permission of Central Queensland University. CRC for Rail Innovation 9 August 2011 Page 2 Track Stability Management Table of Contents Abbreviations and Acronyms ................................................................................................................... v Executive Summary ................................................................................................................................. vi 1. Introduction .......................................................................................................................... 1 1.1 Background and Significance .............................................................................................................. 1 1.2 Objectives ........................................................................................................................................... 2 1.3 Scope and Limitations of the Study .................................................................................................... 2 1.4 Outline of Chapters ............................................................................................................................ 3 2 Literature Review .................................................................................................................................. 4 2.1 Methods for Predicting Weather Conditions ..................................................................................... 4 2.1.1 Predicting Solar Irradiance—Empirical Methods ....................................................................... 4 2.1.2 Spatial and Time Scales of Weather Forecasts ........................................................................... 6 2.1.3 Forecasting Methods ................................................................................................................. 7 2.1.4 NWP Forecasting Procedure .................................................................................................... 10 2.1.5 Australian Community Climate and Earth-System Simulator (ACCESS) Model ......................... 11 2.1.6 ACCESS Products Particulars .................................................................................................... 12 2.1.7 ACCESS-A and Surface-weather Element Verification .............................................................. 12 2.2 Effect of Temperature Change on Buckling ...................................................................................... 14 2.2.1 Minimum Potential Energy Buckling Theory ............................................................................ 14 2.2.2 Three-dimensional Modelling of Forces due to Temperature Fluctuation ............................... 16 2.3 Surface and Internal Temperature of the Rail .................................................................................. 19 2.4 Frictional Heat Generation ............................................................................................................... 21 2.4.1 Curved Track Heat Addition Due to Friction ............................................................................ 21 2.4.2 Tangent Track Heat Addition Due to Friction ........................................................................... 23 2.5 Existing Rail-temperature Models .................................................................................................... 24 2.5.1 Empirical Relationships ........................................................................................................... 24 2.5.2 RSSB UK Rail-temperature Model ........................................................................................... 27 2.5.3 FRA Rail-temperature Model................................................................................................... 32 2.6 Concluding Remarks on Existing Rail-temperature Prediction ......................................................... 35 3. Research Methodology ....................................................................................................... 36 3.1 Weather Predictions......................................................................................................................... 36 3.1.1 Tasks Involved in Producing a Downscaled Weather Forecast ................................................. 36 3.1.2 Network Common Data Format (netCDF) files ........................................................................ 37 3.1.3 Cubic Spline Interpolation ....................................................................................................... 37 3.2 Predicting the Temperature of the Rail Track Due to Weather Conditions ..................................... 38 3.2.1 Tasks Involved in Producing Rail-temperature Prediction ....................................................... 38 3.2.2 Multivariate Linear Regression ................................................................................................ 39 3.3 Frictional Heat Quantification .......................................................................................................... 39 3.4 Statistical Analysis of Measured Data and BoM Data ...................................................................... 39 4. iii Experimental Design ........................................................................................................... 42 Track Stability Management 4.1 Site Layout ........................................................................................................................................ 42 4.2 Thermocouples and Rail-temperature Measurements .................................................................... 43 4.2.1 Thermocouple Set-up on Rail Profile ....................................................................................... 44 4.2.2 Laboratory Test of Thermocouples .......................................................................................... 45 4.3 Weather Station ............................................................................................................................... 46 4.4 Rail Stress Modules (RSMs) .............................................................................................................. 47 5. Rail-temperature Prediction Software ............................................................................... 49 5.1 Operating the Program .................................................................................................................... 49 5.2 Program Disclaimers......................................................................................................................... 52 5.3 Program Run Times .......................................................................................................................... 52 1. 6. Results and Discussion .................................................................................................... 54 6.1 Weather Variables Comparison: Weather Station and BoM data ................................................... 55 6.1.1 Screened Air Temperature ...................................................................................................... 57 6.1.2 Relative Humidity .................................................................................................................... 60 6.1.3 Surface Air Pressure ................................................................................................................ 62 6.1.4 Zonal Winds (U) ....................................................................................................................... 63 6.1.5 Meridional Winds (V) .............................................................................................................. 64 6.1.6 Overall Statistical Weighted Factor ........................................................................... 65 6.2 Comparison of Temperature Difference over the Rail Surface .................................................... 67 6.2.1 Sensor in the Same Orientation but on Different Rails ............................................................ 68 6.2.2 Different Positions on the Profile on the Same Rail ................................................................. 70 6.2.3 Rail Temperatures on Rail Sitting on Sleeper and Rail sitting above Ballast ............................. 72 6.2.4 RSMs and Thermocouple Rail-temperature Comparison ......................................................... 73 6.3 Rail-temperature Prediction ............................................................................................................. 74 6.3.1 Real-time Predictions .............................................................................................................. 75 6.3.1.1Validation Analysis of Real-Time Predictions .......................................................... 75 6.3.2 Future Predictions ................................................................................................................... 78 6.3.2.1 Validation of Future Predictions ............................................................................. 79 6.3.3 BoM Raw Data and BoM Interpolated Predictions .................................................................. 85 6.3.3.1 Interpolated This-day Predictions .......................................................................... 86 6.3.3.2 Interpolated next-day predictions .......................................................................... 88 6.4 Empirical Prediction Drawbacks ....................................................................................................... 91 6.5 Frictional Temperature Increase ...................................................................................................... 92 6.6 Sensors and Prediction: the Argument for Rail-Temperature Prediction ........................................ 94 7. Conclusion .......................................................................................................................... 95 References .............................................................................................................................................. 96 iv Track Stability Management Abbreviations and Acronyms ACCESS ARTC AWS BoM CACWR CFD CSIRO CWR DAQ ECM FEA FRA GCM GMT MOS NCAR NMOC NOAA NWP RSMs RSSB PP SCI WOLO v Australian Community Climate and Earth-System Simulator Australian Rail Track Corporation Automated weather station Bureau of Meteorology (Australia) Centre for Australian Weather and Climate Research Computational fluid dynamics Commonwealth Scientific and Industrial Research Organisation (Australia) Continuous Welded Rail Data acquisition system Expectation condition maximisation Finite element analysis Federal Railroad Association (USA) General circulation model Global mean time Model output statistics National Center for Atmospheric Research (USA) National Meteorological Operations Centre (Australia) National Oceanic and Atmospheric Administration (USA) Numerical weather prediction Rail stress modules Rail Safety and Standards Board (UK) Perfect Prog Statistical climate inversion Welded track—restrictions on speed of operation of locomotive Track Stability Management Executive Summary Background Railway-track buckling occurs due to inadequate rail-stress adjustment, which is greatly influenced by variations in weather-induced rail temperatures and the rigidity of track structures. Climate change and increases in extreme temperature variations have made buckling a more prevalent problem. The ultimate goal of any research into managing track stability is to allow operators to comprehensively manage rail buckling and the management procedures that follow buckling. The first step in developing a comprehensive management plan is to clearly understand how environmental conditions influence changes in rail-track temperatures. The second step is to accurately predict environmental conditions at least 24 hours in advance so that management procedures can be put in place. Study Goal The goal of this study was to develop a model and software to accurately predict rail-track temperatures 24 hours in advance, so that this data can be used to help manage rail-track buckling. Methodology Two distinct and separate mathematical manipulations were performed to achieve this goal. First, weather forecasts from the Australian Bureau of Meteorology (BoM) were used to forecast the weather at specific railtrack locations selected for the study. This involved using three-dimensional cubic interpolation (that is, weather parameters were interpolated in two dimensions geographically, and then in one dimension through time). The result was a series of forecasts updated every 15 minutes for locations every 3.06 km along the rail track. Second, multivariate linear regression was used to predict rail temperatures on the tracks 24 to 48 hours in advance. To validate the rail-temperature predictions, a three-month field test was conducted on a section of Queensland Rail’s coal-network track in central Queensland from June to August 2010. This involved erecting an automated weather station (AWS) and attaching temperature sensors to a section of track. The AWS model WXT520, produced by Vaisala (Vaisala 2009), was used. This is an off-the-shelf product similar to what some rail operators already use for continuous monitoring of critical sites. Temperature sensors (surface thermocouples) and Salient Systems’ rail-stress modules (another off-the-shelf product) were used to measure rail surface temperatures on both rails of the track (Salient Systems Inc 2009). The sensors were attached to the surface of the track to directly measure temperature changes in the rail profile throughout the diurnal cycle. Statistical correlations between the different measured points of the rail profile were evaluated in relation to the diurnal cycle to assess the accuracy of current rail-temperature measuring practices. Statistical evaluation was used to assess how well the BoM predictions compared with weather parameters at the field experimentation site. Similarly, statistical evaluation was used to assess the accuracy of the rail-temperature method developed. Prediction methods were also compared with existing empirical methods identified in the literature review, and with an assessment of track conditions. Conclusions Using a test-case scenario, the researchers concluded that it is possible to accurately predict rail-track temperatures in advance without using on-track weather instrumentation, and that the accuracy of predictions made in this way is as good as, if not better than, predictions made using instrumentation calculation. While the accuracy of the method has been assessed only for the track configuration, materials and location used in this study, further research could develop the method for other tracks. This is a flagship study in Australia, with significant potential benefits for rail operators and their customers. vi 1. Introduction 1.1 Background and Significance For rail tracks to remain stable, a balance must be achieved between environmentally induced changes in rail-track temperature (which cause thermal expansion and subsequent instability), and the counteracting resistive forces provided by sleepers and ballast (which keep tracks in position). Rail tracks become unstable and buckle due to inadequate rail-stress adjustment and weatherinduced track elongation, which can, ultimately, cause derailments. As ambient temperatures have increased and extreme heatwaves have become more prevalent in Australia (Parliament of Australia, 2009), rail temperatures have also increased, and track instability has become more common. While substantial research in the field of track stability has been conducted in the USA and UK, much of this research is not readily transferable to Australia, where weather conditions and track standards are significantly different from those in the northern hemisphere. Australian research in track stability has been hampered due to fragmentation of the railway industry and the lack of any centralised national knowledge-base on track stability. Studies in track stability have not been revised nor progressed since the 1980s (Bartlett et al. 1961; Hunt 1994; Esveld 2001). Considering advances in track standards and weather-forecasting technology in the last 30 years, the issue is overdue for revision and ready for new approaches that engage with current technology. Two distinct areas of research arise naturally out of track-stability studies: first, the stresses that cause instability in rails, and, second, the environmental conditions that cause these stresses. This study focuses on environmental effects on rail-track temperatures. Currently, the railway industry assesses weather parameters by using an empirical formula based on maximum ambient air temperature (Whittingham 1969; Hagaman and Kathage 1988). This is then used to estimate rail temperatures and, if necessary, issue slow orders to operators when the calculated maximums exceed safe levels. A second level of monitoring occurs on sections of track that are known to be particularly susceptible to environmental conditions such as flooding and buckling. When temperatures on these sections exceed alarm levels, monitoring devices communicate this directly to the central railway hub, acting as an emergency warning system. An example of such an alarm-monitoring system is the WOLO speed restriction system implemented by the Australian Rail Track Corporation (ARTC) (2005). The current Australian standards for unsafe temperature increases in rail tracks were developed as a result of a 15-month study conducted by the Australian Bureau of Meteorology (BoM) in 1951. Using the results of the BoM study, Whittingham (1969) developed an empirical relationship between airscreened temperature and rail temperature for sunny cloudless, windless, and light-wind days in the metropolitan area of Brisbane, Queensland. This relationship was interoperated for Australianrecorded extreme maximum screened air temperatures to develop a contoured isothermal map of the expected maximum rail temperatures for Australia, which is still used for alarm-level settings. Empirical weather-prediction methods have a number of shortcomings. A scan of the literature indicates that empirical methods are either inaccurate for rail-temperature purposes, or require a long period to gather observations. _________________________________________________________________________________ CRC for Rail Innovation th 9 August 2011 Page 1 Track Stability Management Furthermore, existing rail-temperature models do not take into account heat transfer on the bottom surface of the rail, or consider frictional heat addition inputs. Both of these areas are explored in this study. Advances in weather forecasting mean that it should now be feasible to develop a predictive simulation model that calculates rail temperatures dynamically for each section of track. The goal of such a model would be to develop more accurate predictions of high rail temperatures. In practical terms, this could mean the difference between blanket speed restrictions in hot weather (with all the costs and inconvenience that they involve), and focused operational management based on localised risk conditions determined by a scientific approach. 1.2 Objectives The main goal of this study was to develop a model and software to predict rail-track temperatures 24 hours in advance, in order to provide data for use in managing rail buckling. Three major tasks were undertaken to achieve this goal: designing field experimentation and procedures, developing a multivariate regression model of rail-track temperatures, and verifying the regression model against measured rail temperatures. These tasks can be further broken down into the following objectives: 1. to measure rail temperature and weather conditions on an in-situ rail track 2. to perform mathematical manipulation of different temperature models reported in the relevant literature 3. to quantify the accuracy of the numerical weather prediction (NWP) product produced by the BoM against weather parameters measured using weather stations 4. to quantify surface-temperature differences over the rail profile 5. to quantify the temperature difference between the same position geographical on different rails 6. to quantify the measurement difference between rail stress modules (RSMs) and thermocouple sensors 7. to quantify the frictional heat generated by train passage over the rail 8. to develop a code in MATLAB software that interacts with the user and produces a graphic representation of rail temperature over the next two days 9. to recommend steps for further development. 1.3 Scope and Limitations of the Study Australia is a large country, with railway networks a prominent feature across its 7,692,030 km² landmass. Because of the limited resources and time available to this study, it was restricted to developing a method that would accurately predict rail temperatures for a section of rail track within the Queensland Rail (QR) coal-network region in central Queensland. Variations in track materials, construction and orientation affect the heating profile of a rail, causing potential temperature variations between different tracks, even when they are in the same geographic location. This study was limited to considering a concrete-sleepered, narrow-gauge track running east–west, in the central Queensland area of Australia. Because any weather model developed would not have equalled the quality of the BoM weather forecast, BoM forecast data was purchased. The BoM data was from the Australian Community Climate and Earth-System Simulator (ACCESS) model, which has been developed in conjunction with Australia’s Commonwealth Scientific and Industrial Research Organisation (CSIRO). CRC for Rail Innovation th 9 August 2011 Page 2 Track Stability Management The study considered a standard 60 kg rail-track profile, which is rated for heavy haul. Track features such as cuttings, bridges, and points, which are known to cause track instabilities, were not considered. 1.4 Outline of Chapters Chapter 2 presents a review of the literature relevant to this study, including techniques and methods commonly used to predict rail temperatures. Chapter 3 describes the study methodology, including the theory and processes of the methods used. Chapter 4 describes instrumentation and field experimentation details, and discusses the type of instrumentation, how it was used, and the accuracy of different types of instrumentation. Chapter 5 discusses the rail-temperature prediction software developed as a part of this study, including how to use it. Screen-shots and descriptions of function files are included. Chapter 6 contains results and discussion, including analysis of data from field instrumentation and the BoM data. This section also discusses limitations in the mathematical manipulations, and outlines further recommended areas of research arising from this study. Chapter 7 outlines the study’s main findings and discusses their implications for the rail industry. CRC for Rail Innovation th 9 August 2011 Page 3 Track Stability Management 2 Literature Review A review was conducted of the literature relating to: available methods for predicting weather conditions the effect of temperature change on rail buckling surface and internal rail temperatures the generation of frictional heat by wheel contact with rails existing rail-temperature models. A separate review of literature related to the rail-buckling mechanism was also conducted, and is presented in other report (Shah’s work). 2.1 Methods for Predicting Weather Conditions Weather studies consider the effects of the atmosphere over a short period of time, while climate research considers long-term atmospheric patterns that may indicate general trends and averages over a number of years (Gutro 2005). The current study focused exclusively on weather prediction for a 24-hour period, and did not include long-term issues such as climate change or monthly average predictions. All weather is caused directly or indirectly by the interactions of the earth, its atmosphere, and the sun. A substantial part of the literature review focused on solar radiation, which is the main source of heating for natural and artificial structures. The review first considered solar-radiation and air-temperature data freely available from BoM national forecasts, and how it could be used to predict weather conditions. It then reviewed empirical, semi-empirical and NWP models for weather prediction. 