WO2024001942A1 - Mountainous area slope displacement prediction method based on mi-gra and improved pso-lstm - Google Patents

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 mountainous slope displacement prediction method based on MI-GRA and improved PSO-LSTM Technical field

The invention relates to the technical field of slope displacement prediction, and specifically relates to a slope displacement prediction method in mountainous areas based on MI-GRA and improved PSO-LSTM.

Background technique

my country's mountainous areas cover a vast area and are affected by external factors such as earthquakes, rainfall, and floods, resulting in frequent slope disasters such as landslides, collapses, and debris flows. Slope displacement is an intuitive representation of slope deformation. It is particularly important to grasp the law of slope displacement changes in mountainous areas, predict the damage of mountainous slopes in advance, and determine the stable state of the slope.

In recent years, with the development of information technology, more and more artificial intelligence prediction methods have been applied in the field of slope displacement prediction, such as SVR, BP, Elman and other intelligent algorithms. However, the above prediction algorithms themselves are static in nature and cannot take into account the historical information of slope displacement, which restricts the improvement of prediction accuracy.

Contents of the invention

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 problem that the existing prediction method cannot take into account the historical information of slope displacement, which restricts the improvement of prediction accuracy. technical problem.

The present invention is a method for predicting slope displacement in mountainous areas based on MI-GRA and improved PSO-LSTM, which includes the following steps: (1) collecting and constructing original data for slope displacement prediction; (2) in the constructed slope displacement prediction Based on the original data, establish the MI-GRA slope displacement feature selection model; (3) Use the feature-selected data as the optimal feature set input for slope displacement prediction, and establish an improved PSO-LSTM slope displacement prediction model; (4) Carry out model prediction and testing on the established slope prediction model.

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

Furthermore, the missing data is imputed using the median imputation method, and its formula is as follows;

In this formula, x _cb is the data after missing value interpolation, x _t-1 is the data at the time before the point to be interpolated, and x _t+1 is the data at the time after the point to be interpolated.

Further, the step (2) includes: using the MI algorithm to select the best historical displacement characteristics based on the displacement data; using the GRA algorithm to select the characteristics of the displacement influencing factors based on the data of the displacement and potential influencing factors of the displacement; comprehensively The best historical displacement characteristics and displacement influencing factor characteristics are used to obtain the optimal feature set.

Further, the use of MI algorithm to optimize the best historical displacement characteristics includes the following steps:

The displacement data is normalized using the following formula:

x _scaled = x _std *(max-min)+min

In this formula, x is the displacement data to be normalized, x _{min (axis = 0)} is a row vector composed of the minimum value in each column of data, and x _{max (axis = 0)} is composed of the maximum value in each column of data. row vector, 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;

Construct the feature matrix S _input and the output sequence S _output of each prediction day. The formulas of the feature matrix S _input and the output sequence S _output are as follows:

S _output =[S(t+1) ₁ ... S(t+1) _n ] ^T

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. F _k (k=1,2...30) corresponds to the kth historical displacement feature. , S _output is the output sequence, consisting of predicted displacement data;

Calculate the mutual information evaluation index I(S _k ; S _output );

Ranking and optimization of historical displacement features.

Further, calculating the mutual information evaluation index includes the following steps:

Calculate information entropy:
H(F _k )＝-p(S _k (i))log ₂ ∫p(S _k (i))dS _k (i)
H(S _output )＝-∫p(S(t+1) _j )log ₂ p(S(t+1) _j )dS(t+1) _j
H(F _k ,S _output )＝-∫∫p _join (S _k (i),S(t+1) _j )log ₂ 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, which are used to measure their respective information content; H(F _k ,S _output ) is the historical displacement feature sequence and the two-dimensional joint entropy of the output sequence, 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;

Calculate 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.

Further, using the GRA algorithm to optimize the characteristics of displacement influencing factors includes the following steps:

Determine the slope displacement characteristics and select the analysis sequence:

After averaging the displacement data and influencing factor data, set the displacement data as the parent sequence Y ₀ and the displacement influencing factor data as the comparison sequence X, recorded as:
Y ₀ =[y ₀ (1),y ₀ (2),…,y ₀ (n)]

In this formula, n is the number of days, m is the number of influencing factor indicators of slope displacement;

Calculate the correlation coefficient:

In this formula, Δx=y ₀ (j)-X _i (j), ρ is the resolution coefficient, generally 0.1 to 1.0, this article takes 0.5;

Calculate relevance:

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;

Characteristic ranking of displacement influencing factors and determination of main influencing factors of displacement.

