Roadbed settlement prediction method based on IGWO-BP and ARIMA

Abstract

The invention discloses a roadbed settlement prediction method based on IGWO-BP and ARIMA. The roadbed settlement prediction method comprises the following steps: firstly, obtaining a seasonal permafrost region settlement data composition, wherein the seasonal permafrost region settlement data composition comprises short-term linear characteristics and long-term nonlinear change characteristics; preprocessing the original monitoring data, dividing the data into a training set and a test set, and constructing an IGWO-BP model based on the training set; then, an IGWO-BP model is trained on the training set, a training residual sequence is further obtained, and meanwhile, the trained IGWO-BP model is adopted to predict the test set; constructing a model ARIMA, and predicting a network residual error based on the model; finally, the prediction result of the IGWO-BP model and the residual error sequence prediction result of the ARIMA model are connected in series, error correction of the prediction result is completed, and a final combined prediction result is obtained.By means of the method, the freezing injury occurrence characteristics of the seasonal frozen soil region can be well captured, and the defect of prediction of a single model is overcome.

Description

Technical Field

[0001] The invention belongs to the technical field of roadbed freezing damage prediction, and in particular relates to a roadbed settlement residual combination prediction method based on IGWO-BP and ARIMA. Background Art

[0002] Among the various railway diseases, roadbed frost damage is widely distributed, lasts for a long time, has a large workload, and has the most serious impact on driving. It is a common disease with the characteristics of regularity and suddenness. The Northwest Plateau of China is a seasonal frozen land area. The surface soil is generally frozen in winter and begins to melt in spring. Under the combined influence of soil, water, and temperature, the roadbed surface of such areas will experience varying degrees of frost heave in winter, and will melt and sink at the turn of spring and summer, causing uneven deformation of the track surface and level of the railway line. Severe sections are often accompanied by mud, ballast grooving, roadbed sinking, and subgrade squeezing. It can be said that frost damage is a common disease that is widely distributed on railway lines in cold regions.

[0003] There are three main methods for predicting railway subgrade frost damage: empirical formula method, graphical method and system analysis method. In actual subgrade frost damage prediction, system analysis method is often used. Common system analysis methods include grey system, ARIAM model (Autoregressive Integrated Moving Average Model) and BP neural network. In Surveying and Mapping and Spatial Geographic Information, Wang Ning et al. published a study on the application of the dynamic GM (1,1) model in settlement prediction. This paper aims to solve the problem of poor long-term prediction effect of the traditional grey model GM (1,1), and uses a dynamic repetition method to continuously update the model to achieve long-term roadbed settlement prediction. In Science, Technology and Engineering, an application of an improved variable weight buffer grey model in settlement prediction was published. Wang Defa et al. proposed a single and double power function weakened buffer operator, and combined with the variable weight background value to establish an improved variable weight buffer GM (1,1) model, which solved the accuracy problem of the grey model in mid- and late-stage settlement prediction. Based on the above analysis, the changes in railway roadbed settlement values ​​in cold regions are different from those in other roadbed settlements. The settlement changes in cold regions have trends and seasonality, and the trend of change is a combination of linear and nonlinear data. The problem cannot be solved by a single analysis method and model. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention proposes a combined prediction method for roadbed settlement residuals based on IGWO-BP and ARIMA, which can make up for the shortcomings of single model prediction, improve the prediction accuracy of the model, and provide roadbed design and maintenance solutions for railway transportation departments in cold areas, thereby reducing the waste of manpower, material and financial resources and increasing the sustainable utilization of railway line equipment.

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

[0006] The roadbed settlement residual combined prediction method based on IGWO-BP and ARIMA of the present invention comprises the following steps:

[0007] S1. Extracting the roadbed settlement observation values ​​from the observation points in the seasonal frozen soil area, and obtaining the seasonal frozen soil area settlement data as the original monitoring data;

[0008] S2, preprocessing the original monitoring data obtained in step S1, and dividing the data into a training set and a test set, and optimizing the structure, initial weight and threshold of the BP neural network using an improved grey wolf optimization algorithm (IGWO) based on the training set to construct an IGWO-BP model;

[0009] S3, train the IGWO-BP model on the training set to further obtain the training residual sequence, and use the trained IGWO-BP model to predict the test set;

[0010] S4. Determine the ARIMA (p, d, q) model based on the stationarity, autocorrelation and partial correlation of the network residual sequence, and predict the network residual sequence based on the model;

[0011] S5. Construct a combined prediction model of IGWO-BP and ARIMA: connect the prediction result of the IGWO-BP model in step S3 and the prediction result of the residual sequence of the ARIMA model in step S4 in series, complete the error correction of the prediction result, and obtain the final combined prediction result.

