Railway roadbed settlement prediction method based on IGM-PSVR model

Abstract

The invention discloses a railway roadbed settlement prediction method based on an IGM-PSVR model, and the method comprises the steps: firstly collecting roadbed settlement data, and carrying out the preprocessing of the collected roadbed settlement data; performing level ratio verification on the data, establishing a corresponding differential equation, solving to obtain a time response function, further optimizing a background value of a gray model, constructing an improved gray model IGM (1, 1), and obtaining a model prediction result; then, a particle swarm optimization algorithm is adopted to optimize hyper-parameters of the support vector regression SVR model, a support vector machine model of particle swarm optimization is constructed, and a model prediction result is obtained; and finally, giving different weights to the prediction results of the two steps by using an error square and reciprocal method, and finally combining to obtain a combined prediction result. Experiments show that compared with a single model, the combined model is higher in prediction precision, can better express the roadbed settlement change trend, and plays an important role in guaranteeing the safety of railway transportation business.

Description

Technical Field

[0001] The invention belongs to the technical field of railway roadbed safety, and in particular relates to a railway roadbed settlement prediction method based on a GM-SVR combined model. Background Art

[0002] During the railway operation stage, the roadbed is affected by many factors, resulting in uneven settlement, which seriously threatens the safety of passengers and drivers, and also affects the normal operation of the railway transportation system. Therefore, it is particularly important to accurately predict the roadbed settlement, which can not only ensure the safety of passengers and drivers, but also provide maintenance plans for the railway transportation department in a timely manner, reduce the waste of manpower, material and financial resources, and play an important role in the smooth operation of trains.

[0003] At present, there are two main methods for railway subgrade settlement prediction: the first is to establish a complex soil model for settlement prediction based on the corresponding parameter information of the subgrade soil; the second is to use the system formula method to establish a time series prediction model based on the measured settlement data to predict the settlement value. In my country's actual subgrade settlement prediction, the system analysis method is often used. Common system analysis methods include exponential curve method, parabola method, hyperbola method, and gray system theory method. The gray system method requires a small sample size, simple calculation and easy operation, but the medium and long-term prediction accuracy is low and it is sensitive to outliers. Based on the literature analysis of existing technologies, it is found that single models have certain limitations when dealing with settlement prediction problems and cannot complete real-time and accurate predictions. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention proposes a railway roadbed settlement prediction method based on the IGM-PSVR model, which can overcome the shortcomings of a single model, improve the settlement prediction accuracy, provide a roadbed design and maintenance plan for the railway transportation department, reduce the waste of manpower, material and financial resources, and improve the sustainable utilization of railway line equipment.

[0005] The above purpose is achieved through the following technical solutions:

[0006] The present invention provides a railway subgrade settlement prediction method based on the IGM-PSVR model, the method comprising the following steps:

[0007] S1. Setting observation points, collecting roadbed settlement data, and preprocessing the collected roadbed settlement data;

[0008] S2. First, perform a level ratio check. If the roadbed settlement data preprocessed in step S1 meets the requirements, establish the corresponding differential equation, solve the time response function, further optimize the background value of the gray model, construct the improved gray model IGM (1,1) and obtain the IGM model prediction result; if the roadbed settlement data preprocessed in step S1 does not meet the requirements, continue to perform preprocessing.

[0009] S3, comprehensively evaluate the accuracy of the prediction model of the grey model through the two indicators of posterior difference ratio C1 and small error probability p; if the accuracy of the prediction model meets the requirements, the prediction result is output, recorded as y1;

[0010] S4, normalizing the roadbed settlement data pre-processed in step S1, and constructing an SVR model;

[0011] S5, using the particle swarm optimization algorithm (PSO) to optimize the hyperparameters of the support vector regression SVR model, constructing the particle swarm optimized support vector machine model (PSVR) model and obtaining the PSVR model prediction result, recorded as y2;

[0012] S6, respectively calculate the sum of squares of the errors between the prediction result y1 of the IGM model and the prediction result y2 of the PSVR model and the true value, and determine the weights w1 and w2 of the grey model IGM model and PSVR model according to the inverse method of the sum of squares of the errors; finally, obtain the prediction result of the IGM-PSVR model, recorded as y;

[0013] Furthermore, the preprocessing in step S1 refers to filling or removing outliers by interpolation. Specifically, for missing values, the average value of the previous item and the next item is taken to fill; for outliers, the 3σ criterion is used to remove them; then the original data is smoothed and denoised by wavelet packet transform (db6 wavelet basis function, rigrsure soft threshold and 5-layer wavelet decomposition).

