A method for constructing a data-driven track structure dynamics prediction model

Abstract

The present invention discloses a method for constructing a track structure dynamics prediction model based on data-driven. The track structure dynamics prediction model based on data-driven is constructed through the steps of constructing a prediction model, conducting model training, conducting model prediction, selecting model performance evaluation indicators, conducting optimization research on the prediction model, and conducting comparative verification of model performance. The constructed prediction model is used for predicting the dynamic response of the track structure. With axle box acceleration and track irregularity information as input, the prediction model can output the dynamic response of the track structure quickly, efficiently and accurately. The constructed prediction model is used for predicting the dynamic response of the track structure of lines such as high-speed railways, urban rail transit and heavy-load railways, thereby realizing rapid evaluation of the dynamic response and dynamic state of the track structure.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit prediction models, and further to a track structure and dynamics prediction model, and in particular to a method for constructing a track structure dynamics prediction model based on data-driven. Background Art

[0002] my country's high-speed railways have gradually transitioned from a large-scale construction period to an operation and maintenance period. Track structure is one of the important factors that directly affect the smoothness, safety and comfort of train operation. Therefore, it is extremely important to strengthen the rapid evaluation of the service status and dynamic response of the track structure. Generally, a simulation model is established to meet the needs of rapid and accurate evaluation of the track structure. Currently, a refined dynamic simulation model is mainly used, but the time cost of refined modeling is huge. Therefore, a new prediction model is needed to replace the traditional simulation model to achieve rapid, accurate and efficient output of the dynamic response of the track structure, thereby achieving a comprehensive evaluation of the dynamic state of the track structure. The present invention provides a method for constructing a data-driven track structure dynamics prediction model to solve the above problems. Summary of the invention

[0003] The present invention provides a method for constructing a track structure dynamics prediction model based on data-driven, and constructs a prediction model. The constructed prediction model is used for predicting the dynamic response of the track structure of lines such as high-speed railways, urban rail transit and heavy-load railways.

[0004] The technical solution adopted by the present invention to solve the above technical problems is:

[0005] A method for constructing a track structure dynamics prediction model based on data-driven, characterized by comprising the following steps:

[0006] S1, build a data-driven track structure dynamics prediction model; the structure of the prediction model includes an input layer, an output layer, a circulation layer and a fully connected layer. The input layer, the output layer, the circulation layer and the fully connected layer are parallel to each other. The data is input into the input layer, and then passes through the circulation layer and the fully connected layer in sequence and then outputted through the output layer to complete the construction of the prediction model structure;

[0007] In the prediction model, the length of a single-layer sequence is t, and both the input and output adopt vector mode. The input and output vectors are x and y respectively, and h0 and h are the initial state of the recurrent layer unit and the hidden layer state respectively;

[0008] S2, training the prediction model: using the timed back propagation algorithm, each gradient calculation randomly selects a subset of the training set, the sample content in the subset is N, the sequence length is T, and the loss function uses the mean square error;

[0009] The training of the prediction model specifically includes the following steps:

[0010] S21, standardize the data: the training set is {x,y}={[x1,x2,...,x N ],[y1,y2,...,y N ]},in n and m represent the dimensions of input and output respectively; the training set is processed by Z-score standardization method, and the data is standardized by mean and standard deviation. The processed data conforms to the standard normal distribution with mean 0 and variance 1;

[0011] The standardization formula is as follows:

[0012]

[0013] In the formula, x* is the standardized data; μ and σ are the mean and standard deviation respectively;

[0014] S22, randomly select and normalize the standardized data subset: randomly select N sequences from the standardized data set as subsets, each sequence length is T, and then normalize the selected data into a 3D tensor form, using {x N ,y N} means, x N and N The dimensions are N×T×n and N×T×m respectively;

[0015] S23, forward propagation: First initialize the model parameters and the initial state of the loop layer, select the training data x N Input into the prediction model and get the output value According to the target value y N Get the loss function;

[0016] The specific formula is as follows:

[0017]

[0018] In order to avoid overfitting of the prediction model during training, the regularization term of the model parameter ξ (including weight and bias) is added to the loss function formula, and the regularized loss function is as follows:

[0019]

[0020] Where λ is the regularization coefficient;

[0021] S24, error propagation: error propagation along the time direction and layer by layer downward direction;

