Mountainous area slope displacement prediction method based on mi-gra and improved pso-lstm

Abstract

Disclosed in the present invention is a mountainous area slope displacement prediction method based on MI-GRA and an improved PSO-LSTM. The method comprises the following steps: (1) collecting and constructing original data for slope displacement prediction; (2) on the basis of the constructed original data for slope displacement prediction, establishing an MI-GRA-based slope displacement feature selection model; (3) using data subjected to feature selection as an optimal feature set input for slope displacement prediction, and establishing an improved-PSO-LSTM-based slope displacement prediction model; and (4) performing model prediction and testing on the established slope prediction model. The present method solves the problems of: a previous prediction algorithm itself having a static characteristic and being unable to consider historical information of slope displacement, thereby restricting the improvement of the prediction precision; previous slope displacement prediction only focusing on the displacement itself and being unable to bring a displacement influence factor into a prediction model, resulting in a poor prediction effect; etc.

Description

A slope displacement prediction method in mountainous areas based on MI-GRA and improved PSO-LSTM Technical Field

[0001] The present invention relates to the technical field of slope displacement prediction, and in particular to a method for predicting slope displacement in mountainous areas based on MI-GRA and improved PSO-LSTM. Background Art

[0002] my country's vast mountainous areas are subject to external factors such as earthquakes, rainfall, and floods, leading to frequent slope disasters such as landslides, collapses, and debris flows. Slope displacement is a direct indicator of slope deformation. Understanding the patterns of slope displacement in mountainous areas is crucial for predicting slope damage and assessing slope stability.

[0003] In recent years, with the development of information technology, an increasing number of artificial intelligence prediction methods have been applied to slope displacement prediction, such as SVR, BP, and Elman algorithms. However, these prediction algorithms are inherently static and fail to take into account historical information about slope displacement, which limits the improvement of prediction accuracy.

[0004] Summary of the Invention

[0005] The main purpose of the present invention is to provide a mountain slope displacement prediction method based on MI-GRA and improved PSO-LSTM to solve the technical problem that the existing prediction method cannot take into account the historical information of slope displacement, which restricts the improvement of prediction accuracy.

[0006] The present invention provides a slope displacement prediction method in mountainous area based on MI-GRA and improved PSO-LSTM, comprising the following steps: (1) collecting and constructing original data for slope displacement prediction; (2) establishing a slope displacement feature selection model of MI-GRA based on the constructed original data for slope displacement prediction; (3) using the data after feature selection as the optimal feature set input for slope displacement prediction, and establishing an improved PSO-LSTM slope displacement prediction model; and (4) performing model prediction and testing on the established slope prediction model.

[0007] Furthermore, step (1) includes: collecting multi-source monitoring data of the slope; interpolating missing data after obtaining the original data of the slope monitoring; and classifying the original data into displacement data and data of potential factors affecting displacement.

[0008] Furthermore, the missing data were interpolated using the median interpolation method, and the formula is as follows;

[0009] In this formula, x cb is the data after missing value interpolation, x t-1is the data of the previous moment of the point to be interpolated, x t+1 The data of the next moment after the point to be interpolated.

[0010] Furthermore, step (2) includes: based on the displacement data, using the MI algorithm to select the best historical displacement features; based on the displacement and displacement potential influencing factor data, using the GRA algorithm to select the displacement influencing factor features; and combining the best historical displacement features and displacement influencing factor features to obtain the optimal feature set.

[0011] Furthermore, the method of selecting the best historical displacement feature by using the MI algorithm includes the following steps:

[0012] The displacement data is normalized using the following formula: x scaled =x std *(max-min)+min

[0013] In this formula, x is the displacement data to be normalized, xmin (axis = 0) is the row vector composed of the minimum value in each column of data, xmax (axis = 0) is the row vector composed of the maximum value in each column of data, max is the maximum value of the interval to be mapped, the default is 1, min is the minimum value of the interval to be mapped, the default is 0, x std is the standardized result, x scaled is the normalized result;

[0014] Construct the feature matrix S for each forecast day input and output sequence S output , feature matrix S input and output sequence S output The formula is as follows: S output =[S(t+1)1 … S(t+1) n ] T

[0015] In this formula, S input is a feature matrix, which is composed of various historical displacement features. n is 30, which means that the number of historical displacement features is 30. k (k=1,2…30) corresponds to the kth historical displacement feature, S output is the output sequence, consisting of predicted displacement data;

[0016] Calculate the mutual information evaluation index I(S k ;S output );

[0017] Sorting and optimization of historical displacement features.

[0018] Furthermore, calculating the mutual information evaluation index includes the following steps:

[0019] Calculate information entropy: H(F k )=-p(S k (i))log2∫p(S k (i))dS k (i) H(S output )=-∫p(S(t+1) j )log2 p(S(t+1) j )dS(t+1) j H(F k ,S output )=-∫∫p join (S k (i),S(t+1) j )log2 p joint (S k (i),S(t+1) j )dS k (i)dS(t+1) j

[0020] In this formula, H(F k ) and H(S output ) are the information entropy of the historical displacement feature sequence and the output sequence, respectively, which are used to measure their respective information contents; H(F k ,S output ) is the two-dimensional joint entropy of the historical displacement feature sequence and the output sequence, which is used to quantify the size of the shared information between variables, p is the marginal probability distribution of a single variable, and p joint is the joint probability distribution between two variables;

[0021] Calculate mutual information I(S k ;S output ):

[0022] In this formula, I(F k ;S output ) is the mutual information between the historical displacement feature sequence and the output sequence.

