A method for constructing fatigue model of track subgrade materials based on neural network

Abstract

The present invention provides a method for constructing a fatigue model of track subgrade materials based on a neural network, comprising: step 1: collecting a data set of permanent deformation of track subgrade materials and their influencing factors; step 2: performing data cleaning on the data set; step 3: determining the input parameters and output parameters of the model; step 4: normalizing the data set; step 5: constructing a BP neural network model; step 6: training according to a training set and testing the prediction accuracy through a validation set; step 7: using an Adam optimization algorithm to obtain an optimal network structure; step 8: constructing a fatigue model for predicting permanent strain of track subgrade materials. The fatigue model constructed by the BP neural network in this method can well solve the problem of complex coupling of multiple influencing factors of permanent strain of track subgrade materials, and realizes rapid, effective, accurate and high-precision prediction of complex permanent strain of track subgrade materials under long-term train loads.

Description

Technical Field

[0001] The invention relates to the field of geotechnical engineering, and in particular to a method for constructing a fatigue model of track roadbed materials based on a neural network. Background Art

[0002] Nowadays, railways have become one of the important means of transportation and play an important role in the national economy. In order to meet the growing social and economic needs, it is necessary to continuously increase train speeds, axle loads or travel volume. Obviously, this will have a significant impact on the substructure of the track. To ensure the normal operation of the train, a large number of maintenance and improvement activities need to be carried out regularly. In order to carry out this work efficiently, it is necessary to deeply study the mechanical behavior of the entire railway substructure, especially the permanent strain of each layer under the influence of long-term train cycles. Therefore, it is necessary to quickly and accurately establish a fatigue model of the track subgrade material.

[0003] At present, the commonly used fatigue model is derived through regression analysis, but the definition of the parameters of the fitted regression model requires a pre-specified relationship and there is currently almost no software that can develop a nonlinear model with more than two influencing factors. Therefore, it is necessary to evaluate a series of linear and nonlinear equations, and the process is very cumbersome. However, a simple fatigue model cannot reflect the complex and highly nonlinear problem of permanent strain of track subgrade materials. In recent years, branch neural networks of machine learning have been increasingly used in geotechnical engineering, such as slope stability prediction, back analysis of geotechnical parameters, and settlement estimation of highly complex cohesive soil foundations. Its strong learning ability and ability to handle highly nonlinear problems can solve complex problems with high accuracy. Therefore, BP neural networks have a high possibility of establishing a fast and accurate fatigue model that considers multiple influencing factors.

[0004] At present, the technology of constructing the fatigue model of track subgrade materials using BP neural network has not been reported. Therefore, a method for constructing the fatigue model of track subgrade materials based on BP neural network is invented, so as to provide an effective basis and reference for the mechanical response of track subgrade materials of railway underground structures under long-term train loads, which plays a vital role in the operation and maintenance of tracks. Summary of the invention

[0005] The purpose of the present invention is to overcome the problems existing in the prior art and to provide a high-precision, high-accuracy and fast method for constructing a fatigue model of track subgrade materials based on a BP neural network.

[0006] A method for constructing a track subgrade material fatigue model based on a neural network, comprising:

[0007] Step 1: Collect the permanent strain and its influencing factor data set required to build the track subgrade material fatigue model;

[0008] Step 2: Data cleaning of permanent strain influencing factor dataset;

[0009] Step 3: Determine the input parameter data set and output parameter data set of the BP neural network model;

[0010] Step 4: Normalize the input parameter data set in step 3;

[0011] Step 5: Divide the input parameter data set and output parameter data set after normalization in step 4 into a training set and a validation set;

[0012] Step 6: Construct BP neural network model;

[0013] Step 7: Train the BP neural network model according to the training set, test the prediction performance of the BP neural network model with the validation set, and obtain the trained BP neural network model;

[0014] Step 8: Based on the optimal BP neural network structure, a fatigue model of permanent strain of track subgrade materials is constructed; wherein the permanent strain influencing factor data set required for the track subgrade material fatigue model in step 1 includes the number of cyclic loadings of the track subgrade materials, the volume content of coarse particles, the moisture content, and the maximum deviatoric stress amplitude. The permanent strain influencing factor data set is used as the input parameter data set of the BP neural network model, and the permanent strain data of the track subgrade materials is used as the output parameter data set of the model.