Further, establishing an improved PSO-LSTM slope displacement prediction model in step (3) includes the following steps: a. Obtaining the time series data of mountainous slope displacement and main influencing factors of displacement and normalizing it, as described The normalization process is consistent with the process in MI feature selection and the formula used is consistent; b. Divide the data set into a training set, a verification set and a test set, and input the training set and verification set into the LSTM network model; c. Preliminary Set the parameters in the improved PSO algorithm and randomly initialize the hyperparameters to be optimized in the LSTM model; d. Calculate particle fitness (fit); e. Update the individual optimal respectively and group optimal f. Update the learning factors c ₁ and c ₂ and the 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 Satisfy the discriminant conditions; h. Carry out iterative training of the model based on obtaining the optimal network model configuration, and save the model.

Further, 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 )

In this formula, i _t is the input gate, f _t is the forgetting 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, and h _t-1 represents the previous The hidden state at the moment, W _i and W _f are the weight matrices to be trained of the input gate and the forget gate respectively, b _i and b _f are the bias terms to be trained of the input gate and the forget gate respectively;

The candidate state represents the new knowledge summarized 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 value of the long-term memory at the previous moment through the forgetting gate. and the sum of the new knowledge summarized at the current moment through the input gate. The specific calculation process can be expressed as:

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, and 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, W _o and _bo are the weight matrix to be trained and the bias term of the output gate respectively, h _t is the hidden state at the current moment;

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

Improved learning factor, the improved formula of the improved learning factor is as follows:

In this formula, m _cur is the current number of iterations, m _max is the maximum number of iterations, c _1b , c _1e , c _2b and c _2e are the initial and final values of c ₁ and c ₂ respectively. Generally, c _1b = 2.5, The algorithm works better when c _1e =0.5, c _2b =0.5 and c _2e =2.5.

Improved inertia factor

The larger the inertia factor w is, the greater the particle flight speed is, and the particles will conduct a global search with a longer step size; the smaller the inertia factor w is, the more precise the local search will be. 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, and F _min represents the minimum value of the objective function;

The objective function uses the mean absolute error MAE on the verification set as the objective function, and its formula is as follows:

In this formula, N represents the number of predicted samples, y (y ₁ , y ₂ ,..., y _N ) is the measured slope displacement value in the verification set, is the predicted slope displacement value on the validation set.

Further, the step (4) of performing 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 saved after training. Predict the model; input the test set and perform prediction testing, and the prediction testing method is rolling prediction; obtain the prediction results and evaluate the prediction accuracy of the model;

The accuracy of the model is evaluated by selecting the goodness of fit R ² and the mean absolute percentage error MAPE, whose formula is as follows:

In this formula, R ² is the goodness of fit. The larger the value, the higher the accuracy of the model. MAPE is the average absolute percentage error. The smaller the value, the smaller the prediction error. N is the number of predicted samples, and y _t is the test set. The measured displacement value of is the predicted displacement value on the test set, is the average of the actual measured values.

This invention is a method for predicting slope displacement in mountainous areas based on MI-GRA and improved PSO-LSTM. The idea is as follows: the change of slope displacement is a dynamic process, and the long and short memory network (LongShort Term Memory, LSTM) has the ability to remember historical information. function, which has great advantages in processing long-term sequence data. In view of this, it is theoretically feasible to apply the LSTM deep learning algorithm to slope displacement prediction in mountainous areas. In the past, the focus of slope displacement prediction was only the displacement itself. The changing patterns of the displacement time series were mined through mathematical methods, but the influencing factors of displacement were not included in the prediction model. This is also an important reason for poor prediction results. Therefore, to accurately predict future slope displacement changes, it is an important research direction to consider integrating multi-source heterogeneous influencing factors for collaborative prediction. The slope displacement prediction model has many input features. Inputting redundant and irrelevant features into the GRU prediction model may obscure the role of important features and increase the difficulty of model training. Therefore, before establishing an accurate slope displacement prediction model, It is necessary to perform feature selection, mining and extracting effective input features. In summary, it is necessary to combine the feature selection algorithm and the displacement prediction model to fuse and collaboratively predict the multi-source data of mountainous slopes. This method has good prediction accuracy and generalization ability, and provides advanced prediction of mountainous slope damage and The prediction of slope stability provides a new idea.