[0022] S25, update model parameters: update the model parameters by calculating the partial derivative of the hidden layer state with respect to the model parameter ξ:

[0023]

[0024] In the formula, η is the learning rate; Hi represents or

[0025] S26, training termination: repeat steps S22-S25 until the training is terminated after the set number of training times;

[0026] S3, perform prediction model prediction; continuously input and output data while saving the state h of the model loop layer unit at the end. When new data is input, the h of the previous set of data is used as the initial state of the new set of data, and a new round of prediction is performed. The reciprocating cycle continuously updates the state of the nodes in the loop layer, so that the nodes in the loop layer fully consider the correlation between the previous and next data;

[0027] S4, selecting the performance evaluation index of the prediction model; using absolute and relative evaluation indexes to evaluate the performance of the prediction model;

[0028] S5, optimize the prediction model to further improve the output accuracy and robustness of the prediction model;

[0029] S6, comparative verification of the performance of the prediction model, including comparative verification of prediction accuracy and comparative analysis of model solution efficiency;

[0030] S7, when the prediction accuracy and model solving efficiency reach the expected level, the construction of the prediction model is completed.

[0031] Furthermore, in step S1, the input data are the axle box acceleration and the track irregularity parameter, and the output data are the dynamic response of the displacement and acceleration of the rail, track plate and bridge, and the number of structural layers of the prediction model is increased by stacking the cyclic layers.

[0032] Further, in step S24, the loss function is propagated downward along the time direction, and the loss function is calculated in reverse order from T to 1 for the hidden layer state at the i-th time step. The partial derivative of :

[0033]

[0034] The error is propagated downward layer by layer, and the loss function is calculated for the hidden layer state. The partial derivative of :

[0035]

[0036] Furthermore, in step S4, the absolute evaluation index refers to the absolute error between the predicted value and the target value, including the root mean square error (RMSE) and the mean absolute error (MAE):

[0037]

[0038] Relative evaluation indicators refer to the relative error between the predicted value and the target value, including the mean absolute percentage error (MAPE) and the correlation coefficient R:

[0039]

[0040] Where Cov(·) and Var(·) represent covariance and variance, respectively.

[0041] Furthermore, in step S5, the prediction model is optimized including model structure parameter optimization and model network training parameter optimization;

[0042] The model structure parameters include the number of hidden layer nodes and the number of loop layers of the prediction model. Taking RMSE as the reference index, the influence of the number of hidden layer nodes and the number of loop layers on the output accuracy of the prediction model is analyzed;

[0043] The model training parameters include batch size, adaptive learning rate and drop probability. RMSE is used as a reference indicator to determine the specific choice of batch size, the specific choice of adaptive learning rate, and the drop probability is determined by the keep_prob parameter.

[0044] Furthermore, the adaptive learning rate is determined by the initial learning rate and the adaptive optimization algorithm, and the optimal combination of the initial learning rate and the adaptive optimization algorithm is determined with RMSE as a reference indicator.

[0045] Furthermore, the adaptive optimization algorithms include AdaGrad algorithm, RMSProp algorithm, Adam algorithm and AdamDelta algorithm;

[0046] The formula of the AdaGrad algorithm is as follows:

[0047]

[0048] Where θ is the parameter to be updated; L(·) is the loss function; ε is the smoothing term to avoid zero division;

[0049] The formula of the RMSProp algorithm is as follows:

[0050]

[0051] In the formula, β is a hyperparameter, which is set to 0.9;

[0052] The formula of Adam algorithm is as follows:

[0053]

[0054] d i =β1d i-1 +(1-β1)g θ

[0055]

[0056] In the formula and Yes i and S i Bias correction; β1 is 0.9, β2 is 0.999;

[0057] The formula of the AdamDelta algorithm is as follows:

[0058]

[0059] In the formula, γ is a hyperparameter.

[0060] Furthermore, the training set is divided into batches of data and input into the model for training. Each batch of data undergoes forward propagation, loss calculation, and error back propagation, and the weights and biases of the model are updated. The amount of data input in each batch is the batch size.

[0061] Furthermore, discarding is used to alleviate the overfitting phenomenon. Discarding means that when the data is propagated forward, some neurons stop working with a certain probability p, thereby enhancing the generalization ability of the model.