[0012] S6: The combined prediction model of IGWO-BP and ARIMA constructed in step S5 is applied to a certain engineering section in Xinjiang for actual verification, and is evaluated using indicators such as mean absolute error, mean absolute percentage error, mean square error, and root mean square error.

[0013] Furthermore, the original monitoring data described in step S2 is preprocessed, specifically, the missing values ​​and abnormal values ​​in the collected samples are replaced by adjacent values ​​in the sequence, and the original noisy data is further denoised by wavelet packet decomposition, and then the denoised data is interpolated by cubic spline interpolation. Finally, the preprocessed data set is divided into a training set and a test set in a ratio of 8:2 to complete the data preprocessing.

[0014] Furthermore, the step S2 described in the above method uses an improved gray wolf optimization algorithm (IGWO) based on the training set to optimize the structure, initial weights and thresholds of the BP neural network to construct an IGWO-BP model; the specific optimization process is: the gray wolf optimization algorithm is a meta-inspiration algorithm that simulates the predation process of the gray wolf population, and the algorithm has good global search capabilities and local optimization capabilities. In the evolution process of the gray wolf population, a core group with three alpha wolves will be formed, and the hunting process of the gray wolves is completed under the guidance of the three alpha wolves. This patent sets the position parameters of the gray wolf as the structural parameters, initial weights and initial thresholds of the BP neural network, and the optimized fitness function is to minimize the mean square error of the BP prediction results. The construction process of the IGWO-BP model is as follows:

[0015] Step 1: Use Logistic chaotic mapping to generate chaotic sequence to initialize the population, initialize the convergence factor a, coefficient vectors A and C, first improve the convergence factor a to make it nonlinear, and further optimize the global search ability of the algorithm. The improvement process is as follows:

[0016]

[0017] A=2ar1-a (2)

[0018] C=2r2 (3)

[0019] Among them, r1 and r2 are random numbers in the range of [0,1], Iter represents the current number of iterations, and Max_Iter represents the maximum number of iterations;

[0020] Step 2: Calculate the individual fitness values ​​of the wolf pack based on the gray wolf population, and determine the positions and fitness values ​​of the three alpha wolves;

[0021] Step 3: Update the current gray wolf position based on the positions of the three alpha wolves and the historical best position of the gray wolf:

[0022]

[0023] Among them, X i (Iter+1) represents the position of the i-th gray wolf in the Iter+1-th iteration, X k and w k Respectively represent the kth wolf and its weight, represents the historical optimal position of the i-th gray wolf, c1 and c2 represent the group update coefficient and the individual update coefficient, b1 and b2 represent random numbers in the interval [0,1];

[0024] Step 4: Update parameter a based on formula (1), update A based on parameter a, and calculate the fitness of all gray wolves in the population.

[0025] Updated the fitness and positions of the three alpha wolves;

[0026] Step 5: Determine whether the maximum number of iterations has been reached. If not, repeat Step 3 and Step 4. If it has been reached, use the position parameters of the first wolf as the parameters of the BP neural network to construct the IGWO-BP model.

[0027] Furthermore, in step S3, the IGWO-BP model is trained on the training set to further obtain a training residual sequence, and the trained IGWO-BP model is used to predict the test set; specifically, the network structure, initial weights and thresholds of the BP model are initialized using the optimal grey wolf position parameters to obtain the IGWO-BP model, and then the model is trained using the training set, and the real sequence of the training set and the predicted sequence of the model training process are subtracted to obtain the model training residual sequence, and then the test set is input into the trained IGWO-BP model to obtain the test set prediction result.

[0028] The IGWO-BP model consists of three parts: input layer, hidden layer and output layer. Its propagation is learned by gradient descent method, and there are two processes: forward propagation and backward propagation. The forward propagation process is: the input signal is input from the input layer, through the hidden layer to the output layer, and if the output result reaches the expected result, it is directly output; if the expected result is not achieved or does not match the preset error value, the error is back-propagated, and the weight and threshold of the neural network are continuously adjusted until the expected value is reached or less than the set error, and the required prediction value is output. The forward propagation process of the IGWO-BP model is expressed based on formula (5):

[0029] z t =f(ω t x t +b t ) (5)

[0030] Among them, x t represents the neuron input, ω t represents the neuron connection weight, b t represents the bias term, z t represents the neural output, f(x) is the activation function;

[0031] After forward propagation, the IGWO-BP model obtains the output value, and the model error is calculated based on the output value and the actual label value. The weight is updated based on the error feedback of the gradient descent algorithm, and the update iteration is continued until the expected value is reached or less than the set error. The weight update process of the gradient descent algorithm is shown in formula (6):

[0032]

[0033] Among them, w iis the initial weight, w′ i is the updated weight, α is the learning rate, J(w i ) is the weight coefficient w i function.