[0023] Furthermore, optimizing the characteristics of displacement influencing factors using the GRA algorithm includes the following steps:

[0024] Determine the slope displacement characteristics and select the analysis series:

[0025] After averaging the displacement data and influencing factor data, the displacement data is set as the parent sequence Y0, and the displacement influencing factor data is set as the comparison sequence X, which can be expressed as: Y0 = [y0(1), y0(2), ..., y0(n)]

[0026] In this formula, n is the number of days, and m is the number of influencing factors of slope displacement;

[0027] Calculate the correlation coefficient:

[0028] In this formula, Δx=y0(j)-X i (j), ρ is the resolution coefficient, which is generally 0.1 to 1.0, and is taken as 0.5 in this paper;

[0029] Calculate the correlation:

[0030] In this formula, γ is the correlation degree. Generally, when it is greater than 0.6, it is considered that the correlation between the sequences is strong. i = 1, 2, ..., m; j = 1, 2, ..., n;

[0031] Ranking of characteristics of factors affecting displacement and determination of main factors affecting displacement.

[0032] Furthermore, the improved PSO-LSTM slope displacement prediction model established in step (3) includes the following steps: a. obtaining the time series data of the mountain slope displacement and the main influencing factors of the displacement and performing normalization processing on them, wherein the normalization processing is consistent with the processing in the MI feature selection and the formula adopted is consistent; b. dividing the data set into a training set, a validation set and a test set, and inputting the training set and the validation set into the LSTM network model; c. preliminarily setting the parameters in the improved PSO algorithm and randomly initializing the hyperparameters to be optimized in the LSTM model; d. calculating the particle fitness (fit); e. updating the individual optimal and group optimality f. Update learning factors c1 and c2, inertia factor w; g. Determine whether the number of iterations is greater than m max If the conditions are met, the improved PSO algorithm optimization ends, otherwise go to step 3 and repeat steps d, e, and f until the judgment conditions are met; h. Perform iterative training of the model based on the optimal network model configuration and save the model.

[0033] Furthermore, the LSTM network model is a deep learning model, and a forward calculation of the LSTM network model cycle unit is: i t =σ(W i ·[h t-1 ,x t ]+b i ) f t =σ(W f ·[h t-1 ,x t ]+b f )

[0034] In this formula, i t is the input gate, f t is the forget gate, σ is the sigmoid activation function, which can make the threshold range between 0 and 1, x t is the input feature at the current moment, h t-1 Represents the hidden state of the previous moment, W i and W f are the weight matrices to be trained for the input gate and forget gate, respectively, b i and b f are the bias items to be trained for the input gate and forget gate respectively;

[0035] The candidate state represents the new knowledge to be stored in the cell state, which is a function of the input features at the current moment and the hidden state at the previous moment. The cell state represents the long-term memory, which is equal to the sum of the value of the long-term memory at the previous moment passing through the forget gate and the value of the new knowledge summarized at the current moment passing through the input gate. The specific calculation process can be expressed as:

[0036] In this formula, is the candidate state, tanh is the activation function, W C is the weight matrix to be trained, b C is the bias term to be trained, C t is the cell state at the current moment, C t-1 is the cell state at the previous moment;

[0037] The output gate selectively outputs the information in the cell state, and the hidden state can be obtained from the current cell state through the output gate. The specific calculation process can be expressed as: t =σ(W o ·[h t-1 ,x t ]+b o ) h t =o t *tanh(C t )

[0038] In this formula, o t is the output gate, W o and b o are the weight matrix and bias term to be trained of the output gate, h t is the hidden state at the current moment;

[0039] The improved PSO algorithm is an optimization algorithm of the traditional PSO algorithm, including:

[0040] Improve the learning factor. The improved formula of the improved learning factor is as follows:

[0041] In this formula, m cur is the current iteration number, m max is the maximum number of iterations, c 1b 、c 1e 、c 2b and c 2e They are the initial and final values ​​of c1 and c2 respectively, usually c 1b =2.5, c 1e =0.5, c 2b =0.5 and c 2e =2.5, the algorithm works better.

[0042] Improved inertia factor

[0043] The larger the inertia factor w, the faster the particle flies, and the particle will perform a global search with a longer step size. The smaller the inertia factor w, the more precise the local search. The improved formula is as follows.

[0044] In this formula, ω max Indicates the maximum value of ω, ω min represents the minimum value of ω, F represents the current objective function value, and F avg Represents the current average objective function value, F min represents the minimum value of the objective function;

[0045] The objective function uses the mean absolute error (MAE) on the validation set as the objective function, and its formula is as follows:

[0046] In this formula, N represents the number of prediction samples, y(y1,y2,…,y N ) is the measured slope displacement value in the validation set, is the predicted slope displacement value on the validation set.

[0047] Furthermore, the step (4) performs model prediction and testing on the established slope prediction model, including the following steps: calling the prediction model, wherein the called prediction model is the improved PSO-LSTM slope displacement prediction model that has been saved after training; inputting the test set and performing prediction testing, wherein the prediction testing method is rolling prediction; obtaining the prediction results and evaluating the model prediction accuracy;

[0048] The model accuracy was evaluated using the goodness of fit R 2 And the mean absolute percentage error MAPE, whose formula is as follows:

[0049]

[0050] In this formula, R 2is the goodness of fit, the larger its value, the higher the model accuracy, MAPE is the mean absolute percentage error, the smaller its value, the smaller the prediction error, N is the number of prediction samples, y t is the measured displacement value in the test set, is the predicted displacement value on the test set, is the average of the measured values.