[0062] The specific operation of discarding is to add a discarding operation based on probability to each unit during the model training phase, determine the discarding probability with the keep_prob parameter, and input the discarding probability into the formula for discarding operation; the formula for discarding operation in the prediction model is as follows:

[0063]

[0064] In the formula, is a probability vector that conforms to the Bernoulli distribution, y (l) is the original input, is the input after discarding, is the weight vector, is the output, and f is the activation function.

[0065] Furthermore, in step S6, the prediction accuracy of the model is determined by comparing the prediction value of the prediction model with the target value, and the model solution efficiency is determined by comparing the prediction time of the prediction model with the solution time of the simulation model.

[0066] The beneficial effects of the present invention are as follows:

[0067] A data-driven track structure dynamics prediction model was constructed for predicting the dynamic response of the track structure. With the axle box acceleration and track irregularity information as input, the prediction model can output the dynamic response of the track structure quickly, efficiently and accurately. The constructed prediction model is used to predict the dynamic response of the track structure of high-speed railways, urban rail transit, heavy-load railways and other lines, realizing rapid evaluation of the dynamic response and dynamic state of the track structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A schematic diagram of the prediction model structure constructed for the present invention;

[0069] Figure 2 It is a schematic diagram of the discarding operation flow of the present invention;

[0070] Figure 3 It is a bar diagram showing the output accuracy of different network structure parameters of the present invention;

[0071] Figure 4 It is a bar diagram of output accuracy under different initial learning rates and optimization algorithm combinations of the present invention;

[0072] Figure 5 It is the output accuracy histogram under different keep_prob combinations of the present invention;

[0073] Figure 6 This is a schematic diagram of the network structure of the prediction model after optimization research of the present invention;

[0074] Figure 7 It is a schematic diagram of multiple irregularities of the present invention;

[0075] Figure 8 It is a schematic diagram comparing the predicted value and the target value of the prediction model of the present invention. DETAILED DESCRIPTION

[0076] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings of the specification. 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 making creative work are within the scope of protection of the present invention.

[0077] In the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship are based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0078] like Figure 1-8 As shown, a method for constructing a data-driven track structure dynamics prediction model is provided. The data-driven track structure dynamics prediction model is constructed by building a prediction model, training the model, predicting the model, selecting model performance evaluation indicators, optimizing the prediction model, and comparing and verifying the model performance. The constructed prediction model is used for predicting the dynamic response of the track structure. With the axle box acceleration and track irregularity information as input, the prediction model can output the dynamic response of the track structure quickly, efficiently and accurately. The specific steps of the method for constructing the prediction model are described as follows.

[0079] like Figure 1 As shown, S1, a data-driven track structure dynamics prediction model is constructed;

[0080] First, the prediction model structure is built. The structure of the prediction model includes input layer, output layer, circulation layer and fully connected layer. The input layer, output layer, circulation layer and fully connected layer are parallel to each other. The data is input into the input layer, and then passes through the circulation layer and the fully connected layer in turn and is output through the output layer. The prediction model structure is built. The number of structural layers of the prediction model is increased by stacking the circulation layers, thereby improving the prediction accuracy of the prediction model.

[0081] In the prediction model, the length of the sequence of the single-layer structural layer is t, the input layer is used to input data, and the input data is the axle box acceleration and track irregularity parameters. The output layer is used to output data, and the output data is the dynamic response of the displacement and acceleration of the rail, track plate and bridge. Both input and output use vector mode, and the input and output vectors are x and y respectively. The recurrent layer is used to improve the prediction accuracy of the prediction model. h0 and h are the initial state and hidden layer state of the recurrent layer unit respectively. The function of the fully connected layer is to convert the high-dimensional input vector into a low-dimensional output vector.

[0082] S2, train the prediction model using the timed back-propagation algorithm. Each gradient calculation randomly selects a subset from the training set. The sample content in the subset is N, the sequence length is T, and the loss function uses the mean square error.