[0034] In step S3, the trained IGWO-BP model is used to predict the test set. The specific process is to obtain the optimal weight and threshold of the model based on the continuous iteration of forward propagation and back propagation of the IGWO-BP model, and the model training is completed; then the test set is input into the trained IGWO-BP model to obtain the test set prediction result.

[0035] Furthermore, in step S4, the model parameters are determined based on the inspection of the stationarity, autocorrelation and partial correlation of the training residual sequence, and an ARIMA (p, d, q) model is constructed. The training residuals are predicted based on the model. Specifically, the ARIMA (p, d, q) model is composed of an autoregressive model, referred to as an AR model, a moving average model, referred to as an MA model, and a difference operation, wherein the expression of the AR model is:

[0036]

[0037] In the formula, y t is the sample value at time t, is the autoregressive coefficient, p is the autoregressive order; ε t is a white noise sequence that obeys an independent normal distribution;

[0038] The expression of the MA model is:

[0039] y t =μ+θ1ε t-1 +θ2ε t-2 +…+θ q ε t-q +ε t (8)

[0040] In the formula, θ i (i=1,2,..,q) is the sliding average coefficient, q is the sliding average order; μ is a constant, ε t is a white noise sequence that obeys an independent normal distribution;

[0041] The expression of the ARIMA (p, d, q) model is:

[0042]

[0043] Where μ is a constant; δ t is the error term between the observed term and its fitted value.

[0044] Furthermore, in step S5, the prediction result of the IGWO-BP model in step S3 and the prediction result of the residual sequence of the ARIMA model in step S4 are connected in series to complete the error correction of the prediction result, and the final combined prediction result is obtained, which is specifically as follows: based on the preprocessed data in step S2, the training set is used to optimize the IGWO-BP model structure and initial parameters, and the model is trained to obtain a training residual sequence, which is recorded as E; the test set is input into the IGWO-BP model to obtain the settlement prediction result on the test set, which is recorded as y j ; Determine the difference order d by testing the stationarity of the training residual sequence E, and determine the autoregressive order p and the sliding average order q by using the autocorrelation coefficient and partial autocorrelation coefficient, so as to construct the residual prediction model ARIMA (p, d, q). Based on the ARIMA (p, d, q) model, predict the residual sequence E, and the prediction result is recorded as e j ; Finally, the two-stage prediction results are fused in series, that is, the combined prediction result is Y j :

[0045] Y j =y j +e j (10)

[0046] The difference order d is determined by testing the stationarity of the training residual sequence E. The specific method is:

[0047] 1) Use the ADF unit root test method to perform a stationary analysis on the residual sequence E. If the residual sequence E is a stationary sequence, proceed directly to the next step of analysis, and the difference order d = 0; if the residual sequence is an unstationary sequence, perform d differences on the sequence until the sequence becomes a stationary sequence; Formula (11) represents the sequence stationary inspection process:

[0048] y t =by t-1 +a+ε t (11)

[0049] In formula (11), y t-1 is the previous item, y t is the lag term, a is the convergence factor, which is used as a constant term here, ε t is a white noise sequence that obeys an independent normal distribution and is used as the error term here. Formula (11) shows that when the lag term coefficient is 1, it indicates an unsteady time series. Otherwise, it is transformed into a stationary series.

[0050] 2) Calculate the autocorrelation function (ACF) and partial autocorrelation function (PACF) to test white noise. If the autocorrelation coefficient and partial autocorrelation coefficient fluctuate within the confidence interval, it means that the residual sequence is a white noise sequence; if the autocorrelation coefficient and partial autocorrelation coefficient exceed the confidence interval, it means that it is not a white noise sequence. Use the autocorrelation coefficient function (ACF) and partial autocorrelation coefficient function (PACF) to determine the value range of the autoregressive order p and the sliding average order q.