2.1.1 Predicting Solar Irradiance—Empirical Methods Solar irradiance is the intensity of solar radiation per unit area, which is affected by the earth’s rotation and orbits around the sun, and by gaseous particles in the atmosphere. Various estimations of solar irradiance are available for engineering purposes. These are based on the Angstrom-Prescott equations, which account empirically for specific locations the amount fraction of average global solar radiation to extraterrestrial radiation. The Angstrom-Prescott equation (Njau 1995) is: G a bS G0 2.1 where: G = average solar radiation [W/m2] G0 = extraterrestrial radiation [W/m2] S = sunshine factor (see Equation 2.1) a = coefficient (between 1 and 0) b = coefficient (between 1 and 0 ) The coefficients a and b are calculated from measured solar radiation, which modifies solar radiation according to the pollutants and atmospheric conditions particular to a location. This is unique for each location. S can be expressed in terms of hours of sunshine (Iqbal 1983): S n Nd 2.2 where: n = monthly average number of instrument-recorded bright sunshine hours per day [h/day] CRC for Rail Innovation th 9 August 2011 Page 4 Track Stability Management N d = average day length [h] For a given month, the average day-length N d can be calculated from (Iqbal 1983): Nd 1 n n2 2 cos 1 tan tan n2 n1 n n1 15 2.3 where: n1 = day number at the beginning of the month (1 to 365) n2 = day number at the end of the month (1 to 365) = latitude [⁰] δ = solar declination [⁰] Numerous modifications have been made to the basic Angstrom-Prescott equation. These aim to relate the equation to climatological variables, rather than keeping it as a purely experiment-based equation. The agricultural industry also uses empirical methods based on air temperature and rainfall to calculate irradiance. A detailed review of these methods in the Australian environment was conducted in 2000 by Liu and Scott (Liu & Scott 2000). After comparing methods that used air temperature only, rainfall only, and a combination of air temperature and rainfall, Liu and Scott found that using air temperature as the main parameter and rainfall as 1 for presence of rainfall and 0 as no rain gave the best results. The equation that best described the Rockhampton region relevant to this study was: Q Q0 a[1 exp(b Dc )](1 dR j 1 eR j fR j 1 ) g 2.4 where: Q = solar radiation reaching the earth’s surface [W/m2] D = diurnal range of air temperature [⁰C] (Equation 2.5) R = transformed rainfall data where if P>0, R=1; P=0, R=0 a,b,c,d,e,f = coefficients determined by regression for Rockhampton (Liu & Scott 2000): a=0.700 b=0.026 c=1.874 d=0.034 e=0.038 f=0.124 g=-0.020 j = the current day J+1 = the next day D Tmax Tmin ( j ) Tmin ( j 1) 2 2.5 where: Tmax = current maximum temperature [⁰C] Tin (j) = minimum temperature current day [⁰C] Tmin( j+1) = minimum temperature the next day [⁰C] SHAZAM software was used for non-linear least square regression (Liu & Scott 2000), and this equation was found to have a regression coefficient R2 of 0.77 between estimated and observed irradiances, and an RMSE of 2.58 MJ m-2. CRC for Rail Innovation th 9 August 2011 Page 5 Track Stability Management The main criticism of these empirical statistical methods is not that they are inaccurate. After all, the R2 findings of Liu and Scott ‘s equations were all 0.69 and above, and the RMSEs were all 2.53 MJm-2 and below. However, their applicability is highly localised—for example, the model developed for Darwin can only be used for Darwin, and cannot be transferred to Cairns, even though Cairns has a similar climate classification. In Liu’s paper, measurements of climatological parameters were taken over a four-year period and repeated for each location of interest. While Liu and Scott tried to develop empirical radiation equations for locations by using climate data from other locations that had a similar climate, their over mean had an R2 of 0.45 and an RMSE of 3.08 MJm-2 (Liu & Scott 2000). This indicates that, although it is possible to develop empirical relationships for locations using data from similar climatic regions, results are not very accurate, and nowhere near accurate enough for a 24-hour advanced forecast model of track temperatures. Furthermore, given that railway networks cover large geographic areas with varied topographical features, it is neither practical nor desirable to implement weather stations in a 20 km grid formation around Australia, collect data for a couple years, and then develop a rail-temperature model. Indeed, models developed in the USA (explained in Section 2.1.4) use NWP to solve an initial value problem (Zhang & Lee 2008). 2.1.2 Spatial and Time Scales of Weather Forecasts In meteorology, the scale or resolution of the forecast is important, because different weather phenomena occur over a range of space and time scales. One boundary-condition measurement may be important in one scale and inconsequential in another (Whiteman 2000; Pielke SR 2002). Meteorology is classified into three basic scales: large-scale or synopticscale, mesoscale, and microscale. Large-scale or synopticscale meteorology considers global circulation systems, including hemispheric wave patterns called Rossby waves; monsoons; high- and low-pressure centres; and fronts. Temperature, humidity, pressure, and wind measurements are collected simultaneously all over the world, and atmospheric dynamics are solved for the entire earth. Synopticscale meteorology has a resolution greater than 200 km and lifetimes (time scales) of days to months (Whiteman 2000). Mesoscale weather events include diurnal systems such as mountain wind systems, including breezes, sea breezes, thunderstorms, and other phenomena with horizontal scales that range from 2 km to 200 km and lifetimes that range from hours to days. Mesoscale meteorologists use networks of surface-based instruments, weather balloon measurements, and remote sensing systems such as radar and aircraft to make observations. Microscale meteorology focuses on local or small-scale atmospheric phenomena with resolutions below 2 km and lifetimes from seconds to hours. These include gusts and turbulence, dust devils, thermals, and certain cloud types (Whiteman 2000). A fourth scale in between mesoscale and synopticscale is also widely used. It is the regional scale, and relates to circulations and weather events occurring on horizontal scales from 500 km to 5000 km (Whiteman 2000). For railway applications, synopticscale and regional scales are too large to allow for local variation of weather parameters on the track. An average section of track between joints is around 3 km, and the required time scale is 24 hours in advance, whereas the timescale for synoptic and regional predictions is days to months, and these models have too coarse a resolution for this application. Given that track features such as orientation and surrounding vegetation can change within a couple CRC for Rail Innovation th 9 August 2011 Page 6 Track Stability Management of kilometres, mesoscale weather prediction is most appropriate for this study. Literature on mesoscale modelling is reviewed below. 2.1.3 Forecasting Methods Similar forecasting methods can be used for climate-change studies and operational forecasts. However, the literature on meteorological modelling is usually published for climate case-studies, such as those related to large eddy motion (Moeng et al. 2006), or the weather particular to one geographic location (Wilby et al. 1999). Therefore, this review focused on modelling techniques used in relevant climate studies that were directly analogous to the techniques required for the current study. Currently, all operational meteorological forecasts start off with a general circulation model (GCM)— a synopticscale NWP model that solves for conservation of mass, momentum and energy equations for the different atmospheric species, where the resolution is 1000 km or greater. GCMs give coarse general information that corresponds to large-scale forcings such as the earth’s orbit, and determine the general order of weather events and characterise the climate of a region (Giorgi & Mearns 1991). To gain meaningful forecasts for a particular city or area, GCM model output is downscaled to a finer resolution, because GCM output is often unreliable at individual grid and sub-grid box scales (Wilby et al. 1999). There are several ways to obtain a finer resolution, including purely empirical methods in which forcing is not explicitly accounted for. Methods are: weather forecasts using instrumental data records semi-empirical methods using GCMs to describe the atmospheric response to large-scale forcings of relevance to climate change empirical techniques to account for the effect of mesoscale forcings dynamic modelling approaches, in which mesoscale forcings are described by increasing the model resolution only over the area of interest. (Giorgi & Mearns 1991) GCMs are NWP models that produce a numerical simulation of atmospheric variables such as temperature and wind for the whole world. Grid sets are divided into latitude and longitude points and vertical levels above the ground, so that the simulated data is three-dimensional. Purely empirical methods involve the assumption that, independent of the nature of the forcing mechanism, under similar lower-boundary conditions (such as ocean to land surface topography), the general circulation will eventually adjust itself to give a similar response to different forces. This assumption is supported by the fact that similar latitudinal near-surface GCM responses are obtained even for increased greenhouse gas concentration and increased values of the solar constant (Giorgi & Mearns 1991). Most empirical methods use data from recent instrumental records. There are two main ways of doing this. One is to group different periods of recorded data that have similar attributes (e.g. warm years or cold years, or different seasons), then develop characteristics such as precipitation and cloudiness for these different groups. A statistical relationship is then developed between the type of year or season and a weather variable, and future information is simulated through this relationship. The second way is to develop linear statistical relationships between climate variables such as temperature and precipitation averaged over a given region and then averaged annually or monthly. These relationships are then used to estimate possible future climate data (Giorgi & Hewitson 2001). CRC for Rail Innovation th 9 August 2011 Page 7 Track Stability Management This is the same approach Whittingham (1969) took in developing a relationship between rail temperature and air temperature. The main problem in using these purely empirical approaches for the current study was their susceptibility to the availability and quality of observational data (Giorgi & Mearns 1991). Records collected over several decades have been used to develop these empirical models. In capital cities such as Melbourne or Sydney, weather data go back to the late 1890s. However, regional and remote areas of Australia have only been collecting weather data since the 1980s, if at all. Also, empirical methods can only be used for the regional climates that they are developed for, as Liu and Scott (2000) found in relation to solar radiation. For rail networks that cover large areas, including regional and remote areas, not enough observational data exists to develop an accurate empirical model. Semi-empirical models or statistical climate inversions (SCI), translate large-scale, coarse-resolution GCM information into local, high-resolution statistics of surface climatic variables of interest, using empirically derived relationships between large-scale and local surface variables. GCMs are used to explicitly account for large-scale forcings, and empirical methods to account for mesoscale forcings (Giorgi & Hewitson 2001). There are four main SCI methodologies: statistical difference schemes regression schemes Perfect Prog (PP) model output statistics (MOS). The underlying assumption for the differences schemes is that the inaccuracy due to the GCM resolution is reduced when simulated GCM-produced and observed high-resolution data are added to the GCM output for forecasting. However, this technique can be misleading, because mesoscale forcing in different locations within a GCM grid box is widely variable and probably nonlinear (Giorgi & Mearns 1991). The same problem identified in using purely empirical methods applies to using differences schemes to account for mesoscale forcing: there is not the necessary quantity of data or density of observation stations to make it viable for this study. In a regression downscaling scheme, multivariate regression is conducted for a series of observed variables in a given region. Another regression is then conducted on a series of the same variables, but averaged. These data-sets are obtained from the same set of observations for the same period. The relationship between the averaged regression and observed regression values is then applied to the forecast GCM produced over that region in order to infer the surface variables (Giorgi & Mearns 1991). Like the methods discussed above, regression schemes depend on the accuracy and validity of the observations used in their development. They also rely on a good theoretical understanding of the surface-variable meteorological interactions, so that relevant variables can be included in the regression. For the purposes of the current study, this would have been too time-intensive, given that that study’s focus was to develop a predictive rail-temperature model rather than a downscaling regression scheme. Therefore, the researchers decided that it would more prudent to combine this method with an already scaled-down NWP product, rather than downscaling from purely observational data. PP and MOS methods are similar to the regression scheme in that both use multivariate regression. However, instead of developing a relationship between two current regressions of averaged and observed values, PP and MOS develop relationships between observed surface-weather variables CRC for Rail Innovation th 9 August 2011 Page 8 Track Stability Management and observed or model-produced suitable free-atmosphere and surface-weather predictors (Giorgi & Mearns 1991). For MOS, the predictors (the independent variables) are model forecast variables; the predictands (dependent variables) are weather-station observations valid at the same time as the forecast. An error function between the predicted weather-station observation and the actual observation is used as a factor that is fed back into a regression relationship, so that the MOS prediction equation continuously becomes closer to the variables observed by the weather station (Kalnay 2003). Whereas MOS uses both forecast model data and observed data, PP only uses observation data. The regression equations are derived using the observed variables, and the outputted model analysis assumes a perfect forecast, so an error function is developed between the regression-predicted forecast and the actual observed forecast. PP uses two sets of observed variables from different intervals in time (Marzban et al. 2005). Again, these two empirical methods suffer from a lack of accurate data for remote and regional areas, and using them would have required at least a few years of observations for the specific regions being studied. However, MOS and PP techniques are also used for post-processing, where atmospheric predicted variables are statistically modified so that they resemble more realistic values near the surface (Kalnay 2003). Dynamic modelling approaches involve increasing the NWP grid resolution to a higher resolution over the region of interest. This is achieved by nesting or embedding a finer-grid NWP model (regional model) inside the coarse-grid NWP model (host model)—that is, the grid points of the coarse NWP model are used as the boundary conditions of the fine NWP model (Giorgi & Mearns 1991). This can be achieved by either one-way nesting or two-way nesting. One-way nesting consists of boundary conditions being fed into the regional model. This leads to abrupt changes in resolution, and there is no modification of the host model by the regional model. This has some advantages, as it allows for independent development of the regional model, and the host model can be run for long integrations without being influenced by the problems associated with non-uniform resolution from the regional model (Kalnay 2003). Two-way nesting is when the solutions of regional models are fed back into the host model and modify the host model. This gives a more accurate result because there is better continuity of information between the two models (Kalnay 2003). The disadvantage of the two-way nested model is that the fine resolution of the regional model may distort the host model and give unrealistic variables (Kalnay 2003). Using a nested NWP downscaling procedure allows predictions to be made for regional and remote areas of Australia, without having to wait for empirical data to be collected using observation or weather stations. Existing GCM and mesoscale model products available from the BoM (see Appendix A) can cut down the computational time of running an NWP model if only a small region is considered (e.g. each city hub for train operations could run their own nested NWP area for surrounding regions). Because NWP nesting procedure does not need empirical data or an advanced knowledge of theoretical meteorology to use the correct variables for regression, it is also easier to implement—although it does require more computational effort. Due to the intensive computation and simulation cost of implementing an NWP model to downscale the GCM points, an existing NWP downscaled product was purchased for the purposes of this study. CRC for Rail Innovation th 9 August 2011 Page 9 Track Stability Management 2.1.4 NWP Forecasting Procedure NWP forecasting requires the solving of equations that govern the movement of the atmosphere for seven unknown variables. While a wide variety of standard numerical procedures are used for different NWP models, only basic concepts of NWP modelling are discussed here. The NWP model used is the ACCESS (Australian Community Climate and Earth-System Simulator) model. ACCESS solves the equations in orthogonal coordinate form, as listed below (Kalnay 2003). 1. Newton’s second law or conservation of momentum (three equations for the three velocity components) 2. Continuity equation or conservation of mass 3. Equation of state for ideal gases 4. First law of thermodynamics or conservation of energy 5. Conservation equation for water mass Into these equations, appropriate boundary conditions at the bottom and top of the atmosphere are used to calculate a full numerical solution. The governing equations are in Lagrangian definition for the movement of a parcel of air in an arbitrary coordinate system origin at the centre of the earth and z-axis along the axis of rotation. The governing equations are (Kalnay 2003): dv p F 2 v dt ( v) t p RT dT dp Q Cp dt dt q ( vq) ( E C ) t (2.6) (2.7) (2.8) (2.9) (2.10) The unknown variables that need to be solved for are: v = the velocity vector v =(u,v,w) u = velocity in the x direction [m/s] v = velocity in the y direction [m/s] w = velocity in the z direction [m/s] T = temperature [K] p = pressure [pa] 3 = density [kg/m ] q = mixing ratio of water vapour and dry air mass The other variables are: 1 the specific volume [m3/kg] i j k = gradient operator x y z g g e 2l = apparent gravity ge e gravitation accelerations vector e = Newtonian gravitational potential of the earth [J/kg] CRC for Rail Innovation th 9 August 2011 Page 10 Track Stability Management = angular velocity [rad/s] l = position vector from the axis of rotation parcel of air F = friction force [N] = compressibility of the air parcel t R = universal gas constant for air [J/kg⁰ K] Q = heat energy [J/kg] Cp= specific heat at constant pressure of air [J/kg⁰K] dT = change in temperature over time dt dp = change in pressure over time dt q = change in mixing water vapour mixing ratio q t E = evaporation [kg/m2s] C = condensation [kg/m2s] These equations are solved for all parcels of air in the atmosphere using numerical methods; solutions themselves correspond to wave forms which relate directly to physical variables. 2.1.5 Australian Community Climate and Earth-System Simulator (ACCESS) Model Each climate-research organisation, government department or research body runs their own NWP model with varying initial conditions, boundary assumptions and numerical schemes designed to serve their own purposes. ACCESS is an Australian government model that solves the abovementioned governing equations to predict weather variables days and months in advance. In August 2010, the Australian BoM switched from their previous in-house model to the ACCESS model for both research and operational forecasts (Bureau of Meteorology 2010). Evening weather forecasts are now based on ACCESS data combined with the experience of forecasters who decipher ACCESS outputs to make a weather prediction. Data is outputted from the ACCESS model in several formats and resolutions, available to the public for a subscription fee. The ACCESS-A product, which has a resolution of 0.11⁰ or 12 km grids for single-level fields, was used in this study. It was chosen because it offered the smallest-resolution weather output that encompassed the central Queensland area relevant to the study. Single-level fields were chosen because multi-level fields had weather data not only on the surface of the earth but at intervals into the earth’s atmosphere, and this vertical information was not relevant to the study. The ACCESS model is based on the UK Met Office Unified Model/Variational Assimilation (UM/VAR) system. It was developed and tested in Australia by Dr Kamal Puri of the Earth System Modelling Programme at the Centre for Australian Weather and Climate Research (CAWCR). It was implemented by the Operational Development Subsection of the National Meteorological Operations Centre (NMOC) (Bureau of Meteorology 2010). Specifications of the ACCESS model are as follows (Bureau of Meteorology 2010). Equation set is non-hydrostatic. Arakawa-C grid is used in the horizontal plane and Charney-Phillips is used in the vertical. CRC for Rail Innovation th 9 August 2011 Page 11 Track Stability Management Advection is solved with two-time-level, semi-Lagrangian integration scheme, with noninterpolating scheme for vertical advection of temperature. An exception for solving is density, which uses a Eulerian scheme. Acoustic terms are treated using a semi-implicit approach. Cloud prediction uses a diagnostic cloud scheme based on conserved variables of liquid/frozen water temperature and total water content (TL and qT), and a sub-grid scale probability distribution of these variables (Smith 1990). Cloud amounts and water content are found using an assumed critical relative humidity. The BoM modifies the scheme such that only water clouds are defined from TL and qT, and a sub-grid probability distribution. Ice water content is determined by the prognostic mixed-phase microphysics scheme, with ice-cloud fraction calculated diagnostically from ice-water content. The radiation scheme used is a modified version of the Edwards and Slingo scheme (Edwards & Slingo 1996), which is based on rigorous solution of the two stream-scattering equations, including partial cloud cover with full treatment of scattering and aerosols and consistent treatment of cloud radiative properties in solar and thermal regions of spectrum. Precipitation is solved by using a single-moment bulk microphysics scheme (Wilson & Ballard 1999), with explicit calculation of transfers between vapour, liquid and ice phases. Convection uses a modified mass-flux scheme based on Gregory and Rowntree (Gregory & Rowntree 1990). 2.1.6 ACCESS Products Particulars The ACCESS model is a GCM model, which is downscaled using NWP nesting by the Australian BoM. As Table 2.1 indicates, several products are available for public consumption in various resolutions, domain sizes, durations, runs, and types. From Table 2.1, ACCESS-A is the product that has the smallest resolution and encompasses the central Queensland region. Its resolution is approximately 12 km, and it can predict weather conditions up to 48 hours in advance, 4 times a day at 00hr, 06hr, 12hr, and 18hr (GMT). This product was chosen for use in this study. Table 2.1: Description of ACCESS Products Provided by the BoM (Bureau of Meteorology 2010) 2.1.7 ACCESS-A and Surface-weather Element Verification After the BoM switched to the ACCESS model in August 2010, several verifications were performed by Tomasz Glowacki of CAWCR to verify that ACCESS-A was as accurate as the BoM’s previous CRC for Rail Innovation th 9 August 2011 Page 12 Track Stability Management MESOLAPS model, using all available Australian surface observations from 10 to 18 July 2010 (Bureau of Meteorology 2010). Figure 2.1 compares the forecasts produced by the two models. It shows: forecast RMS error and bias of mean sea-level pressure screen-level temperature (PT) screen-level dewpoint temperature (D2) zonal (U) and meridional (V) components of the 10 m wind. The blue line in Figure 2.1 is the output of the MESOLAPS model, while the green line is the ACCESS-A output. For any particular hour of the day, the latest available model forecast for that time was used (Bureau of Meteorology 2010). Figure 2.1 gives an estimation of the average errors and biases found in the short-term forecasts available throughout the day. ACCESS-A generally shows smaller RMS errors than MESOLAPS for most hours of the day, particularly for the mean sea-level pressure, temperature, and wind fields. Biases are also significantly better for most fields throughout the day, except for the 10 m zonal wind component, which tends to display a slightly greater (0.1–0.2 m/s) negative bias than MESOLAPS during the evening and overnight (Bureau of Meteorology 2010). CRC for Rail Innovation th 9 August 2011 Page 13 Track Stability Management Figure 2.1: Comparison of Hourly Forecast RMSE (left) and Bias (right) for ACCESS-A (Green) and MESOLAPS (Black) 10 –18 July 2010 2.2 Effect of Temperature Change on Buckling Buckling occurs because of thermal expansion—that is, a steel rail’s natural tendency to expand when temperatures increase. Because rails are continuously welded, they do not have adequate space to expand, and the rail is placed under thermal stress as it becomes warmer. If the stress reaches a critical point, the rail will curve out of shape and buckle (ARTC 2005). Buckling occurs on both straight tangent tracks and on curved tracks, which buckle into different shapes from each other. As this study focuses on well-maintained tangent tracks, the theory discussed is limited to those. “Rail-neutral temperature” (also known as “stress-free temperature”) is the temperature at which a rail does not experience any thermal stresses. This is usually the temperature at which the railway track was built, although neutral temperature can decrease over time due to heating and cooling cycles. The neutral temperature of two rails on the same track can also differ (Chapman et al. 2008). 