Download temperature prediction in timber using artificial neural networks

TEMPERATURE PREDICTION IN TIMBER USING
ARTIFICIAL NEURAL NETWORKS
Paulo Cachim1
ABSTRACT: Neural networks are a powerful tool used to model properties and behaviour of materials in many areas
of civil engineering applications. In the present paper, the models in artificial neural networks for predicting the
temperatures in timber under fire loading have been developed. For building these models, training and testing using the
available numerical results obtained using design methods of Eurocode 5 have been used. The data used in the
multilayer feed forward neural network models are arranged in a format of three input parameters that cover the density
of timber, the time of fire exposure and the distance from exposed side. With these input parameter used in the
multilayer feed forward neural network models the temperatures in timber are predicted. The training and testing results
in the neural network model have shown that neural networks can accurately calculate the temperature in timber
members subjected to fire.
KEYWORDS: Instructions to authors, Proceedings, WCTE 2010
1 INTRODUCTION 1
Artificial neural networks (ANN) have become a very
popular technique in many fields such as medicine,
finance, economics, engineering, etc. The types of
problems to which they are applied to are also extensive
and vary from classification and prediction to data
visualization and compression. The number of neuro-like
models and schemas as well as ways to implement
neural models is permanently increasingly. Within the
field of construction industry, has mostly being used for
estimating concrete properties such as strength, slump or
modulus of elasticity [1-6].
If neural networks could adequately model the
temperature fields within a timber member then, after
network learning, the results of the network can be used
in numerical calculations without the need to use
simultaneously a thermal and mechanical analysis.
Consequently, temperatures in timber can be simply
calculated by applying the network to the appropriate
input values.
The aim of this article is to describe the applicability of
artificial neural networks for the prediction of
temperatures in timber under fire loading.
2 ARTIFICIAL NEURAL NETWORKS
2.1 BASICS
An artificial neural network is basically a large number
of highly interconnected idealized neurons that receives
1
Paulo Cachim, Department of Civil Engineering & LABEST,
University of Aveiro, 3830-193 Aveiro, Portugal. Email:
[email protected]
input from the neurons to which it is connected,
computes an activation level, and transmits that
activation to other processing neurons. The core of
neural network computations is activation. Each input
neuron activates one or several additional neurons with
different levels of efficiency. Subsequently these
activated neurons will activate other neurons until an
output was reached. The final result, the output, of the
betwork is strongly influenced by the interconnection
between neurons, i.e., the strength and layout of the
connections. An ANN must be trained in order to learn
and produce meaningful results. After the learning
process, the network is able to perform computations.
The learning process can be continuous in which case
the network is continuously adapting itself for the new
data.
In a feed forward neural network, as used in this work,
the artificial neurons are grouped in layers. In each layer,
all the neurons are connected to all the neurons in the
next layer (see Figure 1). No connection exists between
neurons of the same layer or the neurons which are not
in successive layers. Basically, a minimum of three
layers of neurons must exist: (i) one input layer; (ii) at
least one hidden layer; and (iii) one output layer of
neurons. Each connection between artificial neurons is
characterized by a weight value. Each neuron of the
input layer receives information (data from experiments
or analysis) that will be the output of this layer and
passes it to the neurons of the following layer weighted
by the weight of the connection layer (see Figure 1). In
all of the subsequent layers, each neuron computes the
weighting sum of all the n neurons of the precedent
layer, sj, according to equation (1). At this stage a bias,
bj, can be introduced.
layer, and the weights are adjusted based on some
learning strategies so as to reduce the network error.
In this study results of numerical finite element
simulations were used as data for the network. Basic
parameters of the model were selected and used as input
neurons while the results, temperatures in timber, are
used as outputs. For each case, a random number of
available points were selected to serve as data for neural
network training while the remaining results were used
to test and validate the model. Details specific for each
networks are given below, depending on the analysed
problem.
In this study, the error occurred during the training and
testing of the network was expressed as a root mean
squared error (RMSE) and as a mean absolute error
(MAE) that can be calculated by equations (3) and (4),
where ti is the desired output (numerical results), oi is the
predicted output (calculated by the network) and p is the
number of points where the temperatures have been
calculated.