[0051] 3) Use the AIC Akaike criterion to best estimate the values ​​of p and q parameters, calculate the AIC value of the ARIMA model, and thus obtain the optimal ARIMA model;

[0052] AIC=2K-2ln(L)(12)

[0053] In formula (12), K is the number of parameters, representing the complexity of the model, and L is the likelihood function, representing the fitting error. The smaller the AIC coefficient value, the closer it is to the true value of the model order.

[0054] 4) Based on steps 1)-3), the residual sequence E is checked to construct an ARIMA (p, d, q) model for residual prediction and obtain the residual sequence prediction result e j .

[0055] Furthermore, the mean absolute error, mean absolute percentage error, mean square error and root mean square error are used for evaluation. The smaller the following evaluation index is, the higher the prediction accuracy of the model is:

[0056] (1) Mean Absolute Error:

[0057]

[0058] (2) Mean Absolute Percentage Error:

[0059]

[0060] (3) Mean Squared Error:

[0061]

[0062] (4) Root Mean Squared Error:

[0063]

[0064] In the formula, represents the observed value, Represents the predicted value.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] 1. The present invention deeply analyzes the variation law of railway subgrade settlement in seasonal frozen soil areas; uses an improved gray wolf optimization algorithm to optimize the BP neural network structure and parameters, further constructs an IGWO-BP model for predicting settlement data with nonlinear variation characteristics; and constructs an ARIMA model for predicting residual data with nonlinear variation characteristics.

[0067] 2. Different from other variable weight combination models ( Figure 5 The combined model proposed in this patent is a secondary correction of the prediction error. The trained IGWO-BP model is used to complete the first-stage result prediction; the model ARIMA (p, d, q) parameters are determined by checking the stationarity, autocorrelation and partial correlation of the residual sequence, and the second-stage residual prediction is completed based on the model; the two-stage prediction results are connected in series to achieve the effect of error correction.

[0068] 3. The constructed combined prediction model is based on the nonlinear characteristics of roadbed settlement changes in seasonal frozen soil areas and the linear characteristics of neural network residual changes. The model is modeled from the essence of data changes. Compared with other deep learning models, this model has strong interpretability and scalability, and can provide reference for solving similar problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Flow chart of combined prediction method of roadbed settlement residual based on IGWO-BP and ARIMA;

[0070] Figure 2 Measured data of settlement changes in a maintenance section in Xinjiang;

[0071] Figure 3 ARIMA single model prediction results;

[0072] Figure 4 BP neural network single model prediction results;

[0073] Figure 5 IGWO-BP and ARIMA optimal weight combination forecast results;

[0074] Figure 6 IGWO-BP and ARIMA neural network residual optimization combined prediction results;

[0075] Figure 7 Comparison of relative errors of four models. DETAILED DESCRIPTION

[0076] The present invention proposes a combined prediction method for roadbed settlement residuals based on IGWO-BP and ARIMA. In order to make the purpose, technical scheme 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 As shown. The verification process of the present invention is implemented by programming in MATLAB R2021b on a laptop computer with Intel Core i7-8750H@2.20GHz six-core, 32G memory, and Windows10 (64-bit). The present invention analyzes the variation characteristics of roadbed settlement data in seasonal frozen soil areas and concludes that the seasonal frozen soil area settlement data composition includes both short-term linear characteristics and long-term nonlinear variation characteristics. A single prediction model cannot meet the prediction accuracy requirements; Figure 1 As shown in the figure, the changes in the observed values ​​of roadbed settlement at eight observation points along the railway in a seasonal frozen soil area of ​​a certain maintenance section in Xinjiang. Figure 1 It can be seen that the frost damage in seasonal frozen soil areas has a trend and seasonality, and the data shows linear and nonlinear changes. The traditional prediction model cannot capture the trend of frost damage changes and cannot deeply explore the characteristics of frost damage. The changes in actual roadbed settlement data meet specific change trends. In short-term predictions, there are both linear changes and nonlinear changes. The experimental data was collected using a real-time monitoring system for railway roadbed frost damage in a seasonal frozen soil area of ​​a certain engineering section in Xinjiang. The process is as follows:

[0077] Step 1: Taking the subgrade settlement of part of the Lanxin Line of China Railway Urumqi Bureau Group Co., Ltd. as an example, the present invention uses subgrade monitoring equipment to obtain a total of 360 periods of settlement data from September 2022 to October 2023. The time interval of each period of settlement data is 1 day. The first 80% of the data is used as the training set, and the last 20% of the data is used as the test set. The settlement data sequence is as follows Figure 2 As shown in the figure, it can be found that frost damage in cold areas has trend and seasonality, and the data shows linear and nonlinear changes. The traditional prediction model (single model prediction method) cannot capture the trend of frost damage changes and cannot deeply explore the characteristics of frost damage. The IGWO-BP and ARIMA combined model integrates the advantages of the ARIMA model and the IGWO-BP model, and can achieve higher prediction accuracy when dealing with numerical prediction problems of seasonal and nonlinear changes.