[0014] Furthermore, the specific method of step S2 is as follows:

[0015] S2.1. Perform a level comparison check on the roadbed settlement data sequence pre-processed in step S1. Specifically, assume that the sequence composed of n roadbed settlement data pre-processed in step S1 is X. (0) ={x1 (0) ,x2 (0) ,…,x n (0)}, by calculating X (0) The level ratio: Check X (0) Are the level ratios in the interval If X (0) The level ratios are in the range If X (0) The level ratio is not in the interval If the roadbed settlement data pre-processed in step S1 is smoothed or transformed until the level ratio verification meets the requirements;

[0016] S2.2, compare the X that has passed the level comparison test (0) The sequence is accumulated to obtain a new sequence X (1) ={x1 (1) ,x2 (1) ,…,x n (1)};

[0017] S2.3, the new sequence obtained in step S2.2 is fitted with the first-order linear constant coefficient differential equation of formula (1) as follows:

[0018]

[0019] In the formula, X (1) Represents the cumulative value of each observation point, a=(a ij ) n×n ,b=[b1,b2,…,b i ,…,b n ] T , both represent coefficient matrices; b i and a ij represents the i-th order coefficient, i=1,2,…,n;

[0020] S2.4. Discretize equation (1) and obtain equation

[0021]

[0022] In the formula, x i (0) (k) represents the grey differential equation; Represents the model base value, and is calculated as shown in formula (3):

[0023] z i (1) (k) = 0.5*[x i (1) (k)+x i (1) (k-1)] (3);

[0024] S2.5. Based on formulas (4)-(6), solve for parameters a and b:

[0025]

[0026]

[0027] In the formula, L and Y are intermediate variables introduced to simplify the calculation, and the superscript T represents the transpose of the matrix;

[0028] S2.6. According to the parameters a and b, the time response function of the grey model is:

[0029]

[0030] Finally, the grey model prediction value is obtained by cumulative reduction of formula (7).

[0031] Furthermore, according to step S2.6, the prediction accuracy of the model is highly dependent on the solved parameters a and b, and the calculation process of the coefficient matrices a and b depends on the model base value constructed by the original sequence in formula (3) The solution of The more accurate, the better the prediction effect, and the base value The calculation is actually solved by using the trapezoidal formula of numerical integration. In order to further enhance the accuracy of basic numerical calculation, the integral formula is used for direct calculation:

[0032]

[0033] Each prediction process of the model adopts an iterative and progressive approach, that is, a and b are calculated based on the original data, and further predictions are made based on the above parameters. Remove the first value of the prediction sequence, use the remaining sequence to rebuild the parameters and update the base value Complete the next prediction task.

[0034] Furthermore, the accuracy of the prediction model is comprehensively evaluated in step S3, specifically, when the posterior difference ratio C≤0.65 predicted by the grey model IGM(1,1) and the small error probability p≥0.70%, the prediction result is output, which is recorded as y1.

[0035] Furthermore, in step S4, the roadbed settlement data pre-processed in step S1 is normalized and an SVR model is constructed; the normalized roadbed settlement data is expressed as:

[0036]

[0037] In the formula, x i represents the ith observation value in the sedimentation sequence, max(x) and min(x) represent the maximum and minimum values ​​of the sedimentation sequence, respectively;

[0038] The support vector regression function is expressed as:

[0039] f(x)=wω(x)+B (10)

[0040] Where w is the weight; B is the bias; ω(x) is the mapping function from low-dimensional space to high-dimensional space;

[0041] According to the principle of structured risk minimization, slack variables are introduced and the objective function of the SVR model is:

[0042]

[0043] The corresponding constraints are:

[0044]

[0045] In the formula, l ε is the insensitive loss function; C is the penalty coefficient; ξ i , They are the upper and lower bounds of the training error under the width ε error constraint of the insensitive loss function;

[0046] Construct the Lagrangian function and transform the objective function optimization problem into solving the following equation:

[0047]

[0048] Finally, it is simplified to:

[0049]

[0050] In the formula, and μ i Both represent Lagrange multiplier variables, K(x i ,x) is called the kernel function, n represents the number of training samples, that is, the n roadbed settlement data after preprocessing in step S1; m represents the number of Lagrange multipliers introduced in the optimization process, usually 2n, corresponding to the Lagrange multipliers of the positive error and negative error of each sample. Common kernel functions include linear kernel function, Gaussian radial basis kernel function, polynomial kernel function and nonlinear kernel function of neurons. In parameter optimization, the kernel function coefficient parameter is only used in Gaussian radial basis kernel function, polynomial kernel function and nonlinear kernel function of neurons.

[0051] Furthermore, step S5 uses a particle swarm optimization algorithm (PSO) to optimize the hyperparameters of the support vector regression SVR model, constructs a particle swarm optimized support vector machine model (PSVR) model and obtains the PSVR model prediction result. The specific process is as follows:

[0052] The performance of the SVR model directly depends on the selection of model hyperparameters. This patent uses the particle swarm optimization algorithm to optimize the kernel function, kernel function parameter (gamma), width ε of the insensitive loss function, and penalty factor C of the SVR model. The fitness calculation of the optimization process uses RMSE (Root Mean Squared Error) to select the optimal parameters to build the PSVR model. The construction steps of the PSVR model are as follows:

[0053] Step 1: Parameter and population initialization. Parameter initialization includes the maximum number of iterations, inertia weight, learning factor, and the speed range and position range of particle updates. The population size is initialized to M, that is, the number of particles in the population. The particle position vector contains the SVR model parameters that need to be optimized.