[0051] The present invention provides a method for predicting mountain slope displacement based on MI-GRA and improved PSO-LSTM. The conception is as follows: the change of slope displacement is a dynamic process, and the long short-term memory network (LSTM) has the function of memorizing historical information and has great advantages in processing long time series (Sequence) data. In view of this, it is theoretically feasible to apply the LSTM deep learning algorithm to the prediction of mountain slope displacement. In the past, the focus of slope displacement prediction was only on the displacement itself. The change law of the displacement time series was mined through mathematical methods, and the factors affecting the displacement were not included in the prediction model. This is also an important reason for the poor prediction effect. Therefore, in order to accurately predict the future changes in slope displacement, considering the integration of multi-source heterogeneous influencing factors for collaborative prediction is an important research direction. The slope displacement prediction model has many input features. Inputting redundant and irrelevant features into the GRU prediction model may mask the role of important features and increase the difficulty of its model training. Therefore, before establishing an accurate slope displacement prediction model, it is necessary to perform feature selection, mine and extract effective input features. In summary, it is necessary to combine the feature selection algorithm with the displacement prediction model to fuse and collaboratively predict multi-source data of mountain slopes. This method has good prediction accuracy and generalization ability, and provides a new idea for the advance prediction of mountain slope failure and the prejudgment of slope stability.

[0052] Compared with the prior art, the present invention's method for predicting mountain slope displacement based on MI-GRA and improved PSO-LSTM has the following beneficial effects: This method solves the problems that previous prediction algorithms themselves are static and cannot take into account historical information on slope displacement, which restricts the improvement of prediction accuracy; and that previous slope displacement prediction focuses only on the displacement itself and fails to incorporate factors affecting displacement into the prediction model, resulting in poor prediction results. In the information age, combining deep learning algorithms and feature selection algorithms, feature selection is performed before establishing an accurate slope displacement prediction model, mining and extracting effective input features to obtain the optimal feature set for slope displacement prediction; then, using metaheuristic algorithms and deep learning algorithms, an improved PSO-GRU collaborative prediction model based on master control factors is established to fuse and collaboratively predict multi-source data of mountain slopes. The in-situ test results based on mountain slope monitoring show that the mountain slope displacement prediction method based on MI-GRA and improved PSO-LSTM has the average mutual information of the historical displacement characteristics of the first five days being 1.33, which is much higher than the average mutual information of the last 25 days being 0.86. The correlation between rainfall and displacement is the largest (0.82), indicating that external rainfall is the main controlling factor affecting the displacement of mountain slopes. The historical displacement and rainfall characteristics of the first five days of the prediction day are selected as the optimal feature set. The improved PSO-GRU prediction model based on rainfall as the main controlling factor has high prediction accuracy at the displacement mutation point, and the goodness of fit R 2 This method has good prediction accuracy and generalization ability, and provides a new approach for the advance prediction of slope failure in mountainous areas and the prejudgment of slope stability.

[0053] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The drawings that constitute part of this invention are intended to assist in understanding the invention. The contents provided in the drawings and their related descriptions in the present invention may be used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0055] Figure 1 is a flow chart of the mountain slope displacement prediction method based on MI-GRA and improved PSO-LSTM.

[0056] Figure 2 is a flowchart for collecting and constructing raw data.

[0057] Figure 3 is a flowchart of the MI-GRA mountain slope displacement feature selection model.

[0058] Figure 4 is a flowchart of establishing the improved PSO-LSTM mountain slope displacement prediction model.

[0059] Figure 5 is a diagram of the optimization process of the improved PSO algorithm.

[0060] Figure 6 shows the evolution diagram of RNN and LSTM.

[0061] Figure 7 is the MI algorithm analysis results.

[0062] Figure 8 shows the results of GRA correlation analysis.

[0063] Figure 9 shows the improved PSO optimization results.

[0064] Figure 10 shows the collaborative prediction and single prediction results. DETAILED DESCRIPTION

[0065] The present invention is described clearly and completely below with reference to the accompanying drawings. A person skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention with reference to the accompanying drawings, it should be noted that:

[0066] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other unless there is any conflict.

[0067] In addition, the embodiments of the present invention described below are generally only part of the embodiments of the present invention, rather than all of the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making any creative efforts should fall within the scope of protection of the present invention.

[0068] Regarding the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and the related parts are intended to cover non-exclusive inclusions.

[0069] The present invention provides a slope displacement prediction method in mountainous area based on MI-GRA and improved PSO-LSTM, comprising the following steps: (1) collecting and constructing original data for slope displacement prediction; (2) establishing a slope displacement feature selection model of MI-GRA based on the constructed original data for slope displacement prediction; (3) using the data after feature selection as the optimal feature set input for slope displacement prediction, and establishing an improved PSO-LSTM slope displacement prediction model; and (4) performing model prediction and testing on the established slope prediction model.

[0070] Furthermore, step (1) of collecting and constructing the original data for slope displacement prediction is mainly divided into three steps including:

[0071] Collection of multi-source slope monitoring data. Specifically, multi-source slope data is acquired in real time through intelligent sensors at the slope monitoring site in mountainous areas, and collected through wireless transmission.