[0083] The training of the prediction model specifically includes the following steps:

[0084] S21, standardize the data: the training set is {x,y}={[x1,x2,...,x N ],[y1,y2,...,y N ]},in n and m represent the dimensions of input and output respectively; the training set is processed by Z-score standardization method, and the data is standardized by mean and standard deviation. The processed data conforms to the standard normal distribution with mean 0 and variance 1;

[0085] The standardization formula is as follows:

[0086]

[0087] In the formula, x* is the standardized data; μ and σ are the mean and standard deviation respectively;

[0088] S22, randomly select and normalize the standardized data subset: randomly select N sequences from the standardized data set as subsets, each sequence length is T, and then normalize the selected data into a 3D tensor form, using {x N ,y N} means, x N and N The dimensions are N×T×n and N×T×m respectively;

[0089] S23, forward propagation: First initialize the model parameters and the initial state of the loop layer, select the training data x N Input into the prediction model and get the output value According to the target value y N Get the loss function;

[0090] The specific formula is as follows:

[0091]

[0092] In order to avoid overfitting of the prediction model during training, the regularization term of the model parameter ξ (including weight and bias) is added to the loss function formula, and the regularized loss function is as follows:

[0093]

[0094] Where λ is the regularization coefficient;

[0095] S24, error propagation: error propagation along the time direction and layer by layer downward direction;

[0096] Propagate downward along the time direction, and calculate the loss function in reverse order from T to 1 for the hidden layer state at the i-th time step The partial derivative of :

[0097]

[0098] The error is propagated downward layer by layer, and the loss function is calculated for the hidden layer state. The partial derivative of :

[0099]

[0100] S25, update model parameters: update the model parameters by calculating the partial derivative of the hidden layer state with respect to the model parameter ξ:

[0101]

[0102] In the formula, η is the learning rate; Hi represents or

[0103] S26, training termination: repeat steps S22-S25 until the training is terminated after the set number of training times.

[0104] S3, perform prediction model prediction; continuously input and output data while saving the state h of the model circulation layer unit at the end. When new data is input, the h of the previous set of data is used as the initial state of the new set of data, and a new round of prediction is performed. The reciprocating cycle continuously updates the state of the nodes in the circulation layer, so that the nodes in the circulation layer fully consider the correlation between the previous and next data.

[0105] The model recurrent layer unit is a single node unit in the recurrent layer of the model structure.

[0106] S4, selecting the performance evaluation index of the prediction model; using absolute and relative evaluation indexes to evaluate the performance of the prediction model;

[0107] Absolute evaluation indicators refer to the absolute error between the predicted value and the target value, including root mean square error (RMSE) and mean absolute error (MAE):

[0108]

[0109] Relative evaluation indicators refer to the relative error between the predicted value and the target value, including the mean absolute percentage error (MAPE) and the correlation coefficient R:

[0110]

[0111] Where Cov(·) and Var(·) represent covariance and variance, respectively.

[0112] The smaller the values ​​of the absolute evaluation indicators RMSE and MAE, the better the performance of the prediction model. The R value indicates the similarity between the output value of the prediction model and the actual value. The closer its value is to 1, the better the performance of the prediction model. Since many data in the track structure response are equal to zero, the denominator will be zero when the MAPE indicator is used, making the indicator meaningless. Therefore, MAPE is not used as an evaluation indicator. Finally, MAE, RMSE and correlation coefficient R are selected as evaluation indicators.

[0113] like Figure 2-6 As shown, S5, the prediction model is optimized. The output accuracy of the prediction model is related to various parameters of the model. The model parameters include structural parameters and model training parameters. Therefore, it is necessary to optimize the structural parameters and model training parameters of the model to further improve the output accuracy and robustness of the prediction model.

[0114] like Figure 3 As shown in the figure, when optimizing the structural parameters of the prediction model, the number of hidden layer nodes and the number of loop layers of the prediction model are important structural parameters of the model. Taking RMSE as a reference indicator, the influence of the number of hidden layer nodes and the number of loop layers on the output accuracy of the prediction model is analyzed to evaluate the output accuracy of the prediction model.

[0115] The prediction model of the present invention is based on the modeling calculation performed by NVIDIA's CUDA neural network accelerator. Therefore, the number of hidden layer nodes is an integer power of 2, the number of hidden layer nodes is {16, 32, 64, 128, 256}, and the number of loop layers is {1, 2, 3, 4}, with a total of 20 combinations. After each combination is repeated 3 times, the error is averaged.