[0015] Preferably, in step 2, the permanent strain influencing factor data set is cleaned by a downsampling method, wherein the downsampling method is specifically as follows: in order to make the data distribution relatively uniform, when acquiring data, some data is extracted from a data category with a large number of samples so that its sample size is equal to that of a data category with a small number of samples.

[0016] Preferably, the normalization process in step 4 is a maximum-minimum normalization process.

[0017] Preferably, the maximum and minimum normalization process described in step 4 is specifically as follows:

[0018]

[0019] in, is the normalized input parameter in the data set, X is the input parameter in the data set, and X max and X min are the maximum and minimum values ​​in the input parameter data set, respectively.

[0020] Preferably, for a small-scale data set, in order to further and more accurately reflect the effectiveness of the model, the data set in step 5 is completely randomly divided into a training set and a validation set using a division ratio of 8:2 commonly used in neural networks. Preferably, the specific process of step 6 is:

[0021] The BP neural network model includes 1 input layer, 3 hidden layers and 1 output layer;

[0022] Step 6-1: Set the number of input layer neurons to 4, the number of neurons in the three hidden layers to N1, N2, and N3 respectively, and the number of neurons in the output layer to 1;

[0023] Step 6-2: Set the activation function of the hidden layer to tanh for nonlinear mapping, and the activation function of the output layer to ReLU;

[0024] Step 6-3: The weights of the three hidden layers are initialized using Xavier, the weights of the output layer are initialized using He, and the biases of the hidden and output layers are initialized to 0;

[0025] Step 6-4: For smaller training set data, the gradient descent method is used, that is, the gradient of the entire data set is calculated in each iteration; at the same time, the Adam optimization algorithm is used to adaptively and dynamically adjust the learning rate and optimize in the gradient direction, setting the initial learning rate Lr.

[0026] Preferably, the specific process of step 7 is:

[0027] Step 7-1: training the BP neural network composed of each parameter generated in step 6-3 by back propagation method, the parameters generated in step 6-3 include weights and biases, and the training adopts the training set generated in step 5, wherein all the data in the training set are randomly input into the BP neural network;

[0028] Step 7-2: Both the training set and the validation set use the mean square error as the loss function to optimize the parameters of each layer of the BP neural network in order to find the parameters with the highest accuracy of the (BP neural) network;

[0029] Step 7-3: During the training process, calculate the loss function of the training set and the validation set. Stop training when the validation set loss function no longer decreases to obtain the optimal BP neural network structure.

[0030] Preferably, the loss function is a mean square error function, specifically:

[0031]

[0032] where y i is the permanent strain value of the track subgrade material in the training set and the validation set, ai It is the permanent strain value of track subgrade material predicted by BP neural network.

[0033] Preferably, the specific process of step 8 is:

[0034] 8-1: Through the optimal structure of BP neural network, the parameters of each layer of BP neural network are obtained;

[0035] 8-2: Establish the general form of fatigue model. The general form of fatigue model is as follows:

[0036]

[0037] Where W1 is the weight of the first layer, W2 is the weight of the second layer, W3 is the weight of the third layer, W4 is the weight of the fourth layer, b1 is the bias of the first layer, b2 is the bias of the second layer, b3 is the bias of the third layer, b4 is the bias of the fourth layer, ε p is the permanent strain of the track subgrade material, are the normalized input parameters.

[0038] The purpose of the present invention can be achieved by the following technical solutions:

[0039] The present invention has the following beneficial effects:

[0040] 1. High precision: The method for constructing the fatigue model of the track subgrade material in the present invention uses a BP neural network to replace the regression analysis in the prior art, which simplifies the process of constructing the fatigue model while ensuring high precision;

[0041] Second, high efficiency: The construction method of the track roadbed material fatigue model based on the BP neural network in the present invention adopts the Adam algorithm, which can adaptively and dynamically adjust the learning rate and optimize the network parameters in the gradient direction compared to optimization algorithms such as RMSprop and Insofar, and has high computational efficiency and low memory requirements. At the same time, the diagonal scaling of the algorithm gradient is invariant, so it is very suitable for solving problems with smaller-scale data or parameters in the roadbed material fatigue model, saving modeling and calculation time, and having higher modeling efficiency.