2.2.1 Minimum Potential Energy Buckling Theory Buckling theory is based on elementary beam theory and the principles of minimum potential energy (Kerr 1976; Samavedam et al. 1993), where the amount of energy needed to cause buckling is then used as a parameter for track stability (Samavedam et al. 1993). The discussion of buckling here is based largely on parametric buckling analysis conducted by the USA Federal Railroad Administration (Samavedam et al. 1993). Two different types of buckling can occur in the horizontal plane of the track, both pictured in Figure 2.2 (Kerr 1975). The focus is on buckling in the horizontal plane because buckling in the vertical plane occurs only when lateral resistance is insufficient, and does not occur when the track is sufficiently maintained (Kerr 1975). Of the two prevalent buckling shapes formed by tangent tracks , the main focus of this study was on the antisymmetric mode. CRC for Rail Innovation th 9 August 2011 Page 14 Track Stability Management Figure 2.2: Mode Shapes of Tangent-track Buckles in Horizontal Plane (Kerr 1975) Energy required for buckling is represented by a potential energy balance equation: (V2 V1 ) W (2.11) where: V1 = strain energy in the rails at a stable pre-buckled [J] V2= strain energy in the rails after a buckle [J] W = work done against resistance by moving track from pre-buckled position to buckled position [J] = potential energy required to move track from pre-buckled position to buckled position [J] Potential energy and temperature can be solved numerically when values for resistance and buckling shape are substituted into the potential energy equation. The result of temperature against energy is shown in Figure 2.3. The resistance values used in solving Equation 2.11 are given in Table 2.2. CRC for Rail Innovation th 9 August 2011 Page 15 Track Stability Management Figure 2.3: Temperature versus Buckling Energy Solution to Equation 2.11 (Samavedam et al. 1993) Table 2.2: Resistance Values Used in Solving Equation 2.11 (Samavedam et al. 1993) In Figure 2.3, a clear maximum temperature and minimum temperature can be seen on the graph. The TB,MAX is about 121⁰F (or 49.4⁰C) and the value of TB,MIN is 76⁰F (or 24.4⁰C). If these values in Equation 2.11 are used in a graph of lateral displacement versus temperature increase (shown in Figure 2.4), they clearly indicate an unsafe band of rail temperatures. Figure 2.4: Graph of Temperature Increase versus Lateral Displacement (Samavedam et al. 1993) The upper critical buckling temperature TB,MAX represents a track position that is infinitesimally stable—that is, without any disturbance or energy input, the track will naturally buckle out to Position C, which is stable. From Position A, the track will buckle to Position S only with sufficient external energy input. The minimum buckling temperature increase is TB,MIN. The absolute temperature of the track is the sum of the critical temperature rise and the rail-neutral temperature (Samavedam et al. 1993). 2.2.2 Three-dimensional Modelling of Forces due to Temperature Fluctuation Another way of evaluating buckling behavior and thermal forces applied to a railway-track structure is to develop a three-dimensional finite element analysis (FEA) model for the track structure (Lim & Sung 2004). CRC for Rail Innovation th 9 August 2011 Page 16 Track Stability Management In Lim and Sung’s model (Lim et al. 2003), the track consisted of two parallel rails resting on a series of sleepers, which were attached to the rail by fasteners. Lim considered the fasteners to have finite rotational and translational resistances; this implies that the movement (translational and rotational) of the sleeper can be different from that of the rails. The sleeper will always exert an opposing force to any displacement of the rails. Lim modeled the non-uniform ballast resistance as non-linear lateral spring elements. Rails were modeled as a thin-walled mono-symmetric opensection beam element with 7 degrees of freedom. The sleepers were modeled as solid beams on elastic foundation elements with 6 degrees of freedom. Through experimentation, it was found that the applied force and displacement on the sleeper varied linearly for small displacements and non-linearly for large displacements. Therefore, Lim modeled ballast as an elastic and inelastic element. Lim modeled the pad-fastener system as an elastic spring element with 6 degrees of freedom per node. The elastic spring element had two nodes but the length of the element is zero. Each pad fastener had six springs with three springs for force-displacement and three springs for moment-rotation. Lim’s configuration is shown in Figure 2.5. Figure 2.5: Cross-section View of CWR Tracks (Lim et al. 2003) In the potential energy study (Samavedam et al. 1993), the lateral and longitudinal resistance of the CWR was represented as an elasto-perfect plastic model (as shown in Figure 2.6), rather than as an infinite series that took into account distributed load and material properties. The lateral and longitudinal resistance was assumed to be linear-elastic until the lateral forces had reached their peak value, then the ballast starts to yield and plastic deformations starts to increase. Figure 2.6: Pad-fastener Element as Represented in Lim (2004) Model The track parameters shown in tables 2.3, 2.4 and 2.5 were used in numerical simulations. CRC for Rail Innovation th 9 August 2011 Page 17 Track Stability Management Table 2.3: FEA Model Track Properties (Lim & Sung 2004) CRC for Rail Innovation th 9 August 2011 Page 18 Track Stability Management Table 2.4: Rail RE132 Properties (Lim & Sung 2004) Table 2.6: Wooden Sleeper Properties (Lim & Sung 2004) Table 2.5: Fastener Material Properties (Lim & Sung 2004) In the tables above, ties are used instead of sleepers. Similar graphs of above-neutral temperature and lateral displacement are plotted for the FEA model as shown in Figure 2.7. Figure 2.7: Graph of Temperature Increase versus Lateral Displacement (Lim & Sung 2004) Both approaches produce a graph with a similar shape; however the TB,MAX and TB,MIN values are a little different due to slight differences in the track parameters used in the two models. A review of the buckling analysis revealed that temperature considerations were limited to a bulk-deformation temperature, with possible flow-on problems for field testing where only the surface temperature of a rail can be measured. These critical rail temperatures are calculated from loading, but how surface temperatures relate to the bulk-deformation temperature is a separate issue that needs to be quantified. 2.3 Surface and Internal Temperature of the Rail Quantifying a single temperature over the whole rail profile is problematic, as it is unclear which temperature measured on the rail corresponds to the bulk-deformation temperature that is calculated in buckling studies. A study was conducted by the UK’s Rail Safety and Standards Board (RSSB) into rail surface temperature and the bulk-deformation temperature of rail steel to quantify a temperature measurement (Ryan 2005). Ryan conducted several laboratory tests using a test rail section (CEN60E1, 898 1 mm long), which was polished to simulate in-situ rail-head wear. The rail was on CRC for Rail Innovation th 9 August 2011 Page 19 Track Stability Management wooden blocks to simulate wooden sleepers, which in turn rested on a small bed of ballast to simulate real track conditions. Rail sleeper and ballast configuration was set up 590 mm off ground height. Two dual-filament radiant heaters rated at 3 kW per heater were used to induce temperature change in the rails. The bulk-deformation temperature was found using thermal expansion with Equation 2.12. (2.12) L LT where: L = the change in length [mm] L = original length of the rail [mm] T =increase in temperature from ambient [⁰C] = thermal expansion coefficient of rail steel ( 11.5 106 m/m⁰C-1) Figure 2.8 shows Ryan’s findings. Figure 2.8: RSSB Study—Temperature versus Time Both Sides Heated (Ryan 2005) It is interesting to note that, except between 90 and 100 minutes, average surface temperature is lower than the bulk temperature, even though the rails were heated externally. Logically, the surface or average surface temperature for rails heated horizontally on both sides should be consistently higher than bulk temperatures. Ryan (2005) does not explain this result; however, it could be due to the polished rail-head, which would have had a higher emissivity than rusted surfaces and might therefore have retained less heat and given a lower result. It might also be due to wind or to a convective heat transfer on the surface of the rail during Test 1. Furthermore, the complex geometric shape of the rail profile was not considered in Ryan’s calculations for bulk temperature, and this may have over-simplified calculations somewhat. However, Ryan does not discuss details of incidents during the test, and any number of external influences could have caused the counter-intuitive result. The main information to take from Ryan is that surface temperature and bulk temperature are closely related, as seen by the R-squared value of 1, which indicates that an experimental design with surface-temperature measurements is possible. However, a discrepancy still exists between CRC for Rail Innovation th 9 August 2011 Page 20 Track Stability Management surface and bulk temperatures, and some post-experiment analysis on temperature variations over the rail profile are performed. 2.4 Frictional Heat Generation Although quantifying frictional heat generation is not a major objective of this study, frictional heat does affect operational rail tracks. Friction, and the subsequent wearing away of the track, is the main by-product of train travel. How much of this friction translates into heating on the overall rail profile is unclear. Many wear studies concentrate on the surface-heating characteristics of rail–wheel interaction for wear purposes (Knothe & Liebelt 1995; Ahlstrom & Karlsson 1999; Ertz & Knothe 2002; Olofsson & Telliskivi 2003). How well these theories translate to overall rail-profile heating has been quantified in various field tests. Two references that include field experimentation were reviewed to give an overview of the conflicting information on frictional heat generation. 2.4.1 Curved Track Heat Addition Due to Friction Tests were conducted by Transnet Freight Rail in South Africa to quantify friction and management of friction on rail-gauge face temperatures on the high rail of a curved track (Frohling et al. 2008). The site had a radius of curvature of 604 m, 59/9 km south of Vryheid on a coal export line. The cant (tilt) of the track was 20 mm. Over a three-day period, 57 trains passed this test site. The temperature sensors used were bead-type thermistors, which were embedded into the gauge corner of the rail and logged using an HOBO external temperature logger. Figure 2.9 shows the sensor configuration. Figure 2.9: Vryheid Field Test Thermistor Location on Rail Profile (Frohling et al. 2008) Trains with different types of wheel axles or bogies passed this curved section, with the increase in temperature grouped for different bogies. A bogie is a structure incorporating suspension elements and fitted with wheels and axles, used to support rail vehicles at or near the ends, and capable of rotation in the horizontal plane. It may have one, two or more axle sets, and may be the common support of adjacent units of an articulated vehicle (IGA 2003). The four different types of bogies identified in the South African study were: 200 wagons at 26-ton axle load [23.58 tonnes], fitted with self-steering three-piece bogies 100 wagons at 20-ton [18.14 tonnes] and 100 wagons at 26-ton [23.58 tonnes] axle load, fitted with self-steering three-piece bogies 85 to 112 general freight wagons with axle loads less than 20 tons [18.14 tonnes], fitted with a mix of standard and self-steering three-piece bogies fewer than 50 general freight wagons with an axle load of less than 20 tons [18.14 tonnes], fitted with standard three-piece bogies. CRC for Rail Innovation th 9 August 2011 Page 21 Track Stability Management The temperature rises recorded on the gauge side of the track directly under the train’s passage were very high—up to 25ºC for 26-ton axle loads and 16ºC for less than 20-ton axle loads (see Figure 2.10a and Figure 2.10b). These peak temperatures even out and remain for up to 400 seconds, a substantial amount of time. Frohling et al. (2008) focused on practical measurements of coefficient and temperature increase, so the time it takes for this temperature to dissipate and its effect on overall track temperature were not discussed. Figure 2.10a (left): Temperature Increase versus Time 26-ton Axle Load Left (Frohling et al. 2008) Figure 2.10b (right): Temperature Increase versus Time 20-ton Axle Load Right (Frohling et al. 2008) Frohling (2008) found: no correlation between increases in rail temperature and the speed of trains a strong correlation between increases in rail temperature and the length of trains that the increase in rail-gauge face temperature on the high rail was dominated by the duration and magnitude of flange forces above a 1.5-ton threshold exerted on the rail that, on average, the high-rail gauge corner increased by 0.000506ºC/ton for 26-ton axle-load trains, 0.000529ºC/ton for 20-ton and 26-ton wagons with self-steering bogies, and 0.01019ºC/ton for a less than 20-ton axle load. Frohling (2008) conducted a second test on six 800 m right-hand curves and one tangent section. For this test, temperature sensors were located at Position 5 in Figure 2.9. The rail was not lubricated for four days; because it rained after one day’s measurement, which changed the rail’s friction and lubrication characteristics, it was regarded as inconclusive (Table 2.6). Table 2.6: Description of Instrumented Rail Sections and Average Speeds (Frohling et al. 2008) CRC for Rail Innovation th 9 August 2011 Page 22 Track Stability Management As can be seen in Figure 2.11, although the tangent track S2 has a lower temperature, the additional heat due to friction is still around 5ºC for each passing train. Curved tracks had higher temperatures, which varied depending on the radius of the curvature. Similar travelling speeds on curved track S1 produced almost double or more the temperature increase found on tangent track S2. Figure 2.11: Rail Temperatures versus Train Passing for Different Sections of Rail (Frohling et al. 2008) Note that Frohling’s test results conflict with Chapman’s findings presented in the RSSB report from the UK (Chapman et al. 2005). 2.4.2 Tangent Track Heat Addition Due to Friction Frictional heat-generation results for tangent tracks presented in Chapman’s report (Chapman et al. 2005) are shown in Figure 2.12. Figure 2.12: Rail Surface Temperature versus Time Tangent Track (Chapman et al. 2005) Again, a large discrepancy exists between the temperature increases reported by Frohling et al. (2008) and those reported by Chapman et al. (2005). Whereas Frohling et al. (2008) found at least a 5⁰C increase in tangent-track measurements, Chapman et al. (2005) found an increase of around 0.1⁰C in rail temperature. Many experimental design factors could have contributed to this difference. For example, Frohling et al. (2008) placed sensors on the gauge corner of the rail, which is much closer to the wheel-contact area than the foot of the rail, where the sensors were located for the study carried out by Chapman CRC for Rail Innovation th 9 August 2011 Page 23 Track Stability Management et al. (2005). Also, while Chapman did not note the type or the bogie of passing trains, the Winterbourne location used for the UK study would not have been a freight line. Furthermore, Frohling et al. used thermistors, whereas Chapman et al. used thermocouples, so there may have been differences in the accuracy of instrumentation. Having said this, however, such a large discrepancy between measurements is unlikely to be due solely to instrument placement or type, given the large thermal conductivity and diffusion factors of rail steel. Frohling et al. (2008) found a strong correlation between train lengths (which are an indication of actual loads that a track experiences) and temperature increase. The current study is specific to a coal rail line in Queensland, which has similar loads to those studied by both Frohling et al. (2008) and Chapman et al. (2005). Therefore, despite the discrepancies between previous studies, the researchers concluded that frictional heat addition should be explored as part of the current study. 2.5 Existing Rail-temperature Models Many models have been devised to quantify changes in rail temperature due to environmental conditions. The most recent models are reviewed below. 2.5.1 Empirical Relationships Hunt (1994) developed an empirical formula for rail to air temperature given below: Trail 1.5 Tair Trail Tair 17 (2.13) (2.14) where: Trail = temperature of the rail track [°C ] Tair = temperature of the air [°C] Equation 2.13 is used for sunny days and Equation 2.14 is used for cloudy days. Esveld (Esveld 2001) developed a similar relationship using finite element software and buckling theory. A comparative study using these results and measured trail temperatures was conducted by Chapman et al. (2005) (see Figure 2.13). Figure 2.13: Temperature of the Foot versus Air Temperature (Chapman et al. 2005) CRC for Rail Innovation th 9 August 2011 Page 24 Track Stability Management It can been seen from Figure 2.13 that, taking only air temperature into account, the empirical formulas are within the same range as the actual measured temperature of the rail foot, but there is a large variance in rail temperature that these equations cannot account for. Chapman et al. hypothesise that a data envelope (or look-up chart) would be more useful than an empirical linear relationship because this would give an indication of the range of the rail temperature. This current empirical relationship would be too inaccurate for a day-to-day real-time prediction of rail temperature, although the equations give an indication of what the range of rail temperatures may be, and could be used for design standards. For example, the analysis by Esveld (2001) came very close to predicting the upper boundaries of the rail temperature relationship, and could be used for design or industry standards. However, it is not accurate enough for real-time prediction. In Australia, similar empirical equations were developed by BoM researcher Whittingham (1969), who conducted a 15-month experiment on a piece of exposed railway rail in an instrumented enclosure at the bureau’s Brisbane office. Details of the experiment are as follows: geographical location latitude 27⁰28’S, longitude 153⁰02’E piece of rail was 82 lb [37.2 kg] and 11 ft [3.35 m] long rail was laid on 18-inch [0.46 m] long sleepers at 2 ft [0.61 m] intervals rail and sleepers were then laid on 1¼-inch [0.032 m] grade ballast head was not polished to replicate the wear band that would be present on in-situ rails. Hourly temperature measurements were taken in two ways. The first involved inserting a dial thermometer into a 1¼-inch [0.032 m] fishbolt hole in the centre of the web. The second used a fishbolt hole 13/16 inch [20.64 mm] in diameter and 1 ¼ inches [0.032 m] in depth on the head surface of the rail. The head hole was filled with mercury, and a standard mercury-in-glass thermometer with a range from 20⁰F to 230⁰F [−6. 67⁰C to 110⁰C] was used. Due to the inaccuracies of the dial thermometer, its measurements were discarded, and the focus was on the mercury-inglass thermometer measurements. The problem was simplified by considering the components of heat balance only at the upper horizontal surface of the rail. This was justified by saying that, under normal conditions, the maximum temperature within the rail would be on the upper surface, which was directly exposed to the sun and would, therefore, experience the maximum temperature conditions. This assumption has some flaws. As Ryan (2005) showed, the surface head temperature was, in fact, cooler than the internal temperature, even when radiant heaters were directly 45⁰ at the head surface. This is because wear on the head or upper horizontal surface causes it to become very polished, so that most short-wave radiation is reflected. In fact, more heat is absorbed on the web and foot because it is rusted and has a much lower albedo than the upper horizontal surface. Again, this is demonstrated in the RSSB report (Ryan 2005). Whittingham (1969) defined heat flow as positive when directed towards the reference level, and used the conservation of energy equation given below. Rn H Q 0 (2.15) where: Rn = radiation component H = convection component Q =conduction component The prediction developed for maximum rail temperatures for Brisbane is shown in Equation 2.16: CRC for Rail Innovation th 9 August 2011 Page 25 Track Stability Management Trx 1.228Tx 9.7 (2.16) where: Trx = maximum temperate in the rail [⁰F] Tx =the screened maximum temperature [⁰F] This equation had a correlation coefficient R of 0.866 and a standard error of estimation of 4.13⁰F [2.3⁰C]. However, it was developed in the 1960s, and instrumentation accuracy has improved dramatically since then. Rail profiles and track structures have also changed substantially. For these reasons, this equation may not be accurate for current track configurations and materials. Whittingham (1969) also used this maximum temperature equation to draw up a map of Australia with an isotherm of recorded average maximum screened air temperatures. The argument for this was that the maximum screened temperature corresponded to when the sun was at its maximum meridian altitude over Brisbane. Whittingham found that the maximum rail temperature coincided with the maximum screened temperature. He also found that, throughout the year, the maximum meridian altitude angle in Brisbane (range greater than 70⁰ to 90⁰) corresponded to the maximum meridian altitude for Southern Tasmania and the tropics respectively. In this way, he extrapolated the Brisbane equation for other areas of Australia. Both the assumptions used by Whittingham were proven incorrect in subsequent experiments conducted by Chapman et al. (2005), who found that rail temperature is affected by air temperature, humidity, and orientation. These factors have a substantial effect on rail temperature, and are very different in Brisbane than they are in the tropics or southern Tasmania. Figure 2.14 shows the maximum expected rail temperatures in Australia as determined by Whittingham, converted to degrees centigrade by Hagaman and Kathage (1988) as a part of rail design standards in Australia. Figure 2.14: Maximum Expected Rail Temperatures in Australia (Hagaman & Kathage 1988) From July 2008 to February 2010, Munro (2009) conducted an experiment similar to that carried out by Whittingham, this time on Victoria’s regional rail network. Munro’s aim was to establish whether the information shown in Figure 2.14 was accurate, and whether a modification of Equation 2.16 would be more accurate for the temperate Victorian climate. CRC for Rail Innovation th 9 August 2011 Page 26 Track Stability Management Munro instrumented six sites around regional Victoria with weather stations and the in-situ stress-monitoring product RSMs. Munro used regression equations with data from weather stations located next to the tracks and from the nearest BoM weather station. Equations 2.17 and 2.18 were used to calculate the rail temperature. Trail a Tair Trail aT . air b.S cW . n d .H (2.17) (2.18) where: Trail &Tair = defined previously a,b,c,d = experimentally determined coefficients S = solar radiation [MJ/m2] Wn = wind intensity [km/h] H = relative humidity [%] Munro‘s findings are given in Table 2.7. Table 2.7: Munro’s Main Findings (Munro 2009) Parameter Rail elevation Rail orientation (N–S or E–W) Sleeper material Relative humidity Wind intensity Data from BoM and from weather station beside track Effect on rail temperature No significant correlation found between the sites with highest and lowest elevation (~400 m difference); however, more investigation is required to increase the sample size. N–S direction has higher rail temperatures relative to E–W rails. Rails on timber sleepers are 7–15% hotter than rails on concrete sleepers. Effects on prediction were minimal (0.5–1% improvements in regression accuracy). Wind effects were non-linear and specific to each site. Rail-temperature regression equations found from BoM data had an average correlation factor of 0.796 with data measured trackside, whereas trackside weather-station data and rail temperature had a correlation factor of 0.918. Both the map of isomers (Figure 2.14) and Munro’s results face the same problems as the methods used by Hunt (1994) and Esveld (2001)—that is, they are not suitable for use as a real-time prediction tool because of the large variations in rail temperature that any location would experience. In fact, Munro notes that real-time temperature calculations using AWSs on sites with critical rail temperatures are an expensive solution to predicting rail temperatures. 