[0116] Table 1 The impact of the number of hidden layer nodes and the number of loop layers on output accuracy

[0117]

[0118] As shown in Table 1 and Figure 3 As shown in the figure, when the number of hidden layer nodes and the number of loop layers change at the same time, the output accuracy of the prediction model will be significantly affected. When the number of hidden layer nodes is small, the output accuracy is significantly reduced. When the number of hidden layer nodes is too large, it also affects the output accuracy of the prediction model. In addition, the change in the number of loop layers will also affect the output accuracy of the prediction model. After calculation, the combination of 3 loop layers and 256 hidden layer nodes is selected as the structural parameters of the prediction model to complete the optimization of the prediction model structure.

[0119] When optimizing the training parameters of the prediction model, the training parameters include batch size, adaptive learning rate, and drop probability; using RMSE as a reference indicator, determine the specific choice of batch size, determine the specific choice of adaptive learning rate, and determine the drop probability with the keep_prob parameter.

[0120] When the prediction model is trained, the training set is input into the model in batches for training. Each batch of data undergoes a forward propagation, loss calculation and error back propagation, and the weights and biases of the model are updated. The amount of data in each batch is the batch size. The prediction model is a complex and highly nonlinear model. The setting of the batch size significantly affects the convergence of the model during training. The batch size cannot be the entire training set. If the entire training set is input into the model to calculate the gradient, it is the traditional gradient descent method; if the batch size is determined to be 1, that is, only one sample is input for training at a time, each gradient update under this training scheme is only for the current sample, the randomness is very high and the convergence speed is significantly slowed down, so it is necessary to determine a reasonable batch size.

[0121] Table 2 Output accuracy of different batch sizes

[0122]

[0123] As shown in Table 2, when selecting the batch size, {16, 32, 64, 128, 256, 512, 1024, 2048} is selected, and the RMSE indicator is used to evaluate the output accuracy of the prediction model. Different batch sizes have a greater impact on the output accuracy. Under the various parameter conditions of the prediction model, the output accuracy corresponding to the batch size of 1024 is the highest, so the specific selection of the batch size is 1024.

[0124] During the model training process, a coefficient is multiplied in the process of updating parameters using the gradient descent method. This coefficient is the learning rate η. When the traditional gradient descent method is used, the learning rate is often set to a constant. When the learning rate is a constant, it cannot converge to the optimal solution and the solution process is slow. The use of an adaptive learning rate can solve the above problem.

[0125] The adaptive learning rate is determined by the initial learning rate and the adaptive optimization algorithm. The initial learning rate is {0.0001, 0.001, 0.01, 0.1, 0.5}. The adaptive optimization algorithms include AdaGrad algorithm, RMSProp algorithm, Adam algorithm and AdamDelta algorithm, with a total of 20 combinations. After three repeated tests for each combination, the error is averaged, and RMSE is used as the reference indicator to determine the optimal combination of the initial learning rate and the adaptive optimization algorithm.

[0126] The AdaGrad algorithm mainly updates low-frequency components by a large margin and updates high-frequency components by a small margin. Therefore, the algorithm is mainly suitable for sparse data. The specific formula is as follows:

[0127]

[0128] Where θ is the parameter to be updated; L(·) is the loss function; ε is the smoothing term to avoid zero division;

[0129] The disadvantage of the AdaGrad algorithm is the accumulation of square gradients in the denominator. As Si increases and the learning rate decreases, this term will eventually become infinitesimal, causing the model to fail to converge.

[0130] The AdamDelta algorithm is developed based on the AdaGrad algorithm, but the AdamDelta algorithm does not accumulate all the past square gradients, but accumulates the decaying average of all the past square gradients, and the AdamDelta algorithm does not need to set the initial learning rate. The specific formula of the AdamDelta algorithm is as follows:

[0131]

[0132] In the formula, γ is a hyperparameter;

[0133] The RMSProp algorithm has the same purpose as the AdamDelta algorithm, both of which are to solve the problem of sharp decline in the AdaGrad algorithm. The specific formula of the RMSProp algorithm is as follows:

[0134]

[0135] In the formula, β is a hyperparameter, which is set to 0.9;

[0136] The Adam algorithm uses the first-order moment estimation and second-order moment estimation of the gradient to dynamically adjust the learning rate of each parameter in the neural network. The specific formula is as follows:

[0137]

[0138] d i =β1d i-1 +(1-β1)g θ

[0139]

[0140] In the formula and Yes i and S i Bias correction; β1 is 0.9, β2 is 0.999;

[0141] Table 3 Effect of initial learning rate and optimization algorithm on output accuracy

[0142]

[0143] As shown in Table 3 and Figure 4 As shown in the figure, after error analysis of different combinations of initial learning rate and adaptive optimization algorithm, under the same optimization algorithm, different initial learning rates have a significant impact on the output accuracy, and under the same initial learning rate, the output accuracy difference of different optimization algorithms is also obvious. Considering the impact of the combination of optimization algorithm and initial learning rate, Adam optimization algorithm and initial learning rate of 0.0001 are selected as the training parameters of the prediction model.