[0042] 3. High accuracy. The present invention targets the highly complex coupling effects of multiple influencing factors of the fatigue model and comprehensively considers their influence on the permanent strain under long-term train loads. Compared with the traditional method of considering a single influencing factor, the model is more in line with the actual situation. Therefore, the model can achieve higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A schematic diagram of the process of constructing a fatigue model of track subgrade materials based on a neural network in the present invention;

[0044] Figure 2 Schematic diagram of the structure of forward and reverse propagation of neural network. DETAILED DESCRIPTION

[0045] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] A method for constructing a fatigue model of track subgrade materials based on a neural network, the process is as follows Figure 1 As shown, it is divided into data processing, model construction, model training, testing model prediction performance and establishing fatigue model, which specifically includes 8 steps, namely S1, step 1, S2, step 2, S3, step 3, S4, step 4, S5, step 5, S6, step 6, S7, step 7 and S8, step 8. The specific process is as follows:

[0047] Step 1: Collect the data set of permanent strain and its influencing factors required to construct the fatigue model of track subgrade materials; the influencing factors include the number of cyclic loading of track subgrade materials, volume content of coarse particles, moisture content, and maximum deviatoric stress amplitude;

[0048] Step 2: Clean the permanent strain influencing factor data set by downsampling to make the data set evenly distributed;

[0049] Step 3: Determine the input parameters and output parameters of the BP neural network model; the influencing factors of the permanent strain of the track subgrade material are used as the input parameters of the BP neural network model, including the number of soil cyclic loading cycles, coarse particle volume content, water content, and maximum deviatoric stress amplitude, and the permanent strain of the track subgrade material is used as the output parameter of the BP neural network model;

[0050] Step 4: Perform maximum and minimum normalization processing on the input parameter data set in step 3;

[0051] The maximum and minimum normalization processing is as follows:

[0052]

[0053] Among them, X is the input parameter in the data set, X max and X min are the maximum and minimum values ​​of the input parameters respectively; Step 5: Divide the normalized input parameter data set and output parameter data set into a training set and a validation set; the data set is completely randomly divided into a training set and a validation set in a ratio of 8:2;

[0054] Step 6: construct a BP neural network model, wherein the BP neural network model includes 1 input layer, 3 hidden layers and 1 output layer;

[0055] Step 6-1: Set the number of input layer neurons to 4, the number of neurons in the three hidden layers to N1, N2, and N3 respectively, and the number of neurons in the output layer to 1;

[0056] Step 6-2: Set the activation function of the hidden layer to tanh for nonlinear mapping, and the activation function of the output layer to ReLU;

[0057] Step 6-3: In order to make the variance of the input and output of each neuron consistent and the error signal not amplified or reduced during the back propagation process, the weights of the three hidden layers are initialized using Xavier, the weights of the output layer are initialized using He, and the biases of the hidden and output layers are initialized to 0;

[0058] Step 6-4: For a smaller training set data, the gradient descent method is used, that is, the gradient of the entire data set is calculated in each iteration; at the same time, the Adam optimization algorithm is selected to dynamically adjust the learning rate adaptively and optimize in the gradient direction, and the initial learning rate Lr is set. The smaller training set data in the present invention refers to a training set data of tens of thousands or less;

[0059] Step 7: Train the BP neural network model based on the training set, test the model prediction performance with the validation set, and obtain the trained model;

[0060] Step 7-1: Use the back propagation method to train the neural network composed of each parameter generated in step 6-3. The parameters generated in step 6-3 include weights and biases. The training data set is all randomly selected from the normalized training set generated in step 5.