[0054] Step 2: Based on the initialization value of each particle in the population, calculate the fitness value of each particle and record the historical optimal solution p of each particle best , get the global optimal position g of the particle swarm best ;

[0055] Step 3: Update the particle velocity based on formula (15), and update the particle position based on formula (16);

[0056]

[0057] in, and are the velocity and position of particle q at iteration t+1, w t is the inertia weight of the tth iteration, represents the speed of particle q in t iterations, c1 and c2 represent learning factors, which are set to 2, r1 and r2 represent random numbers in the range of [0,1], and p best,q represents the best historical position of particle q, represents the position of particle q at iteration t, g best In order to adapt to the nonlinear requirements of roadbed settlement data and further increase the global exploration and local optimization capabilities of the optimization algorithm, this patent uses the nonlinear inertia weight calculation method given by formula (17) to improve the PSO algorithm.

[0058]

[0059] Among them, w begin and w end They represent the inertia weight of the first iteration and the inertia weight of the last iteration respectively, Iter represents the current iteration, and Iter_max represents the maximum iteration;

[0060] Step 4: Calculate the fitness value of each particle, update the historical optimal position of the particle and the global optimal position of the particle swarm, and determine whether the maximum number of iterations has been reached. If so, return g best , if otherwise continue to Step3;

[0061] Step5: The optimal hyperparameter g returned in step 4 best Substitute the SVR model, build the particle swarm optimized support vector machine model (PSVR) and obtain the PSVR model prediction results.

[0062] Furthermore, the specific method of step S6 is: first calculate the prediction error sum of squares e of a single model γ :

[0063]

[0064] Where: x τγ is the τth original data of the γth model; is the τth predicted value corresponding to the γth model; is the prediction error;

[0065] The weight coefficient of a single model is:

[0066]

[0067] In the formula, z represents the total number of models.

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] Aiming at the changing characteristics and laws of roadbed settlement data, the present invention improves the classic grey model to construct an IGM model based on roadbed settlement changes, introduces an improved PSO algorithm to optimize the SVR model to construct a PSVR model, and further completes the evaluation. The proposed IGM-PSVR prediction model can overcome the shortcomings of a single model, improve the settlement prediction accuracy, provide a roadbed design and maintenance plan for the railway transportation department, reduce the waste of manpower, material and financial resources, and improve the sustainable utilization of railway line equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Flow chart of the method of the present invention;

[0071] Figure 2 The roadbed settlement diagram shown in the embodiment of the present invention;

[0072] Figure 3 is the prediction result of a single prediction model based on the grey model GM (1, 1);

[0073] Figure 4It is the prediction result of a single prediction model based on the SVR support vector regression prediction method;

[0074] Figure 5 It is the prediction result based on the IGM-PSVR model prediction method;

[0075] Figure 6 It is a relative error comparison diagram of the prediction values ​​of the grey model GM (1, 1), the SVR support vector regression prediction model and the IGM-PSVR model of the present invention. DETAILED DESCRIPTION

[0076] The present invention proposes a railway roadbed settlement prediction method based on the IGM-PSVR model. In order to make the purpose, technical solution and advantages of the present invention clearer, the implementation scheme of the present invention is further described in detail below with reference to the accompanying drawings. The system flow chart is as follows: Figure 1 shown.

[0077] The present invention provides a railway subgrade settlement prediction method based on the GM-SVR combined model, the method comprising the following steps:

[0078] S1. Set observation points, collect roadbed settlement data, and preprocess the collected roadbed settlement data; the preprocessing refers to using interpolation method to fill or remove outliers. Specifically, for missing values, mean processing is used to take the average of the previous and next items; for outliers, use the 3σ criterion to remove them, and then use wavelet packet transform (db6 wavelet basis function, rigrsure soft threshold and 5-layer wavelet decomposition) to smooth and reduce noise on the original data.