[0144] like Figure 2 As shown, Figure 2 The model on the left side is prone to overfitting during the learning process. Figure 2 The dropout on the right side alleviates the overfitting phenomenon; dropout means that when the data is propagated forward, some neurons stop working with a certain probability p, thereby enhancing the generalization ability of the model.

[0145] like Figure 2 As shown, the specific operation of discarding is that in the model training stage, each unit adds a discarding operation based on probability. When performing the discarding operation, the discarding probability is determined by the keep_prob parameter, and the determined discarding probability is input into the formula for discarding operation; the formula for discarding operation in the prediction model is as follows:

[0146]

[0147] In the formula, is a probability vector that conforms to the Bernoulli distribution. It is essentially a 0-1 vector generated with probability p. (l) is the original input, is the input after discarding, is the weight vector, is the output, and f is the activation function.

[0148] The drop probability is determined by the keep_prob parameter, which includes input keep_prob and output keep_prob. The setting range of input keep_prob and output keep_prob is [0.6, 1.0], with a floating interval of 0.1. If keep_prob is set to 1.0, it means that the data will not be dropped and all will be passed to the next layer. If keep_prob is set to 0.6, it means that there is a 40% probability that the data will be dropped and passed to the next layer. RMSE is used as a reference indicator to determine the impact of the keep_prob parameter on the output accuracy.

[0149] Table 4 The impact of keep_prob on output accuracy

[0150]

[0151] As shown in Table 4 and Figure 5 As shown in the figure, different combinations of input keep_prob and output keep_prob have a significant impact on the output accuracy of the prediction model, and the fluctuations are obvious without significant regularity. If keep_prob is set too large, overfitting will occur. If it is set too small, important information in the data may be lost, affecting the output accuracy. Considering the impact of the combination of input keep_prob and output keep_prob, the discard probability of input keep_prob set to 0.7 and output keep_prob set to 0.9 is selected.

[0152] like Figure 6 As shown in the figure, after the above optimization research, the structural parameters and model training parameters of the prediction model are determined. The specific parameters of the prediction model are set as follows: the loop layer is set to 3 layers, the hidden layer nodes are set to 256, the batch size is set to 1024, the optimization algorithm selects the Adam algorithm, the initial learning rate is set to 0.0001, and the input keep_prob and output keep_prob parameters are set to 0.7 and 0.9 respectively.

[0153] S6, comparative verification of the performance of the prediction model, including comparative verification of prediction accuracy and comparative analysis of model solution efficiency.

[0154] The prediction accuracy of the model is determined by comparing the predicted value of the prediction model with the target value, and the model solution efficiency is determined by comparing the prediction time of the prediction model with the solution time of the simulation model.

[0155] like Figure 7As shown in the figure, when comparing and verifying the performance of the prediction model, the measured track unevenness and axle box acceleration of high-speed railways were used as data sets, 80% of the data sets were used as training sets, 10% as validation sets, and the remaining 10% as test sets. The input parameters of the prediction model were axle box acceleration and track unevenness, and the output results were the dynamic responses of displacement and acceleration of rails, track plates and bridges.

[0156] When comparing and verifying the prediction accuracy, the train speed was set to 300 km / h, the sampling frequency of the model was set to 20 kHz, the input parameters of the prediction model were track irregularity and axle box acceleration, and the output data of the prediction model was the dynamic response of the track structure. The output accuracy was evaluated using three indicators: MAE, RMSE and correlation coefficient R.