[0061] enter;

[0062] Step 7-2: Both the training set and the validation set use the mean square error as the loss function to optimize the parameters of each layer of the BP neural network in order to find the parameters with the highest accuracy of the (BP neural) network;

[0063] Step 7-3: During the training process, the loss function of the training set and the validation set is calculated. When the loss function of the validation set no longer decreases, the training is stopped to obtain the optimal BP neural network structure.

[0064] The neural network loss function is the mean square error function:

[0065]

[0066] where y iis the permanent strain value of the track subgrade material in the training set and the validation set, a i The permanent strain value of the track subgrade material predicted by the BP neural network;

[0067] Step 8: Based on the optimal (BP neural) network structure, a fatigue model of permanent strain of track subgrade materials is constructed;

[0068] Step 8-1: Obtain the parameters of each layer of the BP neural network through the optimal structure of the BP neural network;

[0069] Step 8-2: The general form of establishing a fatigue model is:

[0070]

[0071] Where W1 is the weight of the first layer, W2 is the weight of the second layer, W3 is the weight of the third layer, W4 is the weight of the fourth layer, b1 is the bias of the first layer, b2 is the bias of the second layer, b3 is the bias of the third layer, b4 is the bias of the fourth layer, ε p is the permanent strain of the track subgrade material, are the normalized input parameters.

[0072] Specific application examples:

[0073] In the regular maintenance of railway lines, in order to carry out the work efficiently, the mechanical behavior of the entire railway substructure, especially the permanent strain of each layer under the influence of long-term train cycles, has been studied in depth. The soil samples for the study were taken from the interlayer soil of a railway underground structure in the northwest of Lyon, France. The sampled soil layer is a layer composed of well-mixed coarse / fine-grained soil. When sampling, the line was being restored, so the coarse-grained layer was removed. The sampled soil layer was excavated with a mechanical shovel and transported in soil bags for laboratory multi-stage cyclic loading tests. Fine particles and micro-ballasts were mixed according to 9 fv values ​​to reconstruct simulated interlayer soil materials. Under the conditions of optimal moisture content of 13.7% and maximum dry density of 1.82Mg / m3, fine-grained soil was prepared by dynamic compaction. The data range is shown in Table 1. The present invention now uses a neural network to construct a fatigue model of permanent strain based on the test data.

[0074] Table 1 Value range of influencing factors

[0075]

[0076] According to the range of values ​​shown in Table 1, 1309 sets of data were generated by downsampling, and the permanent strain value of each set of data was also included. Figure 2 Establish a good neural network structure for training and verification, in which Figure 2 In the neural network structure, the input layer consists of 4 neurons

[0077] The first hidden layer consists of 18 neurons. The second hidden layer consists of 15 neurons The third hidden layer consists of 14 neurons The number of neurons in each hidden layer is the number of weights in each layer of the BP neural network. The output layer consists of 1 neuron The composition is the permanent strain data.

[0078] The optimal network structure and the values ​​of the parameters of each layer are used to construct the fatigue model of permanent strain:

[0079]

[0080] Where W1 is the weight of the first layer, W2 is the weight of the second layer, W3 is the weight of the third layer, W4 is the weight of the fourth layer, b1 is the bias of the first layer, b2 is the bias of the second layer, b3 is the bias of the third layer, b4 is the bias of the fourth layer, ε1 p is the permanent strain of the track subgrade material, are the influencing factors after normalization.

[0081] The error between the permanent strain value of the track subgrade material predicted by the fatigue model constructed based on the neural network and the permanent strain value measured by the test and the error of the validation set are shown in Table 2. Table 2 Comparison of the error between the predicted value and the measured value of the fatigue model and validation set

[0082]