[0079] S2. First, perform a level ratio check. If the roadbed settlement data pre-processed in step S1 meets the requirements, establish the corresponding differential equation, solve the time response function, further optimize the background value of the gray model, construct the improved gray model IGM (1,1) and obtain the IGM model prediction result; if the roadbed settlement data pre-processed in step S1 does not meet the requirements, continue to perform pre-processing; the specific method is as follows:

[0080] S2.1. In order to ensure that the grey GM (1, 1) model can be established, the original data needs to be checked. Therefore, firstly, the sequence of roadbed settlement data preprocessed in step S1 is checked by level comparison. Specifically, let the sequence composed of n roadbed settlement data preprocessed in step S1 be X. (0) ={x1 (0) ,x2 (0) ,…,x n (0)}, by calculating X (0) The level ratio: Check X (0)Are the level ratios in the interval If X (0) The level ratios are in the range If X (0) The level ratio is not in the interval If the roadbed settlement data pre-processed in step S1 is smoothed or transformed until the level ratio verification meets the requirements;

[0081] X that has passed the level comparison test (0) The sequence is accumulated to obtain a new sequence X (1) ={x1 (1) ,x2 (1) ,…,x n (1)};

[0082] S2.3, the new sequence is monotonically increasing data, which approximately conforms to exponential growth. Therefore, the new sequence obtained in step S2.2 is fitted with the first-order linear constant coefficient differential equation of formula (1) as follows:

[0083]

[0084] In the formula, X (1) Represents the cumulative value of each observation point, a=(a ij ) n×n ,b=[b1,b2,…,b i ,…,b n ] T , both represent coefficient matrices; b i and a ij represents the i-th order coefficient, i=1,2,…,n;

[0085] S2.4. Discretize equation (1) and obtain equation

[0086]

[0087] In the formula, x i (0) (j) represents the grey differential equation; Represents the model base value, and is calculated as shown in formula (3):

[0088] z i (1) (k) = 0.5*[x i (1) (k)+x i (1) (k-1)] (3);

[0089] S2.5. Based on formulas (4)-(6), solve for parameters a and b:

[0090]

[0091] In the formula, L and Y are intermediate variables introduced to simplify the calculation, and the superscript T represents the transpose of the matrix;

[0092] S2.6. According to the parameters a and b, the time response function of the grey model is:

[0093]

[0094] Finally, the grey model prediction value is obtained by cumulative reduction of formula (7).

[0095] According to step S2.6, the prediction accuracy of the model is highly dependent on the solved parameters a and b, and the calculation process of the coefficient matrices a and b depends on the model base value constructed by the original sequence in formula (3) The solution of The more accurate, the better the prediction effect, and the base value The calculation is actually solved by using the trapezoidal formula of numerical integration. In order to further enhance the accuracy of basic numerical calculation, the integral formula is used for direct calculation:

[0096]

[0097] Each prediction process of the model adopts an iterative and progressive approach, that is, a and b are calculated based on the original data, and further predictions are made based on the above parameters. Remove the first value of the prediction sequence, use the remaining sequence to rebuild the parameters and update the base value Complete the next prediction task.

[0098] S3. The accuracy of the prediction model of the grey model IGM (1,1) is comprehensively evaluated by using two indicators: the posterior difference ratio C1 and the probability of small error p; see Table 1 for details. When the C value is small, the dispersion of the original data is large, while the dispersion of the residual is small, which indicates that the prediction accuracy is high. In addition, the increase in the p value of the indicator indicates that there are more points where the difference between the residual and the residual mean is less than 0.6745, so a larger p value represents a better prediction model. If the accuracy of the prediction model meets the requirements, the prediction result is output, recorded as y1.

[0099] S4, normalizing the roadbed settlement data pre-processed in step S1, and constructing an SVR model; the normalized roadbed settlement data is expressed as:

[0100]

[0101] In the formula, x irepresents the ith observation value in the sedimentation sequence, max(x) and min(x) represent the maximum and minimum values ​​of the sedimentation sequence, respectively;

[0102] The support vector regression function is expressed as:

[0103] f(x)=wω(x)+B (10)

[0104] Where w is the weight; B is the bias; ω(x) is the mapping function from low-dimensional space to high-dimensional space;

[0105] According to the principle of structured risk minimization, slack variables are introduced and the objective function of the SVR model is:

[0106]

[0107] The corresponding constraints are:

[0108]

[0109] In the formula, k ε is the insensitive loss function; C is the penalty coefficient; ξ i , They are the upper and lower bounds of the training error under the width ε error constraint of the insensitive loss function;

[0110] Construct the Lagrangian function and transform the objective function optimization problem into solving the following equation:

[0111]

[0112] Finally, it is simplified to:

[0113]

[0114] In the formula, and μ i Both represent Lagrange multiplier variables, K(x i ,x) is called the kernel function, n represents the number of training samples, that is, the n roadbed settlement data after preprocessing in step S1; m represents the number of Lagrange multipliers introduced in the optimization process, usually 2n, corresponding to the Lagrange multipliers of the positive error and negative error of each sample. Common kernel functions include linear kernel function, Gaussian radial basis kernel function, polynomial kernel function and nonlinear kernel function of neurons. In parameter optimization, the kernel function coefficient parameter is only used in Gaussian radial basis kernel function, polynomial kernel function and nonlinear kernel function of neurons.