2.5.2 RSSB UK Rail-temperature Model Chapman et al. (2005) developed a rail-temperature model using a simplified profile of the rail shown in Figure 2.2a. Chapman et al. validated their findings by conducting two field tests. Site 1 was at Winterbourne, with a small section of rail clamped onto two sleepers sitting on a bed of ballast to UK standards, fitted with screened air temperature sensors. Three Type K magnetic thermocouples were adhered CRC for Rail Innovation th 9 August 2011 Page 27 Track Stability Management to the head, web and foot1 of the rail, and the head of the rail was polished to simulate the wear band present on in-situ rails. Site 2 was at Leominster, next to a ”live” track, where a weather station was installed and rail temperature was measured using a temperature sensor secured to the rail foot (Hima Sella sensor, with the sensor electrically insulated from the track to prevent interference with signalling).The study team collected data over a 12-month period from June 2003 to June 2004. The study found that it was not uncommon for the temperature of the rail-head to be twice that of the air temperature (⁰C) in the afternoon, but that it was more common for the rail to be cooler than the ambient air temperature because of the high thermal conductivity and diffusivity of the rail steel’s microstructure. The largest difference in profile temperatures was between the head and the foot in summer months. This difference reached a maximum of 3.7⁰C, with similar differences found between the web and the foot temperatures. Chapman et al. also found that the differences in profile temperatures of tracks orientated north– south were greatest in the afternoon because the west-facing side of the web and head was in direct sunlight. The highly reflective polished head absorbed less direct-beam radiation, whereas the unpolished and rusted rail web received more radiation and heated up more. Chapman et al. observed that rail-profile temperature differences increased throughout the day and peaked in late afternoon, then decreased with the onset of dusk. After sunset, the profile temperature differences became negligible as the rail rapidly cooled. Profile temperature differences were short-lived and the differences minimal. Chapman et al. found that the presence of moisture was very important. The large difference between air and rail temperature in summer was not observed when heavy rainfall and high humidity caused convective cooling of the rail and clouds blocked beam radiation. When there were intervals of rainfall and sunshine, the rail adjusted to changes in incoming solar radiation and moisture, although time lags in heating and cooling were observed. Chapman et al. found a non-linear relationship existed between maximum rail and air temperatures as a result of environmental factors such as track orientation, exposure to sun or wind, humidity, precipitation and cloud cover. While empirical relationships such as those stated by Hunt (1994) and Esveld (2001) provide good results for tracks from which data can be collected, they cannot be used for tracks where similar direct-measurement data cannot be collected, because of these environmental factors. Chapman et al. proposed a more sophisticated method using a zerodimension energy balance approach to predict an equilibrium service temperature with the simplified rail track geometry seen in Figure 2.15b. 1 Note that Chapman et al. use the term “soffit” to imply the whole rail foot, even though “soffit” is generally used to refer only to the underside of the rail foot. In this discussion, the term “foot” is used to refer to what was called “the soffit” in the original work. CRC for Rail Innovation th 9 August 2011 Page 28 Track Stability Management Figure 2.15a: Cross-section of Rail Profile (Chapman et al. 2005) Figure 2.15b: Schematic of the simplified model rail (Chapman et al. 2005) CRC for Rail Innovation th 9 August 2011 Page 29 Track Stability Management By balancing the energy of three types of heat transfer—conduction, convection and radiation—net radiation flux of the rail web and the rail-head can be calculated. The governing equations are shown in Equation 2.19 to Equation 2.21. RN H H H LEH QSH 0 (2.19) RNWsun HWsun LEWsun QSWsun 0 (2.20) RNWshade HWshade LEWsun QSWshade 0 (2.21) where: RN = net radiation flux [W/m2] H = sensible heat flux [W/m2] L E= latent heat flux [W/m2] QS = thermal conduction [W/m2] Subscript W = rail web Subscript H = rail-head Subscript shade = rail track surface in shade Subscript sun = rail track surface in sun Chapman et al. further developed a prediction equation for the rail foot, as they believed that the rail foot was the most practical place for rail personnel to measure rail temperatures. However, they admitted that it might not be the most representative of rail temperatures—as confirmed by Ryan (2005). A two-dimensional diffusion equation was used to calculate heat flow within the track, which could be used for the head and web of the rail: 2T 2T T K S 2 2 t z x where: Ks = thermal diffusivity of rail T= temperature (2.22) t = the local apparent solar time x and z = dimensions shown in Figure2.19b Chapman et al. simplified the problem by assuming that: there was no heat exchange between underneath the foot and the air some parts of the foot surface would be exposed to direct beam radiation. This prediction equation was tested against the physical measurements over a 200-day period at the Winterbourne site. Weather data was collected from the weather station located at the site, but cloud conditions were not measured at Winterbourne, so those from the nearest UK meteorological office (Coleshill— 9 miles [14.48 km] from Winterbourne) were used. Chapman et al. used statistical analysis on predicted temperature and actual measured temperature to find the overall bias and root mean square error as shown in equations 2.23 and 2.24. Overall bias equation is presented in Equation 2.23: Modeli Actuali n i 1,24 n (2.23) where: Every 24 measurement was taken Overall bias = 0.2°C CRC for Rail Innovation th 9 August 2011 Page 30 Track Stability Management Maximum temperature bias = −0.36°C Minimum temperature bias = −0.21°C. Root means square error was calculated: n i 1,24 Modeli Actuali 2 (2.24) n Chapman et al.’s overall root mean squared error (RMSE) = 2.5°C, maximum temperature RMSE = 2.53°C, and minimum temperature RMSE = 2.02°C. The mean maximum temperature lag was −44 minutes, and mean minimum temperature lag was −19 minutes. The Chapman et al. model tends to underestimate rail temperatures, which may make it problematic to use as part of a buckling-prevention system. The actual temperature of the rail may be higher than the predicted temperature, and the time that the actual maximum occurs may be sooner than predicted. This could result in a rail experiencing a larger-than-expected temperature increase sooner than expected. Also, Chapman’s simplification of the model may artificially reduce the heat-transfer properties of the rail, as an actual rail has a much larger surface area than the simplification. This makes the model susceptible to underestimating a rail’s convective heat transfer. However, because wind does not move at high speeds near the ground, this may not be a problem. Chapman et al. also performed a sensitivity test on the model, using the methodology developed by Thornes and Shao (1991) to assess the impact of various parameters in the model on rail-temperature forecast curves.(Thornes and Shao 1991) Chapman et al. used hypothetical data, consisting of constant values of relative humidity = 70%, wind speed = 3 ms-1, precipitation = 0, cloud cover = 4 oktas, and cloud height = medium, with rail and air temperatures varying throughout the day consistent with real data. The results from the sensitivity test were: 1. Latitude: did not change maximum temperatures but increased minimum temperatures at higher latitudes, because increases in latitude result in longer hours of sunlight. 2. Rail orientation: magnitude of maximum temperatures varied only slightly, but the maxima occurred at different times of the day. A double peak is clearly seen in the rails oriented north–south, where the reflective properties of the rail-head reduced the temperature of the rail at midday. The hottest rails were found in the north–west/south–east orientations. In explaining this, Chapman et al. noted that direct-beam radiation coincided with the maximum air temperatures for the day, creating slightly higher rail temperatures. Rails oriented north–east/south–west were found to be the coldest. 3. Rail inclination: the simplification made at the beginning of the model made any subtle changes to the rail geometry minimal; the result of difference is negligible. 4. Air temperature: decrease or increase in air temperature resulted in a decrease or increase in air temperature. Any constant change in air temperature had no effect on the timing of the forecast rail-temperature maxima and minima. 5. Relative humidity: increase or decrease in relative humidity resulted in a small increase or decrease in forecast rail temperatures. The model was most sensitive to changes in humidity when forecasting minimum temperatures in winter, where an increase or decrease in humidity of 20% could change the temperature by around 1°C. CRC for Rail Innovation th 9 August 2011 Page 31 Track Stability Management 6. Cloud cover: change from 3–5 oktas of cloud cover to 8 oktas reduced the maximum temperature forecast by 6.15°C; a change from 3–5 oktas to clear skies increased the forecast by 1.27°C. Cloud cover had negligible effects on the minimum temperature forecast, the time at which neither maxima occurred, and the general shape of the temperature variation of the rail over the diurnal cycle. 7. Cloud height: a small increase in rail temperatures was seen when cloud height was increased from medium to high, and a small decrease in temperature occurred when cloud height was changed from medium to low. There was also a reduction in the magnitude of the curve; the double peak seen with the north–south orientation was far less obvious. 8. Wind speed: increase and decrease in wind speed produced lower maximum and overall rail temperatures. Variations in wind speed appeared to have no effect on the timing of maximum temperatures. 9. Precipitation: rain had a significant impact on suppressing maximum temperature. When the rail was wet, there was an 8.16°C decrease in average and maximum temperatures compared with dry conditions. Temperatures tended to peak slightly earlier when there was rain. Although the model used by Chapman et al. was quite accurate, with a 0.2 overall bias and 2.5 RMSE, simplifying the rail profile to a rectangular structure resulted in negligible effects for rail elevation. The prediction equation was conducted for the rail foot. However, as Ryan (2005) demonstrated, variations of up to 3.7°C can arise between the rail-head and foot because of rail-head emissivity and direct-beam radiation. Potentially, there can be an under-estimate of approximately 5°C between the predicted foot temperature and the head temperature of the rail, which corresponds better to the bulk-deformation temperature (Ryan 2005). Chapman et al. also omitted the ballast and track structure from the energy balance equation, and assumed no heat transfer on the bottom of the foot, so any long-wave ballast inputs were not accounted for. No heat transfer on the bottom of the foot can be justified for rails sitting entirely on sleepers, because sleepers are non-conductive materials, but in-situ rails would have 130 mm sections in contact with sleepers and then 550 mm without contact (and so on), so the proportion of rail not in contact with sleepers would be much higher than that in contact with sleepers. This assumption will be tested in this study. 2.5.3 FRA Rail-temperature Model A model predicting rail-track temperatures for up to nine hours in advance was developed for the northeastern region of the United States by the Federal Railroad Association (FRA) in conjunction with Ensco, Inc (Kesler & Zhang 2007; Zhang & Lee 2008). The model uses existing numerical weather model temperatures, and the transient heat transfer of a floating body to represent a finite rail element. The energy equilibrium equation used is a first-order, non-linear, non-homogeneous, ordinary differential equation as stated in Equation 2.23 (Kesler & Zhang 2007; Zhang & Lee 2008): Eabsorbed Eg Eout Est (2.23) where: Eabsorbed = rate of energy absorbed by rail from the sun and atmospheric irradiation [W/m2] 2 Eout = rate of energy emitted from the rail through convection, conduction and radiation [W/m ] 2 Eg = rate of energy generation due to conversion of energy forms (latent heat) [W/m ] CRC for Rail Innovation th 9 August 2011 Page 32 Track Stability Management Est = rate of energy change [W/m2] The energy balance is affected by weather conditions, rail metallurgical properties, rail size, shape factors and other environmental parameters k s AsGs cos( ) hconv AC (Tr T ) Ar (Tr 4 Tsky 4 ) Eother cV dTr dt (2.24) where: k = atmospheric filtering factor [ #] s = solar absorptivity [#] As = area of rail surface exposed to the sun [mm2] Gs= solar constant [W/m2] = solar angle [⁰] hconv= convective coefficient [W/m2K] AC = area of rail surface subject to convection heat transfer [mm2] Tr = rail temperature [⁰K] T = ambient air temperature [⁰K] = emissivity of rail [#] = Stefan-Boltzmann constant [ W/m2K4] Ar= area of rail surface subject to radiation heat transfer [mm2] Tsky = atmospheric sky temperature above the cloud level [⁰k] Eother = term for heat exchange at the interface of the rail–sleeper and rail–ballast interfaces = density of rail steel [kg/m3] c = specific head of rail steel [J/KgK] V = volume of rail [mm3] dTr = change of rail temperature over time dt Zhang et al. (2008) used a dedicated weather-prediction service to provide a short-wave solar radiation factor so that the factors that modify incoming environmental radiation were automatically calculated. Zhang et al. would have needed to take a similar approach to Chapman et al. (2005) if MetwiseTM (a commercial division of the USA National Weather Service) had not been used. The convective heat transfer coefficient was found using Equation 2.25. a bvwin , for v win 5m/s hconv 0.78 c(vwin ) , for v win > 5m/s where: a = 5.6 b = 4.0 c = 7.2 Vwin = wind velocity m/s CRC for Rail Innovation th 9 August 2011 (2.25) Page 33 Track Stability Management Equation 2.25 is an empirical equation, developed by the USA’s National Institute of Standards and Technology. As Zhang et al. noted, there was no standard method for determining the heat-transfer coefficient, but it was sufficient for rail predictions. Like Chapman et al. (2005), Zhang et al. simplified the model so that the heat exchange between the sleeper and the ballast was assumed to be zero (no heat transfer). Zhang et al. assumed that there was no energy generation due to energy conversion. However, because of the height of the rails, there would be phase transformations in atmospheric species from evaporation, so it is unclear why Zhang et al. assumed no energy conversion in the energy balance. Sky temperature was used to find outgoing net heat from the rail; this was estimated to be −20°C below air temperature. The true value for this variable would have been affected by cloud, aerosols, and particles in the atmosphere, so this simplification was used. As Zhang et al. admit, this is highly inaccurate, but there were no other simple ways to quantify this top-of-atmosphere temperature. Zhang et al. developed a flow chart (shown in Figure 2.16), to show where rail-temperature prediction could be used in the operation and management architecture of railways. Figure 2.16: Flow Chart of Rail Representation of Influencing Factors (Kesler & Zhang 2007) The forecast results produced by Zhang et al. were validated against results obtained from a 9 km x 9 km area covering 10 north-eastern USA states. There was a maximum difference of 2°C and 4°C for windy days between predicted temperature and measured temperature. The discrepancy was largest on windy days because the forecast wind speed differed significantly from local values. This could have been due to a number of factors. Wind speed and direction at the point where an anemometer is installed can vary significantly from track level, while obstacles such as trees, bushes and buildings can shield the track from wind so that it is not cooled as much as expected. The correlation of forecast rail temperature and actual measured rail temperature is shown in Figure 2.17: CRC for Rail Innovation th 9 August 2011 Page 34 Track Stability Management Figure 2.17: Predicted and Measured Daily Maximum Rail Temperatures (Zhang & Lee 2008) Both Chapman et al. (2005) and Zhang et al. (2008) have developed models that are relatively accurate for predicting rail temperature. However, improvements can be made by more realistically modelling the surface of the rail, and by taking into account the bottom surface of the rail foot and its heat transfer. Both models were also developed for sections of rail, rather than for in-situ rails with passing trains. While Chapman et al. had a temperature sensor on the rail foot, it was used only for validation rather than to collect data to develop the model. The current study will be the first to use in-situ rail profile temperatures. 2.6 Concluding Remarks on Existing Rail-temperature Prediction This review of the literature has found that empirical weather-prediction methods are either inaccurate for the purpose of predicting rail temperature, or require an observation-gathering period that is too long for the time available for this study. The review has also found that existing rail-temperature models do not take into account heat transfer on the bottom surface of the rail, or the additional heat inputs of frictional heat . Chapman et al. (2005) did consider friction, but ruled it out as a heat source because their empirical data showed only a very small increase in temperature caused by friction. However, this was contrary to empirical data later collected by Frohling et al. (2008). In addition, the placement of sensors on the in-situ track used by Chapman et al. (2005) was shown to be not the most representative of rail temperature in the railtemperature report produced by Ryan (2005). The current study aims to: verify if there is heat exchange on the bottom of the rail foot quantify if heat generated by friction should be considered in a rail-temperature model. CRC for Rail Innovation th 9 August 2011 Page 35 Track Stability Management 3. Research Methodology 3.1 Weather Predictions Australia’s railway networks extend over large, often remote, geographic areas, where there are no permanent weather stations operated by the BoM or other enterprises. Therefore, weather predictions must be accurate over large geographic areas to meet the operational needs of the railway industry. Furthermore, the horizontal resolution of the forecast is also important. Railway networks pass over and through various topological features (e.g. mountains, valleys, built-up areas), all of which may influence weather patterns and must be accounted for in weather predictions. Thus, any resolution chosen must take into account the orographic forcing caused by topology (Pielke SR 2002). In the initial stages of this study, the available weather services and forecasts provided by the BoM were audited. From this audit, it emerged that the BoM offers a subscription service providing 48-hour advance weather predictions for all locations in Australia, with an 11 km resolution. The predictions are generated using BoM’s ACCESS-A NWP product (Bureau of Meteorology 2010). For the purposes of the study, the aims of the weather prediction were to: verify the accuracy of the unmodified ACCESS-A NWP product against the measured weather variables at the field experiment site downscale the ACCESS-A NWP data at a specific location into a 3.06 km horizontal and 15-minute time resolution from the original 11 km horizontal and 1-hour time resolution. This would allow it to be applied to more specific track locations. 3.1.1 Tasks Involved in Producing a Downscaled Weather Forecast Figure 3.1 shows a flow chart of the tasks involved in producing a downscaled weather forecast. BOM forecasted data at Relevant location is found close to the field experiment al site Interpol ation Forecast data at approximatel y 3km horizontal Data is rearranged from a geographic location Data can be used for multivari ate Figure 3.1: Flow Chart of Predictive Weather Model CRC for Rail Innovation th 9 August 2011 Page 36 Track Stability Management Figure 3.1 shows both unmodified (or raw) BoM data as well as the interpolated BoM data. The accuracy of a weather prediction is important to any subsequent rail-temperature predictions, so any modifications needed to be as accurate as the unmodified product. Different function codes in MATLAB were written to transform ACCESS-A into a useable format for multivariate regression. Functions were written to: 1. extract the relevant weather variables from netCDF format into a .mat format, which is easily processed by MATLAB 2. target the geographic locations of interest within the ACCESS-A domain 3. interpolate all the weather variables in two dimensions 4. rearrange a matrix field of weather variables in the geographic domain into a matrix field of weather variables in the time domain 5. interpolate all weather variables in time. 3.1.2 Network Common Data Format (netCDF) files The netCDF format was chosen for the BoM weather prediction data because this format has a set of access libraries for C, and MATLAB software Version 2008b has functions that use these C libraries, in particular for indexing files. netCDF is a set of interfaces for array-oriented data access, with a freely distributed collection of dataaccess libraries for C, Fortran, C++, Java, and other languages (Rew 2010). According to Rew (2010), the main features of netCDF are as follows: netCDF files include information about the data they contain netCDF files can be accessed by computers with different ways of storing integers, characters, and floating-point numbers a small subset of a large dataset may be accessed efficiently data may be appended to a properly structured netCDF file without copying the dataset or redefining its structure one writer and multiple readers may simultaneously access the same netCDF file. The netCDF file format and subsequent software were developed by Glenn Davis, Russ Rew, Ed Hartnett, John Caron, Steve Emmerson, and Harvey Davies at the Unidata Program Centre in Boulder, Colorado, with contributions from many other netCDF users (Rew 2010). 3.1.3 Cubic Spline Interpolation Cubic spline interpolation was used to interpolate between the latitude and longitude points within the horizontal BoM data, in order to find a resolution of 3.06 km from the original 11 km resolution. The MATLAB function for bi-cubic spline interpolation ‘griddata’, with the method ‘cubic’, was used. This was decided in consultation with Mr Ivor Blockley from Operations Development at the BoM’s NMOC (Blockley 2010), who advised that a more advanced scheme similar to cubic interpolation is used for operational forecasts. CRC for Rail Innovation th 9 August 2011 Page 37 Track Stability Management The theory behind the MATLAB function is the quick hull algorithm for convex hulls (Barber et al. 1996). The one-dimensional interpolation through time uses the MATLAB function ‘spline’, which in turn uses the spline interpolation algorithm described by de Boor (1978).(De Boor 1978) 3.2 Predicting the Temperature of the Rail Track Due to Weather Conditions ACCESS-A weather variables were used in a multivariate linear regression analysis with the measured averaged rail temperatures to find a rail-temperature regression equation. A selection of the full ACCESS-A weather variable fields was used for the rail-temperature regression analysis. Variables such as below-ground soil temperatures, horizontal visibilities, etc., were not used because they would not affect rail temperature. ACCESS-A variables used in the regression analysis were: 1. v10: meridional component wind at 10 m height [m/s] 2. u10: zonal component wind at 10 m height [m/s] 3. temp_scrn: screen level temperature [⁰k] 4. dewpt_scrn: dewpoint screened temperature 5. sfc_pres: surface pressure [Pa] 6. accum_prcp: accumulated precipitation [kg m-2] 7. mslp: mean sea-level pressure [Pa] 8. accum_evap: accumulated evaporation [kg m-2] 9. av_lat_hflx: average surface latent heat flux [Wm-2] 10. av_lwsfcdown: average downwards longwave radiation at the surface [Wm-2] 11.av_netlwsfc: average net longwave radiation at the surface [Wm-2] 12.av_netswsfc: average net shortwave radiation at the surface [Wm-2] 13. av_olr: average outgoing longwave radiation at the surface [Wm-2] 14.av_sens_hflx: average sensible heat flux [Wm-2] 15.av_sfc_sw_dif: average surface shortwave diffuse radiation flux [Wm-2] 16.av_sfc_sw_dir: average surface shortwave direction radiation flux [Wm-2] 17.av_swirrtop: average incoming shortwave radiation flux [Wm-2] 18.av_swsfcdown: average downwards shortwave radiation at the surface [Wm-2] 19. mid_cld: mid cloud cover [0–1] 20.qsair_scrn: screen level (1.5 m) specific humidity [kg kg-1] 21.sens_hflx: surface sensible heat flux [Wm-2] 22.sfc_temp: surface temperature [⁰K] 23.soil_mois: soil moisture [kg m-2] 24.soil_temp: soil temperature [⁰K] 25. tmax_scrn: screen level (1.5 m) maximum temperature [⁰K] 26.tmin_scrn: screen level (1.5 m) minimum temperature [⁰K] 27.ttl_cld: total cloud cover [0–1] 28.z0: roughness length [m]. 3.2.1 Tasks Involved in Producing Rail-temperature Prediction Figure 3.2 is a flow chart of the tasks involved in producing a rail-temperature prediction. CRC for Rail Innovation th 9 August 2011 Page 38 Track Stability Management Weather data formatted by MATLAB into the time domain Multivariate linear regression Rail temperatur es Figure 3.2: Flow Chart of Predictive Rail-Temperature Model Figure 3.2 shows the linear progression of inserting the weather data and generating rail-temperature predictions. One function in MATLAB was written to perform regression analyses on the weather variables. 3.2.2 Multivariate Linear Regression Multivariate linear regression was chosen as the method to calculate rail temperatures from the weather variables. This is this same method used by Whittingham (1969) and Munro (2009) to calculate rail temperatures. The MATLAB function used for multivariate linear regression is ‘mvregress’. ‘mvregress’ uses an expectation condition maximisation (ECM) algorithm, which is an iterative method that finds maximum likelihood in incomplete data-sets (Meng & Rubin 1993). In this study, the ECM algorithm was used for a full data-set; thus, the ECM is a specialised case of a cyclic coordinate accent method for function maximisation in the optimisation literature on iterative proportional fitting (Zangwill 1969; Haberman 1974). 