ECNN-based high-speed railway roadbed accumulated deformation prediction method

Abstract

The invention discloses a high-speed railway roadbed accumulated deformation prediction method based on ECNN, and the method comprises the following steps: inputting roadbed accumulated deformation data at a historical moment into a trained ECNN model for processing, and obtaining an accumulated deformation value of a roadbed at a future moment; wherein the ECNN model is constructed after a machine learning model and a stable cumulative plastic strain curve are coupled. The method is ingenious in conception, simple and easy to operate, achieves the technical purpose of high external generalization performance, effectively solves the technical problems that a traditional machine learning roadbed cumulative prediction model only has generalization ability in distribution and has poor time distribution external generalization, and can provide a new reference for high-speed railway roadbed cumulative deformation prediction.

Description

Technical Field

[0001] The invention relates to the technical field of prediction of cumulative deformation of high-speed railway roadbed, and in particular to a method for predicting cumulative deformation of high-speed railway roadbed based on ECNN. Background Art

[0002] Under the action of train loads, the high-speed railway subgrade will produce irreversible permanent deformation. Excessive permanent deformation can easily lead to uneven subgrade settlement or excessive settlement damage, which seriously threatens the safety of high-speed train operation. Therefore, high-speed railways have strict restrictions on the permanent deformation of subgrades. If the long-term deformation development of high-speed railway subgrades can be grasped through prediction methods, it will be of great significance for deformation disease control and operation management.

[0003] The prediction model of the cumulative deformation of the roadbed is an important means to obtain the long-term deformation development of the high-speed railway roadbed. At present, the prediction model of the cumulative deformation of the roadbed mainly includes four aspects: empirical method, numerical simulation method, statistical analysis method and machine learning method. The empirical method establishes a mathematical equation for predicting the cumulative deformation of the roadbed based on the test results, which has the disadvantage of being unable to quantify nonlinear problems; the numerical simulation method can consider a variety of simulation conditions, and the statistical analysis method establishes a mathematical model based on saturated soil theory or deformation law, but both have the disadvantages of difficulty in setting internal parameters and over-reliance on assumptions. In contrast, the machine learning method has the advantages of nonlinear mapping, adaptive learning, and high prediction accuracy, and is gradually being promoted and applied to cumulative deformation prediction. Existing studies have proved the applicability of machine learning methods in predicting the cumulative deformation of roadbeds and their high prediction accuracy, which has promoted the application of machine learning methods in high-speed railway projects.

[0004] Machine learning methods require a large number of training samples to support them. However, high-speed railways are fast, have heavy passenger transport tasks and are closed. Therefore, in actual projects, there may be insufficient training data, which places high demands on the generalization performance of the prediction model outside the time distribution. In the traditional machine learning roadbed cumulative deformation prediction model, the training set and the test set (used to test the prediction accuracy of the model) are divided from the data set in chronological order, usually accounting for 70% and 30% or 80% and 20% respectively. This method makes the training set and the test set have similar distribution in time. Therefore, although the obtained prediction model performs well on the test set, it often only has the generalization ability within the distribution and has the disadvantage of poor generalization outside the time distribution.

[0005] Physical information neural networks (PINNs) developed in recent years can provide a solution to this problem. PINNs usually incorporate physical information in a specific field as a constraint into the loss function, which can improve the generalization of the machine learning model. At present, this method has been widely used in many fields such as mechanics, medicine, and engineering. However, due to the many factors affecting the cumulative deformation of high-speed railway subgrades, it is difficult to find a physical equation that can support machine learning modeling. In contrast, empirical information briefly summarizes the complex development process of the cumulative deformation of high-speed railway subgrades, and has been verified by long-term experiments and engineering examples; although it is not as accurate as physical information, it can also reveal the development trend and potential laws of the cumulative deformation of the subgrade to a certain extent. Therefore, under the condition that physical information cannot be quickly obtained and effectively quantified, empirical information is relatively more suitable as a constraint in the machine learning subgrade cumulative deformation prediction model. Therefore, how to use the existing empirical knowledge in the field of high-speed railway engineering and incorporate the empirical knowledge as a constraint into the loss function of the machine learning model based on the PINNs theory to construct a subgrade cumulative deformation prediction model with generalization outside the time distribution is a problem worth exploring. Summary of the invention

[0006] The main purpose of the present invention is to provide a high-speed railway roadbed cumulative deformation prediction method based on an experience-constrained neural network (ECNN) to solve the technical problem of poor out-of-distribution generalization performance of machine learning models in the prior art.