[0115] S5. Use the particle swarm optimization algorithm (PSO) to optimize the hyperparameters of the support vector regression SVR model, build a particle swarm optimized support vector machine model (PSVR) and obtain the PSVR model prediction results. The specific process of S5 is as follows: The performance of the SVR model directly depends on the selection of the model hyperparameters. This patent uses the particle swarm optimization algorithm to optimize the kernel function, kernel function parameter (gamma), width of the insensitive loss function (ε) and penalty factor (C) of the SVR model. The fitness calculation of the optimization process uses RMSE (Root Mean Squared Error) to select the optimal parameters to build the PSVR model. The steps for building the PSVR model are as follows:

[0116] Step 1: Parameter and population initialization. Parameter initialization includes the maximum number of iterations, inertia weight, learning factor, and the speed range and position range of particle updates; the population size is initialized to M, that is, the number of particles in the population, and the particle position vector contains the SVR model parameters that need to be optimized;

[0117] Step 2: Based on the initialization value of each particle in the population, calculate the fitness value of each particle and record the historical optimal solution p of each particle best , get the global optimal position g of the particle swarm best ;

[0118] Step 3: Update the particle velocity based on formula (15), and update the particle position based on formula (16);

[0119]

[0120] in, and are the velocity and position of particle q at iteration t+1, w t is the inertia weight of the tth iteration, represents the speed of particle q in t iterations, c1 and c2 represent learning factors, which are set to 2, r1 and r2 represent random numbers in the range of [0,1], and p best,q represents the best historical position of particle q, represents the position of particle q at iteration t, g best In order to adapt to the nonlinear requirements of roadbed settlement data and further increase the global exploration and local optimization capabilities of the optimization algorithm, this patent uses the nonlinear inertia weight calculation method given by formula (17) to improve the PSO algorithm.

[0121]

[0122] Among them, w begin and w endThey represent the inertia weight of the first iteration and the inertia weight of the last iteration respectively, Iter represents the current iteration, and Iter_max represents the maximum iteration;

[0123] Step 4: Calculate the fitness value of each particle, update the historical optimal position of the particle and the global optimal position of the particle swarm, and determine whether the maximum number of iterations has been reached. If so, return g best , if otherwise continue to Step3;

[0124] Step5: The optimal hyperparameter g returned in step 4 best Substitute the SVR model, build the particle swarm optimized support vector machine model (PSVR) and obtain the PSVR model prediction result, which is recorded as y2.

[0125] S6. This embodiment adopts the IGM-PSVR parallel model to predict the railway subgrade settlement. The grey IGM model has better linear prediction capability, and the PSVR has better nonlinear data prediction capability. The two models are combined in parallel to make up for the shortcomings of a single model, improve the prediction accuracy of subgrade settlement, and provide technical support for the safe and smooth operation of trains.

[0126] This embodiment adopts the GM-SVR parallel model to predict the railway embankment settlement. The grey GM (1, 1) model has better linear prediction ability, and the SVR has better nonlinear data prediction ability. The two models are combined in parallel to make up for the shortcomings of a single model, improve the prediction accuracy of the embankment settlement, and provide technical support for the safe and smooth operation of trains.

[0127] In the combined prediction model, it is crucial to determine the weight coefficient. Generally, the arithmetic mean method, the optimal weighted method or the inverse error sum of squares method are used to determine the weight coefficient. The arithmetic mean method is usually used when the importance of the model is not well understood, but because it assigns the same weight to all models and does not consider priority, it may lead to poor prediction results. The optimal weighted method is complex to calculate and has great limitations in practical applications. The inverse error sum of squares method reflects the importance of each model in the combined prediction by calculating the sum of squares of the errors of the prediction model. The weights assigned are more reasonable and effective, and are easy to operate and can obtain good prediction results. Therefore, this embodiment uses the inverse error sum of squares method to determine the optimal combined weight size of the prediction model.

[0128] The sum of square errors between the prediction result y1 of the grey model GM(1,1) and the prediction result y2 of the SVR model and the true value are calculated respectively. The weights w1 and w2 of the grey model GM(1,1) and the SVR model are determined according to the inverse method of the sum of square errors. The specific method is:

[0129] First, calculate the sum of squared prediction errors e for a single model γ :

[0130]

[0131] Where: x τγ is the τth original data of the γth model; is the τth predicted value corresponding to the γth model; is the prediction error;

[0132] The weight coefficient of a single model is:

[0133]

[0134] In the formula, z represents the total number of models.

[0135] It can be seen that the larger the sum of squares of the prediction model errors, the larger the prediction error value of the prediction model, and the smaller the weight coefficient in the combined model. The smaller the sum of squares of the prediction model errors, the smaller the prediction error value of the prediction model, and the larger its weight coefficient in the combined model. Finally, the prediction result y is obtained:

[0136] y=w1*y1+w2*y2 (20)

[0137] Experimental verification: This experiment takes the subgrade settlement of the Xinjiang Kuitun Letuyi section railway line as the research object. The poor geological bodies distributed in the Kuitun Letuyi section railway are mainly loess, and the soil quality has a great impact on the stability of the subgrade. Figure 2 shown.