[0083] The above description does not limit the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not used to limit the present invention. Any technician familiar with the profession can use the above disclosed technical content to make different forms of neural networks and construct different prediction models. Change or modification to equivalent embodiments with equivalent changes without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification of any neural network structure, input parameters and optimization method made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for constructing a fatigue model of track subgrade materials based on a neural network, characterized in that: The construction method comprises: Step 1: Collect the permanent strain and its influencing factor data set required to build the track subgrade material fatigue model; Step 2: Data cleaning of permanent strain influencing factor dataset; Step 3: Determine the input parameter data set and output parameter data set of the BP neural network model; Step 4: Normalize the input parameter data set in step 3; Step 5: Divide the input parameter data set and output parameter data set after normalization in step 4 into a training set and a validation set; Step 6: Construct BP neural network model; Step 7: Train the BP neural network model according to the training set, test the prediction performance of the BP neural network model with the validation set, and obtain the trained BP neural network model; Step 8: Based on the optimal BP neural network structure, a fatigue model of permanent strain of track subgrade materials is constructed; wherein the permanent strain influencing factor data set required for the track subgrade material fatigue model in step 1 includes the number of cyclic loadings of the track subgrade materials, the volume content of coarse particles, the moisture content, and the maximum deviatoric stress amplitude. The permanent strain influencing factor data set is used as the input parameter data set of the BP neural network model, and the permanent strain data of the track subgrade materials is used as the output parameter data set of the model.

2. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 1, characterized in that: In step 2, the permanent strain influencing factor data set is cleaned by downsampling, wherein the downsampling method is as follows: in order to make the data distribution relatively uniform, when acquiring data, some data is extracted from the data category with a large number of samples so that its sample size is equal to that of the data category with a small number of samples.

3. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 1, characterized in that: The normalization process in step 4 is maximum and minimum normalization process.

4. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 3, characterized in that: The maximum and minimum normalization process described in step 4 is specifically as follows: in, is the normalized input parameter in the data set, X is the input parameter in the data set, and X max and X min are the maximum and minimum values ​​in the input parameter data set, respectively.

5. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 1, characterized in that: For small-scale data sets, in order to further and more accurately reflect the effectiveness of the model, the data set in step 5 is completely randomly divided into a training set and a validation set using the 8:2 division ratio commonly used in neural networks.

6. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 1, characterized in that: The specific process of step 6 is as follows: The BP neural network model includes 1 input layer, 3 hidden layers and 1 output layer; Step 6-1: Set the number of input layer neurons to 4, the number of neurons in the three hidden layers to N1, N2, and N3 respectively, and the number of neurons in the output layer to 1; Step 6-2: Set the activation function of the hidden layer to tanh for nonlinear mapping, and the activation function of the output layer to ReLU; Step 6-3: The weights of the three hidden layers are initialized using Xavier, the weights of the output layer are initialized using He, and the biases of the hidden and output layers are initialized to 0; Step 6-4: For smaller training set data, the gradient descent method is used, that is, the gradient of the entire data set is calculated in each iteration; at the same time, the Adam optimization algorithm is used to adaptively and dynamically adjust the learning rate and optimize in the gradient direction, setting the initial learning rate Lr.

7. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 6, characterized in that: The specific process of step 7 is as follows: Step 7-1: training the BP neural network composed of each parameter generated in step 6-3 by back propagation method, the parameters generated in step 6-3 include weights and biases, and the training adopts the training set generated in step 5, wherein all the data in the training set are randomly input into the BP neural network; Step 7-2: Both the training set and the validation set use the mean square error as the loss function to optimize the parameters of each layer of the BP neural network in order to find the parameters of the BP neural network with the highest accuracy; Step 7-3: During the training process, calculate the loss function of the training set and the validation set. Stop training when the validation set loss function no longer decreases to obtain the optimal BP neural network structure.

8. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 7, characterized in that: The loss function is a mean square error function, specifically: where y i is the permanent strain value of the track subgrade material in the training set and the validation set, a i It is the permanent strain value of track subgrade material predicted by BP neural network.

9. The method for constructing a track subgrade material fatigue model based on a neural network according to claim 1, characterized in that: The specific process of step 8 is as follows: 8-1: Through the optimal structure of BP neural network, the parameters of each layer of BP neural network are obtained; 8-2: Establish the general form of fatigue model. The general form of fatigue model is as follows: Where W1 is the weight of the first layer, W2 is the weight of the second layer, W3 is the weight of the third layer, W4 is the weight of the fourth layer, b1 is the bias of the first layer, b2 is the bias of the second layer, b3 is the bias of the third layer, b4 is the bias of the fourth layer, ε p is the permanent strain of the track subgrade material, are the normalized input parameters.

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