[0007] In order to achieve the above object, the present invention provides a method for predicting the cumulative deformation of high-speed railway subgrade based on ECNN as follows:

[0008] The ECNN-based high-speed railway embankment cumulative deformation prediction method comprises the following steps: inputting the embankment cumulative deformation data at historical moments into a trained ECNN model for processing, so as to obtain the cumulative deformation value of the embankment at future moments; wherein the ECNN model is constructed by coupling a machine learning model with a stable cumulative plastic strain curve.

[0009] As a further improvement of the above-mentioned ECNN-based high-speed railway subgrade cumulative deformation prediction method: the acquisition process of the ECNN model is as follows:

[0010] Obtain the roadbed cumulative deformation data set and divide it into a training set and a test set;

[0011] Use at least three machine learning models to train the training set, then use the trained machine learning model to process the test set and output the corresponding prediction results;

[0012] Comprehensively evaluate the prediction performance of the machine learning model through prediction accuracy, prediction error, and prediction uncertainty, and select the machine learning model with the best prediction performance;

[0013] The ECNN model was constructed by coupling the machine learning model with the best prediction performance with the stable cumulative plastic strain curve.

[0014] As a further improvement of the above-mentioned ECNN-based high-speed railway subgrade cumulative deformation prediction method: the evaluation index of the prediction accuracy includes goodness of fit; the evaluation index of the prediction error includes mean absolute error and mean absolute percentage error; the evaluation index of the prediction uncertainty includes expanded uncertainty, t-statistical test, standardized mean difference and SI value.

[0015] As a further improvement of the above-mentioned ECNN-based high-speed railway subgrade cumulative deformation prediction method: the Loss function of the ECNN model consists of a data-driven loss term and an empirical loss term.

[0016] The ECNN-based high-speed railway subgrade cumulative deformation prediction method of the present invention has the following advantages:

[0017] First, based on the PINNs theory, the present invention uses the cumulative plastic strain relationship curve as the empirical knowledge constraint condition, and successfully constructs an ECNN method that integrates the PINNs theory and the cumulative plastic strain relationship curve. This method uses the optimal machine learning model to drive the data information of the cumulative deformation of the roadbed, incorporates the existing empirical knowledge in the field of high-speed railway engineering into the loss function of the machine learning model, and embeds the stable cumulative plastic strain relationship curve in the form of loss function correction, so as to realize the constraints on the optimal machine learning model parameters and loss function, taking into account the particularity of the prediction of the cumulative deformation of the high-speed railway roadbed and the advantages of the PINNs theory. Secondly, the present invention establishes a machine learning model based on the training set, and determines the optimal machine learning model by combining the prediction accuracy and error and prediction uncertainty results on the test set.

[0018] The present invention verifies the effectiveness of the proposed method with the help of a specific high-speed railway subgrade test section. The results show that: first, the ECNN model constructed by coupling the screened Bi-GRU model with the stable cumulative plastic strain curve is better than the Bi-GRU model in terms of prediction accuracy, error and prediction uncertainty, indicating that the ECNN model that considers the cumulative plastic strain relationship constraint has significantly stronger prediction performance. Secondly, when the time span covered by the training set is small, the ECNN model has better generalization performance of time distribution than the Bi-GRU model, which can effectively improve the prediction accuracy of long-term cumulative deformation.

[0019] In summary, the ECNN-based high-speed railway subgrade cumulative deformation prediction method of the present invention is ingenious in conception, simple and easy to operate, and achieves the technical purpose of strong external generalization performance. It effectively solves the technical problems that the traditional machine learning subgrade cumulative prediction model has only the generalization ability within the distribution and has poor generalization performance outside the time distribution. It can provide a new reference for the prediction of high-speed railway subgrade cumulative deformation.

[0020] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The drawings constituting a part of the present invention are used to assist the understanding of the present invention. The contents provided in the drawings and their related descriptions in the present invention can be used to explain the present invention, but do not constitute improper limitations on the present invention.