[0157] Table 5 Prediction accuracy evaluation indicators

[0158]

[0159] As shown in Table 5 and Figure 8 As shown in the figure, the evaluation results are as follows: the displacement and acceleration results of the rails, track plates and bridges predicted by the track structure dynamics prediction model have a high degree of consistency with the target values, which not only accurately predicts the change trend of displacement and acceleration, but also reflects the change of numerical values; the root mean square error RMSE and the absolute mean error MAE in the evaluation indicators of the prediction accuracy of the track structure dynamics prediction model are both kept at a low value, and the correlation coefficient R shows a high level, indicating that the prediction results have a high accuracy. The conclusion is that the prediction model predicts the displacement and acceleration response of the rails, track plates and bridges with high accuracy, which also proves the effectiveness of the prediction model built based on the prediction model.

[0160] Table 6 Comparison of model solution efficiency

[0161]

[0162] As shown in Table 6, when comparing and verifying the model solution efficiency, the prediction time of the prediction model is compared with the solution time of the simulation model. When the hardware is the same, the prediction model constructed and trained can efficiently output the dynamic response of the track structure while ensuring the prediction accuracy. The solution time is only 1 / 30 of that of the traditional dynamic simulation model, which further illustrates that the data-driven track structure dynamics prediction model can achieve fast, accurate and efficient output of the track structure dynamic response.

[0163] S7, when the prediction accuracy and model solving efficiency reach the expected level, the construction of the prediction model is completed. The constructed prediction model is used to predict the dynamic response of track structures of high-speed railways, urban rail transit, heavy-duty railways and other lines, and provides a reference basis and theoretical support for the rapid evaluation of the dynamic response and dynamic state of the track structure.

[0164] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be regarded as exemplary and non-limiting from any point of view, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

Claims

1. A method for constructing a data-driven track structure dynamics prediction model, characterized in that: The following steps are involved: S1, build a data-driven track structure dynamics prediction model; the structure of the prediction model includes an input layer, an output layer, a circulation layer and a fully connected layer. The input layer, the output layer, the circulation layer and the fully connected layer are parallel to each other. The data is input into the input layer, passes through the circulation layer and the fully connected layer in sequence, and then is output through the output layer to complete the construction of the prediction model structure; In the prediction model, the length of a single-layer sequence is t, and both the input and output adopt vector mode. The input and output vectors are x and y respectively, and h0 and h are the initial state of the recurrent layer unit and the hidden layer state respectively; S2, training the prediction model: using the timed back propagation algorithm, each gradient calculation randomly selects a subset of the training set, the sample content in the subset is N, the sequence length is T, and the loss function uses the mean square error; The training of the prediction model specifically includes the following steps: S21, standardize the data: the training set is {x,y}={[x1,x2,...,x N ],[y1,y2,...,y N ]},in n and m represent the dimensions of input and output respectively; the Z-score standardization method is used to process the training set, and the mean and standard deviation are used to standardize the data. The processed data conforms to the standard normal distribution with a mean of 0 and a variance of 1; The standardization formula is as follows: In the formula, x* is the standardized data; μ and σ are the mean and standard deviation respectively; S22, randomly select and normalize the standardized data subset: randomly select N sequences from the standardized data set as subsets, each sequence length is T, and then normalize the selected data into a 3D tensor tensor form, using {x N ,y N } means, x N and N The dimensions are N×T×n and N×T×m respectively; S23, forward propagation: First initialize the model parameters and the initial state of the loop layer, select the training data x N Input into the prediction model and get the output value According to the target value y N Get the loss function; The specific formula is as follows: In order to avoid overfitting of the prediction model during the training process, a regularization term of the model parameter ξ including weights and biases is added to the loss function formula, and the regularized loss function is obtained as follows: Where λ is the regularization coefficient; S24, error propagation: error propagation along the time direction and layer by layer downward direction; S25, update model parameters: update the model parameters by calculating the partial derivative of the hidden layer state with respect to the model parameter ξ: In the formula, η is the learning rate; Hi represents or S26, training termination: repeat steps S22-S25 until the training is terminated after the set number of training times; S3, perform prediction model prediction; continuously input and output data while saving the state h of the model circulation layer unit at the end. When new data is input, the h of the previous set of data is used as the initial state of the new set of data, and a new round of prediction is performed. The state of the model circulation layer unit node is continuously updated in a reciprocating cycle, so that the model circulation layer unit node fully considers the correlation between the previous and next data; S4, selecting the performance evaluation index of the prediction model; using absolute and relative evaluation indexes to evaluate the performance of the prediction model; S5, optimize the prediction model to further improve the output accuracy and robustness of the prediction model; S6, comparative verification of the performance of the prediction model, including comparative verification of prediction accuracy and comparative analysis of model solution efficiency; S7, when the prediction accuracy and model solving efficiency reach the expected level, the construction of the prediction model is completed.