[0138] In areas with severe settlement and deformation, static levels are set up to collect roadbed settlement data with an accuracy of up to 0.01mm, and there are 10 observation points in total. Due to space limitations, the present invention selects the most representative set of settlement observations, namely the K2047+750 observation pile data for experimental verification. The time span is 160 days from March 2022 to August 2022. Due to the long time, missing values ​​and outliers are inevitable in the collected data. For missing values, mean processing is adopted to take the average of the previous and next items; for outliers, the 3σ criterion is used to eliminate singular values ​​in the monitoring data to prevent erroneous conclusions.

[0139] Since the grey model requires that the input data must be equidistant, after preliminary data screening, a total of 56 settlement data were obtained, and the time interval between each settlement data was 3 days. The first 80% of the data set was used as the training set, and the last 20% of the data set was used as the test set.

[0140] When predicting railway subgrade settlement, the prediction accuracy and reliability of the evaluation model play a vital role. The smaller the following evaluation index is, the higher the prediction accuracy of the model represented is. The present invention mainly evaluates through the following evaluation indexes:

[0141] (1) Mean Absolute Error

[0142]

[0143] (2) Mean Absolute Percentage Error

[0144]

[0145] (3) Mean Squared Error

[0146]

[0147] (4) Root Mean Squared Error

[0148]

[0149] Among the above evaluation indicators, is the predicted value; i is the true value.

[0150] Depend on Figure 2 It can be seen that the roadbed settlement is a time series with a trend. For the improved grey model IGM (1,1), the original data sequence is checked for level ratios, and it is determined that all level ratios fall within the acceptable coverage interval. The model was established and used to predict the railway subgrade settlement data for the next 11 periods. The improved grey model IGM (1,1) was rated for accuracy, with the posterior error ratio being 0.17 and the probability of small error being 0.89. According to the classification in Table 1, the accuracy of the grey model is good.

[0151] For the PSVR model, the input data is normalized, the model is further trained, the model parameters are determined, the PSVR model is established, and the output results of the model are denormalized to obtain the settlement prediction value.

[0152] Table 1 Improved grey model IGM (1,1) accuracy comparison table

[0153] Model accuracy level Posterior difference ratio C1 Small error probability p / % Level 1 (Excellent) C1≤0.35 p≥0.95 Level 2 (Good) 0.35＜C1≤0.50 0.80≤p≤0.95 Level 3 (Pass) 0.50＜C1≤0.65 0.70≤p≤0.80 Level 4 (Unqualified) 0.65＜C1 p＜0.70

[0154] In order to verify the prediction performance of the combined prediction method proposed in this invention, the grey model GM (1, 1), the SVR support vector regression model and the IGM-PSVR model prediction method of this invention are used to predict and analyze the roadbed settlement data series. The result curves of the three prediction methods are shown in Figure 2. Figures 3 to 5 shown.

[0155] Figure 3 is the prediction result of a single prediction model based on the grey model GM (1, 1). Figure 3 It can be seen that the changing trend of the fitting value of the roadbed settlement based on the grey model GM (1, 1) is consistent with the changing trend of the actual value, but the predicted value deviates from the true value and the error is large.

[0156] Figure 4 is the prediction result of a single prediction model based on the SVR support vector regression prediction method. Figure 4 It can be seen that the predicted values ​​of the first few periods based on SVR support vector regression are very close to the actual values ​​of settlement, but the errors between the data of the last few periods and the actual values ​​are large.

[0157] Figure 5 This is the prediction result of the IGM-PSVR combined model prediction method of the present invention. Compared with the single GM (1, 1) grey model prediction method and the SVR support vector regression prediction method, the prediction result of the IGM-PSVR model is closer to the actual value of the railway subgrade settlement, and the prediction accuracy and precision are improved. Only in the 7th period, the prediction accuracy has declined, but the error is only 0.1mm, which does not interfere with the actual engineering tasks and can meet the actual scene application.

[0158] Figure 6 This is a comparison chart of the relative errors of the prediction values ​​of the three models. Figure 6 It can be seen that the prediction results of the grey model prediction method have the largest error and the least ideal prediction results. Specifically, the error is small in the first few periods, and the error of the data in the latter few periods gradually increases. This also shows that the grey model is only suitable for short-term predictions, not for medium- and long-term predictions. Compared with the grey prediction model, the error of the SVR model is reduced, and the prediction results are significantly better than the grey prediction model; the prediction method based on the IGM-PSVR model has the smallest error, and the relative error always fluctuates within the range of 0.1 mm, indicating that this method can well predict the law of railway subgrade settlement changes and meet the actual engineering application.