[0078] Step 2: The gray wolf optimization algorithm is a meta-inspiration algorithm that simulates the hunting process of gray wolf populations. The algorithm has good global search capabilities and local optimization capabilities. During the evolution of the gray wolf population, a group with three alpha wolves as the core will be formed. The hunting process of the gray wolf is completed under the guidance of the three alpha wolves. This patent uses the improved gray wolf optimization algorithm (IGWO) to optimize the structure, initial weights and thresholds of the BP neural network to construct the IGWO-BP model; the specific process is as follows:

[0079] Step 1: Use Logistic chaotic mapping to generate chaotic sequences to initialize the population. The population size is set to 30 and the maximum number of iterations is set to 100. First, the convergence factor a is improved to make it nonlinear, and the global search capability of the algorithm is further optimized. The parameters a, A and C are initialized based on formula (1). The improvement process is as follows:

[0080]

[0081] A=2ar1-a (2)

[0082] C=2r2 (3)

[0083] Among them, r1 and r2 are random numbers in the range of [0,1], Iter represents the current number of iterations, and Max_Iter represents the maximum number of iterations;

[0084] Step 2: Calculate the individual fitness values ​​of the wolf pack based on the gray wolf population, and determine the positions and fitness values ​​of the three alpha wolves;

[0085] Step 3: Update the current gray wolf position based on the positions of the three alpha wolves and the historical best position of the gray wolf in formula (30):

[0086]

[0087] In formula (4), the parameters c1=0.6, c2=0.4, w k Calculated by the following formula:

[0088]

[0089] Step 4: Update parameter a based on formula (1), update A and C based on parameter a, calculate the fitness of all gray wolves in the population, and update the fitness and position of the three alpha wolves;

[0090] Step 5: Determine whether the maximum number of iterations has been reached. If not, repeat Step 3 and Step 4. If it has been reached, use the position parameters of the first wolf as the parameters of the BP neural network to construct the IGWO-BP model.

[0091] Step 3: Use the optimal gray wolf position parameters to initialize the network structure, initial weights and thresholds of the BP model to obtain the IGWO-BP model. Then use the training set to train the model. Difference the real sequence of the training set and the predicted sequence of the model training process to obtain the model training residual sequence. Then input the test set into the trained IGWO-BP model to obtain the test set prediction result. The model uses 5 input nodes and one output node during the training process. The number of hidden layers and nodes is obtained by the improved gray wolf optimization algorithm. The number of hidden layers is 3 and the number of nodes is 10-20-10 respectively. During initialization, the number of training times is set to 1000, the learning rate is set to 0.01, and the minimum error of the training target is set to 1E-5.

[0092] Step 4: Using the ADF unit root test method, it can be seen that this time series is an unsteady time series. After a series of processing, the optimal parameters of the ARIMA model are ARIMA (3, 1, 1), and this model is used to predict the railway subgrade settlement data for the next 72 days. In order to verify the predictive performance and prediction accuracy of the combined prediction method proposed in this patent, the BP, ARIMA models, the IGWO-BP and ARIMA optimal weight combination prediction method, and the IGWO-BP and ARIMA network residual optimization combination prediction method are used to predict and analyze the subgrade settlement data series. The result curves of the four prediction methods are shown in the figure below. Figures 3 to 7 shown.

[0093] Step 5: Single forecasting model experiment based on ARIMA forecasting method. Figure 3 is the forecast result of a single forecast model based on the ARIMA forecasting method. Figure 3 It can be seen that the change trend of the predicted value of roadbed settlement based on the ARIMA prediction method is consistent with the change trend of the actual value on the whole, but the predicted value deviates from the true value, the error is large, and the maximum error value exceeds 1mm, which seriously interferes with the actual production work arrangement of the maintenance section personnel.

[0094] Step 6: Single prediction model experiment based on BP neural network prediction method. Figure 4 is the prediction result of a single prediction model based on the BP neural network prediction method. Figure 4 It can be seen that the predicted value based on the BP neural network is quite different from the actual settlement value, especially near the inflection point where the deviation from the actual value is the largest. The error value is almost 1mm, causing great trouble to the construction.