[0072] After obtaining the original data of slope monitoring, the missing data are interpolated. Specifically, after obtaining the original data of multi-source monitoring of mountain slopes, the median interpolation method is used to interpolate the missing data to ensure the integrity and quality of the original data and provide guarantee for subsequent data analysis.

[0073] The original data are classified into displacement data and data of potential influencing factors of displacement. Specifically, the original data can be classified into displacement data and data of potential influencing factors of displacement, wherein the data of potential influencing factors of displacement may include possible influencing factors such as rainfall, groundwater level, pore water pressure, water content, slope gradient, slope top load, soil pressure, crack width, etc.

[0074] Furthermore, the missing data were interpolated using the median interpolation method, and the formula is as follows;

[0075] In this formula, x cb is the data after missing value interpolation, x t-1 is the data of the previous moment of the point to be interpolated, x t+1 The data of the next moment after the point to be interpolated.

[0076] Furthermore, in the step (2), the idea of ​​establishing the MI-GRA mountain slope displacement feature selection model mainly refers to the slope displacement prediction feature, which can be divided into the displacement itself and the displacement influence feature. That is, the historical displacement feature will mask other features, so the historical displacement and the displacement influence factor are considered separately, and the MI algorithm and the GRA algorithm are used to optimize the two different types of features respectively. It is mainly divided into three steps: based on the mountain slope displacement data, the MI algorithm is used to optimize the best historical displacement feature; based on the mountain slope displacement and displacement potential influencing factor data, the GRA algorithm is used to optimize the displacement influencing factor feature; the best historical displacement feature and the displacement influencing factor feature are combined to obtain the optimal feature set;

[0077] The above-mentioned method of selecting the best historical displacement feature using the MI algorithm includes the following steps:

[0078] In order to ensure the operation speed and accuracy in the subsequent feature selection process, the mountain slope displacement data is normalized to the range of [0,1]. The normalization of the data adopts the formula: x scaled =x std *(max-min)+min (3)

[0079] In this formula, x is the displacement data to be normalized, xmin (axis = 0) is the row vector composed of the minimum value in each column of data, xmax (axis = 0) is the row vector composed of the maximum value in each column of data, max is the maximum value of the interval to be mapped, the default is 1, min is the minimum value of the interval to be mapped, the default is 0, x std is the standardized result, x scaled is the normalized result;

[0080] In order to analyze the information between the historical displacement characteristics and the displacement characteristics to be predicted, the characteristic matrix S of each prediction day is constructed. input and output sequence S output , feature matrix S input and output sequence S output The formula is as follows: S output =[S(t+1)1 … S(t+1) n ] T (5)

[0081] In this formula, S input is a feature matrix, which is composed of various historical displacement features. n is 30, which means that the number of historical displacement features is 30. k (k=1,2…30) corresponds to the kth historical displacement feature, S output is the output sequence, consisting of predicted displacement data;

[0082] Calculate the mutual information evaluation index I(S k ;S output ), the mutual information I(S k ;S output ) is the mutual information between the historical displacement feature sequence and the output sequence;

[0083] The historical displacement feature sorting and optimization is specifically performed by sorting the mutual information values ​​from large to small, and finally the top five mutual information values ​​are selected as the best historical displacement features.

[0084] Furthermore, calculating the mutual information evaluation index includes the following steps:

[0085] Calculate information entropy: H(F k )=-p(S k (i))log2∫p(S k (i))dS k (i) (5) H(S output )=-∫p(S(t+1) j )log2p(S(t+1)j )dS(t+1) j (6) H(F k ,S output )=-∫∫p joint (S k (i),S(t+1) j )log2p joint (S k (i),S(t+1) j )dS k (i)dS(t+1) j (7)

[0086] In this formula, H(F k ) and H(S output ) are the information entropy of the historical displacement feature sequence and the output sequence, respectively, which are used to measure their respective information contents; H(F k ,S output ) is the two-dimensional joint entropy of the historical displacement feature sequence and the output sequence, which is used to quantify the size of the shared information between variables, p is the marginal probability distribution of a single variable, and p joint is the joint probability distribution between two variables;

[0087] Calculate mutual information I(S k ;S output ):

[0088] In this formula, I(F k ;S output ) is the mutual information between the historical displacement feature sequence and the output sequence.

[0089] Furthermore, optimizing the characteristics of displacement influencing factors using the GRA algorithm includes the following steps:

[0090] Determine the slope displacement characteristics and select the analysis series:

[0091] After averaging the displacement data and the influencing factor data, the displacement data is set as the parent sequence Y0, and the displacement influencing factor data is set as the comparison sequence X, which can be expressed as: Y0 = [y0(1), y0(2), ..., y0(n)] (9)

[0092] In this formula, n is the number of days, and m is the number of influencing factors of slope displacement;

[0093] Calculate the correlation coefficient:

[0094] In this formula, Δx=y0(j)-X i (j), ρ is the resolution coefficient, which is generally 0.1 to 1.0, and is taken as 0.5 in this paper;

[0095] Calculate the correlation:

[0096] In this formula, γ is the correlation degree. Generally, when it is greater than 0.6, it is considered that the correlation between the sequences is strong. i = 1, 2, ..., m; j = 1, 2, ..., n;

[0097] Ranking of characteristics of factors affecting displacement and determination of main factors affecting displacement.