[0159] Table 2 shows the prediction results of different prediction methods

[0160] Evaluation index model GM Model SVR Model IGM-PSVR combined model MAE 0.178 0.093 0.060 MAPE 1.932 0.687 0.501 MSE 0.039 0.011 0.005 RMSE 0.198 0.099 0.071

[0161] Table 2 shows the prediction statistics of the three models. The MAE, MAPE, MSE and RMSE of the IGM-PSVR combined model prediction method are 0.06, 0.501, 0.005 and 0.071 respectively. Compared with the prediction results of the GM (1, 1) grey model, the MAE, MAPE, MSE and RMSE of the GM-SVR combined model prediction results are reduced by 66.3%, 74.1%, 87.1% and 64.1% respectively; compared with the prediction results of the SVR model, the MAE, MAPE, MSE and RMSE are reduced by 35.5%, 27.1%, 54.6% and 28.3% respectively.

[0162] The prediction results of the three prediction models are compared through statistical data: in the field of roadbed settlement prediction, the prediction method based on the IGM-PSVR combined model is better than the SVR support vector regression model and the GM (1, 1) grey model.

Claims

1. The railway subgrade settlement prediction method based on the IGM-PSVR model is characterized by: The method comprises the following steps: S1. Setting observation points, collecting roadbed settlement data, and preprocessing the collected roadbed settlement data; S2, first perform level ratio verification. If the roadbed settlement data after S1 preprocessing does not meet the requirements, continue to perform preprocessing; If the roadbed settlement data preprocessed in step S1 meets the requirements, the corresponding differential equation is established, the time response function is solved, the background value of the grey model is further optimized, and the improved grey model IGM (1,1) is constructed; S3, comprehensively evaluate the accuracy of the prediction model of the improved grey model IGM (1,1) through the two indicators of posterior difference ratio C1 and small error probability p; and output the prediction result, recorded as y1; S4, normalizing the roadbed settlement data pre-processed in step S1, and constructing an SVR model; S5, using the particle swarm optimization algorithm (PSO for short) to optimize the hyperparameters of the support vector regression model (SVR for short), constructing a particle swarm optimized support vector machine model (PSVR model for short), and obtaining the prediction result of the PSVR model, recorded as y2; S6. Calculate the sum of squares of the errors between the prediction result y1 of the IGM (1,1) model and the prediction result y2 of the PSVR model and the true value respectively. According to the inverse method of the sum of squares of the errors, determine the weights w1 and w2 of the grey model IGM (1,1) model and the PSVR model. Finally, obtain the prediction result y of the IGM-PSVR model.

2. The railway subgrade settlement prediction method based on the IGM-PSVR model according to claim 1 is characterized in that: The preprocessing in step S1 refers to filling or removing outliers by interpolation. Specifically, for missing values, the average value of the previous and next items is used to fill them; for outliers, the 3σ criterion is used to remove them; and then the original data is smoothed and denoised by wavelet packet transform.

3. The railway subgrade settlement prediction method based on the IGM-PSVR model according to claim 1 is characterized in that: The specific method of step S2 is as follows: S2.

1. Perform a level comparison check on the roadbed settlement data sequence pre-processed in step S1. Specifically, assume that the sequence composed of n roadbed settlement data pre-processed in step S1 is X. (0) ={x1 (0) ,x2 (0) ,…,x n (0) }, by calculating X (0) The level ratio: Check X (0) Are the level ratios in the interval If X (0) The level ratios are in the range If X (0) The level ratio is not in the interval If the roadbed settlement data pre-processed in step S1 is smoothed or transformed until the level ratio verification meets the requirements; S2.2, compare the X that has passed the level comparison test (0) Sequence accumulation to obtain a new sequence S2.3, the new sequence obtained in step S2.2 is fitted with the first-order linear constant coefficient differential equation of formula (1) as follows: In the formula, X (1) Represents the cumulative value of each observation point, a=(a ij ) n×n ,b=[b1,b2,…,b i ,…,b n ] T , both represent coefficient matrices; b i and a ij represents the i-th order coefficient, i=1,2,…,n; S2.

4. Discretize equation (1) and obtain equation In the formula, x i (0) (k) represents the grey differential equation; Represents the model base value, and is calculated as shown in formula (3): z i (1) (k)=0.5*[x i (1) (k)+x i (1) (k-1)] (3); S2.

5. Based on formulas (4)-(6), solve for parameters a and b: In the formula, L and Y are intermediate variables introduced to simplify the calculation, and the superscript T represents the transpose of the matrix; S2.

6. According to the parameters a and b, the time response function of the grey model is: Finally, the grey model prediction value is obtained by cumulative reduction of formula (7).