[0095] Step 7: Experiment on the forecasting method based on the optimal weight combination of IGWO-BP and ARIMA. Figure 5This is the prediction result based on the IGWO-BP and ARIMA optimal weight combination prediction method. Compared with the single BP neural network prediction method and the ARIMA prediction method, it is closer to the actual value of railway subgrade settlement, and the accuracy and precision of the prediction have been improved. However, there is a certain degree of fluctuation between the predicted value and the actual value, and there is still a large error at the inflection point. In particular, the predicted trend at some points is completely opposite to the actual trend.

[0096] Step 8: Experiment on network residual optimization combined prediction method based on IGWO-BP and ARIMA. Figure 6 It is a network residual optimization combined prediction method based on IGWO-BP and ARIMA. As can be seen from the figure, this method can well predict the changes in railway subgrade settlement and achieve good prediction results. Compared with other models, the prediction error at the inflection point is significantly reduced. The prediction accuracy is the highest in the short and medium term, and only in the long term does the prediction accuracy decline.

[0097] Step 9: Relative error comparison experiment of four models. Figure 7 This is a comparison chart of the relative errors of the prediction values ​​of the four models. Figure 7 It can be seen that the prediction result based on the ARIMA prediction method has the largest error and the least ideal prediction result. Compared with the BP and ARIMA single prediction models, the error of the combined prediction model has been reduced, and the prediction result is significantly better than the single prediction model; in the combined prediction model, compared with the optimal weighted combined prediction method based on IGWO-BP and ARIMA, the network residual combined prediction method based on IGWO-BP and ARIMA has the smallest error, and the relative error always fluctuates within the range of 0.4 mm, indicating that this method can well predict the change law of railway subgrade settlement.

[0098] Table 1 shows the statistical results of the four prediction methods. The MAE, MAPE, MSE and RMSE of the network residual combination model prediction method based on IGWO-BP and ARIMA are 0.097, 6.62%, 0.017 and 0.132 respectively. Compared with the single model based on ARIMA prediction method, MAE, MAPE, MSE and RMSE are reduced by 78.8%, 78.4%, 94.7% and 76.9% respectively; compared with the single model based on BP neural network prediction method, MAE, MAPE, MSE and RMSE are reduced by 65.4%, 57.7%, 83.1% and 58.6% respectively. Under the same conditions, compared with the optimal weight combination prediction method based on ARIMA-BP neural network, the evaluation indicators MAE, MAPE, MSE and RMSE are reduced by 48.1%, 41.1%, 78.5% and 45.9% respectively.

[0099] Table 1 Comparison of the results of four models

[0100]

[0101] Through statistical data comparison, among the four prediction models, the prediction results are: in the field of roadbed settlement prediction, the network residual combination prediction method based on IGWO-BP and ARIMA is better than the network weight combination prediction method based on IGWO-BP and ARIMA, the network weight combination prediction method based on IGWO-BP and ARIMA is better than the single model of BP neural network, and the single model of BP neural network is better than the single model of ARIMA.

Claims

1. The roadbed settlement prediction method based on IGWO-BP and ARIMA is characterized by: It includes the following steps: S1. Extracting the roadbed settlement observation values ​​from the observation points in the seasonal frozen soil area, and obtaining the seasonal frozen soil area settlement data as the original monitoring data; S2, preprocessing the original monitoring data obtained in step S1, and dividing the data into a training set and a test set, and optimizing the structure, initial weight and threshold of the BP neural network using an improved grey wolf optimization algorithm (abbreviated as IGWO) based on the training set to construct an IGWO-BP model; S3, train the IGWO-BP model on the training set to further obtain the training residual sequence, and use the trained IGWO-BP model to predict the test set; S4, based on the inspection of the stationarity, autocorrelation and partial correlation of the training residual sequence obtained in step S3, determine the model ARIMA (p, d, q), and predict the training residual sequence based on the model; S5. Construct a combined prediction model of IGWO-BP and ARIMA: connect the prediction result of the IGWO-BP model in step S3 and the prediction result of the ARIMA (p, d, q) model on the training residual sequence in series, complete the error correction of the prediction result, and obtain the final combined prediction result.

2. The roadbed settlement residual combined prediction method based on IGWO-BP and ARIMA according to claim 1 is characterized in that: The method also includes applying the IGWO-BP and ARIMA combined prediction model constructed in step S5 to the roadbed maintenance section in the seasonal frozen soil area for actual verification, and using the mean absolute error, mean absolute percentage error, mean square error and root mean square error indicators for evaluation.