[0098] Furthermore, the improved PSO-LSTM slope displacement prediction model in step (3) is mainly divided into three aspects: data set construction, improved PSO-GRU neural network architecture construction, model training and preservation. The establishment of the improved PSO-LSTM slope displacement prediction model in step (3) includes the following steps:

[0099] a. Obtain time series data of mountain slope displacement and main influencing factors of displacement and perform normalization processing on them. The normalization processing is consistent with the processing and formula used in MI feature selection. The purpose of the normalization processing is to make the input features all within the range of 0 to 1 to ensure the operation and convergence speed of the neural network; the processing is consistent with the processing in MI feature selection and also uses the formula:

[0100] b. Divide the dataset into training, validation, and test sets, and input the training and validation sets into the LSTM network model. Specifically, the training and validation sets are used to train the model and optimize the configuration, while the test set is used for prediction and testing. The dataset is divided into training, validation, and test sets in a ratio of 6:2:2, and input the training and validation sets into the LSTM network model. The LSTM model is an improved version (variant) of the RNN. LSTM introduces memory cells based on the RNN and designs three gates: the input gate, the forget gate, and the output gate. The gate mechanism controls the flow and loss of information, effectively solving the long-term dependency problem of the RNN.

[0101] c. Preliminary setting of parameters in the improved PSO algorithm, random initialization of hyperparameters to be optimized in the LSTM model, and preliminary setting of population size n and maximum number of iterations m in the improved PSO algorithm max , learning factors c1 and c2, inertia factor w and other parameters, and randomly initialize the hyperparameters α and Neuron to be optimized in the LSTM model. The improved PSO algorithm is a meta-heuristic algorithm. To ensure the prediction accuracy of the LSTM network model, the hyperparameters (learning rate α and number of neurons Neuron) of the LSTM network model are optimized to achieve their adaptive determination;

[0102] d. Calculate the particle fitness (fit), using the mean absolute error (MAE) on the validation set as the objective function to calculate the particle fitness (fit);

[0103] e. According to the principle of minimizing fitness, update the individual optimal and group optimality

[0104] f. Update the learning factors c1 and c2, and the inertia factor w. Nonlinearly update the learning factors c1 and c2 so that they evolve co-evolvingly with the number of iterations, thereby avoiding premature maturation. Adaptively optimize the inertia factor w according to formula (21) so that it evolves co-evolvingly with the number of iterations, thereby avoiding premature maturation.

[0105] g. Determine whether the number of iterations is greater than m max If the conditions are met, the improved PSO algorithm optimization ends, otherwise go to step 3 and repeat steps d, e, and f until the judgment conditions are met;

[0106] h. Perform iterative training of the model based on the optimal network model configuration and save the model. Perform iterative training of the model based on the optimal network model configuration. The number of iterations is usually set between 100 and 200, and the model is saved in the form of .ckpt.

[0107] Furthermore, the LSTM network model is a deep learning model, and a forward calculation of the LSTM network model cycle unit is: i t =σ(W i ·[h t-1 ,x t ]+b i ) (13) f t =σ(W f ·[h t-1 ,x t ]+b f ) (14)

[0108] In this formula, i t is the input gate, f t is the forget gate, σ is the sigmoid activation function, which can make the threshold range between 0 and 1, x t is the input feature at the current moment, h t-1 Represents the hidden state of the previous moment, W i and W f are the weight matrices to be trained for the input gate and forget gate, respectively, b i and b f are the bias items to be trained for the input gate and forget gate respectively;

[0109] The candidate state represents the new knowledge to be stored in the cell state, which is a function of the input features at the current moment and the hidden state at the previous moment. The cell state represents the long-term memory, which is equal to the sum of the value of the long-term memory at the previous moment passing through the forget gate and the value of the new knowledge summarized at the current moment passing through the input gate. The specific calculation process can be expressed as:

[0110] In this formula, is the candidate state, tanh is the activation function, W C is the weight matrix to be trained, b C is the bias term to be trained, C t is the cell state at the current moment, C t-1 is the cell state at the previous moment;

[0111] The output gate selectively outputs the information in the cell state, and the hidden state can be obtained from the current cell state through the output gate. The specific calculation process can be expressed as: t =σ(W o ·[h t-1 ,x t ]+b o ) (17) h t =o t *tanh(C t ) (18)

[0112] In this formula, o t is the output gate, W o and b o are the weight matrix and bias term to be trained of the output gate, h t is the hidden state at the current moment;

[0113] The improved PSO algorithm is an optimization algorithm of the traditional PSO algorithm, including:

[0114] Improve the learning factor. The improved formula of the improved learning factor is as follows:

[0115] In this formula, m cur is the current iteration number, m max is the maximum number of iterations, c 1b 、c 1e 、c 2b and c 2e They are the initial and final values ​​of c1 and c2 respectively, usually c 1b =2.5, c 1e =0.5, c 2b =0.5 and c 2e =2.5, the algorithm works better.

[0116] Improved inertia factor

[0117] The larger the inertia factor w, the faster the particle flies, and the particle will perform a global search with a longer step size. The smaller the inertia factor w, the more precise the local search. The improved formula is as follows.

[0118] In this formula, ω max Indicates the maximum value of ω, ω min represents the minimum value of ω, F represents the current objective function value, and F avg Represents the current average objective function value, F min represents the minimum value of the objective function;

[0119] The objective function uses the mean absolute error (MAE) on the validation set as the objective function, and its formula is as follows:

[0120] In this formula, N represents the number of prediction samples, y(y1,y2,…,y N ) is the measured slope displacement value in the validation set, is the predicted slope displacement value on the validation set.

