VERTICAL TEMPERATURE DIFFERENCE PREDICTION ABOUT UNBALLASTED TRACK BASED ON ARTIFICIAL NEURAL NETWORK

Bin YAN，Shi LIU，Ping LOU，Hao PU，Zhiping ZENG，Wei LI

School of Civil Engineering，Central South University，Changsha 410075

Abstract：Based on the test data of unballasted track temperature field，the local meteorological data was used as input parameters and the multilayer artificial neural network（BP neural network）was established by error back-propagation algorithm.It is for the purpose of predicting vertical temperature gradient distribution of unballasted track and investigating the influence of the parameters including network structure，selection method and quantity of sample，excitation function and error back-propagation algorithm.The measured data was used to verify the accuracy of the predicted results.The relationship between daily temperature change range and vertical temperature difference of unballasted track was studied on this basis.Studies show that：the relationship between vertical temperature difference of unballasted track and daily temperature change range is nonlinear，with-2 ℃ to-15 ℃ negative temperature difference at 6：00 a.m.and-2 ℃ to 9 ℃ positive temperature difference at 3：00 p.m.In order to further improve the predictive ability of the model，it is necessary to add the test data of the local temperature model.

Keywords：track engineering，unballasted track，temperature field，artificial neural network，prediction model

Email：binyan@csu.edu.cn

1　Introduction

The heat exchange between the concrete structure and the outside can be divided into three kinds of sun direct radiation，convective heat and radiation heat exchange[1，2].In the process of heat exchange with the outside，there is a non-linear temperature field in the concrete structure due to the poor thermal conductivity of concrete.In order to study concrete box section and channel section temperature field distribution of sunlight[3-5]，as well as CWR longitudinal force on the continuous bridge caused by sunshine temperature field[6]，the heat exchange was converted by scholars into the thermodynamic simulation model of loading heat flux boundary conditions to the bridge section.However，the temperature field was closely related to the earth revolution position，sun azimuth，latitude and longitude，structure orientation，atmospheric transparency coefficient，concrete surface absorption rate and other parameters[7，8].Because there were many theoretical assumptions and calculation parameters were difficult to obtain，the reproducibility of existing research was often poor and there was a certain gap between it and engineering practice.

There was also the nonlinear temperature field in unballasted track structure on the bridge，the vertical temperature gradient of which on the one hand caused track plate buckling deformation and mortar layer away from the joint to influence the durability of track structure，on the other hand increased instability of the track structure and track plate was liable to arch under the sustained high temperature to threaten traffic safety.However，the vertical temperature gradient distribution of unballasted track was still unclear.

In order to predict the vertical temperature gradient distribution of unballasted track，based on a multilayer perceptron artificial neural network of error back-propagation algorithm（BP neural network）by this paper，measured results of the unballasted track temperature field were used as sample library to establish nonlinear relationship between local temperature，weather condition and vertical temperature field of unballasted track，and to compare the influence of network structure，sample selection method，transfer function and error feedback algorithm parameters on prediction accuracy of network.On this basis，the vertical temperature field distribution of unballasted track and time-variant characteristics were predicted by the local temperature and weather condition，prediction results being in good agreement with the measured values.

2　Unballasted Track Temperature Field Test

CRTSⅡ slab-type unballasted track temperature field on a passenger dedicated line were continuously observed by Central South University for 4 months.The temperature interval was 0.5 h，and the test site was located at 28°N and 115°E，a subtropical monsoon climate.The temperature sensor was embedded in the base plate and track plate joint，as shown in Figure 1.

Each measuring point temperature and the local daily maximum and minimum temperature distribution（local atmospheric temperature data from meteorological）was as shown in Figure 2.

Diurnal variation of temperature on the unballasted track surface caused by the sun direct radiation and convection heat transfer was significant，the difference 5℃ to 14℃ between the highest temperature and daily maximum temperature；The internal temperature of unballasted track lagged behind the upper surface with the amplitude of variation smaller，and the bottom surface temperature was 2 ℃ to 14 ℃ higher than the daily minimum temperature.The daily distribution of temperature difference between the upper and lower surface of the track was shown in Figure 3.

The temperature difference between the upper and the lower surface of the track could reach-10 ℃ to 15 ℃ ，and the larger the daily temperature difference was，the larger the vertical temperature difference of the track plate was.The maximum positive temperature difference occurred at 3：00 p.m.，while the maximum negative temperature difference occurred at about 6：00 a.m.