3. The roadbed settlement residual combined prediction method based on IGWO-BP and ARIMA according to claim 1 is characterized in that: In step S2, the original monitoring data is preprocessed. Specifically, the missing values ​​and abnormal values ​​in the collected samples are replaced by the adjacent values ​​in the sequence, and the original noisy data is further denoised by wavelet packet decomposition. Then, the denoised data is interpolated by cubic spline interpolation. Finally, the preprocessed data set is divided into a training set and a test set in a ratio of 8:2 to complete the data preprocessing.

4. The roadbed settlement residual combined prediction method based on IGWO-BP and ARIMA according to claim 1 is characterized in that: In step S2, based on the training set, the improved grey wolf optimization algorithm (IGWO for short) is used to optimize the structure, initial weights and thresholds of the BP neural network to construct the IGWO-BP model; the specific optimization process is: the position parameters of the grey wolf are set as the structural parameters, initial weights and initial thresholds of the BP neural network, and the optimized fitness function is to minimize the mean square error of the BP prediction result. The construction process of the IGWO-BP model is as follows: Step 1: Use Logistic chaotic mapping to generate chaotic sequence to initialize the population, initialize the convergence factor a, coefficient vectors A and C, first improve the convergence factor a to make it nonlinear, and further optimize the global search ability of the algorithm. The improvement process is as follows: A=2ar1-a (2) C＝2r2 (3) Among them, r1 and r2 are random numbers in the range of [0,1], Iter represents the current number of iterations, and Max_Iter represents the maximum number of iterations; Step 2: Calculate the individual fitness values ​​of the wolf pack based on the gray wolf population, and determine the positions and fitness values ​​of the three alpha wolves; Step 3: Update the current gray wolf position based on the positions of the three alpha wolves and the historical best position of the gray wolf: Among them, X i (Iter+1) represents the position of the i-th gray wolf in the Iter+1-th iteration, X k and w k Respectively represent the kth wolf and its weight, represents the historical optimal position of the i-th gray wolf, c1 and c2 represent the group update coefficient and the individual update coefficient, b1 and b2 represent random numbers in the interval [0,1]; Step 4: Update parameter a based on formula (1), update A based on parameter a, calculate the fitness of all gray wolves in the population, and update the fitness and position of the three alpha wolves; Step 5: Determine whether the maximum number of iterations has been reached. If not, repeat Step 3 and Step 4. If it has been reached, use the position parameters of the first wolf as the parameters of the BP neural network to construct the IGWO-BP model.

5. The roadbed settlement residual combined prediction method based on IGWO-BP and ARIMA according to claim 1 is characterized in that: In step S3, the IGWO-BP model is trained on the training set to further obtain the training residual sequence. Specifically, the network structure, initial weight and threshold of the BP model are initialized using the optimal gray wolf position parameters to obtain the IGWO-BP model. Then, the model is trained using the training set, and the real sequence of the training set and the predicted sequence of the model training process are subtracted to obtain the model training residual sequence. Then, the test set is input into the trained IGWO-BP model to obtain the test set prediction result. Specifically: The IGWO-BP model consists of three parts: input layer, hidden layer and output layer; Its propagation is learned by gradient descent method, and there are two processes: forward propagation and back propagation. The forward propagation process is: the input signal is input from the input layer, through the hidden layer to the output layer, if the output result reaches the expected result, it is directly output; if the expected result is not achieved or does not match the preset error value, the error is back propagated, and the weights and thresholds of the neural network are continuously adjusted until the expected value is reached or less than the set error, and the required prediction value is output. The forward propagation process of the IGWO-BP model is expressed based on formula (5): z t =f(ω t x t +b t ) (5) Among them, x t represents the neuron input, ω t represents the neuron connection weight, b t represents the bias term, z t represents the neural output, and f(x) is the activation function; After forward propagation, the IGWO-BP model obtains the output value, and the model error is calculated based on the output value and the actual label value. The weight is updated based on the error feedback of the gradient descent algorithm, and the update iteration is continued until the expected value is reached or less than the set error. The weight update process of the gradient descent algorithm is shown in formula (6): Among them, w i is the initial weight, w i ′ is the updated weight, α is the learning rate, J(w i ) is the weight coefficient w i Function of In step S3, the trained IGWO-BP model is used to predict the test set. The specific process is to obtain the optimal weight and threshold of the model based on the continuous iteration of forward propagation and back propagation of the IGWO-BP model, and the model training is completed; then the test set is input into the trained IGWO-BP model to obtain the test set prediction result.