2. The method for constructing a data-driven track structure dynamics prediction model according to claim 1, characterized in that: In step S1, the input data are the axle box acceleration and track irregularity parameters, and the output data are the dynamic response of the displacement and acceleration of the rails, track plates and bridges. The number of structural layers of the prediction model is increased by stacking the cyclic layers.

3. The method for constructing a data-driven track structure dynamics prediction model according to claim 1, characterized in that: In step S24, the loss function is propagated downward along the time direction, and the loss function is calculated in reverse order from T to 1 for the hidden layer state at the i-th time step. The partial derivative of : The error propagates downward layer by layer, and the loss function is calculated for the hidden layer state. The partial derivative of :

4. The method for constructing a data-driven track structure dynamics prediction model according to claim 1, characterized in that: Step S4 In the above, the absolute evaluation index refers to the absolute error between the predicted value and the target value, including the root mean square error RMSE and the mean absolute error MAE: Relative evaluation indicators refer to the relative error between the predicted value and the target value, including the mean absolute percentage error MAPE and the correlation coefficient R: Where Cov(·) and Var(·) represent covariance and variance, respectively.

5. The method for constructing a data-driven track structure dynamics prediction model according to claim 4, characterized in that: In step S5, the prediction model is optimized including model structure parameter optimization and model training parameter optimization; The model structure parameters include the number of hidden layer nodes and the number of loop layers of the prediction model. Taking RMSE as the reference index, the influence of the number of hidden layer nodes and the number of loop layers on the output accuracy of the prediction model is analyzed; The model training parameters include batch size, adaptive learning rate and drop probability. RMSE is used as a reference indicator to determine the specific choice of batch size, the specific choice of adaptive learning rate, and the keep_prob parameter to determine the drop probability.

6. The method for constructing a data-driven track structure dynamics prediction model according to claim 5, characterized in that: The learning rate is determined by the initial learning rate and the adaptive optimization algorithm, and the optimal combination of the initial learning rate and the adaptive optimization algorithm is determined with RMSE as the reference indicator.

7. The method for constructing a data-driven track structure dynamics prediction model according to claim 6 is characterized by: The optimization algorithms include AdaGrad algorithm, RMSProp algorithm, Adam algorithm and AdamDelta algorithm; The formula of the AdaGrad algorithm is as follows: Where θ is the parameter to be updated; L(·) is the loss function; ε is the smoothing term to avoid zero division; The formula of the RMSProp algorithm is as follows: In the formula, β is a hyperparameter, which is set to 0.9; The formula of Adam algorithm is as follows: d i =β1d i-1 +(1-β1)g θ In the formula and Yes i and S i Bias correction; β1 is 0.9, β2 is 0.999; The formula of the AdamDelta algorithm is as follows: In the formula, γ is a hyperparameter.

8. The method for constructing a data-driven track structure dynamics prediction model according to claim 5, characterized in that: The training set is divided into batches of data and input into the model for training. Each batch of data undergoes a forward propagation, loss calculation and error back propagation, and the weights and biases of the model are updated. The amount of data input in each batch is the batch size.

9. The method for constructing a data-driven track structure dynamics prediction model according to claim 5, characterized in that: Discarding is used to alleviate the overfitting phenomenon. Discarding means that when the data is propagated forward, some neurons stop working with a certain probability p, thereby enhancing the generalization ability of the model. The specific operation of discarding is to add a discarding operation based on probability to each unit during the model training phase, determine the discarding probability with the keep_prob parameter, and input the discarding probability into the formula for discarding operation; the formula for discarding operation in the prediction model is as follows: In the formula, is a probability vector that conforms to the Bernoulli distribution, y (l) is the original input, is the input after discarding, is the weight vector, is the output, and f is the activation function.

10. The method for constructing a data-driven track structure dynamics prediction model according to claim 1, characterized in that: In step S6, the prediction accuracy of the model is determined by comparing the prediction value of the prediction model with the target value, and the model solution efficiency is determined by comparing the prediction time of the prediction model with the solution time of the simulation model.

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