RMSE =
Figure 1: Feed forward neural network scheme (top) and
individual neuron calculation scheme (bottom)
Afterwards each neuron activates the output, oj, by using
an activation function, f. One of the most used activation
functions is the sigmoid function leading to an output as
described in equation (2), where α is a parameter
controlling the rate of changing of the sigmoid. In a feed
forward network, the inputs and output variables are
normalized to be in the range [0, 1]. For practical
purposes, however, the applicable range is usually [0.1,
0.9] to avoid small slopes of the activation function.
n
s j = b j + ∑ wij oi
(1)
i =1
1
o j = f (s j ) =
1 + exp(− α s j )
(2)
2.2 CHOICE OF NETWORK
Because there is no reliable method for deciding the
number of neural units required for a particular problem,
the choice of the number of hidden layers and of neurons
per layer must be based on experience and a few number
of trials is usually necessary to determine the best
configuration of the network.
Back propagation algorithm, as one of the most wellknown training algorithms for the multilayer perceptron,
is a gradient descent technique to minimize the error for
a particular training pattern in which it adjusts the
weights by a small amount at a time. The network error
is passed backwards from the output layer to the input
MAE =
1 p
(ti − oi )2
∑
p i =1
(3)
1 p
∑ ti − oi
p i =1
(4)
In addition, accuracy of the network predictions were
also assessed by the coefficient of distribution (R2) and
by the mean absolute percentage error (MAPE)
calculated according to equations (5) and (6),
respectively. In equation (5),
desired outputs.
t represents the average of
p
R2 = 1 −
∑ (t
i =1
p
2
∑ (t
i =1
− oi )
i
i
−t
)
(5)
2
1 p t i − oi
MAPE = ∑
p i =1 t i
(6)
3 TIMBER TEMPERATURES UNDER
FIRE LOADING
In this work, the temperature evolution within a timber
member under fire loading was calculated using the
conductive model presented in Eurocode 5, Part 1-2
(EC5) [7]. The conductive model presented in EC5 is
based on the calculation of the two- or threedimensional, transient, heat transfer differential equation,
incorporating thermal properties that vary with
temperature. Effects such as mass transfer within the
structure, reaction energy released inside the wood due
to pyrolysis or degradation of material, cracking of
charcoal, which increases the heat transfer of the char
layer are not accounted for. Thus, EC5 proposes
properties that are equivalent properties taking these
effects into account.
The coefficient of heat transfer by convection on
unexposed surfaces was considered 9 W/m2K and on
heated surfaces with standard temperature-time curves
25 W/m2K, as defined in Eurocode 1, Part 1-2 [7]. The
surface emissivity of wood used in calculations was 0.8
[8]. Thermal conductivity, specific heat capacity and
density ratio were used with values defined in EC5
(Figure 2 and 3). Moisture content of wood was
considered equal to 0.12.
The calculation of temperatures in timber was performed
by using a finite element mesh with square elements
(side is 5 mm); this will allow an adequate
characterization of the thermal field within timber.
Default EC5 thermal properties for timber as described
in previous section were used. Numerical finite element
calculations were carried out using the finite element
code SAFIR [9], which is a special purpose finite
element code, developed at University of Liege for
studying structures subjected to fire. Figure 4 shows the
temperature distribution for t = 30 minutes and 450
kg/m3 density with the abscissa distance measured from
the face exposed to fire obtained using SAFIR and
standard properties of EC5.
Figure 2: Specific heat in timber [7]
Figure 4: Temperature profile in timber for t = 30 and 60
minutes and 450 kg/m3 density
Figure 3: Relative density and conductivity [7]
4 PREDICTION OF TEMPERATURES
IN TIMBER UNDER FIRE LOADING
USING ARTIFICIAL NEURAL
NETWORKS
The use of artificial neural networks to predict
temperatures in timber members will be presented in this
article by using the following approach:
a) for a specific timber density, several network
models were tested by training them using
randomly selected data;
b) for the network model with best training results
additional information regarding network
behaviour was investigated.