3.3 Frictional Heat Quantification Heat generated by train passage was captured by the field experimentation described in Chapter 4. The data from this the field experiment was analysed statistically to quantify the temperature increase due to train passage over the rail. The variance and standard deviation of the measurements were used to indicate heat added to the track as a result of the train passage. The formulas used to calculate variance and standard deviation are listed below in Equation 3.1 and Equation 3.2 respectively (Weisstein 2010). (3.1) 1 N 2 2 S S where: S = variance S2= standard deviation N =total number of samples [#] N 1 N x x i 1 i N xi x 2 (3.2) i 1 i = the sample number within the set of data x = the value of the data x = the mean of the data-set 3.4 Statistical Analysis of Measured Data and BoM Data Some information is repeated between field experimentation data (as described in Chapter 4) and purchased BoM data. Both the weather station and the BoM provided weather information about the site, and both the thermocouple sensors and the RSMs provided rail-temperature information. CRC for Rail Innovation th 9 August 2011 Page 39 Track Stability Management Repeated values were checked for consistency, and then used in further analysis. Consistency checks included: comparing predicted BoM variables with those measured by the weather station for the month comparing the surface profile temperature over the measurement period (this included the RSMs rail-temperature data). Data from both the weather station and the BoM were used in the regression analysis. The weather station provided a set of real-time weather variables, while the BoM provided a set of predictive variables. Statistical comparisons between measured and calculated temperatures included: 1. comparing real-time, future predictive rail temperatures and empirical methods for accuracy 2. comparing BoM-interpolated temperatures with the raw BoM-predicted rail temperatures for accuracy. In addition, statistical comparisons included: taking the difference between the variables measuring the same phenomenon finding the correlation, overall average bias and overall average root mean squared error (RMSE) between the calculated and measured rail temperatures. The equations to calculate correlation, overall average bias, and overall average RMSE are listed in equations 3.3, 3.4 and 3.5 respectively. (3.3) 1 N ( xi x )( yi y ) N 1 i 1 r N 1 1 N ( xi x ) 2 ( yi y ) 2 N 1 i 1 N 1 i 1 (3.4) x y Biasoverall RMSEoverall where: N = total number of samples [#] x = measured variable x = mean of the measured variables N x y 2 (3.5) N y = predicted variable y = mean of the predicted variable i = the sample number within the set of data Figure 3.3 shows the statistical comparisons and analyses carried out during the study. CRC for Rail Innovation th 9 August 2011 Page 40 Track Stability Management BOM forecasted data at 11km Data is reduced to relevant geographic area Interpolatio n Forecast data at 3km horizontal resolution for specific site location Comparison 1 BOM forecasted data at 11km Data is reduced to relevant geographic area Data is rearranged from geographic domain to time domain Weather measured data Multivariate regression Comparison 3 Comparison 2 List of rail temperature values from interpolated BoM data List of rail temperature values from unmodified BoM data List of rail temperature values (from weather station regression) Measured rail temperatures from thermocouples Measured rail temperatures from RSM Figure 3.3: Flow Chart of Methodology Figure 3.3 shows that statistical analysis was performed at several stages of the study, and that data sources and the study results were evaluated. CRC for Rail Innovation th 9 August 2011 Page 41 Track Stability Management 4. Experimental Design The aim of this study was to develop software to enable the accurate prediction of rail-track temperatures. While other Australian projects have attempted to calculate rail temperatures (Whittingham 1969; Munro 2009), this is the first attempt to predict rail temperatures using an NWP product. An important part of the current study was to compare the accuracy of the new software with that of existing technology and methods for predicting rail temperatures. In order to compare the new method to previous research (Whittingham 1969; Munro 2009), an experimental design similar to that used by Munro (2009) was devised. This field experiment employed: an automated weather station (AWS) to measure weather variables thermocouple temperature sensors to measure rail surface temperatures RSMs (rail stress modules), an off-the-shelf product to measure rail temperatures. Each played a different function in the study. The weather station provided the screened air temperatures and wind velocities used by Whittingham (1969). It also provided the necessary information to check the accuracy of the NWP product, ACCESS-A, purchased from the BoM. The thermocouples provided rail surface temperatures across the profile of the rail. The RSMs allowed the researchers to compare the accuracy of the program developed for this study to an existing product that monitors rail temperature. The equipment and configuration of the field experiment are described in more detail below. 4.1 Site Layout The field test site was at Edungalba, central Queensland, on the QR national coal network, located at latitude 23.7⁰, longitude 49.9⁰. The thermocouples and RSMs were installed on a 4 m section of the right rail and a 6 m section of the left rail. The different rail lengths were chosen for ease of identification (the thermocouple configurations were different on the two rails). The rail track was located on an embankment approximately 3 m above the ground level of the rail corridor. Under QR National’s track-safety protocol, none of the data acquisition system (DAQ) equipment or power supply could be installed within 3 m of the track centre-line (known as the “danger zone”). Accordingly, the DAQ box was installed just outside of the danger zone, and the power supply (which was larger) was installed in the rail corridor below the embankment. A network cable connecting the DAQ box to the power supply enabled study personnel to download the thermocouple data without having to walk near the danger zone. A diagram of the instrumentation rail sections as installed on the real track is shown in Figure 4.1. CRC for Rail Innovation th 9 August 2011 Page 42 Track Stability Management Figure 4.1: Instrumented Rail Sections Installed on the Track (NB: Figure 4.1 also includes strain gauges, which were not used for this study but related to another study that also used the track instrumentation.) 4.2 Thermocouples and Rail-temperature Measurements A thermocouple is a device that converts thermal energy into electrical energy. Thermocouples work on the Seebeck, Peltier and Thomson effect (Pollock 1993). The type of thermocouple sensor used for this study is shown in Figure 4.2. Figure 4.2: Cement on Polyimide Thin-film Thermocouple (TC Direct 2009) The thermocouple sensors chosen for this study are cement on polyimide thin-film thermocouples— aerostructure grade (TC Direct 2009). Their specifications are as follows: Type T Class 1 CRC for Rail Innovation th 9 August 2011 Page 43 Track Stability Management temperature measurement range of −250⁰C to 300⁰C accuracy of +/−0.004*(temperature measured) or 0.5⁰C at all other temperatures dimensions are 20 mm x 10 mm x 0.13 mm thick. Before field installation, the thermocouples were compared with existing Type K thermocouples to check for consistency of temperature measurement. 4.2.1 Thermocouple Set-up on Rail Profile Fifteen thermocouples were adhered to the surface of the two rail sections. The configuration of the set-up is shown in figures 4.3a and 4.3b. Figure 4.3a: Position of Thermocouples on Rail Profile Figure 4.3b: Numbered Thermocouple Sensors for Easy Identification CRC for Rail Innovation th 9 August 2011 Page 44 Track Stability Management There were 17 surface thermocouples in total, with 15 sensors actively taking measurements and 2 residual sensors in Position 8 and Position 16. The two residual sensors were backups in case Sensor 7 or Sensor 17 was damaged during installation. The left rail does not have a bottom-of-rail foot sensor because this section of the rail is placed on top of a sleeper, whereas the right thermocouple has a bottom-of-rail foot sensor (Sensor 13) because it sits on top of the ballast. This was to gauge whether temperature transfers from the bottom surface were significant to the heating pattern of the rail overall. Thermocouple measurements were recorded in the field by a National Instrument Compact Rio DAQ (NI 2011). The saved file format was ‘.tdms’. A MATLAB program was written using a National Instrument ‘tdms’ wrapper to import and analyse the results. 4.2.2 Laboratory Test of Thermocouples Thin-film surface thermocouples were installed in the laboratory using adhesive proxy. They were checked for operation by placing two 500 W lamps at a 45⁰ angle approximately 10–20 cm from the sensors. The experimental set-up is shown in Figures 4.4a and 4.4b. Figure 4.4a: Laboratory Experimental Set-up Right rail Figure 4.4b: Thermocouple Sensors Four additional Type K surface thermocouples (lab thermocouples) for each rail were temporarily adhered to the rail with masking tape, and read at 10-minute intervals to check for consistency. An example of the data produced by this comparison is shown in Figure 4.5. CRC for Rail Innovation th 9 August 2011 Page 45 Track Stability Management sensor comparison 80 75 70 Temp deg C 65 60 55 DAQ channel 4 Thermocouple sensor 2 50 45 40 35 0 200 400 600 800 time intervals (/10s) 1000 1200 1400 Figure 4.5: Graph of Thermocouple on Right Web Figure 4.5 shows good correlation between the installed thermocouples and the lab thermocouples (although, because the thermocouples were in different positions and had different accuracies, an exact match was not expected). From Figure 4.5, it was concluded that the field-experiment thermocouples were in working order and the rails could be installed in the field. 4.3 Weather Station Weather variables were measured using a standard weather station WXT50, produced by Vaisala. This was installed approximately 20 m away from the instrumented track section and 10 m above ground level. The weather station measured: screened air temperature [⁰C] relative humidity [%] wind speed [m/s] wind direction [⁰ from north] rainfall—intensity [mm/h], accumulation [mm], and duration [s]. This automated weather station (AWS) conforms to the regulations in the World Meteorological Organisation standard for installing an AWS (WMO 2008). It took measurements every 10 minutes, which were logged in the DAQ and downloaded once every 4 weeks. An image of the weather station and DAQ configuration is shown in Figure 4.6. CRC for Rail Innovation th 9 August 2011 Page 46 Track Stability Management Figure 4.6: Weather Station and DAQ Set-up The measurement range and accuracy of the weather variables measured are listed in Table 4.1 below. Table 4.1: Variables Measured by Weather Station: Measurement Range and Accuracy Weather variable Measurement range Accuracy Barometric pressure 600~1100 hPa Air temperature Wind speed −52⁰C~60⁰C 0~60 m/s Wind direction Relative humidity 0~360⁰ (from azimuth) 0~100% Rainfall accumulation Rain duration Rain intensity 0.01 mm 10-second increments 0~200 mm/h +/− 0.5 hPa at 0⁰C to30⁰C +/− 1hPa at −52⁰C to 60⁰C +/− 0.3⁰C +/−0.3 m/s or +/−3% between 0–35 m/s +/−5% between 36–60 m/s +/−3.0⁰ +/−3% at 0–90%RH +/−5% at 90–100%RH 5% (NB: Where lines are blank in the “Accuracy” column, it is because accuracy in these cases depends largely on other measured variables, such that accuracy is greatly variable.) The recorded weather measurements were saved in a ‘.csv’ format with a date stamp per measurement. 4.4 Rail Stress Modules (RSMs) Two RSMs (see Figure 4.7) were installed alongside the thermocouples as a second way to measure rail surface temperature. The RSMs were designed to measure both surface strain and surface temperature on the neural axis of the rail, but, for this study, only the rail temperature was used. CRC for Rail Innovation th 9 August 2011 Page 47 Track Stability Management RSMs use an integrated temperature sensor, which has: an accuracy of +/−10C from −200C to +600C a battery life of 10 years a storage memory of 7.5 months when using 10-minute measurement intervals (Salient Systems Inc 2009). The wayside weather monitor shown in Figure 4.6 contained a radio that communicated with the RSMs shown in Figure 4.7. The wayside monitor allowed the data stored in each RMS to be downloaded remotely via the phone network. Figure 4.7: RSMs Installed on the Rail in the Field Experiment The RSMs outputted their files in Excel format. A program was written in MATLAB to import and analyse the results. CRC for Rail Innovation th 9 August 2011 Page 48 Track Stability Management 5. Rail-temperature Prediction Software As a part of this study, interactive rail-temperature prediction software was written in MATLAB. The software converts the ACCESS-A netCDF files from the BoM into a graphical forecast of rail temperatures based on Equation 6.15 and Table 6.10 as outlined in Section 6.4. The software consists of one main program, three main functions and an update to the numberconservations program written by Ameya Deoras (Deoras 2010), which is covered by a Berkeley Software Distribution licence and is free for public use. The script for the program is: 1. main.m 2. readncfile.m 3. interpolate.m 4. resize.m 5. dynamicDateTicks.m. (Deoras 2010) A library file beta.mat also needs to be included for the software to run. The user is prompted for the path to this file in the main program. All the above-mentioned files need to be saved in the same directory for the program to run. The program was developed using the July 2010 weather-parameter data-set for the track in the east– west orientation. In addition, it was developed for a Linux system. If it was to be run on a Windowsbased system, alterations to the path import/export routines would need to be made. In the future, these program scripts could be developed into a stand-alone program or excitable software by using the MATLAB compiler (Mathworks 2008). The program is designed to be read in one run of ACCESS-A from BoM at a time. 5.1 Operating the Program The file ‘main.m’ is the main file program that controls all operations and interacts with the user. It calls up the function ‘readncfile’ to read ACCESS-A files in netCDF format, and uses the functions ‘resize’ or ‘interpolate’ depending on whether the user wants to use raw ACCESS data or interpolated ACCESS data. At the start, the program asks the user for the location of ACCESS-A files on the computer, as shown in Figure 5.1a and Figure 5.1b. Figure 5.1a: Program Prompt to Specify Path to Files CRC for Rail Innovation th 9 August 2011 Page 49 Track Stability Management Figure 5.1b: Folder Selection Prompt for Location of ACCESS-A Files The program then asks the user to specify the location of interest in latitude and longitude in degrees. The latitude is positive in the northern hemisphere and negative in the southern hemisphere. ACCESS-A has domain limits of latitude −55.00S to 4.73 N, longitude 95.00E to 169.69E. Figure 5.2 shows the prompt for the user to enter the location of the rail. Figure 5.2: Prompt to Enter Latitude and Longitude of the Location of the Rail After the prompt, the program asks the user if they would like to save the output of the file in the current working directory. This is shown in Figure 5.3. Figure 5.3: Prompt for Location to Save Output Files CRC for Rail Innovation th 9 August 2011 Page 50 Track Stability Management If ‘Yes’, is selected, the output results are saved to the MATLAB working directory, where the program scripts are located. If ‘No’ is selected, another location-selection window prompt will appear, in the same format as Figure 5.1b. The main program then inserts the location of the specified folder and the geographic location of interest in the ‘readncfile’ function. The ‘readncfile’ function imports the netCDF file format into a MATLAB multidimensional structure array format, with a domain of 5.39⁰x5.39⁰ of latitude and longitude surrounding the geographic location of interest. The MATLAB array ‘varnc’ is passed back to the main program, then main asks the user if interpolation of the data is required, as shown in the prompt box in Figure 5.4. Figure 5.4: Prompt Asking if Data Should Be Interpolated If ‘interpolate’ is chosen, the ‘varnc’ variable and the latitudes and longitudes previously entered by the user are fed into the function ‘interpolate’, which interpolates the ACCESS-A variables in the geographical plain and then in the time plain. The function ‘interpolate’ then rearranges the ACCESS-A variables into time-dependent variables in a multidimensional structure array ‘vars’, which has as its fields the variable names from ACCESS (i.e. vars.temp_scrn, vars.v10, vars.sfc_temp, etc.). If ‘raw’ is chosen, the 'varnc' variable and the latitudes and longitudes entered by the user are fed into the function ‘resize’, which rearranges the raw ACCESS-A variables into the multidimensional structural array ‘vars’. If ‘both’ is chosen, the ‘varnc’ is fed both into the ‘interpolate’ and the ‘resize’ function and the operations described above are performed. Once the variable ‘vars’ is passed back to the main program, it prompts the user for the location of the library file ‘beta.mat’, which contains the regression coefficients listed in Table 6.10 in Chapter 6 of this report. After the location of ‘beta.mat’ is established, the main program loads the ‘beta.m’ file. The main program then asks the user if they would like to include Whittingham’s equation calculations (Whittingham 1969) or Hunt’s sunny- and cloudy-day equation calculations (Chapman et al. 2005). If option ‘all’ is chosen, the screened-temperature variable from the ACCESS-A files is used in the empirical relationships to calculate a rail temperature. The main program then calculates rail temperatures accordingly and produces a graph (an example of which can be seen in Figure 5.5). The graph depicts rail temperatures over the period specified in the ACCESS-A files, and saves to the user-specified folder in the ‘.mat’ format of date and time and rail temperatures. CRC for Rail Innovation th 9 August 2011 Page 51 Track Stability Management Figure 5.5: Sample Output of Software with Options of Using Raw BoM Data 5.2 Program Disclaimers The program was developed using data from July 2010, for rail in an east–west orientation, with steel sleepers and fist-clip fasteners, in the central Queensland area. Using the program outside of these parameters may produce results that are not as accurate as the rail predictions listed in Section 6.4 of this report. However, the program could be made more generic if statistical regression factors are found for each season and more samples of rail temperatures and rail configurations are entered as different options. 5.3 Program Run Times The run time of the program was calculated using a quad core Linux system. Run times were approximately: 1. 2 minutes to read in 49 ACCESS-A files 2. 5 seconds to rearrange the ACCESS-A variables into the time domain 3. 3 minutes for the two-dimensional cubic interpolation 4. 19 minutes for the one-dimensional cubic spline interpolation of the already interpolated twodimensional data. It took approximately 25 minutes to run the program interpolating the raw BoM data, and 2 minutes to run the program with only the raw BoM data. Depending on a user’s computer, run times could be faster or slower. CRC for Rail Innovation th 9 August 2011 Page 52 Track Stability Management CRC for Rail Innovation th 9 August 2011 Page 53 Track Stability Management 1. 6. Results and Discussion All field experiments carry the risk of equipment damage. In the case of this study, out of the three data-collection methods (weather station, thermocouples, and RSMs) only the RSMs (a commercial product designed for the railway environment) survived the three-month period in the field. The weather station recorded the full set of weather variables from 31 March 2010 to 8 August 2010. On 18 August 2010, study personnel found a DAQ malfunction that had occurred on 8 August 2010. A visual inspection of the DAQ revealed that the only noticeable fault related to the memory card. A new memory card was installed on the next track visit on 13 October 2010; however, on the next site visit on 11 November 2010, the weather station was found to be recording only wind and precipitation variables. Air temperature, relative humidity, and air pressure were not recorded after 8 August 2010. Due to time constraints, no attempt was made to repair the weather station DAQ. The thermocouples recorded the full set of rail temperatures at one-hour intervals from 30 May 2010 to 13 August 2010. On the track visit on 18 August 2010, study personnel found that the thermocouple DAQ was not recording because the memory card was full, and had stopped recording on 13 August 2010. Also on 18 August 2010, personnel noted that Thermocouple 9, located on the side of the railhead on the right rail (shown in Figure 4.3b), was damaged. Unfortunately, Thermocouple 9 was not repaired and the DAQ was not restarted because the main electrical technician who implemented the DAQ system was not present. On a track visit on 13 October 2010, the DAQ was restarted with new software. The measurement interval was 1 sample per minute and the DAQ was automatically triggered to take 70 samples per second when trains passed the instrumented site. On the track visit on 11 November 2010, the thermocouple DAQ was found to have recorded only three days of data from 13 October 2010 to 16 October 2010. Because of time constraints, no attempt was made to repair the thermocouple DAQ. The RSMs, which also record rail temperature, were installed on 8 March 2010, and are still recording data. ACCESS-A data from the BoM before 26 May 2010 was validation-stage data, as the BoM had only recently moved to ACCESS-A from its previous LAPS NWP product. From 1 March 2010 to 26 May 2010, the ACCESS-A model was running on an SX6 supercomputer and the 6-hour run and 18-hour run were only forecast to +9 hours. Full ACCESS-A data from the BoM was available from 27 May 2010 to 05 December 2010. The period for which all data-sets are available is 30 May 2010 to 8 August 2010—that is, two full months of data in the winter 2010 period. This is not ideal for a study investigating rail buckling due to high temperatures. The data-sets for each analysis are listed below: July 2010 data-set (31 days, 744 samples ) was used for rail-temperature regression analysis June 2010 data-set (30 days, 720 samples ) was used to validate the regression analysis July 2010 data-set (30 days 744 samples) was used to check for consistency between BoM data and weather-station data 30 May 2010 to 13 August 2010 data-set (76 days 1824 samples) was used to check for consistency between thermocouple data and RSMs data CRC for Rail Innovation th 9 August 2011 Page 54 Track Stability Management 30 May 2010 to 13 August 2010 data-set (76 days 1824 samples) was used to quantify the temperature change over the rail profile and between the left and right rail. 6.1 Weather Variables Comparison: Weather Station and BoM data The BoM prediction data was compared with actual measured data from the weather station. The BoM data came in a gridded format, where the weather station is located at latitude −23.7⁰, longitude 149.9⁰. BoM data geographically closest to this location were chosen, and several other surrounding BoM points were chosen to gauge how much the weather variables differed within a 0.2⁰ change in latitude and longitude. Figure 6.1 shows the configuration of BoM data-points in relation to the weather station. Lon:149.67 Lat:-23.65 Lon:149.7 8lat:-23.65 Lon:149.89 Lat:-23.65 Lon:150 Lat:-23.65 Weather station Lat:-23.71 Lon:149.9 Lon:149.67 Lat:-23.76 Lon:149.67 Lat:-23.87 Lon:149.78 Lat:-23.76 Lon:149.78 Lat:23.87 Lon:149.89 Lat:-23.76 Lon:149.89 Lat:-23.87 Lon:150 Lat:-23. Lon:150 Lat:-23.87 Figure 6.1: Location of Weather Station Between Grid Locations of BoM Data The BoM data also came in several runs, with a new prediction file for the next 48 hours made available four times a day, so there is considerable overlap between each prediction file. This is shown in detail in Figure 6.2. CRC for Rail Innovation th 9 August 2011 Page 55 Track Stability Management 0 6 1 1 24 3 3 4 H H 2 8 H 0 6 2 R R H H R H H H R R R R R 4 8 H R Figure 6.2: ACCESS-A Predictions of Each Run and Their Overlap Figure 6.2 shows that the prediction data in Run 1 overlaps 42 hours with Run 2, 36 hours with Run 3 and 32 hours with Run 4. How accurately each run predicts the measured weather variables is not constant; there are slight variations in accuracy between each run. This may be because of variations in the observational data gathered for various runs. For example, Run 1 is a morning run, with the largest number of observations included for the prediction output. On the other hand, night-time runs do not include observation data from radiosonde balloons, which are launched only in the morning in most Australian cities. The correlation coefficients, bias, and root mean squared errors of each run for each location were performed. Overall, Run 1 was found to be most accurate in forecasting most weather variables. The comparisons between each weather-station-measured variable and the BoM equivalent are detailed in sections 6.2.1 to 6.2.6. Run 1 itself had some overlap in predictions, as shown in Figure 6.3. The BoM provides its NWP model with observational data before each run, so shorter-term forecasts should be more accurate than longer-term forecasts (because a longer time elapses between when observational data is taken and when predicted weather will occur for longer-term forecasts). This was confirmed by separating Run 1 into a 1–24-hour forecast and a 25–49-hour forecast. CRC for Rail Innovation th 9 August 2011 Page 56 Track Stability Management 0 6 1 18 24 30 HR H 2 H HR H R H RUN R 1 (dayR1) R 3 42 48 6 H H H R R R RUN 1 (day2) 0 6 HR H R 1 18 poi 30 2 H H R H R R 3 42 48 6 H H H R R R Figure 6.3: ACCESS-A Predictions of the First Run of Each Day and Its Overlaps BoM data forecasts are also in one-hour intervals; that is, only one instantaneous prediction measurement is given for the hour, with the measured weather-station variables gathered every 10 minutes (i.e. the BoM forecast is not an average, but an instantaneous point prediction). Therefore, to compare data-sets, weather-station data was not averaged but was sampled for every sixth 10-minute measurement (i.e. every hour). Thus the time of the measured variable corresponds to the time of the predicted variable. 