[0121] Furthermore, the step (4) performs model prediction and testing on the established slope prediction model, including the following steps: calling the prediction model, wherein the called prediction model is the improved PSO-LSTM slope displacement prediction model that has been trained and saved in step (3); inputting the test set and performing prediction testing, inputting the test set into the improved PSO-LSTM slope displacement prediction model for rolling prediction; obtaining the prediction results, and evaluating the model prediction accuracy;

[0122] The model accuracy was evaluated using the goodness of fit R 2 and mean absolute percentage error (MAPE), R 2 The larger its value, the higher the model accuracy, and the smaller the MAPE value, the smaller the prediction error. The formula is as follows:

[0123] In this formula, R 2 is the goodness of fit, the larger its value, the higher the model accuracy, MAPE is the mean absolute percentage error, the smaller its value, the smaller the prediction error, N is the number of prediction samples, y t is the measured displacement value in the test set, is the predicted displacement value on the test set, is the average of the measured values.

[0124] The present invention will be further described below with reference to specific examples.

[0125] The embodiment and implementation process of the complete method according to the present invention are as follows:

[0126] Collect and construct raw data for slope displacement prediction

[0127] At a mountain slope construction site, inclinometers were deployed at various locations and depths to measure slope displacement. Rain gauges, hygrometers, water level observation holes, and pore water pressure gauges were also deployed to obtain data on potential influencing factors. Wireless transmission was used to collect multi-source slope monitoring data, resulting in a total time series sample length of 146 items. Some of the data is shown in Table 1 below.

[0128] After obtaining the original data of multi-source monitoring of mountain slopes, the median interpolation method shown in formula (1) is used to interpolate the missing data to ensure the integrity and quality of the original data and provide guarantee for subsequent data analysis;

[0129] The original data can be classified into displacement data and data of potential influencing factors of displacement. The data of potential influencing factors of displacement include rainfall, groundwater level, pore water pressure, water content, slope gradient, top load of slope, and soil pressure (as shown in Table 1 below).

[0130] Table 1 Slope multi-source monitoring data

[0131] Establishment of MI-GRA model for selecting displacement characteristics of mountain slopes

[0132] The mountain railway slope displacement data obtained in step 1) is input into the MI model, and the MI algorithm is used to select the best historical displacement characteristics. The detailed process is as follows:

[0133] ① In order to ensure the operation speed and accuracy in the subsequent feature selection process, the mountain slope displacement data are normalized to the range of [0, 1].

[0134] ② Input the normalized data into the MI model and calculate the mutual information evaluation index I. The results are shown in Figure 7.

[0135] ③ According to the calculation results, the displacement characteristics are sorted, and the top five historical displacement characteristics are S1 (1.58) > S2 (1.34) > S4 (1.27) > S3 (1.25) > S5 (1.21). Therefore, the five characteristics of S1 to S5 are regarded as the best historical displacement characteristics.

[0136] The mountain railway slope displacement data and displacement influencing factor data obtained in step 1) are input into the GRA model, and the GRA algorithm is used to select the best historical displacement characteristics. The detailed process is as follows:

[0137] ① To ensure the computational speed and accuracy in the subsequent feature selection process, the displacement data of mountain railway slopes and the data of displacement influencing factors are averaged;

[0138] ② Input the averaged data into the GRA model and calculate the correlation between each influencing factor and slope displacement. The results are shown in Figure 8.

[0139] ③' According to the calculation results, the displacement characteristics are ranked as follows: rainfall (0.82) > moisture content (0.76) > pore water pressure (0.70) > groundwater level (0.63) > slope gradient (0.58) > soil pressure (0.54) > slope top load (0.53). Rainfall has the strongest correlation with displacement, with a correlation degree of 0.82. Therefore, rainfall is regarded as the main controlling factor affecting slope displacement.

[0140] In summary, the historical displacement and rainfall features of the first five days of the forecast day are selected as the optimal feature set and input into the improved PSO-GRU forecast model;

[0141] Establishment of an improved PSO-LSTM model for slope displacement prediction in mountainous areas

[0142] Normalize the time series data of slope displacement and rainfall so that the input features are all within the range of 0 to 1 to ensure the operation and convergence speed of the neural network

[0143] The dataset is divided into training set, validation set and test set in a ratio of 6:2:2, and the training set and validation set are input into the LSTM network model.

[0144] Initially set the population size n in the improved PSO algorithm to 25 and the maximum number of iterations m max =50, learning factors c1=2.5 and c2, inertia factor w and other parameters, and randomly initialize the hyperparameters α and Neuron to be optimized in the LSTM model.

[0145] In the improved PSO algorithm, the optimization range for the number of units in the first and second hidden layers was set to 0-200, with values ​​randomly and uniformly selected on the linear axis. The optimization range for the learning rate was set to 10-4-100, with a logarithmic scale used for the search. The loss function for both model optimization and training was the mean absolute error (MAE), the optimizer was the Adam algorithm, and the number of iterations was set to 50. The optimization results are shown in Figure 9. The optimal LSTM network model configuration was determined as follows: the number of units in the first hidden layer, Neuron1, was 80, the number of units in the second hidden layer, Neuron2, was 100, and the learning rate α was 0.001.

[0146] After obtaining the optimal network model configuration, the model is iteratively trained. The number of iterations is usually set to 200, and the best model is saved in the form of .ckpt.