[0022] Figure 1 Schematic diagram of the linear rectification function ReLU.

[0023] Figure 2 Schematic diagram of time series cross validation.

[0024] Figure 3 Schematic diagram of the cumulative deformation law of the roadbed during the test.

[0025] Figure 4 A graph showing changes in fitness values ​​during the PSO algorithm's optimization of hyperparameters for each machine learning model.

[0026] Figure 5 This is the global distribution diagram of the absolute error of the prediction results of the Bi-GRU model.

[0027] Figure 6 This is the global distribution diagram of the absolute error of the prediction results of the ECNN model.

[0028] Figure 7 R of the Bi-GRU model and the ECNN model under different training set lengths 2 Change graph.

[0029] Figure 8 This is the MAE change diagram of the Bi-GRU model and the ECNN model under different training set lengths.

[0030] Fig. 9 This is the MAPE change diagram of the Bi-GRU model and the ECNN model under different training set lengths. DETAILED DESCRIPTION

[0031] The present invention is described clearly and completely below in conjunction with the accompanying drawings. A person skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0032] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other if there is no conflict.

[0033] In addition, the embodiments of the present invention involved in the following description are generally only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0034] About the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and related parts are intended to cover non-exclusive inclusions.

[0035] The specific implementation method of the high-speed railway roadbed cumulative deformation prediction method based on ECNN of the present invention includes the following steps: inputting the roadbed cumulative deformation data at historical moments into a trained ECNN model for processing, that is, obtaining the cumulative deformation value of the roadbed at a future moment; wherein, the ECNN model is constructed by coupling a machine learning model with a stable cumulative plastic strain curve.

[0036] The acquisition process of the ECNN model includes steps 100-400, which are as follows:

[0037] Step 100: Dataset construction and division

[0038] The method of obtaining the roadbed cumulative deformation data set and dividing it into a training set and a test set is as follows: based on the engineering site or indoor test data, the roadbed cumulative deformation S1, S2, S3...S t-1 As the input feature, the roadbed cumulative deformation S at time t t As the output feature, the roadbed cumulative deformation prediction dataset D is constructed.

[0039] The dataset D is divided into a training set and a test set in a ratio of 8:2. The training set is used to establish the machine learning model, and the test set is used to select the optimal machine learning model.

[0040] Step 200: Machine learning model training

[0041] Three machine learning models are used to train the training set, and then the trained machine learning models are used to process the test set to output the corresponding prediction results.

[0042] The three selected machine learning models are Back Propagation (BP), Extreme Learning Machine (ELM), and Bidirectional Gate Recurrent Unit (Bi-GRU), which are three typical machine learning models.

[0043] In order to ensure accurate prediction accuracy, it is necessary to find the optimal hyperparameters. However, the traditional manual parameter adjustment is inefficient and labor-intensive. Therefore, after the training set is input into the machine learning model, the PSO algorithm is introduced to optimize its hyperparameters.

[0044] Step 300, optimal machine learning model determination

[0045] The prediction performance of the machine learning model is comprehensively evaluated by prediction accuracy, prediction error, and prediction uncertainty, and the machine learning model with the best prediction performance is selected.

[0046] The evaluation index of the prediction accuracy is the goodness of fit (R 2 ), the evaluation indicators of the prediction error are mean absolute error (MAE) and mean absolute percentage error (MAPE).

[0047] The evaluation indicators of prediction uncertainty include expanded uncertainty, t-statistical test, standardized mean difference and SI value, and the calculation expressions are:

[0048]

[0049]

[0050]

[0051]

[0052] Where: U 95 is the expanded uncertainty at 95% confidence level; SD is the standard deviation of the difference between the predicted value and the measured value of the roadbed cumulative deformation; RMSE is the root mean square error, SMD is the standardized mean difference; y t is the measured value of the cumulative deformation of the roadbed; is the mean of the measured values ​​of the roadbed cumulative deformation; is the predicted value of the roadbed cumulative deformation; is the mean of the predicted cumulative deformation of the roadbed; S y is the standard deviation of the measured value of the roadbed cumulative deformation; is the standard deviation of the predicted value of the roadbed cumulative deformation; T statis t statistical test; N t is the total number of samples used for evaluation; MBE is the average residual of the difference between the predicted value and the measured value of the cumulative deformation of the roadbed; Regarding the SI value, if SI < 0.1, the machine learning model is considered to have "excellent performance"; if SI < 0.2, the machine learning model is considered to have "good performance"; if SI > 0.3, the machine learning model is considered to have "air performance".

