Download Application of Artificial Neural Network in Fluid Mechanics Teaching Evaluation System

Application of Artificial Neural Network in Fluid Mechanics
Teaching Evaluation System
ZHU Changjun, ZHOU Jihong
College of Urban Construction Hebei University of Engineering, Handan Hebei 056038
[email protected]
Abstract: Based on the neural network method, a neural network model for comprehensive evaluation
of teaching levels in fluid mechanics is built because the classic statistics method and static model can
not meet the demand of precision to the nonlinear and uncertain system.. The structure of the neural
network model is described. The model is trained with fifty samples and tested with twenty samples.
The test results agree well with the actual situation, showing that the model is effective in evaluating the
teaching levels.
Keywords: neural network; teaching evaluation; fluid mechanics
1. Introduction
The artificial neural network model is an intellectual discipline that rose rapidly in the eighties. It
is one non-linear system that simulates human brain structure and encourage behavior at the same time.
It has been successfully applied to many fields. In recent years, the artificial neural network has been
used to evaluate teaching level, and has achieved better results. Higher education has been the hot spot
which people pay attention. In recent years, the Ministry of Education has carried on the level appraisal
every year to several dozens universities, so right evaluation of teaching quality is also the topic which
has been studied in recent years. During the evaluation of teaching level, because the factors affecting
teaching level are more and the affecting degree is different, it is difficult to express the measure result
using mathematical expression which belongs to the nonlinear problem. According to the characters, a
neural network model for teaching evaluation system is built.
2. Principle of neural network
After the first simple neural network developed by McCulloch and Pitts (1943), many types of
ANN have been proposed. The neural network model with multi-hierarchic structure which is based on
back-propagation (BP) arithmetic, the most widely used ANN in hydrologic modeling, is used in this
study. The BP network has all the functions of the neural network and its unique advantages such as the
good mapping ability of processing the rainfall-runoff partitioning with more flexibility. In addition, its
network model contains a highly parallel inter-connection structure, fast self-learning and handling
ability of self-adaptation, which provide foundations for the application in hydrology, especially in
rainfall-runoff modeling using the incomplete material. Therefore, the BP neural network is a popular
choice in the field of hydrology with various complex physical processes.
In recent years, neural network has been widely applied to the teaching evaluation , in which BP
network is commonly used . The model created in this paper is a BP neural network with three-layer
network (Figure1),
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Figure 1.
Three-layer BP network structure
In the Figure 1, p is input of neuron. Each layer has its own weight matrix W , its bias vector b , a
net input vector n , and an output vector a . W is an S × R matrix, and a and b are vectors of
length S respectively. The superscripts of symbols identify the layers. Also shown in Figure 1 are R
1
2
input, S neurons in the first layer, and S neurons in the second layer. Different layers can have
different numbers of neurons. The outputs of layers one and two are the inputs for layers two and three.
1
Thus layer 2 can be viewed as a one-layer network with R = S inputs, S = S
1
2
1
1
2
neurons, and
2
an S × S weight matrix W . The input of layer 2 is a , and the output is a . The other layer also
can be drawn using same abbreviated notation.
First, the output of the network will be computed.In the hidden and output layers, the net input to
unit I is of the form:
s i = ∑ w ji y i + θ i
(1)
Several types of transfer functions are used; however, the most frequently used is the sigmoid
function. This transfer function is usually a steadily increasing S-shaped curve. The sigmoid function is
continuous, differentiable everywhere, and monotonically increasing. In this study, two S-shaped
transfer functions in a MATLAB neural network toolbox were used: the tansig function and logsig
function. The two functions are of the form:
2
−1
1 + e − 2n
1
tan sig (n ) =
1 + e −n
tan sig (n ) =
(2)
(3)
These accumulated inputs are then transformed to the neuron output. This output is generally
distributed to various connection pathways to provide inputs to the other neurons; each of these
connection pathways.
3. Teaching evaluation model
Though neural network can be seen as one kind of “black box” model, the process of building the
model is as complex as other model. During the building the model, the main contents should be
considered as follows: type of neural network, data pre-process, training sample, input pattern, network
topology, parameter estimation, model examination. It is a very important work to choose the model
structure. One good structure can reduce the training times and improve learning precision.
3.1 Data pre-processing
Data pre-processing is an important initial work. The process includes training sample's size,
criterion unitizing transforms (unification replacement), the statistical property research, spatial
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information processing as well as singular value processing and so on. Before the data is processed, the
data should be divided into two groups: training sample and examining sample. There are several types
of preprocessing methods. All the training data are rescaled to a specific range (e.g., [-1, 1] or [0, 1]).
However, the BP model is based on the gradient descent algorithm and the transfer function which
determines the relationship between inputs and outputs of a node and a network has an asymptotic
nature. When the extreme values of discharge are utilized, the gradient of the transfer function will
approximate to zero, consequently, leading to slow the training down.