3　BP Neural Network Prediction Model of Unballasted Track Temperature Field

3.1　BP neural network

Artificial neural network（ANN）was a network[9]，which was abstracted and simplified from the human brain network structure，and was composed of a large number of processing unit interconnection（neurons，Figure 4）.In fact，it was a kind of nonlinear fitting algorithm[10].

Among them，xm（m=1，2，…，M）was the input signal of the neuron i（training sample），wmithe connection strength between xmand neuron i（weight），bithe threshold for the neuron i，f（·）the excitation function and yithe output of the neuron：

Taking sigmoid excitation function as an example：

After the error signal was obtained by comparing the model output with the target sample，the weight and threshold were iteratively adjusted to eventually reduce the difference between the model output and target sample to an acceptable range.

BP neural network belonged to the multilayer neural network（Figure 5）.The input signal（training sample）from the input layer went through the hidden layer and generated the output signal at the output end；not getting the target sample，the output layer transferred to the error signal back-propagation，adjusting the network weight simultaneously.Through the constant revision of the weight，the actual output of the network was closer to the target sample[10].

The strong nonlinear relation between the input samples and the target ones could be stored in the weight matrix of the BP neural network by inputting multiple samples.When containing multiple hidden layers，more information could be extracted from the input mode so as to make the BP neural network to accomplish more complex tasks.In theory，arbitrary nonlinear fitting was completed by adjusting the number of hidden layer neurons[11].

3.2　BP neural network model of unballasted track temperature field

A certain amount of the A-E point temperature records were selected as the target samples from 4368 unballasted track temperature test data（5 items in total）.The day meteorological data were selected as training samples，including the daily maximum temperature，minimum temperature，sunny/rainy（respectively expressed as 1/0），and time（0-24），a total of 4 items.Daily temperature was related to both convection and radiation heat exchange，while both weather and time to the intensity of solar radiation.

The random initial weight and the sigmoid transfer function were used to improve the convergence speed and avoid the local minimum（the initial learning rate 0.001）by the gradient descent learning algorithm of additional momentum factor.Mean square error was adopted as an error performance function（the permissible error of the target 0.001）.Powell-Beale conjugate gradient method was used by error propagation algorithm to establish double hidden layer BP neural network mode of unballasted track temperature field prediction（Figure 5）.

4　BP Neural Network Parameter Selection

4.1　Network structure

In order to study the influence of the network structure on network prediction accuracy，the number of neurons in the first and second hidden layers was respectively set to 1-30，the 4368 unballasted track temperature test records were taken as target samples，the corresponding meteorological parameters were taken as training samples，and then network training was carried out by 1000 iterative times.The maximum absolute error between the network calculation results and target samples（at any time and any point，similarly hereinafter）was shown in Figure 6.

When the double hidden layer neural nodes were larger than 3，the maximum error was less than 7 ℃ ，but floating up and down.Considering the prediction accuracy and computational energy consumption，the hidden layer structure of double 16 neurons was ultimately chosen，the maximum error 5.7 ℃.The overall structure of the network was 4（input layer）-16-16-5（output layer）.

4.2　Training sample selection method

To facilitate validation of neural network prediction accuracy，it was often necessary to retain part of the records as test samples.To study the effect of training sample selection method and number of samples，10％-100％ test records were orderly and randomly selected respectively to carry out network training，as shown in Figure 7.

Because the sequential extraction of training samples easily made the network fall into the local minimum，and there was excessive learning phenomenon，it was needful to constantly increase the number of training samples to ensure network prediction accuracy.However，random extraction of training samples could skip the local minimum.When the number of samples was more than 30％，the accuracy requirements were completely able to be met.For safety reasons，the first 80％ test records of disrupting the order were selected as the training samples，and the remaining 20％was used to verify the accuracy of neural network simulation.

4.3　Excitation function

Randomly selecting 80％ test records as training samples，the ① competition type，② threshold type，③ S type，④ linear，⑤ radial basis and ⑥ Sigmoid function were respectively used as excitation function[12，13]to study its effect on the prediction accuracy of the network，as shown in Figure 8.

When using the Sigmoid transfer function，the maximum absolute error and average one of the network were all the lowest，which were respectively 5.7 ℃ and 0.01 ℃.

4.4　Error back-propagation algorithm

The ① quasi Newton method，② Bayesian normalization method，③ Powell-Beale conjugate gradient method，④ Rolak-Ribiere variable gradient method，⑤ gradient descent method，⑥ adaptive learning rate gradient descent method and ⑦ adaptive learning rate and momentum factor gradient descent method[14，15]were respectively chosen as the error back-propagation algorithm of the model so as to study its impact on prediction accuracy.