[0053] Step 400: ECNN model construction

[0054] The optimal machine learning model is used to drive the cumulative deformation data information, and the stable cumulative plastic strain curve is embedded in the form of loss function correction to realize the constraints on the optimal machine learning model parameters and loss function. That is, the ECNN model is constructed by coupling the machine learning model with the best prediction performance with the stable cumulative plastic strain curve.

[0055] The Loss function of the ECNN model consists of a data-driven loss term and an empirical loss term, and its calculation expression is:

[0056] Loss = (1-λ) Loss Data +λLoss Phy

[0057] Where: λ is the weight parameter; Loss Data is the data-driven loss term; Loss Phy is the experience loss term.

[0058] The data-driven loss term Loss Data It is the deviation between the predicted cumulative deformation of the roadbed obtained based on the optimal machine learning model and the measured cumulative deformation of the roadbed. Its calculation expression is:

[0059]

[0060] Where n is the number of input features, x1 represents the first input feature, x n represents the nth input feature; y(x1,x2…x n ) is the measured value of the cumulative deformation of the roadbed; is the predicted value of the roadbed cumulative deformation; N d The total number of training samples for the data-driven loss term.

[0061] In order to conform to the variation pattern of the stable cumulative plastic strain relationship curve, the roadbed cumulative deformation must meet the following constraints:

[0062] (1) The cumulative deformation of the roadbed increases with the number of loading times and should meet the following requirements:

[0063] (2) The cumulative deformation of the roadbed increases rapidly at the initial stage of loading, and the rate may increase with time.

[0064] (3) The cumulative deformation of the roadbed slows down or stagnates in the later stage of loading, which should meet the following requirements:

[0065] (4) The rate gradient decreases over time and should satisfy

[0066] The empirical loss term Loss Emp Extracted from the stable cumulative plastic strain relationship curve, the calculation expression is:

[0067]

[0068] Where: Indicates partial derivative; y p is the predicted value of the roadbed cumulative deformation; N is the number of loading times, in ten thousand times; f R is the expression of the linear rectification function ReLU. When the input value is x, its specific expression is The overline indicates that f R () function to obtain the arithmetic mean.

[0069] Figure 1 It is a schematic diagram of the linear rectification function ReLU. Figure 1 As shown, in the empirical loss term Loss Phy The ReLU function used in the calculation process is a linear rectification function. If the prediction result meets the constraints, the penalty term is 0. Otherwise, the penalty term will be linearly proportional to its size.

[0070] In order to achieve the purpose of sufficient training, the gradient iterative optimization algorithm is used in the process of Loss function calculation to minimize the Loss value, and the weight parameter w and bias vector b of the neural network are synchronously updated to w* and b*, and the expression is:

[0071]

[0072] After completing the ECNN model training, the prediction results of the ECNN model are analyzed from three aspects: weight parameter analysis, prediction performance evaluation and comparison, and time distribution generalization performance verification, as follows:

[0073] 1) Weight parameter analysis: Set different weight parameters λ from 0 to 0.9 with an interval of 0.1. Output the stable loss value on the training set and the R on the test set. 2 , MAE and MAPE, and determine the optimal weight parameters by comparing these three evaluation indicators, which are used as important parameters in subsequent forecasting analysis.

[0074] 2) Prediction performance evaluation and comparative analysis: Under the optimal weight parameter λ, the prediction results of the ECNN model on the test set are output, and the prediction performance of the ECNN model and the Bi-GRU model are compared from the two levels of prediction accuracy and error, and prediction uncertainty.

[0075] 3) Verification and analysis of time distribution out-generalization performance: Under the optimal weight parameter λ, time series cross-validation (TSCV) is used to verify the time distribution out-generalization performance of the ECNN model.