6.1.1 Screened Air Temperature The BoM variable of screened air temperature is predicted at 1.5 m above ground in degrees Kelvin. Screened air temperature does change with elevation above ground level; however, as a 10 m elevation is within 0.1⁰C of the screened temperature at 1.5 m (Blockley 2010), this was assumed to be insignificant. The BoM variable temp_scrn was converted to degrees Celsius by subtracting 273.15. The graph for July 2010 is shown in Figure 6.4. CRC for Rail Innovation th 9 August 2011 Page 57 Track Stability Management Figure 6.4: Screened Air Temperature July 2010 The temperature variation plotted corresponds very well with the measured temperature, although there are some minimum temperature extremes around 19 and 20 July and 23 and 24 July that the predicted temperature does not account for. After checking the rain-gauge measurement for these days, study personnel found that there were large amounts of precipitation on those days, which could account for the temperature difference in predicted and measured values. The screened temperature corresponded well with the actual measured air temperature; the correlation factor, overall average bias, and overall root mean squared error are tabulated in Table 6.1. The formula for calculating the correlation coefficient is explained in Chapter 3 of this report. Table 6.1: Correlation Coefficients of Screened Air Temperature Screened Air Temperature Correlation Coefficient Run 1 (1–24-hour prediction) Run 1 (25–49-hour prediction) lon:149.67 lat:–23.65 0.945 0.916 lon:149.78 lat–23.65 0.943 0.918 lon:149.89 lat:–23.65 0.940 0.921 lon:150 lat:–23.65 0.938 0.923 lon:149.67 lat:–23.76 0.943 0.915 lon:149.78 lat:–23.76 0.941 0.916 lon:149.89 lat:–23.76 0.940 0.920 lon:150 lat:–23.76 0.939 0.923 lon:149.67 lat:–23.87 0.938 0.913 lon:149.78 lat:23.87 0.938 0.913 lon:149.89 lat:–23.87 0.936 0.916 lon:150 lat:–23.87 0.936 0.919 From Figure 6.4, it can be seen that screened air temperature is a very stable variable, reflected in the consistently high correlation coefficients shown in Table 6.1. The fact that the geographically closest CRC for Rail Innovation th 9 August 2011 Page 58 Track Stability Management points do not have the highest correlation coefficients (which are bolded) is unexpected but not impossible, because the difference in correlation is within +/−0.025 at about 0.942 and the variable does not vary overly much across the landscape. It is possible that a grid point had very similar temperatures, which coincidently corresponded slightly better with the measured temperature. The correlation was separated into the first 1–24-hour prediction and the 25–49-hour prediction. As expected, the forecast decreased in accuracy over time. For a detailed explanation of overall bias calculation, see Chapter 3 of this report. The overall biases in degrees Celsius are listed in Table 6.2. Table 6.2: Screened Air Temperature Overall Bias Screened Air Temperature Overall Bias Run 1 (1–24-hour prediction) Run 1 (25–49-hour prediction) lon:149.67 lat:–23.65 –0.816 –0.889 lon:149.78 lat:–23.65 –0.792 –0.856 lon:149.89 lat:–23.65 –0.677 –0.751 lon:150 lat:–23.65 –0.550 –0.632 lon:149.67 lat:–23.76 –0.739 –0.809 lon:149.78 lat:–23.76 –0.719 –0.770 lon:149.89 lat:–23.76 –0.585 –0.642 lon:150 lat:–23.76 –0.478 –0.547 lon:149.67 lat:–23.87 –0.604 –0.667 lon:149.78 lat:23.87 –0.642 –0.687 lon:149.89 lat:–23.87 –0.482 –0.534 lon:150 lat:–23.87 –0.365 –0.396 From the overall bias, it can be seen that the location with the highest correlation factors actually has the highest bias, which indicates that the reasoning behind the discrepancy of correlation is sound. Overall RMSE was performed on the data-sets to see what difference existed between the measured and predicted samples. This is presented in Table 6.3. Table 6.3: Screened Air Temperature Overall RMSE Screened Air Temperature Overall RMSE Run 1 (1–24-hour prediction) Run 1 (25–49-hour prediction) lon:149.67 lat:–23.65 1.980 2.343 lon:149.78 lat:–23.65 1.992 2.303 lon:149.89 lat:–23.65 1.976 2.243 lon:150 lat:–23.65 1.954 2.172 lon:149.67 lat:–23.76 1.992 2.331 lon:149.78 lat:–23.76 1.992 2.305 lon:149.89 lat:–23.76 1.969 2.234 lon:150 lat:–23.76 1.934 2.160 lon:149.67 lat:–23.87 2.051 2.347 lon:149.78 lat:23.87 2.031 2.330 lon:149.89 lat:–23.87 2.029 2.280 lon:150 lat:–23.87 1.997 2.207 CRC for Rail Innovation th 9 August 2011 Page 59 Track Stability Management Table 6.3 shows that the lowest overall RMSE is at the BoM data-point longitude 150, latitude –23.65, which corresponds to one of the nearest geographical locations of the BoM data-points. It should be noted that correlation coefficient, although a good indicator of correlation, does not necessarily indicate the closest geographic location when the variable is highly stable across the landscape. Statistically, the geographic BoM data-points do not vary greatly for screened air temperature. This indicates that a weighted combination of the statistical factors needs to be considered when deciding which raw BoM data-point should be used, because correlation alone is not the best indication in this instance. A weighted correlation, bias, RMSE factor for screened air temperature is calculated using Equation 6.1 below. (6.1) R Correlation 10 bias RMSE screen _ temp where Rscreen_temp is the weighted factor for screened air temperature. A factor table is included below. Table 6.4: Weighted Factor for Screened Air Temperature Rscreen_temp lon:149.67 lat:–23.65 lon:149.78 lat:–23.65 lon:149.89 lat:–23.65 lon:150 lat:–23.65 lon:149.67 lat:–23.76 lon:149.78 lat:–23.76 lon:149.89 lat:–23.76 lon:150 lat:–23.76 lon:149.67 lat:–23.87 lon:149.78 lat:23.87 lon:149.89 lat:–23.87 lon:150 lat:–23.87 Run 1 (1–24-hour prediction) 6.656 6.645 6.751 6.881 6.696 6.703 6.845 6.980 6.723 6.710 6.850 6.995 Run 1 (25–49-hour prediction) 5.924 6.024 6.212 6.428 6.009 6.089 6.324 6.520 6.115 6.115 6.345 6.591 From the weighted factor Rscreen_temp, it can be seen that the geographic location of the BoM data closest to the location of the actual weather station does correspond; however, this could not be used to decide which raw BoM data-point should be used in analysis until other weather variables had been checked. 6.1.2 Relative Humidity Relative humidity is not a quantity in the BoM data fields; however, the BoM data fields do include dewpoint temperature and screened air temperature, which can be used to calculate relative humidity. The relative humidity conversion formula (Lowe & Fickle 1974) in equations 6.2, 6.3, and 6.4 was used to convert the two BoM field quantities into relative humidity. Relative humidity is a calculation of the moisture content in the atmosphere, so both the dewpoint (the temperature at which air can no longer hold all of its water vapour, and some must condense into liquid) and the actual air temperature need to be considered. RH (6.2) e(TD ) 100 e(T ) CRC for Rail Innovation th 9 August 2011 Page 60 Track Stability Management e a0 T a1 T a2 T a3 T a4 T a5 T a6 e min ewater , eice , 50C T 100C (6.3) (6.4) where: RH = relative humidity [%] TD = dewpoint temperature [⁰C] T = the screened air temperature [⁰C] e = vapour pressure of water (Equation 6.3) Table 6.5: Coefficients to Calculate Vapour Pressure of Water Vapour pressure of water factors Water Ice a0 6.107799961 6.109177956 a1 4.436518521x10-1 5.034698970x10-1 a2 1.428945805x10-2 1.886013408x10-2 -4 a3 2.650648471x10 4.176223716x10-4 a4 3.031240396x10-6 5.824720280x10-6 a5 2.034080948x10-8 4.838803174x10-8 -11 a6 6.136820929x10 1.838826904x10-10 After the BoM fields of dewpoint temperature and screened air temperature were converted into relative humidity, they were graphed in Figure 6.5 below for the month of July 2010. Figure 6.5: Relatively Humidity July 2010 Relative humidity is, again, a very stable weather variable, with no large sudden fluctuations over the month of July. The BoM raw data have similar results to screened air temperature when the two are statistically compared. The correlation coefficient, overall bias and overall RMSE are calculated in the same way as for screened air temperature and can be found in Appendix I. As the prediction moves further out in time from the observation input, the relative humidity bias has in some cases doubled in magnitude from the 1–24-hour to the 25–49-hour predictions for the same BoM geographic location. Again, the BoM data location closest to the weather station did not have the lowest CRC for Rail Innovation th 9 August 2011 Page 61 Track Stability Management bias; however, as in the case of screened air temperature, this is due to the stable nature of the variable. Further information is needed to decide on the best raw BoM data-point to use for calculations. The RMSE of relative humidity is far larger than that for screened air temperature, due mostly to relative humidity being a percentage variable. Overall, the RMSE is out by approximately 10%. If a percentage calculation was taken for screened air temperature, a number similar in magnitude would be observed. Taking the percentage into account, a weighted factor analysis was performed on relative humidity, shown in Equation 6.5 below. (6.5) RRH Correlation 10 0.1 bias 0.1 RMSE The weight factor of relative humidity is listed in Appendix I. The weighted factor RRH of the geographic location of the BoM data-point closest to the location of the actual weather station does correspond well. However, this is not conclusive, as the weighted factors are all very close to each other. A more dynamic weather variable needs to be considered for a final analysis. 6.1.3 Surface Air Pressure Surface pressure is the air pressure at the surface. The weather-station pressure unit was the hectorPascal (hPa), while the BoM field output was supplied in Pascals, so the BoM field was multiplied by 10 to provide consistent units. A graph of surface air pressure for the month of July 2010 is show in Figure 6.6 below. Figure 6.6: Surface Air Pressure July 2010 In Figure 6.6, the measured pressure is consistently around 5 hPa higher than predicted pressures. Although there is a slight elevation in the weather-station measurement, this would not equate to a 5 hPa increase. This is due to the discrepancy between the BoM model topography elevation at the location and the elevation. Pressure typically drops by about 1 hPa for every 10 m increase in altitude. This suggests that the model topography is in the order of 40–50 m higher in elevation than the real topographic height at the weather-station location. This discrepancy seems large but not impossible (Blockley 2010). The correlation coefficient, overall bias, and overall RMSE were calculated in the same way as for screened air temperature. The pressure bias and RMSE for surface air pressure were constantly 4 hPa and 15 hPa respectively less than the measured pressure. Therefore, for surface pressure, the weight factor should take into account CRC for Rail Innovation th 9 August 2011 Page 62 Track Stability Management the correlation more than the bias or RMSE, as these are consistently large. The weight factor for pressure is shown in Equation 6.6. This factor weights the correlation coefficient more heavily than either bias or RMSE compared to the weighted factor for screened air temperature and surface air pressure. Rsurface _ pres Correlation 10 0.01 bias 0.01 RMSE (6.6) From the weighted factor Rsurface_pres, it can be seen that the geographic location of the BoM data on the latitude line –23.65⁰ corresponds most closely to the actual weather-station data. However, this is not conclusive, as the weighted factors are all very close to each other. A more dynamic weather variable needs to be considered in the final analysis. 6.1.4 Zonal Winds (U) Zonal wind components are the wind magnitudes parallel to lines of constant latitude, that is, along the x-axis in the Cartesian plane, while meridional wind components are parallel to lines of constant longitude—that is, along the y-axis in the Cartesian plane. The weather station measured winds in magnitude and wind direction in degrees from north. However, if the zonal and meridional winds were transformed into magnitude and direction, analysing the two data-sets would be problematic, because when the wind direction is nearing 0⁰ it is also nearing 360⁰. Thus, the decision was made to transform the wind magnitude and wind direction measured by the weather station into the zonal and meridional wind fields that BoM fields provide. This task was carried out using equations 6.7 and 6.8 (Blockley 2010). (6.7) U r sin( ) (6.8) V r cos( ) where: U = zonal winds [m/s] V = meridional winds [m/s] r = wind magnitude [m/s] θ = wind direction [⁰] The graph of the zonal winds in Figure 6.7 shows large deviations and a very noisy wind pattern. Although the general trend of wind is present, there is too much fluctuation for the prediction data to be as close to the measured data as that for the other weather variables. This does not affect the results greatly, because the rail track is located near the ground surface, where wind effects are greatly reduced (whereas the data-sets compared in this section are elevated 10 m above the ground surface). CRC for Rail Innovation th 9 August 2011 Page 63 Track Stability Management Figure 6.7: Zonal Winds July 2010 The correlation coefficient, overall bias, and overall RMSE are calculated and listed in tables 6.14, 6.15 and 6.17 below. As expected from Figure 6.7 above, the correlation coefficients for zonal winds are far less than those of screened air temperature, surface pressure, or relative humidity. The correlation coefficient, overall bias, and overall RMSE are calculated in the same way as for screened air temperature. The overall bias and the overall RMSE of zonal winds reflect a not very skilful forecast, but, due to the nature of wind and the strong influences of topology, this is not surprising. The BoM model from which the data is extracted has a grid resolution of 11 km. With a low-topology resolution, the wind variable prediction would be smoothed out compared to measured winds. Although the wind forecast is not very skilful, it does give some information about the forecast, so a similar weighted factor is found for the zonal wind magnitudes as shown in Equation 6.9. (6.9) RU Correlation 10 0.1 bias 0.1 RMSE From the weighted factor RV, it can be seen that, similar to surface pressure, the geographic location of the BoM data on the latitude line –23.65⁰ corresponds better to the actual weather-station data. 6.1.5 Meridional Winds (V) A similar process was performed for meridional winds. Surprisingly, the meridional winds graphed in Figure 6.8 below appear to be better correlated with the measured data than the zonal winds. CRC for Rail Innovation th 9 August 2011 Page 64 Track Stability Management Figure 6.8: Meridional Winds July2010 Calculations using the correlation coefficient listed in Appendix G show that the correlation coefficient of meridional winds is indeed much larger than those for the zonal winds. However, a large overall bias and large overall RMSE exist, as shown in tables 6.19 and 6.20 below. Similar to the zonal winds, a weighted factor is calculated for the meridional winds, using the formula as for zonal wind calculation and listed in Appendix G. (6.10) RV Correlation 10 0.1 bias 0.1 RMSE From the weighted factors RV and RU, it can be seen that forecasting wind is not very effective for the BoM model; however, wind prediction can be used as an indication of a closer geographic location. Thus a combined and overall weighted statistical factor was found to indicate how well the BoM data forecast the weather at the field location and which raw BoM data-point was to be used in further analysis. 6.1.6 Overall Statistical Weighted Factor An overall weighted factor for all of the weather variables was calculated using Equation 6.11 and the values in Table 6.6. (6.11) Rscreen _ temp RRH Rsurface _ pres RV RU Roverall 5 This weighted overall factor averages all the weighted factors, so that an overall indication of “goodness” of prediction can be found for the raw BoM data. Table 6.6: Weighted Overall Goodness of Prediction Factor Roverall lon:149.67 lat:–23.65 lon:149.78 lat:–23.65 lon:149.89 lat:–23.65 lon:150 lat:–23.65 lon:149.67 lat:–23.76 lon:149.78 lat:–23.76 CRC for Rail Innovation Run 1 (1–24-hour prediction) 6.505 6.495 6.465 6.500 6.431 6.446 th 9 August 2011 Run 1 (25–49-hour prediction) 6.132 6.078 6.064 6.108 6.102 6.053 Page 65 Track Stability Management lon:149.89 lat:–23.76 lon:150 lat:–23.76 lon:149.67 lat:–23.87 lon:149.78 lat:23.87 lon:149.89 lat:–23.87 lon:150 lat:–23.87 6.426 6.507 6.261 6.324 6.266 6.315 6.021 6.103 5.980 5.982 5.903 5.950 The closest geographic locations to the actual weather station have higher goodness of prediction factors for Run 1 (1–24-hour predictions) than those located further way from the geographic location, with the exception of a few locations such as longitude 149.67, latitude −23.65. Latitude −23.87, although only one latitude grid away, gives a noticeable margin of 0.2–0.3 less in the goodness of prediction factor compared to the other location for Run 1 (1–24-hour predictions). This could be because of the hilly nature of the area, where the BoM data has a low resolution of the terrain, which affects the wind variables the most and other variables to a lesser extent. This could also be why some locations near latitude −23.65, longitude 149.67 have high goodness of prediction factors, because the BoM model has terrain that better matches the weather station’s location. This does not imply that that location is closer to the actual weather station, rather that there are terrain differences between the actual field site and what the BoM model expects to be there. Goodness of prediction is noticeably less for Run 1 (25–49-hour prediction) than for Run 1 (1-24-hour prediction). This indicates that, as prediction time becomes further away from the model run, it becomes less accurate. Also, as accuracy decreases, the variation in the goodness predictor decreases. Thus the decision was made that the BoM data-point at latitude −23.76, longitude 150 should be used as the example of the ”raw BoM data”. It was also decided that interpolated data-points surrounding the weather station’s location would be used for comparison, to see whether interpolation in between geographic- and time-interpolated data-sets would reduce the accuracy of the rail-temperature prediction. The following points around the weather station were used: longitude 149.9725, latitude −23.7050 longitude 150, latitude −23.7050 longitude 149.9725, latitude −23.7325 longitude 150, latitude −23.7325. The interpolated data-points can be seen in Figure 6.9 below. CRC for Rail Innovation th 9 August 2011 Page 66 Track Stability Management Lon:149.89 Lat:-23.65 Lon:149.9175 lat:-23.65 Lon:149.9450 Lat:-23.65 Lon:149.9725 Lat:-23.65 Lon:149.89 Lat:-23.6775 Lon:149.9175 lat:-23.6775 Lon:149.9450 Lat:-23.6775 Lon:149.9725 Lat:-23.6775 Lon:149.89 Lat:-23.7050 Lon:149.9175 lat:-23.7050 Lon:149.9450 Lat-23.7050 Lon:149.9725 Lat-23.7050 Weather station Lon:149.87 Lat:-23.71 Lon:149.89 Lat:-23.7325 Lon:149.89 Lat:-23.76 Lon:149.9175 Lat:-23.7325 Lon:149.9175 lat:-23.76 Lon:149.9450 Lat:-23.7325 Lon:149.9450 Lat-23.76 Lon:149.9725 Lat:-23.7325 Lon:149.9725 Lat-23.76 Figure 6.9: Configuration of Interpolated BoM Data-points in Relation to Weather Station 6.2 Comparison of Temperature Difference over the Rail Surface Fifteen surface thermocouples were attached over two rails (see Chapter 4 of this report for a detailed description of sensor placement). It was theorised that: sensors on the same sides of the rail should have the same heating pattern as each other CRC for Rail Innovation th 9 August 2011 Page 67 Track Stability Management over the profile of any one rail, there should be distinct differences in temperature at critical points in the day such as sunrise, sunset and at maximum air temperatures there should be some slight variation between the rail sitting directly on a sleeper and the rail suspended above the ballast. For this reason, the following analysis of rail temperature over the surface profile is divided into three sections relating to: 1. sensors in the same orientation but on different rails 2. sensors in different positions on the profile on the same rail 3. rail temperatures of rail sitting on sleeper and rail sitting on ballast. 6.2.1 Sensor in the Same Orientation but on Different Rails Corresponding sensors on the left and right rails are graphed together in Figure 6.10 below. From this figure, it can be seen that, between 12 July 2010 and 14 July 2010, although there is a slight difference between maximum temperatures, it is not consistent or large. Further analyses in terms of overall bias and root mean squared error between the two sensors were done using equations 6.12 and 6.13. (6.12) T T Biasoverall RMSEoverall left _ rail right _ rail no.samples (T left _ rail (6.13) Tright _ rail )2 no.samples where: Tleft_rail is the rail-temperature sensor on the left rail Tright_rail is the corresponding rail-temperature sensor on the right rail no.samples is the number of samples CRC for Rail Innovation th 9 August 2011 Page 68 9 August 2011 th Rail temperature deg C Rail temperature deg C 5 10 15 20 25 30 10 20 30 40 5 10 15 20 25 30 06/12-2010 06/12-2010 06/12-2010 Date 06/13 Date 06/13 Date 06/13 Left rail field side web Right rail gauge side web 06/14 06/14 Left rail gauge side top of foot Right rail field side top of foot 06/14 Left rail gauge side under side of head Right rail field side under sid eof head Rail temperature deg C Rail temperature deg C CRC for Rail Innovation Rail temperature deg C Rail temperature deg C 5 10 15 20 25 30 10 15 20 25 30 5 10 15 20 25 30 06/12-2010 06/12-2010 06/12-2010 Left rail field side top of foot Right rail gauge side top of foot 06/14 06/14 Left rail gauge side web Right rail field side web Date Left rail field side under side of head Right rail gauge side under side of head 06/13 06/14 Date 06/13 Date 06/13 Rail surface thermocouple sensor measurement Track Stability Management In these calcula tions, bias is the consist ent tempe rature differe nce betwe en two sensor s at the same orient ation on the left and right rail, which can be either a negati ve or positiv e numbe r, and the RMSE is a measu re of the absolu te differe nce betwe en the Page 69 Track Stability Management two sensors. The results of the overall bias and RMSE appear in Table 6.7. Table 6.7: Overall Bias and RMSE of Thermocouples in Same Orientation but on Different Rails Overall bias (⁰C) Overall RMSE (⁰C) Left rail gauge side under head and 0.206 0.737 right rail field side under head left rail gauge side web and right rail 0.108 0.673 field side web left rail gauge side top foot and right 0.016 0.710 rail field side top food left rail field side top foot and right rail 0.056 0.654 gauge side top foot left rail field side web and right rail 0.136 0.628 gauge side web left rail field side under head and right 0.180 0.693 gauge side under head Overall, calculating the bias and RMSE from 30 May to 13 August 2010 (1824 samples), there is less than a +/−1 ⁰C difference for both bias and RMSE. This magnitude is within sensor accuracy range, indicating that two sensors in the same orientation and on the same position of the profile have virtually the same heating profiles. This occurs even when the two sensors are placed 300 mm apart longitudinally and on different rails. It is conclusive that, within small distances such as sleeper spacing and crib distances, the temperature profiles of both rails can be regarded as the same at different positions on the profile. 6.2.2 Different Positions on the Profile on the Same Rail Sensors placed in different positions across the surface of the same rail record a different result. There is a noticeable and consistent variation between the thermocouples across the profiles of both rails as shown in Figure 6.11 below. This is consistent with past research (Ryan 2005), which showed distinct heating differences between different areas on the rail’s surface. On the east–west rail used for this study, the differences in temperature were more pronounced at sunrise, as seen around 5am (19:00 GMT) on 12 and 14 June. At this time of day, some sensors would be in direct sunlight and others not. Also, as demonstrated by the maximum temperatures around 1pm (3:00 GMT) on 12, 13 and 14 June, at this time of day, the sensors under the head of the rail would be in direct shade and would record lower temperatures than those exposed to direct sunlight. Statistically, the percentage variance and percentage standard deviation in degrees Celsius are graphed in Figure 6.12 below. CRC for Rail Innovation th 9 August 2011 Page 70 Rail temperature deg C 9 August 2011 th 0 -1 10 20 30 40 -0.5 10 15 20 25 30 35 0 -1 5 10 15 20 25 30 35 40 45 50 0.5 1.5 12:00 2 18:00 Degree C variance 1 3 06/13-00:00 2.5 06:00 3.5 12:00 0 -1 10 20 30 40 -0.5 18:00 0.5 1 1.5 06/14-00:00 06:00 Degree C standard deviation 0 12:00 2 18:00 2.5 Gauge side under head Gauge side web Gauge side top foot Field side top foot Field side web Field side under head Field side side head Left rail percentage standard deviation from mean May-August2010 -0.5 06:00 0 0.5 1.5 12:00 2 18:00 Degree C variance 1 3 06:00 3.5 12:00 0 -1 Date and time (GMT) 06/13-00:00 2.5 5 10 15 20 25 30 35 40 -0.5 Right rail surface temperatures 45 50 18:00 0.5 1 1.5 06/14-00:00 06:00 Degree C standard deviation 0 12:00 2 18:00 2.5 Field side side head Field side under head Field side web Field side top foot Bottom foot middle Gauge side top foot Gauge side web Gauge side under head Date and time (GMT) Right rail percentage variance from mean May-August2010 Right rail percentage standard deviation from mean May-August2010 06:00 0 Percentage % of occurance over the May-August 2010 period 50 Left rail surface temperatures Left rail percentage variance from mean May-August2010 5 06/11/10-18:00 06/12-00:00 Rail temperature deg C 5 06/11/10-18:00 06/12-00:00 10 15 20 25 30 Percentage % of occurance over the May-August 2010 period Percentage % of occurance over the May-August 2010 period CRC for Rail Innovation Percentage % of occurance over the May-August 2010 period 50 Track Stability Management Page 71 Figure 6.12 shows that although there are instances where the variation and deviation of temperature indicate a real difference in temperature across the profile (that is, above 1⁰C), the vast majority of the time, variance and standard deviation are within 0.5⁰C of the mean rail temperature. Therefore, as in the study conducted by Ryan (2005), the current study took the mean surface temperature as the rail temperature for further calculations involving rail temperature as a variable. 