[0147] The established slope displacement prediction model is used for model prediction and testing

[0148] Call the improved PSO-LSTM slope displacement prediction model saved in step 3);

[0149] The improved PSO-LSTM slope displacement prediction model was fed a test set for rolling predictions. The predictions were compared with the single predictions from the GRU model, the support vector machine regression (SVR) model, and the back propagation neural network (BP) model. To ensure the reliability of the comparison results, the improved PSO algorithm was also used for model optimization. The prediction results are shown in Figure 10. It can be seen that while the single predictions from the GRU, SVR, and BP models can reflect the general displacement trend, they perform poorly at displacement mutation points and are unable to cope with displacement changes caused by unexpected external events, resulting in low overall prediction accuracy. The predictions from the LSTM collaborative prediction model are the most consistent with the actual values.

[0150] The prediction accuracy of the model is evaluated using formulas (23) and (24). The results are shown in Table 2. It can be seen that the prediction results of the GRU collaborative prediction model are most consistent with the actual values, and the goodness of fit R 2 The prediction error MAPE is 0.496%, which is higher than the prediction accuracy evaluation results of each single variable prediction model (the goodness of fit R 2 The BP model achieved a 0.528% and a MAPE of 0.696%, both superior to the BP model's 0.267% and 1.283% and the SVR model's 0.284% and 1.229% respectively. This is because the collaborative prediction model considers the influence of rainfall, a primary controlling factor, on mountain slope displacement, and can better reflect the displacement changes caused by external factors. In summary, the proposed slope displacement prediction method based on MI-GRA and improved PSO-LSTM, which introduces a primary controlling factor for displacement, exhibits certain advantages in prediction accuracy and generalization ability, and can effectively support mountain slope displacement prediction.

[0151] Table 2 Prediction accuracy evaluation results

[0152] The above describes the relevant contents of the present invention. Based on this description, a person skilled in the art will be able to implement the present invention. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without making any creative efforts should fall within the scope of protection of the present invention.