4. The railway subgrade settlement prediction method based on the IGM-PSVR model according to claim 3 is characterized in that: The calculation process of coefficient matrices a and b depends on the model base value constructed from the original sequence in formula (3) The solution of The more accurate, the better the prediction effect, and the base value The calculation is actually solved by numerical integration. In order to further enhance the accuracy of the basic numerical calculation, the integral interval is further refined into H, and [k-1, k] = [c, d] is recorded. The interval [c, d] is divided into H equal parts, and the node x k =c+kh, where Using the complex trapezoidal formula to solve: Each prediction process of the model adopts an iterative and progressive approach, that is, a and b are calculated based on the original data, and further predictions are made based on the above parameters. Remove the first value of the prediction sequence, use the remaining sequence to rebuild the parameters and update the base value Complete the next prediction task.

5. The railway subgrade settlement prediction method based on the IGM-PSVR model according to claim 1 is characterized in that: The comprehensive evaluation of the accuracy of the prediction model in step S3 specifically means that when the posterior difference ratio C ≤ 0.65 predicted by the grey model IGM (1, 1) and the small error probability p ≥ 0.70%, the prediction result is output and recorded as y1.

6. The railway subgrade settlement prediction method based on the IGM-PSVR model according to claim 1 is characterized in that: Step S4 normalizes the roadbed settlement data preprocessed in step S1 and constructs an SVR model; the normalized roadbed settlement data is expressed as: In the formula, x i represents the ith observation value in the sedimentation sequence, max(x) and min(x) represent the maximum and minimum values ​​of the sedimentation sequence, respectively; The support vector regression function is expressed as: f(x)=wω(x)+B (10) Where w is the weight; B is the bias; ω(x) is the mapping function from low-dimensional space to high-dimensional space; According to the principle of structured risk minimization, slack variables are introduced and the objective function of the SVR model is: The corresponding constraints are: In the formula, l ε is the insensitive loss function; C is the penalty coefficient; ξ i , They are the upper and lower bounds of the training error under the width ε error constraint of the insensitive loss function; Construct the Lagrangian function and transform the objective function optimization problem into solving the following equation: Finally, it is simplified to: In the formula, and μ i Both represent Lagrange multiplier variables, K(x i ,x) is called the kernel function, n represents the number of training samples, that is, the n roadbed settlement data after preprocessing in step S1; m represents the number of Lagrange multipliers introduced in the optimization process, usually 2n, corresponding to the Lagrange multipliers of the positive error and negative error of each sample.

7. The railway subgrade settlement prediction method based on the IGM-PSVR model according to claim 1 is characterized in that: Step S5 uses a particle swarm optimization algorithm (PSO) to optimize the hyperparameters of the support vector regression SVR model, constructs a particle swarm optimized support vector machine model (PSVR) model and obtains the PSVR model prediction results. The specific process is as follows: The performance of the SVR model directly depends on the selection of model hyperparameters. This patent uses the particle swarm optimization algorithm to optimize the kernel function, kernel function parameter (gamma), width ε of the insensitive loss function, and penalty factor C of the SVR model. The fitness calculation of the optimization process uses RMSE (Root Mean Squared Error) to select the optimal parameters to build the PSVR model. The construction steps of the PSVR model are as follows: Step 1: Parameter and population initialization. Parameter initialization includes the maximum number of iterations, inertia weight, learning factor, and the speed range and position range of particle updates. The population size is initialized to M, that is, the number of particles in the population. The particle position vector contains the SVR model parameters that need to be optimized. Step 2: Based on the initialization value of each particle in the population, calculate the fitness value of each particle and record the historical optimal solution p of each particle best , get the global optimal position g of the particle swarm best ; Step 3: Update the particle velocity based on formula (15), and update the particle position based on formula (16); in, and are the velocity and position of particle q at iteration t+1, w t is the inertia weight of the tth iteration, represents the speed of particle q in t iterations, c1 and c2 represent learning factors, which are set to 2, r1 and r2 represent random numbers in the range of [0,1], and p best,q represents the best historical position of particle q, represents the position of particle q at iteration t, g best In order to adapt to the nonlinear requirements of roadbed settlement data and further increase the global exploration and local optimization capabilities of the optimization algorithm, this patent uses the nonlinear inertia weight calculation method given by formula (17) to improve the PSO algorithm. Among them, w begin and w end They represent the inertia weight of the first iteration and the inertia weight of the last iteration respectively, Iter represents the current iteration, and Iter_max represents the maximum iteration; Step 4: Calculate the fitness value of each particle, update the historical optimal position of the particle and the global optimal position of the particle swarm, and determine whether the maximum number of iterations has been reached. If so, return g best , if otherwise continue to Step3; Step5: The optimal hyperparameter g returned in step 4 best Substitute the SVR model, build the particle swarm optimized support vector machine model (PSVR) and obtain the PSVR model prediction results.

8. The railway subgrade settlement prediction method based on the IGM-PSVR model according to claim 1 is characterized in that: The specific method of step S6 is: first calculate the prediction error sum of squares e of a single model γ : Where: x τγ is the τth original data of the γth model; is the τth predicted value corresponding to the γth model; is the prediction error; The weight coefficient of a single model is: In the formula, z represents the total number of models.

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