[0076] Figure 2 This is a schematic diagram of time series cross validation. Figure 2 As shown in the figure, this method retains the time series order and divides the data set into 10 groups. The data volume of each group accounts for 10% of the data set D. According to the different data proportions of the training set and the test set, 9 types of division are obtained. Taking Fold 1 as an example, the first 10% of the data set D is used as the training set, and the remaining 90% of the data is used as the test set for prediction analysis; in the remaining division types, the proportion of the training set is expanded by 10% each time, and the corresponding test set is reduced by 10%.

[0077] The beneficial effects of the present invention are described below through specific examples.

[0078] Relying on specific high-speed railway subgrade engineering examples, a subgrade test section was selected. After the subgrade was completed, a large-scale vibration exciter was used to quickly simulate the cyclic load of a high-speed train. The main technical parameters of the vibration test were set as follows: the vibration frequency was 15 Hz and the number of vibrations was 2 million times. In order to monitor the cumulative deformation value of the subgrade under cyclic loads, measuring points were set on the diagonal and near-side loading plates to monitor the cumulative deformation value of the subgrade under fatigue loads.

[0079] Step 100: Dataset construction and division

[0080] Figure 3 This is a schematic diagram of the cumulative deformation law of the roadbed during the test. Figure 3 It can be seen that the cumulative deformation rate of the roadbed gradually slows down and finally tends to a stable state, which means that the dynamic stress of the roadbed is less than its critical dynamic stress, and the cumulative deformation of the roadbed is effectively controlled. When the number of excitations reaches 900,000 times, the cumulative deformation rate of the roadbed decreases and gradually tends to be stable. It can be determined that the cumulative deformation of the roadbed obtained in this test conforms to the law of the stable curve, and the data of the C-1 measuring point is used as the data set, which is divided into a training set and a test set in a ratio of 8:2.

[0081] Step 200: Machine Learning Model Training

[0082] Figure 4 The fitness value change diagram of the PSO algorithm in the process of optimizing the hyperparameters of each machine learning model. Figure 4 It can be seen that through the iterative optimization of the PSO algorithm, the fitness of each machine learning model is significantly reduced and all tend to be stable before the 20th generation. Among them, the fitness of the Bi-GRU model is the lowest, which to some extent shows that this model has more advantages. After the iteration is completed, the optimal hyperparameters of each machine learning model are saved and input into the model again to perform subsequent optimal machine learning model screening operations.

[0083] Step 300: Determine the optimal machine learning model

[0084] 1) Prediction accuracy and prediction error

[0085] Use goodness of fit (R 2 The summary calculation results of evaluating the prediction results by using the mean absolute error (MAE) and the mean absolute percentage error (MAPE) are listed in Table 1. As shown in Table 1, the three machine learning models have strong prediction capabilities for the cumulative deformation of the roadbed. Among them, the most prominent one is the Bi-GRU model, whose R 2 The highest, MAE and MAPE are the smallest.

[0086] Table 1

[0087]

[0088] 2) Forecast uncertainty

[0089] Using extended uncertainty (U 95 ), t statistical test (T stat ), standardized mean difference (SMD) and SI value were used as evaluation indicators of prediction uncertainty to evaluate the prediction results, and the calculation results are summarized in Table 2.

[0090] As shown in Table 2, the U 95 It can be seen that the Bi-GRU model has the lowest uncertainty, and its U 95 is only 0.0156. At the same time, T stat The values ​​show that there are significant differences in the performance of each model, among which the Bi-GRU model has the least difference. In terms of SMD value, the Bi-GRU model is the best. SI values ​​below 0.1 were observed in the Bi-GRU, ELM, and BP models, indicating that each model has excellent performance in predicting output.

[0091] Table 2

[0092]

[0093] Based on the evaluation results of prediction accuracy, prediction error and prediction uncertainty, it can be obtained that the Bi-GRU model has the best overall performance, so it is used as the optimal machine learning model.

[0094] Step 400: ECNN model construction

[0095] The final loss of the ECNN model in the training set and the evaluation results on the test set under different weight parameters are shown in Table 3. Analysis shows that the final loss of the training set decreases with the increase of λ, indicating that the increase of the weight parameter can increase the fitting ability of the ECNN model for the cumulative deformation of the roadbed. In contrast, when λ is 0.3, the R 2 The highest, MAE and MAPE are the lowest. In summary, the optimal weight parameter λ of the ECNN model is determined to be 0.3.