6. The method for combined prediction of roadbed settlement residuals based on IGWO-BP and ARIMA according to claim 1, characterized in that: In step S4, the model parameters are determined based on the inspection of the stationarity, autocorrelation and partial correlation of the training residual sequence, and an ARIMA (p, d, q) model is constructed. The training residuals are predicted based on the model. Specifically, the ARIMA (p, d, q) model is composed of an autoregressive model, referred to as an AR model, a moving average model, referred to as an MA model, and a difference operation, wherein the expression of the AR model is: In the formula, y t is the sample value at time t, is the autoregressive coefficient, p is the autoregressive order; ε t is a white noise sequence that obeys an independent normal distribution; The expression of the MA model is: In the formula, θ i (i=1,2,..,q) is the sliding average coefficient, q is the sliding average order; μ is a constant, ε t is a white noise sequence that obeys an independent normal distribution; The expression of the ARIMA (p, d, q) model is: Where μ is a constant; δ t is the error term between the observed term and its fitted value.

7. The roadbed settlement residual combined prediction method based on IGWO-BP and ARIMA according to claim 1 is characterized in that: In step S5, the prediction result of the IGWO-BP model in step S3 and the prediction result of the residual sequence of the ARIMA model in step S4 are connected in series to complete the error correction of the prediction result, and the final combined prediction result is obtained, which is specifically as follows: based on the preprocessed data in step S2, the training set is used to optimize the IGWO-BP model structure and initial parameters, and the model is trained to obtain a training residual sequence, which is recorded as e; the test set is input into the IGWO-BP model to obtain the settlement prediction result on the test set, which is recorded as y j ; Determine the difference order d by testing the stationarity of the training residual sequence E, and determine the autoregressive order p and the sliding average order q by using the autocorrelation coefficient and partial autocorrelation coefficient, so as to construct the residual prediction model ARIMA (p, d, q). Based on the ARIMA (p, d, q) model, predict the residual sequence E, and the prediction result is recorded as e j ; Finally, the two-stage prediction results are fused in series, that is, the combined prediction result is Y j : AND j =and j +e j (10)。 8. The combined prediction method for roadbed settlement residuals based on IGWO-BP and ARIMA according to claim 7 is characterized in that: The difference order d is determined by testing the stationarity of the training residual sequence E. The specific method is: 1) Use the ADF unit root test method to perform a stationary analysis on the residual sequence E. If the residual sequence E is a stationary sequence, proceed directly to the next step of analysis, and the difference order d = 0; if the residual sequence is an unstationary sequence, perform d differences on the sequence until the sequence becomes a stationary sequence; Formula (11) represents the sequence stationary inspection process: and t = b and t-1 +a+ε t (11) In formula (11), y t-1 is the previous item, y t is the lag term, a is the convergence factor, which is used as a constant term here, ε t is a white noise sequence that obeys an independent normal distribution, which is used as the error term here. Formula (11) shows that when the lag term coefficient is 1, it indicates an unsteady time series, otherwise, it is transformed into a stationary series; 2) Calculate the autocorrelation function graph and partial autocorrelation function graph to test white noise. If the autocorrelation coefficient and partial autocorrelation coefficient fluctuate within the confidence interval, it means that the residual sequence is a white noise sequence; if there are autocorrelation coefficients and partial autocorrelation coefficients that exceed the confidence interval, it means that it is not a white noise sequence. Use the autocorrelation coefficient function and partial autocorrelation coefficient function to determine the value range of the autoregressive order p and the sliding average order q. 3) Use the AIC Akaike criterion to best estimate the values ​​of p and q parameters, calculate the AIC value of the ARIMA model, and thus obtain the optimal ARIMA model; AIC=2K-2ln(L) (12) In formula (12), K is the number of parameters, representing the complexity of the model, and L is the likelihood function, representing the fitting error. The smaller the AIC coefficient value is, the closer it is to the true value of the model order; 4) Based on steps 1)-3), the residual sequence E is checked to construct an ARIMA (p, d, q) model for residual prediction and obtain the residual sequence prediction result e j .

9. The roadbed settlement residual combined prediction method based on IGWO-BP and ARIMA according to claim 1, characterized in that: The mean absolute error, mean absolute percentage error, mean square error and root mean square error are used for evaluation. The smaller the following evaluation indicators are, the higher the prediction accuracy of the model is: (1) Mean Absolute Error: (2) Mean Absolute Percentage Error: (3) Mean Squared Error: (4) Root Mean Squared Error: In the formula, represents the observed value, Represents the predicted value.

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