To assess the possibility of using artificial neural
networks for prediction of temperature in timber, several
networks were tested. The input parameters were the
time of exposure, t; (and the distance from exposed
surface, s. Output was defined by a single neuron that
represents the temperature in timber, T. The procedure
was defined as follows. Temperatures were calculated
every 60 seconds during one hour, meaning that a total
of 60 time points are available. Since the finite element
mesh had elements with 5 mm side and the maximum
distance from exposed surface is 200 mm a total of 41
points where temperatures were calculated existed. Thus,
a total of 2460 time-distance-temperature points are
available. For network training, 30 % of these points
were randomly selected. The remainder were used for
network assessment. Since there is no rule of thumb for
the selection of artificial network layouts, several (in this
case 11) network layouts were tested where the number
of hidden layers and the number of neurons in these
layers were changed (see Table 1). For network training,
sigmoid activation functions were used with the αparameter equal to 2, the number of iterations was
100000, the learning rate was 0.3 and the momentum
was 0.1. Timber density used for assessing the ability of
artificial neural networks for temperature prediction was
450 kg/m3.
Table 1: ANN characterization
Network
name
H1500
H1700
H1900
H2550
H2750
H2950
H2570
H2770
H2970
H2990
H3575
Number of
hidden
layers
1
1
1
2
2
2
2
2
2
2
3
Neurons in hidden layer
1
2
3
5
7
9
5
7
9
5
7
9
9
5
5
5
5
7
7
7
9
7
5
process. The results of the testing are shown in Table 3.
Again it can be observed that network H2570 gives the
best results with a RMSE of 3.5 ºC and an R2 equal to
0.9997. In Figure 5 the results calculated using SAFIR
are compared with the outputs of the network H2570. It
can be observed that a very good correspondence
between both results was achieved.
Table 2 presents the errors and accuracy measures for
the analysed cases. It can be shown that the network
H2570 gives the best results for the training process.
This network has two hidden layers with 5 neurons in the
first layer and 7 neurons in the second hidden layer. It
can also be observed that one layer networks give the
worst results.
Table 2: Training results
Network name
H1500
H1700
H1900
H2550
H2750
H2950
H2570
H2770
H2970
H2990
H3575
MAE
ºC
3.2
3.1
3.6
1.4
1.3
1.6
1.2
1.7
1.5
1.7
1.4
2
MAPE
0.0568
0.0683
0.0759
0.0210
0.0190
0.0320
0.0169
0.0318
0.0253
0.0291
0.0260
RMSE
ºC
7.5
6.4
8.2
3.3
3.2
3.5
3.3
3.6
3.5
3.9
3.4
R
0.9987
0.9991
0.9985
0.9997
0.9998
0.9997
0.9998
0.9997
0.9997
0.9997
0.9997
MAPE
0.0542
0.0703
0.0708
0.0218
0.0193
0.0306
0.0170
0.0307
0.0255
0.0276
0.0255
RMSE
ºC
8.2
7.6
8.6
4.0
4.2
4.4
3.8
4.2
4.0
4.4
3.6
R2
0.9986
0.9988
0.9985
0.9997
0.9996
0.9996
0.9997
0.9996
0.9997
0.9996
0.9997
Figure 5: Comparison of SAFIR calculated temperatures
and ANN output temperatures for H2570 network
The evolution of the error during the iteration process
can be observed in Figure 6. It can be observed that the
convergence process is relatively efficient. It should be
noted that, since the initial estimation of the network
parameters are randomly selected and then corrected
through the iterative process, two sequential runs of the
process may lead to different network parameters and
error values (although similar).
Table 3: Testing results
Network name
H1500
H1700
H1900
H2550
H2750
H2950
H2570
H2770
H2970
H2990
H3575
MAE
ºC
3.1
3.3
3.5
1.4
1.4
1.7
1.2
1.7
1.5
1.7
1.4
After training, the network was tested by using the
remainder 70% of the results not used for the training
Figure 6: Evolution of the error during the iterative
process for H2570 network
5 CONCLUSIONS
Artificial neural networks are a powerful tool for solving
some of the complex civil engineering problems because
they can learn and generalize from examples and
experiences. In this study, using these beneficial
properties, artificial neural networks are used in order to
predict the temperatures in timber under fire loading.
The use of artificial neural networks allow designers to
easily calculate the temperatures in a timber member at
any time and to use these results into structural analysis
and design without the need to use a thermal and
mechanical model.
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