Claims

1. A method for predicting the displacement of mountain slopes based on MI-GRA and improved PSO-LSTM, characterized in that, It includes the following steps: (1) Collect and construct the original data for slope displacement prediction; (2) Based on the constructed original data for slope displacement prediction, establish a slope displacement feature selection model of MI-GRA; (3) Input the data after feature selection as the optimal feature set for slope displacement prediction, and establish an improved PSO-LSTM slope displacement prediction model; (4) Conduct model prediction and testing on the established slope prediction model; The step (2) includes: on the basis of displacement data, use the MI algorithm to optimize the best historical displacement features; on the basis of displacement and potential influencing factor data of displacement, use the GRA algorithm to optimize the displacement influencing factor features; Integrate the best historical displacement features and displacement influencing factor features to obtain the optimal feature set; The use of the MI algorithm to optimize the best historical displacement features includes the following steps: Normalize the displacement data, and the normalization of the data adopts the following formula: x scaled = x std *(max - min)+min In this formula, x is the displacement data to be normalized, xmin(axis = 0) is the row vector composed of the minimum values in each column of data, xmax(axis = 0) is the row vector composed of the maximum values in each column of data, max is the maximum value of the interval to which it is to be mapped, the default is 1, min is the minimum value of the interval to which it is to be mapped, the default is 0, and x std is the standardized result, and x scaled is the normalization result; Construct the feature matrix S for each prediction day input and the output sequence S output , the feature matrix S input and the output sequence S output are formulated as follows: S output = [S(t + 1)1…S(t + 1) n T ​ In this formula, S input is the feature matrix, which is composed of various historical displacement features. n is taken as 30, representing that the number of historical displacement features is 30. F k (k = 1, 2... 30) corresponds to the k-th historical displacement feature, and S output is the output sequence, which is composed of predicted displacement data; Calculate the mutual information evaluation index I(S k ; S output ); Sorting and optimizing historical displacement features; The calculation of the mutual information evaluation index includes the following steps: Calculating the information entropy: H(F k ) = -p(S k (i)) log2 ∫ p(S k (i)) dS k (i) H(S output ) = -∫p(S(t + 1) j ) log2 p(S(t + 1) j ) dS(t + 1) j H(F k ,S output )=-∫∫p joint (S k (i),S(t+1) j )log2 p joint (S k (i),S(t+1) j )dS k (i)dS(t+1) j In this formula, H(F k ) and H(S output ) are the information entropy of the historical displacement feature sequence and the output sequence respectively, used to measure their respective information contents; H(F k , S output ) is the two-dimensional joint entropy of the historical displacement feature sequence and the output sequence, used to quantify the size of the common information between variables, p is the marginal probability distribution of a single variable, and p joint is the joint probability distribution between two variables; Calculate the mutual information I(S k ; S output ): In this formula, I(F k ; S output ) is the mutual information between the historical displacement feature sequence and the output sequence; The use of the GRA algorithm to optimize the displacement influencing factor features includes the following steps: Determine the analysis sequence of slope displacement feature selection: After averaging the displacement data and influencing factor data, set the displacement data as the mother sequence Y0, and the displacement influencing factor data as the comparison sequence X, denoted as: Y0 = [y0(1), y0(2), …, y0(n)] In this formula, n is the number of days, and m is the number of displacement influencing factor indexes of the slope; Calculate the correlation coefficient: In this formula, Δx = y0(j) - X i (j), ρ is the resolution coefficient, generally taking a value of 0.1 to 1.0, and in this paper, 0.5 is taken; Calculate the correlation degree: In this formula, γ is the correlation degree. Generally, when it is greater than 0.6, it can be considered that the correlation between sequences is strong, i = 1, 2,..., m; j = 1, 2,..., n; Sorting of displacement influencing factor features and determination of main displacement influencing factors; The establishment of the improved PSO-LSTM slope displacement prediction model in step (3) includes the following steps: a. Obtain the time series data of the mountain slope displacement and the main influencing factors of the displacement, and perform normalization processing on it. The normalization processing is consistent with that in MI feature selection and uses the same formula; b. Divide the data set into a training set, a validation set, and a test set, and input the training set and the validation set into the LSTM network model; c. Initially set the parameters in the improved PSO algorithm and randomly initialize the hyperparameters to be optimized in the LSTM model; d. Calculate the particle fitness (fit); e. Update the individual optimum respectively and group optimum f. Update the learning factors c1 and c2, and the inertia factor w; g. Determine whether the number of iterations is greater than m max , if the condition is met, the improvement of the PSO algorithm optimization ends; otherwise, go to step 3 and repeat steps d, e, and f until the discrimination condition is met; h. Perform iterative training of the model based on the obtained optimal network model configuration and save the model; The LSTM network model is a deep learning model. One forward calculation of the LSTM network model's recurrent unit is: i t = σ(W i · [h t-1 , x t + b i ) f t = σ(W f · [h t-1 , x t + b f ) In this formula, i t is the input gate, f t is the forget gate, σ is the sigmoid activation function, which can make the threshold range between 0 and 1, x t is the input feature at the current moment, h t-1 represents the hidden state at the previous moment, W i and W f are the weight matrices to be trained for the input gate and the forget gate respectively, b i and b f are the bias terms to be trained for the input gate and the forget gate respectively; The candidate state represents the newly learned knowledge of the cell state to be stored, which is a function of the input features at the current time and the hidden state at the previous time; the cell state represents long-term memory, which is equal to the sum of the value of the long-term memory at the previous time passed through the forget gate and the value of the newly learned knowledge at the current time passed through the input gate. The specific calculation process can be expressed as: In this formula, is in the candidate state, tanh is the activation function, W C is the weight matrix to be trained, b C is the bias term to be trained, C t is the cell state at the current moment, C t-1 is the cell state at the previous moment; The output gate selectively outputs the information in the cell state, and the hidden state can be obtained from the current cell state through the output gate. The specific calculation process can be expressed as: o t = σ(W o · [h t-1 , x t + b o ) h t = o t *tanh(C t ) In this formula, o t is the output gate, and W o and b o are the weight matrix to be trained and the bias term of the output gate respectively, and h t is the hidden state at the current moment; The improved PSO algorithm is an optimized algorithm of the traditional PSO algorithm, including: Improving the learning factor, and the improvement formula of the improved learning factor is as follows: In this formula, m cur is the current iteration number, and m max is the maximum iteration number. c 1b , c 1e , c 2b and c 2e are the initial value and the final value of c1 and c2 respectively. Generally, when c 1b = 2.5, c 1e = 0.5, c 2b = 0.5, and c 2e = 2.5, the algorithm has better performance. Improving the inertia factor The larger the inertia factor w is, the greater the flying speed of the particle, and the particle will conduct a global search with a longer step length; if the inertia factor w is smaller, it tends to conduct a fine local search. The improved formula is as follows: In this formula, ω max represents the maximum value of ω, ω min represents the minimum value of ω, F represents the current objective function value, F avg represents the current average objective function value, F min represents the minimum value of the objective function; The objective function uses the mean absolute error (MAE) on the validation set as the objective function, and its formula is as follows: In this formula, N represents the number of prediction samples, and y(y1, y2, …, y N ) is the measured slope displacement value in the validation set, It is the predicted slope displacement value on the validation set.

2. The method for predicting the displacement of mountain slopes based on MI-GRA and improved PSO-LSTM according to claim 1, characterized in that Step (1) includes: collection of multi-source monitoring data of the slope; after obtaining the original slope monitoring data, interpolate the missing data; classify the original data into displacement data and potential displacement influencing factor data.

3. The method for predicting the displacement of mountain slopes based on MI-GRA and improved PSO-LSTM according to claim 2, wherein The imputation of missing data adopts the method of median imputation, and its formula is as follows; In this formula, x cb is the data after missing value imputation, and x t-1 is the data at the previous moment of the point to be imputed, and x t+1 is the data at the next moment of the point to be imputed.

4. A method for predicting the displacement of mountain slopes based on MI-GRA and improved PSO-LSTM according to claim 1, characterized in that: The step (4) of conducting model prediction and testing on the established slope prediction model includes the following steps: calling the prediction model, and the called prediction model is the improved PSO-LSTM slope displacement prediction model saved after training; inputting the test set and conducting prediction testing, and the prediction testing method is rolling prediction; obtaining the prediction result and evaluating the prediction accuracy of the model; The evaluation of the model prediction accuracy uses the selection of the goodness of fit R 2 and the mean absolute percentage error MAPE, and their formulas are as follows: In this formula, R 2 is the goodness of fit. The larger its value, the higher the model accuracy. MAPE is the mean absolute percentage error. The smaller its value, the smaller the prediction error. N is the number of prediction samples, and y t is the measured displacement value in the test set, is the predicted displacement value on the test set, It is the average of the measured values.