[0096] Table 3

[0097]

[0098] The following is an evaluation and comparison of the prediction performance of the ECNN model and the Bi-GRU model under the optimal weight parameter λ.

[0099] 1) Prediction accuracy, prediction error, and prediction uncertainty

[0100] Figure 5 This is the global distribution diagram of the absolute error of the prediction results of the Bi-GRU model. Figure 6 This is the global distribution diagram of the absolute error of the prediction results of the ECNN model. Figure 5-6 It can be seen that both the Bi-GRU model and the ECNN model can reflect the trend of the measured value of the cumulative deformation of the roadbed, but the absolute error of the ECNN model is about half of that of the Bi-GRU model, and its MAE is only 0.00349 mm, which is 34.40% better than that of the Bi-GRU model. This shows that the ECNN model is more in line with the trend of the measured value of the cumulative deformation of the roadbed and is better in error control.

[0101] The prediction performance comparison results of Bi-GRU and ECNN models are shown in Table 4. In terms of prediction accuracy and prediction error, the R 2 , MAE and MAPE are all better, showing stronger prediction performance. In terms of prediction uncertainty, the U 95 , T stat , SMD, and SI improved by 39.23%, 73.49%, 70.64%, and 47.72%, respectively, indicating that the ECNN model has stronger control ability in predicting uncertainty.

[0102] In summary, the prediction performance of the ECNN model considering the cumulative plastic strain relationship constraint is better than that of the Bi-GRU model.

[0103] Table 4

[0104]

[0105]

[0106] 2) Verification of time distribution external generalization performance

[0107] The TSCV method was used to test and compare the temporal distribution generalization performance of the Bi-GRU model and the ECNN model, and the R 2 , MAE and MAPE's changing rules.

[0108] Figure 7 R of the Bi-GRU model and the ECNN model under different training set lengths 2 Change graph. Figure 8 This is the MAE change diagram of the Bi-GRU model and the ECNN model under different training set lengths. Fig. 9 The MAPE change diagram of the Bi-GRU model and the ECNN model under different training set lengths. Analysis shows that when only 10% and 20% of the data are used as the training set, the prediction accuracy of the Bi-GRU model is poor, R 2 are all lower than 0; while the ECNN model can obtain relatively ideal prediction results, and its R 2 They are 0.76474 and 0.83205 respectively, MAE is 0.12117mm and 0.07042mm respectively, and MAPE is 4.18743% and 2.31076% respectively. When the data length of the training set exceeds 30% of the overall data set, as the roadbed cumulative deformation tends to the stable stage, the Bi-GRU model and the ECNN model both perform well in the prediction of long-term roadbed cumulative deformation, but the prediction performance of the ECNN model is always better than that of the Bi-GRU model.

[0109] In summary, when the time span covered by the training set is large, both the Bi-GRU model and the ECNN model can make good predictions, because the cumulative deformation of the roadbed of the stable curve will eventually tend to be flat. When the time span covered by the training set is small, the purely data-driven Bi-GRU model completely loses its predictive ability, and the ECNN model with cumulative plastic strain relationship constraints performs better.

[0110] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without creative work shall fall within the scope of protection of the present invention.

Claims

1. The ECNN-based high-speed railway subgrade cumulative deformation prediction method is characterized by: The following steps are involved: The accumulative deformation data of the roadbed at the historical moment is input into the trained ECNN model for processing, that is, the accumulative deformation value of the roadbed at the future moment is obtained; The ECNN model is constructed by coupling a machine learning model with a stable cumulative plastic strain curve.

2. The method for predicting the cumulative deformation of high-speed railway roadbed based on ECNN as claimed in claim 1, characterized in that: The acquisition process of the ECNN model is as follows: Obtain the roadbed cumulative deformation data set and divide it into a training set and a test set; Use at least three machine learning models to train the training set, then use the trained machine learning model to process the test set and output the corresponding prediction results; Comprehensively evaluate the prediction performance of the machine learning model through prediction accuracy, prediction error, and prediction uncertainty, and select the machine learning model with the best prediction performance; The ECNN model was constructed by coupling the machine learning model with the best prediction performance with the stable cumulative plastic strain curve.