6.2.3 Rail Temperatures on Rail Sitting on Sleeper and Rail sitting above Ballast The literature review (Chapter 2) noted that previous studies have found that a rail’s location on sleepers or above ballast is largely insignificant in overall considerations of rail temperature. This somewhat surprising finding was deemed worthy of further investigation in the current study. Therefore, care was taken to mount sensors on one rail sitting on a sleeper with fist clips, and on another rail that was above ballast. This could be one reason for greater variance and standard deviation on the right rail, which sat above ballast, than on the left, which sat on a sleeper. The difference between thermocouples has been plotted in Figure 6.13 below. From Figure 6.13, it can be seen that there is a larger percentage of foot top differences between 0⁰C and −1⁰ C (i.e. the right rail is consistently warmer than the left rail, as the difference was Tleft_rail-Tright_rail). Distrubiton of difference between left and right rail sensors 11 Left rail gauge under head, right rail field under head left rail gauge web and right rail field web left rail gauge top foot and right rail field top food left rail field top foot and right rail gauge top foot left rail field web and right rail gauge web left rail field under head and right gauge under head The foot sensors have 10percentage larger difference 9 Percentage occurance 8 7 6 5 4 3 2 1 0 -2 -1 0 1 2 3 Degrees difference between left and right rail Figure 6.13: Differences between Thermocouples Results from the sensors on the foot of the rails indicate that the right rail (rail above ballast) is generally marginally warmer than the left rail (rail on sleeper). However, this difference is within the range of sensor accuracy and the results are not conclusive. Therefore, more analysis was performed on the daily maximum and minimum temperatures and the difference between the mean temperature and the bottom-of-foot temperature. This is graphed in Figure 6.14. In the 76-day period, the foot of the right rail, which was never exposed to direct sunlight, could, at maximum rail temperature, be warmer than the average surface temperature of the rail. Around 10% of the time, it was more than 1⁰C warmer than the average rail temperature. However, for a majority of the time, the rail temperature on the bottom surface was cooler than the average rail temperature. This distributed temperature difference between mean and foot temperature was closely related to weather phenomena. If rain was falling or winds were high, the right rail top _________________________________________________________________________________ CRC for Rail Innovation th 9 August 2011 Page 72 Track Stability Management surface was exposed to more convective cooling than the foot, which was insulated by the ballast, resulting in a higher foot temperature than the mean. Where there was incident radiation on the other surface, the foot in shade was lower in temperature. This is an important issue for further research if a generic model of rail temperature is to be attempted. Daily minimum temperature differences between the foot and the mean right-rail temperature were also calculated. The distribution of the daily minimum temperatures was more regular than that of daily maximum temperatures. This issue would also need to be researched further in the development of any more generic rail-temperature model. Maximum temperature differences right rail mean- bottom of foot sensor Percentage % of maximum temperature difference 6 5 4 3 2 1 0 -3 -2 -1 0 1 Degree C difference 2 3 4 Minimun temperature differences right rail mean- bottom of foot sensor Percentage % of minimum temperature difference 12 10 8 6 4 2 0 -1.5 -1 -0.5 0 Degree C difference 0.5 1 1.5 Figure 6.14a (top): Difference of Maximum Rail Temperatures between Mean and Bottom of Foot Figure 6.14b (bottom): Difference of Minimum Rail Temperatures between Mean and Bottom of Foot Generally, then, the rail sitting on sleepers was marginally warmer than the rail sitting above ballast. For maximum average temperatures, the sleepered rail was overall 0.7⁰C warmer than the rail on ballast. However, as this is in the same magnitude as the sensor accuracy range, it is not a conclusive finding. A more generic model, using thermodynamic principles, needs to be developed for this finding to be verified. While it can hypothesised that smaller sleeper spacing would have an overall effect on rail temperature, this would also need further investigation. 6.2.4 RSMs and Thermocouple Rail-temperature Comparison RSMs are a commercially available product that was used in this study partly as robust instrumentation to verify thermocouple measurements. The RSMs are encased in a hollow metal casing as protection for their sensors. The average left- and right-rail temperatures were compared with the sampled results from the RSMs. From the graphs (as seen in Figure 6.15), it was found that RSMs data was noisier than the thermocouple measurements. This noise corresponded to the times when a train passed over the sensors. The RSMs recorded a noisy signal at train passage that was not present in the thermocouple data. There was also a time delay between the measurements recorded by the thermocouples and those recorded by the RSMs. At times there was a 1.5- to 2-hour difference between the measured maximums of the day, as can be seen in Figure 6.15. CRC for Rail Innovation th 9 August 2011 Page 73 Track Stability Management Left rail temperatures 4th -6th June 2010 Temperature deg C 45 RSM rail temp mean thermocouple rail temp measured air temp 40 35 30 25 20 15 10 06/04/10-00:00 06:00 12:00 18:00 06/05-00:00 06:00 12:00 18:00 06/06-00:00 06:00 Date and time (GMT) Right rail temperatures 4th -6th June 2010 45 RSM rail temp mean thermocopule rail temp measured air temp Temperature deg C 40 35 30 25 20 15 10 5 06/04/10-00:00 06:00 12:00 18:00 06/05-00:00 06:00 12:00 18:00 06/06-00:00 06:00 12:00 Date and time (GMT) Figure 6.15a (top): Mean, RSMs Left-rail Temperature and Air Temperature, 4–6 June 2010 Figure 6.15b (bottom): Mean, RSMs Right-rail Temperature and Air Temperature, 4–6 June 2010 This is in part due to the thermal mass of the RSMs unit, which insulates its rail-temperature sensors from the elements, and in part due to the fact that the changes in rail temperature are most pronounced on the surface of the rail, where the thermocouples were located. This second factor was mitigated somewhat by taking the average temperature of the thermocouple measurements. Readings showing the actual air temperature of the day are the red line in Figure 6.15 above. Air temperature maximums correspond well with the maximum RSMs measurements but, again, this can be deceptive. As seen in results from Chapman et al. (2005), the timing of rail temperature maximums in relation to air temperature depends largely on rail orientation and seasonal changes. Both of these factors would have contributed to the time difference between the RSMs and thermocouple measurements. The RSMs and thermocouples correlate well, with the left rail having a coefficient of correlation of 0.902 and the right rail 0.879. However, further analysis of the RSMs measurements would be required in order to validate the RSMs product in Australia. 6.3 Rail-temperature Prediction Rail-temperature regression equations for both BoM and weather-station data were formulated using multivariate linear regression (as outlined in Chapter 2). July 2010 was chosen as the month for use because it was the only month where data from all four sources was available. Previous research (Chapman et al. 2005) indicates that one month of regression data is not robust enough for future prediction. However, with the limited data available, a distinction between the formulation data-set and the validation data needed to be maintained for a non-biased assessment of the accuracy of any regression equation developed. The average left-rail temperature was chosen to represent measured rail temperature because it had less variance and deviation (as explained in Section 6.3.2 below). CRC for Rail Innovation th 9 August 2011 Page 74 Track Stability Management 6.3.1 Real-time Predictions A real-time predictions equation was formulated from weather-station measurements. It was called “real-time” because the weather-station measurements occurred at the same time as the railtemperature measurements, so there was no lead time between predicting rail temperature and it occurring. Real-time rail-temperature prediction was developed for the July 2010 data-set (31 days at 744 samples). Equation 6.14 (with coefficients in Table 6.8) was the result. Trail 1Tair 2U wstat 3Vwstat 4 RH 5 Pr es where: Tair = screened air temperature [⁰C] Uwstat = zonal winds [m/s] Pres = air pressure [hPa] (6.14) Vwstat = meridional winds [m/s) RH = relative humidity [%] Table 6.8: Real-time Rail-temperature Prediction Coefficients Variable Coefficient α1 −0.653448202389647 α2 0.637206478633606 α3 0.218464524148432 α4 2.12553852746129 α5 −0.0545025911532638 This weather-station regression equation is compared for the month of June with the empirical relationships of Whittingham’s maximum-rail-temperature equation (1969) and Hunt’s sunny- and cloudy-day equations ( 1994). These four different rail-temperature predictions are all classified as real-time, because their empirical relationships use a real-time air-temperature measurement from the weather station. This is discussed further in Section 6.4.1.1 below. 6.3.1.1Validation Analysis of Real-Time Predictions The coefficients in Table 6.9 above are used for the weather-station data in June 2010, and compared to the mean left-rail temperature in June 2010. Temperatures from 9 –12 June 2010 are graphed in Figure 6.16. June validation rail temperatures 35 Temperature deg C 30 25 20 15 10 5 average left rail temperature Hunt's cloudy rail temp Hunt's sunny rail temp Whittingham's max rail temp weather station regressoin air temperature 0 06/09/10-18:00 06/10-00:00 CRC for Rail Innovation 06:00 12:00 18:00 06/11-00:00 06:00 12:00 18:00 Date and Time (GMT) th 9 August 2011 06/12-00:00 06:00 12:00 18:00 Page 75 06/13-00:00 Track Stability Management Figure 6.16: Validation Graph of Real-time Rail-temperature Predictions 9–13 June 2010 Figure 6.16 shows that all the empirical relationships consistently overestimate the rail temperature, even when real-time air temperature is used. This is consistent with the purpose of the empirical relationships, which was to find a critical maximum temperature of the day using predicted air temperature. The correlation coefficient of the empirical equations is only slightly lower (0.858 compared with the weather station equation of 0.896). However, the overall bias and RMSE of the empirical relationships (listed in columns 2 and 3 of Table 6.9) show that the bias is magnitudes larger than the weather-station equation. An exception is Hunt’s sunny-day equation, which performs better than both Whittingham’s equation and Hunt’s cloudy-day equation, because most of the days in June 2010 were sunny. The overarching concern with the empirical real-time equations is that there is no accurate time of critical temperature. An empirical relationship may find a satisfactory maximum rail temperature, but these equations do not accurately indicate when this maximum temperature will be reached and how long the maximum will remain. Table 6.9: Statistical Comparison of Real-time Rail-temperature Predictions Correlation Coefficient Average overall bias Average overall R2 ⁰C RMSE ⁰C Real-time prediction (air temperature is measured at the same time as rail temperature) Whittingham’s 0.858 −8.722 10.149 equation Hunt’s sunny-day 0.858 −3.227 5.806 equation Hunt’s cloudy-day 0.858 −12.497 13.742 equation Weather-station 0.896 0.659 4.193 prediction Over the 720 measurements that were taken in the month of June 2010, the difference between the measured mean temperature and various relationships were calculated and graphed in Figure 6.17 below. Figure 6.17b shows that Hunt’s sunny-day equation performs better than previous empirical relationships; however, the weather-station equation for the site is better distributed around 0⁰ C differences, whereas Hunt’s sunny-day equation has maximum occurrence at around 5⁰C higher than actual rail temperature. This is as expected, because the weather-station relationship was developed for the site of validation, whereas the other equations were developed in other locations around the world. CRC for Rail Innovation th 9 August 2011 Page 76 Track Stability Management Hunt sunny day equation Occurences within the June 30 days Occurences within the June 30 days Whittingham equation 120 100 80 60 40 20 0 -20 -15 -10 -5 0 5 10 15 Temperature difference measured -predicted degC 20 100 80 60 40 20 0 -20 -15 -10 -5 0 5 10 15 Temperature difference measured -predicted degC Weather station regression 400 Occurences within the June 30 days Occurences within the June 30 days Hunt cloudy day equation 350 300 250 200 150 100 50 0 -20 -15 -10 -5 0 5 10 15 Temperature difference measured -predicted degC 20 20 100 80 60 40 20 0 -20 -15 -10 -5 0 5 10 15 Temperature difference measured -predicted degC 20 Figure 6.17a (top left): Real-time Rail-temperature Prediction using Whittingham’s Equation (Measured Minus Predicted) Figure 6.17b (top right): Real-time Rail-temperature Prediction using Hunt’s Sunny-day Equation (Measured Minus Predicted) Figure 6.17c (bottom left): Real-time Rail-temperature Prediction using Hunt’s Cloudy-day Equation (Measured Minus Predicted) Figure 6.17d (bottom right): Real-time Rail-temperature Prediction Using Weather-station-regression Equation (Measured Minus Predicted) The purpose of the research conducted by Hunt (1994) and Whittingham (1969) was to develop a gauge for maximum rail temperatures so that maximum rail temperatures could be investigated. The difference between the maximum rail temperature and the maximum predicted temperatures is graphed in Figure 6.18. Figure 6.18 shows that, as expected, Whittingham’s equation performs better at predicting maximum temperatures than all other relationships. Whittingham’s equation predicts the maximum within a +/−5 ⁰C range 28 out of the 30 days, whereas even the weather-station prediction is in the 0–10⁰C interval less than measured rail temperature for the majority of June 2010. This could be problematic for operational usage, if the predicted temperature is consistently 5–10⁰C less than the actual rail temperature. This could be improved if more data-sets were used in the regression process, given that Whittingham had 15 months of data-sets for his empirical analysis. This was not possible for the current study, but a hybrid program using Whittingham’s equation for maximumtemperature estimation and the weather-station equation for temperature timings could be a less time-intensive method of producing a better timed forecast. CRC for Rail Innovation th 9 August 2011 Page 77 Track Stability Management Whittingham equation Hunt sunny equation 7 Occurances of maximum temperature differences Occurances of maximum temperature differences 10 8 6 4 2 0 -20 -15 -10 -5 0 5 10 15 6 5 4 3 2 1 0 -20 20 Temperature difference measured -predicted degC Hunt cloudy equation -10 -5 0 5 10 15 20 Weather station regression equation 6 Occurances of maximum temperature differences 6 Occurances of maximum temperature differences -15 Temperature difference measured -predicted degC 5 4 3 2 1 0 -20 -15 -10 -5 0 5 10 15 5 4 3 2 1 0 -20 20 Temperature difference measured -predicted degC -15 -10 -5 0 5 10 15 20 Temperature difference measured -predicted degC Figure 6.18a (top left): Daily Maximum Rail-temperature Differences between Measured and Whittingham’s Prediction Figure 6.18b (top right): Daily Maximum Rail-temperature Differences between Measured and Hunt’s Sunny Day Prediction Figure 6.18c (bottom left): Daily Maximum Rail-temperature Differences between Measured and Hunt’s Cloudy Day Prediction Figure 6.18d (bottom right): Daily Maximum Rail-temperature Differences between Measured and Weather Station Regression Prediction 6.3.2 Future Predictions The BoM predicts weather variables 1–48 hours in advance. Practically speaking, files are not uploaded onto the BoM ftp server for subscribers to download until the third hour of the prediction because of the size and the number of services that the BoM offers (Blockley 2010). This shortens the prediction to 1–45 hours; however, this does not detract from the predictive nature of the files. Thus the runs from BoM have still been separated into 1–24-hour forecasts and 25–48-hour forecasts as shown in Figure 6.2 in Section 6.2. The multi-variant regression for the 1–24 hour equation was developed for July 2010 and is shown in Equation 6.15. The BoM predictions for weather variables that are used in this section are from the location latitude −23.76, longitude 150, and have not been modified in any way. Trail 1v10 2u10 3temp _ scrn 4 dewpt _ scrn 5 sfc _ pres (6.15) 6 accum _ prcp 7 mslp +8 accum _ evap 9 av _ lat _ hflx 10 av _ lwsfcdown 11av _ netlwsfc 12 av _ netswsfc 13 av _ olr 14 av _ sens _ hflx 15 av _ sfc _ sw _ dif 16 av _ sfc _ sw _ dir 17 av _ swirrtop 18 av _ swsfcdown 19 mid _ cld 20 qsair _ scrn 21sens _ hflx 22 sfc _ temp 23 soil _ mois 24 soil _ temp 25t max_ scrn 26t min_ scrn + 27ttl _ cld + 28 z 0 CRC for Rail Innovation th 9 August 2011 Page 78 Track Stability Management where the symbols used are the same as those explained in Section 3.2. The β coefficients are listed in Table 6.10. Table 6.10: Coefficients of Regression β Coefficient Number β1 0.0349214685860181 β2 0.300803117783424 β3 3.26127609691842 β4 0.548680299876555 β5 −0.0176241478356276 β6 0.296859695855778 β7 0.0190721105766093 β8 1.08266611560058 β9 − 0.00968231367160908 β10 0.114534168536698 β11 –0.133276582471754 β12 7.95797683959537 β13 0.00914604669678778 β14 0.0120850138461365 β15 –1725.67323763576 β16 –1725.67801531730 β17 0.00230863771581154 β18 1718.97342606071 β19 0.390794423357368 β20 –1002.22138885324 β21 –0.00394730467453745 β22 0.189313674908339 β23 –0.0616725597039408 β24 0.221087658354270 β25 –0.105847604257958 β26 –2.95880644076632 β27 0.635764475671435 β28 –17880.8512663862 6.3.2.1 Validation of Future Predictions The graph of 13–16 June 2010 appears in Figure 6.19 below. As can be seen in the figure, the BoM prediction is variable. On 13 June 2010, the prediction is very close to the actual rail temperatures; on 14 June, it is greater than actual; on 15 June, the prediction is less than actual; and so on. Hunt’s and Whittingham’s equations were calculated using the BoM screened temperature field (temp_scrn) and graphed in the figure. Much of Figure 6.19 shows empirical relationships overestimating rail temperatures when using real-time measured air temperatures. This also occurs when using the predicted screened air temperatures. Again, the timing of the maximum temperatures is not well-interpreted by the empirical formulas; at times, the peaks occur three to four hours after the measured rail temperatures. CRC for Rail Innovation th 9 August 2011 Page 79 Track Stability Management Future prediction temperature validation 40 Temperature deg C 35 30 25 20 15 average left rail temperature Hunt's cloudy day rail temp Hunt's sunny day rail temp Whittingham's rail temp BoM 1-24 predicted rail temp air temperature 10 06/13/10-06:0012:00 18:00 06/14-00:00 06:00 12:00 18:00 06/15-00:00 06:00 12:00 18:00 06/16-00:00 06:00 12:00 18:00 Date and time (GMT) Figure 6.19: Future Predicted Rail Temperature 13–16 June 2010 The correlation coefficient, overall average bias and RMSE were found for the three empirical formulas by Hunt and Whittingham and for the BoM regression equation and are listed in Table 6.11 below. Table 6.11: Statistical Comparison of Future Predictions Correlation Average Overall Average Overall Coefficient R2 bias ⁰C RMSE ⁰C Future predictions (air temperature is predicted 1–24 hours in advance of rail-temperature measurement) BoM prediction equation 0.963 –0.136 2.560 (1–24hr) Whittingham’s equation 0.852 –9.717 11.345 Hunt’s sunny-day equation 0.853 –4.44 6.952 Hunt’s cloudy-day equation 0.853 –13.308 14.758 Table 6.11 indicates that the BoM predictions are far better in terms of correlation coefficient bias and RMSE; Hunt’s sunny-day equations have double the bias and RMSE of the BoM prediction. Even when compared with the weather-station real-time numbers, the raw BoM prediction correlates better than the weather-station regression output (correlation coefficient of 0.963 to 0.806 respectively), has an average overall bias of −0.136⁰C compared to 0.659⁰C, and has an RMSE of 2.560⁰C compared to 4.193⁰C. Even though the BoM regression had only July 2010 data in its formulation, it is still more robust than either the Hunt or Whittingham equations. Figure 6.20 graphs the temperature difference (measured minus predicted) versus the number of such occurrences for the four methods shown. CRC for Rail Innovation th 9 August 2011 Page 80 100 80 60 40 20 0 -20 -15 -10 -5 0 5 10 15 20 Temperature difference measured -predicted degC Hunt cloudy day equation 400 350 300 250 200 150 100 50 0 -20 -15 -10 -5 0 5 10 15 20 Temperature difference measured -predicted degC Occurences within the June 30 days Whittingham equation 120 Hunt sunny day equation 100 Occurences within the June 30 days Occurences within the June 30 days Occurences within the June 30 days Track Stability Management 80 60 40 20 0 -20 -15 -10 -5 0 5 10 15 20 Temperature difference measured -predicted degC BoM predicted rail temperature 100 80 60 40 20 0 -20 -15 -10 -5 0 5 10 15 20 Temperature difference measured -predicted degC Figure 6.20a (top left): Occurrence Difference Graph—Whittingham’s Equation as Prediction Figure 6.20a (top right): Occurrence Difference Graph—Hunt’s Sunny-day Equation as Prediction Figure 6.20a (bottom left): Occurrence Difference Graph—Hunt’s Cloudy-day Equation as Prediction Figure 6.20a (bottom right): Occurrence Difference Graph—BoM Regression Equation as Prediction Figure 6.20 shows that, similar to the real-time prediction, Hunt’s sunny-day equation outperforms the other empirical equations. Hunt’s sunny-day equation predicts the rail temperature at around 5 ⁰C above the measured rail temperature the majority of the time, whereas Hunt’s cloudy-day equation and Whittingham’s empirical equation are around 15⁰C higher and 10⁰C higher respectively than the measured temperature. The BoM prediction again outperforms Hunt’s sunny-day equation. The majority of BoM predictions are within the −5⁰C to 5⁰C range, with the largest occurrences centring around a +/−2 ⁰C difference, whereas predictions using Hunt’s sunny-day equation are centred around −6⁰C, with the majority ranging from 10⁰C to 5⁰C above the measured temperature. The day maximum temperature differences are also plotted in Figure 6.21 for the future predictions. The figure shows that, again, the BoM prediction has less variation and is closer to the actual measured temperature than all of the empirical relationships. It is conclusive that the raw BoM prediction out-performs any existing empirical relationship currently available for industry use. Also of interest is whether the BoM’s 25–48-hour prediction is as accurate as the 1–24-hour prediction. This is investigated in the next section. CRC for Rail Innovation th 9 August 2011 Page 81 Track Stability Management Hunt sunny day equation Whittingham equation 4 Occurences of maximum temperature differences Occurences of maximum temperature differences 6 5 4 3 2 1 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Hunt cloudy day equation BoM prediction equation 6 Occurences of maximum temperature differences Occurances of maximum temperature differences 6 5 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC 5 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Figure 6.21a (top left): Daily Maximum Rail-temperature Difference (Measured minus Whittingham’s Prediction) Figure 6.21b (top right): Daily Maximum Rail-temperature Difference (Measured minus Hunt’s Sunny-day Prediction) Figure 6.21c (bottom left): Daily Maximum Rail-temperature Difference (Measured minus Hunt’s Cloudy-day Prediction) Figure 6.21d (bottom right): Daily Maximum Rail-temperature Difference (Measured minus BoM Regression Equation Prediction) 6.3.2.2 1–24-hour and 25-48-hour Predictions The BoM ACCESS model depends on weather observations collected by the BoM on a daily to hourly basis. Thus, as the time period for a forecast increases, its accuracy decreases, because the weather changes and the initial observations become less valid as the initial conditions of the model. Considering this, and the fact that each day’s BoM output runs overlap with each other, this study investigated how the accuracy of BoM predictions changes as the forecast time moves further into the future. The BoM prediction at latitude −23.76, longitude 150 was separated into “this-day” predictions (1–24 hours) and “next-day” predictions (25–48 hours). Equation 6.15 and the coefficients (Table 6.10) from Section 6.4.1 were used to predict rail temperature using both this-day and next-day variables. The validation analysis for June 2010 graphed in Figure 6.22 shows that the next-day predictions are smoother in form than this-day predictions, showing fewer perturbations an exaggerate the inaccuracies in the BoM predictions. Where the this-day predictions for 20 June predict a higher maximum rail temperature, the next-day predictions (i.e. temperatures for 20 June as predicted on 18 June, rather than 19 June) show an even higher maximum temperature. CRC for Rail Innovation th 9 August 2011 Page 82 Track Stability Management 20th to 23rd June 2010 validation of BoM raw prediction accuracy 35 Temperatures deg C 30 25 20 15 average left rail temperature BoM predicted (1-24 hr) rail temp BoM predicted (25-48hr) rail temp air temperature 10 5 06/20/10-00:0006:00 12:00 18:00 06/21-00:00 06:00 12:00 18:00 06/22-00:00 06:00 12:00 18:00 06/23-00:00 06:00 12:00 Date and time (GMT) Figure 6.22: BoM Regression-equation Rail-temperature Predictions This-day and Next-day Comparing this-day and next-day statistics shows that the correlation