The next issue is the division of the data into the training and testing data set. The training data set
is presented repeatedly to the network until the weight values are determined while the testing data set is
used for the final evaluation of the BP model performance. Sometimes to overcome the problem of
overfiting or to determine the stopping point of the training process, the validation set is also required.
The testing data set is used for both validation and testing in this study. Although there are no general
solutions to the selection of the training and testing set which may affect the performance of the BP
model, both the training and testing sets representative of the evaluation system data should be carefully
evaluated in the decision making.
3.2 Neuron determination of input layer
According to the indicator system, the main index affecting teaching quality is 12 (table.1),so the
number of input layer can be adopted as 12. the determination of input pattern is the key for the
successful neural network model. If the input neurons are more, the structure of model is more complex
and training period is long. Otherwise, it is difficult to get the nonlinear relationship.
First-level target
Teaching manner
Course content
Teaching method
Teaching effect
Table.1 comprehensive evaluation indicators of fluid mechanics
Number
Second-level target
1
Prepare and plan of a lesson
2
Teaching style and patience
3
Corrects students' papers and Question/answer
4
Foundation and specialization
5
Innovation and comprehension
6
Emphasis
7
Performance and velocity of language
8
Blackboard writing
9
Teaching way
10
Theory test
11
Experiment skill
12
Practice
3.3The number of hidden layers and nodes
ANNs perform complicated nonlinear mapping between input and output variables through the
hidden nodes in the hidden layer. It can capture the pattern in the data. So the hidden layer and nodes
play very important roles in the network architecture. Most studies indicate that a single hidden layer
network tends to be used to the modeling problem and if the number of hidden nodes is enough, we can
obtain any desired accuracy. However, other studies demonstrated the benefits of an ANN comprised of
two hidden layers . In the recognizance of these studies, a single hidden layer is used in this study.
The number of hidden nodes has comparatively great difficulty in determining. The neuron
selection in the hidden layer affects the precise calculation and learning efficiency for the whole BP
network, up till now, there are still no unified ways to identify the number of the hidden layer neuron,
which is at the stage of research and exploration. If a small number of the hidden layer neurons are
chosen, the self-adaptability of the BP neural network will be reduced, thus the training results are not
ideal. However, if the large number is chosen, it is generally believed that the time for network training
will be greatly increased, and some meaningless information in training data will be remembered, thus it
will reduce precise calculation in a sense. The most common way in determining the number of hidden
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nodes is by using experiments or by trial-and-error. Thus in this study the more appropriate number of
the hidden layer neuron is fixed for six through testing and comparing.
Therefore, the chosen configuration for the BP model is 12–6–1: eight inputs, six hidden neurons in
one hidden layer and one output.
3.4 learning rate
In ANNs, the gradient descent algorithm is called learning rate which determine the speed of the
learning phase. Thus the learning rate is crucial for the BP learning algorithm. The learning rate can be
very different in different applications. If the value chosen is excessively large, a divergence will occur;
if the value chosen is excessively small, the learning will be inefficient. A number of recent publications
have proposed new adaptive methods which are commonly based on a trial-and-error heuristic where
global learning rates are adjusted according to the error rates to improve the learning rate. They are
fundamentally different from the traditional adaptive methods which include an additional momentum
parameter for automatically improving the original gradient descent.
In this study, we adopted a traditional method. Since there are few systematic ways of selecting the
learning rate and momentum simultaneously, the ‘‘best’’ values of these learning parameters are usually
chosen through experimentations. As the learning rate and momentum can take on any value between 0
and 1, it is actually impossible to do an exhaustive search to find the best combinations of these training
parameters. For better performance in our experiments, we use a small learning rate of 0.13 and the
associated momentum factor of 0.95 in the training.
4. Results
number
1
2
3
4
5
6
7
8
9
10
ANN
0.991
0.812
0.596
0.421
0.811
0.798
0.610
0.989
0.799
0.603
Table2 testing result
Expert’s value
1.0
0.8
0.6
0.4
0.8
0.8
0.6
1.0
0.8
0.6
Grade
Excellent
Good
Medium
Pass
Good
Good
Medium
Excellent
Good
Medium
5. Conclusions
Neural network is adopted to the evaluation of the “fluid mechanics” course, which victory the
subjective factors of experts. The results are effective and objective. But the neural network method has
its own disadvantages. The number and quality of learning sample can affect the study performance. the
choice of the layer numbers and hidden neurons also affect the study ability and study efficiency. For all
this, the neural network can be seen as an excellent method to evaluate the teaching quality.
References
[1] Zhang heng. Application of artificial neural network in electrical engineering teaching evaluation
system. Journal of wuhan university of science and engineering, 2007,20(3):110-112.
[2] Martin T.Hagan, Howard B.Demuth, Mark H.Beale, Neural network design. Beijing China Machine
Press,2004,239-255.
[3] Han Liqun. Neural network model of teaching quality evaluation system. Journal of Beijing institute
of light industry,2000,18(2):34-38.
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