3. The method for predicting the cumulative deformation of high-speed railway roadbed based on ECNN as claimed in claim 2, characterized in that: Constructing a roadbed cumulative deformation data set based on engineering site or indoor test data; the at least three machine learning models include a BP model, an ELM model and a Bi-GRU model; The training process uses the PSO algorithm to optimize the hyperparameters of the machine learning model.

4. The method for predicting the cumulative deformation of high-speed railway subgrade based on ECNN as claimed in claim 3 is characterized by: The evaluation index of the prediction accuracy includes goodness of fit; the evaluation index of the prediction error includes mean absolute error and mean absolute percentage error.

5. The method for predicting the cumulative deformation of high-speed railway roadbed based on ECNN as claimed in claim 3 is characterized by: The evaluation indicators of prediction uncertainty include expanded uncertainty, t-statistical test, standardized mean difference and SI value.

6. The method for predicting the cumulative deformation of high-speed railway subgrade based on ECNN as claimed in claim 5, characterized in that: The calculation expressions of expanded uncertainty, standardized mean difference, t-statistic test and SI value are: Where: U 95 is the expanded uncertainty at 95% confidence level; SD is the standard deviation of the difference between the predicted value and the measured value of the roadbed cumulative deformation; RMSE is the root mean square error, SMD is the standardized mean difference; y t is the measured value of the cumulative deformation of the roadbed; is the mean of the measured values ​​of the roadbed cumulative deformation; is the predicted value of the roadbed cumulative deformation; is the mean of the predicted cumulative deformation values ​​of the roadbed; S y is the standard deviation of the measured value of the roadbed cumulative deformation; is the standard deviation of the predicted value of the roadbed cumulative deformation; T stat is t statistical test; N t is the total number of samples used for evaluation; MBE is the average residual of the difference between the predicted value and the measured value of the cumulative deformation of the roadbed; Regarding the SI value, if SI<0.1, the machine learning model is considered to have "excellent performance"; if SI<0.2, the machine learning model is considered to have "good performance"; if SI>0.3, the machine learning model is considered to have "air performance".

7. The method for predicting the cumulative deformation of high-speed railway subgrade based on ECNN as claimed in claim 2, characterized in that: The Loss function of the ECNN model consists of a data-driven loss term and an empirical loss term, and its calculation expression is: Loss=(1-λ)Loss Data +λLoss Emp Where: λ is the weight parameter; Loss Data is the data-driven loss term; Loss Emp is the experience loss term.

8. The method for predicting the cumulative deformation of high-speed railway subgrade based on ECNN as claimed in claim 7, characterized in that: The data-driven loss term Loss Data The calculation expression is: Where n is the number of input features, x1 represents the first input feature, x n Represents the nth input feature; y(x1,x2…x n ) is the measured value of the cumulative deformation of the roadbed; is the predicted value of the roadbed cumulative deformation; N d The total number of training samples for the data-driven loss term.

9. The method for predicting the cumulative deformation of high-speed railway subgrade based on ECNN as claimed in claim 7, characterized in that: In order to conform to the variation pattern of the stable cumulative plastic strain relationship curve, the roadbed cumulative deformation must meet the following constraints: (1) The cumulative deformation of the roadbed increases with the number of loading times and should meet the following requirements: (2) The cumulative deformation of the roadbed increases rapidly at the initial stage of loading, and the rate may increase with time. (3) The cumulative deformation of the roadbed slows down or stagnates in the later stage of loading, which should meet the following requirements: (4) The rate gradient decreases over time and should satisfy The empirical loss term Loss Emp Extracted from the stable cumulative plastic strain relationship curve, the calculation expression is: Where: Indicates partial derivative; y p is the predicted value of the roadbed cumulative deformation; N is the number of loading times, in ten thousand times; f R is the expression of the linear rectification function ReLU. When the input value is x, its specific expression is The overline indicates that f R () function to obtain the arithmetic mean.

10. The method for predicting the cumulative deformation of high-speed railway roadbed based on ECNN as claimed in claim 7, characterized in that: In the process of calculating the Loss function, the gradient iterative optimization algorithm is used to minimize the Loss value, and the weight parameter w and bias vector b of the neural network are updated synchronously: Where: w* and b* are the updated weight parameters and bias vectors respectively.

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