coefficient reduces by 0.021, the overall bias increases by 1.246⁰C, and the overall RMSE increases by 0.82⁰C (as seen in Table 6.13). Table 6.12: Statistical Comparison of BoM This-day and Next-day Predictions Correlation Average Overall bias Average Overall RMSE 2 Coefficient R ⁰C ⁰C Future predictions BoM this-day 0.963 −0.136 2.560 BoM next-day 0.942 −1.382 3.381 The next-day predictions are less accurate than the this-day predictions. However, the next-day predictions are still more accurate than the weather-station predictions. The weather station has a correlation coefficient of 0.896 compared with 0.942 for the next-day prediction, 0.659⁰C bias compared with −1.382⁰C next-day bias, and 4.193⁰C RMSE compared to 3.381⁰C next-day RMSE (see Section 6.4.1.1). The rail temperatures calculated by the weather-station variables at the same time as measured rail temperatures are less correlated and have a larger RMSE than a prediction that was calculated by BoM data 24 hours before the event. This indicates that the BoM predictions are more accurate than weather-station predictions. Similar “occurrences versus difference” graphs have been produced for this-day and next-day predictions, and are shown in Figure 6.23 below. CRC for Rail Innovation th 9 August 2011 Page 83 Track Stability Management Occurences within the June 30 days BoM predicted (1-24 hours) 150 100 50 0 -20 -15 -10 -5 0 5 10 15 20 15 20 Temperature difference measured -predicted degC Occurences within the June 30 days BoM predicted (25-48 hours) 100 80 60 40 20 0 -20 -15 -10 -5 0 5 10 Temperature difference measured -predicted degC Figure 6.23a (top): Rail Temperatures Occurrences versus Difference (Measured minus BoM This-day Predictions) Figure 6.23b (bottom): Rail Temperatures Occurrences versus Difference (Measured minus BoM Next-day Predictions) Figure 6.23 shows that the next-day prediction has shifted the difference distribution to predicting 3⁰C above the measured rail temperature rather than centring on the 0⁰C difference. Generally, the next-day predictions increase the variance of measured-predicted rail temperatures compared with this-day BoM predictions; however, the next-day predictions differences are similar to the weatherstation predictions. The daily maximum rail temperature versus occurrence is also graphed in Figure 6.24. As in the occurrence difference graphs, the maximum daily temperatures for next-day predictions have a larger variance when compared with this-day predictions. BoM prediction (25-48 hours) BoM predicted (1-24 hours) 5 Occurences of maximum temperature differences Occurences of maximum temperature differences 6 5 4 3 2 1 0 -20 -10 0 10 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 -20 20 -10 0 10 20 Temperature difference measured -predicted degC Temperature difference measured -predicted degC Figure 6.24a (left): Daily Maximum Rail-temperature Difference (Measured Minus BoM This-day Prediction) Figure 6.24b (right): Daily Maximum Rail-temperature Difference CRC for Rail Innovation th 9 August 2011 Page 84 Track Stability Management (Measured Minus BoM Next-day Prediction 6.3.3 BoM Raw Data and BoM Interpolated Predictions The interpolated BoM data located weather parameters much closer to the geographic location of the actual weather station and also increased the time frequency of the prediction. That is, instead of a rail-temperature prediction for every hour, a prediction was made for every 15 minutes. Provided that the accuracy of a prediction is not diminished by interpolation, then a prediction using a smaller time resolution will more accurately indicate when the maximum temperature will be reached. The accuracy of the interpolated values was checked using the thermocouple readings, which only existed for every hour (i.e. the interpolated results were sampled every hour and compared to the thermocouple readings). The daily maximum temperature comparison used the full set of interpolated results, found the maximum value of those for each day, and then compared these with the daily thermocouple maximums. The location of the interpolated BoM points is shown in Figure 6.25 below. They are 0.0275⁰ to 0.05⁰ in latitude (3.06 km to 6.12 km) closer to the weather station. Lo Lo n:1 n: We 49. ath 1 Lo 97 5 Lo n:125 0 n: 49.Lat La1 Lon 97 5 t:-Raw :15 25 23. 0 2BoM 0 Lat70 La 3.data Lat: :- 50 7 t:23. 02 23. 73 5 3. 76 25 07 3 2 5 Figure 6.25: Configuration of Interpolated BoM Prediction and Raw BoM Prediction in Relation to Location of Weather Station The weather variables were multiplied using the regression coefficients listed in Table 6.10 in Section 6.4.2.Once again, the predictions were separated into this-day and next-day predictions. CRC for Rail Innovation th 9 August 2011 Page 85 Track Stability Management 6.3.3.1 Interpolated This-day Predictions Figure 2.6 shows graphs of rail-temperature predictions and actual measured rail temperatures for 8–10 June 2010. The figure shows that, although all the predictions are similar, the raw BoM prediction appears to be a closer fit than the other interpolated predictions. Of the interpolated predictions, the BoM latitude −23.705, longitude 149.4725 outputs appear to be closer to the measured temperatures than the rest. The correlation coefficient, overall bias, and overall RMSE are listed in Table 6.14. Interpolated BoM validation (1-24hr prediction) mean left rail temperature raw BoM prediction BoM lat 023.705 lon:149.4725 predict BoM lat-23.705 lon:150 predict BoM lat-23.7325 lon:149.4725 predict BoM lat-23.7235 lon:150 predict 40 Rail temperature deg C 35 30 25 20 15 10 5 06/08/10-21:00 06/09-00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 06/10-00:00 03:00 Date and time (GMT) 06:00 09:00 12:00 15:00 Figure 6.26: Interpolated, Raw BoM Prediction and Measured This-day Rail Temperature 8–10 June Table 6.13: Statistical Comparison of Interpolated and Raw BoM This-day Rail-Temperature Prediction Equations Correlation Average Overall Average Overall Coefficient R2 bias ⁰C RMSE ⁰C Future predictions (1–24 hours in advance of rail-temperature measurement) Raw BoM prediction equation 0.963 −0.136 2.560 (1–24-hour) BoM lat–23.705 lon:149.4725 0.942 0.645 3.198 BoM lat–23.705 lon:150 0.942 4.718 5.667 BoM lat–23.7325 lon:149.4725 0.941 −1.940 3.699 BoM lat–23.7235 lon:150 0.941 2.173 3.834 Table 6.13 indicates that all of the interpolated predictions correlate well with the measured rail temperature; the correlation is slightly bettered by the raw BoM prediction by 0.022. However, when considering bias and RMSE, the raw BoM predictions outperform the other interpolated results, with the interpolated location at BoM latitude −23.705, longitude 149.4725 performing better than the rest of the interpolated results. The temperature differences between predicted and measured are graphed in Figure 6.27. CRC for Rail Innovation th 9 August 2011 Page 86 Track Stability Management raw BoM predicted (1-24 hours) BoM lat:-23.705 lon:149.4725 120 100 Occurences within the June 30 days Occurences within the June 30 days 150 100 50 0 -20 -10 0 10 80 60 40 20 0 -20 20 Temperature difference measured -predicted degC 0 10 BoM lat-23.7325 lon:149.4725 BoM lat-23.705 lon:150 120 100 100 100 60 40 20 0 -20 -10 0 10 Temperature difference measured -predicted degC 20 Occurences within the June 30 days 120 80 80 60 40 20 0 -20 20 BoM lat-23.7235 lon:150 120 Occurences within the June 30 days Occurences within the June 30 days -10 Temperature difference measured -predicted degC -10 0 10 Temperature difference measured -predicted degC 20 80 60 40 20 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Figure 6.27a (top left): Rail Temperatures Occurrences versus Difference (Measured minus Raw This-day BoM Predictions) Figure 6.27b (top right): Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.705 lon:149.4725 Predictions) Figure 6.27c (bottom left): Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.705 lon:150 Predictions) Figure 6.27d (bottom middle): Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.7325 lon:149.4725 Predictions) Figure 6.27e (bottom left): Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.7235 lon:150 Predictions) Figure 6.27 shows that the range of the measured minus predicted values is similar, between +/−10⁰C. However, the interpolated predictions tend to skew the maximum occurrences from 0⁰C difference in the case of both raw BoM prediction and BoM latitude −23.705, longitude 149.4725 to 4⁰C for both BoM latitude –23.705, longitude 150 and BoM latitude –23.7235, longitude 150. –2⁰C for BoM prediction latitude –23.7325, longitude 149.4725. The daily maximum differences between measured and predicted temperatures are graphed in Figure 6.28. CRC for Rail Innovation th 9 August 2011 Page 87 5 4 3 2 1 -10 Interpolated BoM lat:-23.705 lon:150 5 4 3 2 1 -10 0 10 0 10 Temperature difference measured -predicted degC Temperature difference measured -predicted degC 20 20 5 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Interpolated BoM lat:-23.7325 lon:149.4725 Interpolated BoM lat:-23.7235 lon:150 5 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Occurences of maximum temperature differences Occurences of maximum temperature differences 0 -20 0 -20 Interpolated BoM lat:-23.705 lon:149.4725 raw BoM predicted (1-24 hours) Occurences of maximum temperature differences 6 Occurences of maximum temperature differences Occurences of maximum temperature differences Track Stability Management 5 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Figure 6.28a (top left): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus This-day Raw BoM Predictions) Figure 6.28b (top right): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.705 lon:149.4725 Predictions) Figure 6.28c (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.705 lon:150 Predictions) Figure 6.28d (bottom middle): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.7325 lon:149.4725 Predictions) Figure 6.28e (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus This-day BoM lat-23.7235 lon:150 Predictions) Figure 6.28 shows the variance of difference is still within a 10⁰C range. However, there is a shift in the range. Whereas the range is from –2⁰C to 8⁰C in the raw BoM prediction, the interpolated predictions range from –3⁰C to 8⁰C for BoM latitude –23.705, longitude 149.4725 and BoM latitude –23.705, longitude 149.4725; and from 1⁰C to 12⁰C for BoM latitude –23.705, longitude 150 and BoM latitude –23.705, longitude 150. It is conclusive that the raw BoM predictions are more accurate for this-day predictions. However, the interpolated BoM prediction latitude –23.705, longitude 149.4725 comes close to the accuracy of the raw BoM prediction and can be used to better understand the time at which maximum rail temperatures occur. 6.3.3.2 Interpolated next-day predictions Figure 6.29 shows a graph of rail-temperature predictions and actual measured temperatures for 8 – 10 June 2010 for next-day predictions. This figure shows that all of the next-day predictions, whether interpolated or raw, look similar. The raw BoM prediction does not appear to be a closer fit than any of the other interpolated predictions as was the case with the this-day predictions. The correlation coefficient, overall bias, and overall RMSE are listed in Table 6.14. CRC for Rail Innovation th 9 August 2011 Page 88 Track Stability Management Interpolated BoM validation (25-48hr prediction) mean left rail temperature raw BoM prediction BoM lat 023.705 lon:149.4725 predict BoM lat-23.705 lon:150 predict BoM lat-23.7325 lon:149.4725 predict BoM lat-23.7235 lon:150 predict 40 Rail temperature deg C 35 30 25 20 15 10 5 06/08/10-18:00 06/09-00:00 06:00 12:00 18:00 06/10-00:00 06:00 12:00 18:00 Date and time (GMT) Figure 6.29: Interpolated, Raw BoM Prediction and Measured Next-day Rail Temperature 8–10 June Table 6.14: Statistical Comparison of Interpolated and Raw BoM Next-day Rail-temperature Prediction Equations Correlation Average Overall Average Overall 2 Coefficient R bias ⁰C RMSE ⁰C Future predictions (24–48 hours in advance of rail-temperature measurement) BoM prediction equation 0.942 –1.382 3.381 (25–48-hour) BoM lat –23.705 lon:149.4725 0.942 –0.425 3.841 BoM lat –23.705 lon:150 0.911 3.669 5.302 BoM lat –23.7325 lon:149.4725 0.942 –3.014 4.859 BoM lat –23.7235 lon:150 0.942 1.117 3.983 Table 6.14 shows that the accuracy of the raw BoM prediction and interpolated BoM predictions for the next day are not very different. With the exception of BoM latitude –23.705, longitude 150, correlation coefficients are the same. With regard to bias, all the predictions are of the same magnitude; the interpolated BoM latitude –23.705, longitude 149.4725 actually has a lower bias than the raw BoM next-day predictions. With regard to RMSE, all the predictions are again of the same magnitude. Figure 6.30 graphs the temperature differences between predicted and measured for next-day rail temperatures. CRC for Rail Innovation th 9 August 2011 Page 89 Track Stability Management raw BoM predicted (25-48 hours) BoM lat:-23.705 lon:149.4725 80 Occurences within the June 30 days Occurences within the June 30 days 100 80 60 40 20 0 -20 -10 0 10 60 40 20 0 -20 20 Temperature difference measured -predicted degC BoM lat-23.705 lon:150 40 20 -10 0 10 Temperature difference measured -predicted degC 20 80 60 40 20 0 -20 20 BoM lat-23.7235 lon:150 Occurences within the June 30 days 60 10 100 100 Occurences within the June 30 days Occurences within the June 30 days 0 BoM lat-23.7325 lon:149.4725 80 0 -20 -10 Temperature difference measured -predicted degC -10 0 10 Temperature difference measured -predicted degC 20 80 60 40 20 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Figure 6.30a (top left): Rail Temperatures Occurrences versus Difference (Measured minus Next-day Raw BoM Predictions) Figure 6.30b (top right): Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.705 lon:149.4725 Predictions) Figure 6.30c (bottom left): Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.705 lon:150 Predictions) Figure 6.30d (bottom middle): Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.7325 lon:149.4725 Predictions) Figure 6.30e (bottom left): Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.7235 lon:150 Predictions) In Figure 6.30, the range of measured minus predicted values for the interpolated predictions have a marginally larger range than those of the raw BoM predictions. As in the case of the this-day prediction, the next-day interpolated predictions tend to skew the maximum occurrences. Figure 6.31 graphs the daily maximum differences between measured and predicted for next-day predictions. CRC for Rail Innovation th 9 August 2011 Page 90 Track Stability Management 5 Interpolated BoM lat:-23.705 lon:149.4725 Occurences of maximum temperature differences Occurences of maximum temperature differences raw BoM predicted (25-48 hours) 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC 5 4 3 2 1 0 -20 -10 0 10 20 5 4 3 2 1 0 -20 -10 0 10 Temperature difference measured -predicted degC 20 5 Occurences of maximum temperature differences 6 Occurences of maximum temperature differences Occurences of maximum temperature differences Temperature difference measured -predicted degC Interpolated BoM lat:-23.705 lon:150 Interpolated BoM lat:-23.7325 lon:149.4725 Interpolated BoM lat:-23.7235 lon:150 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC 6 5 4 3 2 1 0 -20 -10 0 10 20 Temperature difference measured -predicted degC Figure 6.31a (top left): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus Next-day Raw BoM Predictions) Figure 6.31b (top right): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.705 lon:149.4725 Predictions) Figure 6.31c (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.705 lon:150 Predictions) Figure 6.31d (bottom middle): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.7325 lon:149.4725 Predictions) Figure 6.31e (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference (Measured minus Next-day BoM lat-23.7235 lon:150 Predictions) Figure 6.31 shows the variance of difference is still within a 15⁰C range; however, there is a shift in the range. Whereas the range was from –7⁰C to 8⁰C in the raw BoM prediction, the interpolated predictions range from –8⁰C to 5⁰C for BoM latitude –23.705, longitude 149.4725; from –4⁰C to 11⁰C for BoM latitude –23.705, longitude 150; from –8⁰C to 5⁰C for BoM latitude –23.3725, longitude 179.4725; and from –4⁰C to 11⁰C for BoM latitude –23.7235, longitude 150. It is conclusive that, for next-day predictions, the interpolated BoM predictions are as skilful as the raw BoM prediction. There is almost no difference in accuracy between the raw BoM prediction and the interpolated BoM latitude –23.705, longitude 149.4725. 6.4 Empirical Prediction Drawbacks The rail-temperature prediction completed in this study depended heavily on empirical data collected in the field. Although the BoM data is from a dynamic NWP model, the ultimate accuracy of the rail temperature is based on empirical downscaling. The field experimentation for this study was oriented in the east–west direction, but it is known that rail oriented north–south has a distinctly different heating pattern, with higher maximum rail temperatures (Whittingham 1969; Munro 2009). Track in cuttings, on bridges and in urban areas would also have a distinctly different heating pattern from that observed in this study. Different track constructions (such as timber sleepers, larger sleeper spacing, different gauge distances, and different fasteners) also affect the heating pattern of a rail. Therefore, the findings of this study are CRC for Rail Innovation th 9 August 2011 Page 91 Track Stability Management limited to straight track on embankment configuration, with narrow-gauge distances, concrete sleepers and fist-clip fasteners. Beyond this scenario, the accuracy of rail-temperature prediction would differ greatly from what is reported in this study. The volume of data available for this study also reduces the accuracy of the rail-temperature prediction described here. Only 744 samples from July 2010 were used to formulate the railtemperature prediction equation, compared with previous research by Whittingham (1969) that used 15 months of data, Chapman et al. (2005) that used 12 months of data, and Munro (2009) that used 9 months of data. Due to time constraints and its academic nature, the current study did not use enough data for a robust empirical analysis. Therefore, the rail-temperature prediction developed lacks the empirical data to be a truly robust prediction. The July period in which the data was collected is also problematic. July is winter in Australia, while most track buckles (which are caused by large rail-temperature variations) occur in spring or autumn. In a different season, the rail may have had a very different heating pattern. This could not be considered because of the study’s time constraints. 6.5 Frictional Temperature Increase On a site visit on 18 October 2010, study personnel found that Thermocouple 9, on the field side of the right rail-head, was loose and may not have been reading correctly. However, a visual inspection suggested that the other sensors were intact. During this visit, the triggering mechanism of the DAQ system was implemented. That is, as a train passed the instrumented site, measurements of temperature were taken at 70 Hz for 5 minutes, which was enough time to record any temperature increase due to the train passage. The rail temperature was averaged over both rails, so a uniform increase in temperature could be gauged. The variances in rail temperature and standard deviation in rail temperature were found to gauge the effect of a train passage on the overall temperature of the rail. The measurement for the train passage was a very noisy signal, so, in lieu of filtering the data, variance and standard deviation were taken as an indication of the increase in rail temperature. It was found that temperature change due to train passage varied depending on whether the train was loaded or empty. Empty trains had no effect on the overall temperature of the rails, regardless of rail temperature. Average rail temperature during the train passage, variance of rail temperature, and standard deviation of rail temperature are plotted in Figure 6.32. CRC for Rail Innovation th 9 August 2011 Page 92 Track Stability Management Figure 6.32: Rail-temperature Mean, Variance, and Standard Deviation of Empty Train Passage over Instrumentation A total of 25 empty trains passed the instrumented site and temperature changes were recorded. The average, variance, and standard deviation of rail temperature during the passage show that, on average, the variation was 0.2⁰C (0.6% of average rail temperature), and the standard deviation was, on average, 0.3⁰C (1% of average rail temperature), regardless of the average rail temperature. The range of the variance and standard deviation is within 1% of the average rail temperature, indicating that an empty train has virtually no effect on rail temperature regardless of whether it is day or night or what the temperature of the rail is at the time of the train’s passage. Ten loaded trains with various total wagon numbers passed the instrumented site. The average, variance, and standard deviation of rail temperatures during the train passage are plotted and shown in Figure 6.33. Figure 6.33: Rail-temperature Mean, Variance, and Standard Deviation of Loaded Train Passage over Instrumentation The plot of loaded trains (Figure 6.33) shows a very different result from the empty trains. Depending on the number of wagons, the average overall temperature variance was 4.7⁰C (20.6% of average rail temperature) and 2⁰C in standard deviation (8.7% of average rail temperature). However, these large increases were not observed in the next interval measurement of rail temperature after the train had passed. That is, the high temperatures were sustained for only a short period and did not add to the rail’s overall temperature increase. This is similar to the findings of Chapman et al. (2005). The increase in rail temperature due to train passage varied according to the weight of the train (or loaded wagons). From the results, it is conclusive that temperature increase due to train passage does not depend on the rail’s initial temperature. Temperature increase due to the passage of loaded trains could be problematic when rail temperature is near critical and a loaded train passes and increases the rail temperature above the critical limit. Of course, the rail-buckling mechanism depends both on the forces that the train induces (due to traction) and the residual stress in the rail (which is highly dependent on rail temperature). CRC for Rail Innovation th 9 August 2011 Page 93 Track Stability Management An attempt was made to quantify the frictional heat generated by train passage over the rail in this study by calculating the variance and mean of rail temperature at the time of train passage. However, this is not the usual method for calculating heat addition due to friction. There were some limitations: First, the sensor placement in the field experiment was located at least 10 mm away from the contact patch. Therefore, the intense heat produced by friction and its subsequent transfer into the rail could not be studied. Second, the sampling rate of 70 Hz was not fast enough to capture the frequencies that are developed within the wheel rail contact. Third, the configuration of the passing trains (i.e. how many wagons were loaded and what kind of locomotive was present) was not known, so what temperature increase was generated by what load could not be assessed. Fourth, the rail-temperature data-set was not filtered because of the study’s time constraints, so exactly how much overall rail temperature increased was not quantified. Therefore, it is not clear whether temperature increase due to train passage can initiate a buckling event, or if it is the traction forces of a train that initiate buckling. This is beyond the scope of this study and could be a future area for research. 6.6 Sensors and Prediction: the Argument for Rail-Temperature Prediction The rail-temperature prediction developed for this study had an accuracy of: +/– 5⁰C approximately 95% of the time for this-day predictions +/– 5⁰C approximately 89% of the time for next-day predictions. Measurement devices currently used to measure rail temperature include Type K Class 1 or Class 2 hand-held surface thermocouples, which have an accuracy of +/– 1.5 ⁰C and +/– 2.5 ⁰C respectively. Prediction using the NWP product ACCESS is less accurate, but is within the same magnitude as data gathered by sending personnel to physically measure rail temperatures, or that collected through continuous monitoring. Therefore, the rail-temperature prediction is on a par with physical measurement, and is well worth further future development. CRC for Rail Innovation th 9 August 2011 Page 94 Track Stability Management 7. Conclusion This study developed a piece of software to predict rail temperatures using data from the BoM NWP ACCESS-A product. It is a flagship study for the use of an NWP product in a railway-engineering application in Australia. The researchers concluded that ACCESS-A can be used to accurately predict rail temperatures 24 to 48 hours in advance. While the accuracy of the prediction decreases as the length of the prediction time increases, this decrease in accuracy is within the same magnitudes as that experienced when using rail-temperature measurements taken by instrumentation. Ultimately, this software could be used to provide the rail industry with at least one day’s warning of when rail temperatures could become critical. The accuracy of the method has been tested only for the track configuration, materials and location used in this study. If the research is further developed for different track configurations, materials and locations, it could provide rail-network controllers and schedulers with a powerful tool to help decide if it is safe to run trains at certain speeds. It could also lead to better customer satisfaction for both rail commuters and freight customers, allowing trains to operate with fewer delays and cancellations, and less uncertainty. 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