The prediction result errors in the other algorithms were relatively smaller，except unsatisfactory prediction results in the ①，⑤and ⑥.However，considering that Algorithm② was time-consuming for 139 s，④ and ⑤9s，and ⑤-⑦ 3 s，Powell-Beale conjugate gradient back-propagation algorithm was finally chosen，its maximum error 5.7 ℃ and the average error 0.01 ℃，as shown in Figure 9.

4.5　Number of iterations

The neural network training iteration number was set to 100-2000 to study the impact of the iteration number on the network prediction accuracy（Figure 10）.The calculation results showed that：when the number of iterations was over 600，the error was basically stable，and the network prediction accuracy could meet the engineering needs.

5　Validation of Neural Network Prediction Model in Unballasted Track Temperature Field

Comparing with the above parameters，the first 80％ test records of disrupting the order were selected as the target samples and its corresponding meteorological data as the training samples，the remaining 20％ test records as the validation data.BP neural network with 4-16-16-5 structure was established by the sigmoid excitation function and the Powell-Beale conjugate gradient back-propagation algorithm.The iteration number was set to 800 times to train the network，and the contrast between the predicted values of A measuring point temperature and the measured ones was shown in Figure 11.

Based on average error 9.4％ of predicted results and the maximum absolute error 5.7 ℃，it was proved that BP neural network model proposed in this paper could be used to predict the unballasted track temperature distribution and had better generalization ability.The error on October 31 was larger in Figure 11，the reason for which was that the day’s weather parameters were extremely close to ones on October 19.Network prediction results were similar to ones on October 19，showing that the neural network had certain robustness.

6　Vertical Temperature Difference Prediction of Unballasted Track

Based on the trained BP neural network prediction model of unballasted track temperature field，the daily maximum and minimum temperature and weather condition were regarded as the initial conditions so as to calculate the temperature difference between the upper and lower edge of unballasted track within the range of both daily maximum temperature 0 to 50 ℃ and daily minimum temperature 0 to 30 ℃，as shown in Figure 12.

Figure 12 showed that unballasted track vertical temperature difference was not a direct ratio with the daily temperature difference，and presented nonlinear distribution characteristics.At 6 a.m.，the negative temperature gradient was often presented in the unballasted track，its value-2 ℃ to-15 ℃；at 3：00 p.m.，the positive temperature gradient was often presented in the unballasted track，its value-2 ℃ to 9 ℃.

For the part outside the training sample interval，the predicted value was also given by the neural network，based on the existing nonlinear relationship between the input and output.However，for the extreme case of similar daily temperature change 0 to 50 ℃，the accuracy of the network prediction value was not proven.

7　Conclusions

Based on the measured data in unballasted track temperature field，taking meteorological data easily got as input parameters，BP neural network prediction model of unballasted track vertical temperature distribution was established，the influence of various network parameters on the neural network prediction accuracy was compared and the vertical temperature difference distribution pattern of unballasted track was investigated in various temperature and weather conditions.The main conclusions are as follows：

In order to improve the BP neural network prediction accuracy of unballasted track vertical temperature distribution and reduce the calculated energy consumption，it is suggested that：the neural network structure is chosen for 4-16-16-5，80％ test records are randomly extracted as the target samples and the corresponding meteorological data are used as training samples，sigmoid excitation function and Powell-Beale conjugate gradient back-propagation algorithm are adopted，and more than 800 times are required for the number of iterations.

Unballasted track vertical temperature gradient，the average error 9.4％，is predicted by the BP neural network to be able to meet the engineering needs.

The relationship of unballasted track vertical temperature and daily temperature difference is nonlinear.In the unballasted track，the negative temperature difference，-2 ℃ to-15 ℃，appears at about 6：00 a.m.，while the positive temperature difference，-2 ℃ to 9 ℃，at around 3：00 p.m.

Compared with unballasted track thermodynamic simulation model of too much theoretical assumptions and key parameter values difficult to be got，it is a comparatively simple and feasible scheme that the meteorological data is used to predict unballasted track vertical temperature difference based on BP neural network，with the characteristics of both good fault tolerance and strong generalization.In order to further improve the accuracy of model prediction，it is necessary to supplement the test data of containing the local main temperature model.

Acknowledgement

The authors wish to acknowledge the support and motivation provided by Project（No.51578552）of National Natural Science Foundation of China.

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ICRE2016-International Conference on Railway Engineering