Compared with the existing technology, the present invention's method for predicting slope displacement in mountainous areas based on MI-GRA and improved PSO-LSTM has the following beneficial effects: This method solves the problem that previous prediction algorithms themselves have static characteristics and cannot take into account the history of slope displacement. Information has restricted the improvement of prediction accuracy, and the previous slope displacement prediction focused only on the displacement itself, failing to incorporate displacement influencing factors into the prediction model, resulting in poor prediction results and other problems. In the information age, deep learning algorithms and feature selection algorithms are combined to perform feature selection before establishing an accurate slope displacement prediction model, mine and extract effective input features, and obtain the optimal feature set for slope displacement prediction; and then use Metaheuristic calculations and deep learning algorithms are used to establish an improved PSO-GRU collaborative prediction model based on main control factors to fuse and collaboratively predict multi-source data on mountainous slopes. In-situ test results based on mountainous slope monitoring show that with the help of this mountainous slope displacement prediction method based on MI-GRA and improved PSO-LSTM, the average mutual information value of the historical displacement characteristics in the first 5 days is 1.33, which is far from the It is higher than the average mutual information value of 0.86 in the next 25 days; the correlation between rainfall and displacement is the largest (0.82). It is found that external rainfall is the main controlling factor affecting mountainous slope displacement. The historical displacement and rainfall characteristics of the first 5 days of the prediction day are selected. As the optimal feature set; the improved PSO-GRU prediction model based on rainfall as the main control factor has high prediction accuracy at the displacement mutation point, and the goodness of fit R ² is 0.928. This method has good prediction accuracy and generalization ability, and provides a new idea for advance prediction of slope damage in mountainous areas and prediction of slope stability.

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Description of drawings

The drawings that form a part of the present invention are used to assist the understanding of the present invention. The contents provided in the drawings and their relevant descriptions in the present invention can be used to explain the present invention, but do not constitute an improper limitation of the present invention. In the attached picture:

Figure 1 is a flow chart of the slope displacement prediction method in mountainous areas based on MI-GRA and improved PSO-LSTM.

Figure 2 is a flow chart of collecting and constructing original data.

Figure 3 is a flow chart for building a slope displacement feature selection model in MI-GRA mountainous areas.

Figure 4 is a flow chart for establishing the improved PSO-LSTM slope displacement prediction model in mountainous areas.

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

Figure 6 shows the evolution diagram of RNN and LSTM.

Figure 7 shows the analysis results of the MI algorithm.

Figure 8 shows the results of GRA correlation analysis.

Figure 9 shows the optimization results of the improved PSO.

Figure 10 shows the results of collaborative prediction and single prediction.

Detailed ways

The present invention will be clearly and completely described below in conjunction with the accompanying drawings. A person of ordinary skill in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly pointed out that:

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

In addition, the embodiments of the present invention mentioned in the following description are generally only some embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, those of ordinary skill in the art can obtain the results without any creative efforts. There are other embodiments, which should all fall within the protection scope of the present invention.

Regarding terms and units in this invention. The terms "including", "having" and any variations thereof in the description and claims of the present invention and related parts are intended to cover non-exclusive inclusion.

The present invention is a method for predicting slope displacement in mountainous areas based on MI-GRA and improved PSO-LSTM, which includes the following steps: (1) collecting and constructing original data for slope displacement prediction; (2) in the constructed slope displacement prediction Based on the original data, establish the MI-GRA slope displacement feature selection model; (3) Use the feature-selected data as the optimal feature set input for slope displacement prediction, and establish an improved PSO-LSTM slope displacement prediction model; (4) Carry out model prediction and testing on the established slope prediction model.

Further, step (1) collects and constructs the original data for slope displacement prediction, which is mainly divided into three steps including:

The collection of slope multi-source monitoring data, specifically, obtains the multi-source data of the slope in real time through intelligent sensors at the mountain slope monitoring site, and collects the multi-source monitoring data of the slope through wireless transmission;

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

Classify the original data into displacement data and data of potential influencing factors of displacement. Specifically, classify the original data into data of displacement data and data of potential influencing factors of displacement. The data of potential influencing factors of displacement may include rainfall, groundwater, etc. Possible influencing factors include position, pore water pressure, moisture content, slope gradient, slope top loading, earth pressure, crack width, etc.

Furthermore, the missing data is imputed using the median imputation method, and its formula is as follows;

In this formula, x _cb is the data after missing value interpolation, x _t-1 is the data at the time before the point to be interpolated, and x _t+1 is the data at the time after the point to be interpolated.

Further, in step (2), the idea of establishing the MI-GRA mountain slope displacement feature selection model mainly refers to the slope displacement prediction features, which can be divided into displacement itself and displacement influence features, that is, historical displacement features will To cover up other features, the historical displacement and displacement influencing factors are considered separately, and the MI algorithm and the GRA algorithm are used to optimize two different types of features, which are mainly divided into three steps: based on the mountainous slope displacement data, use MI The algorithm selects the best historical displacement characteristics; based on the mountainous slope displacement and displacement potential influencing factor data, the GRA algorithm is used to select the displacement influencing factor characteristics; the best historical displacement characteristics and displacement influencing factor characteristics are combined to obtain the optimal feature set;

The above-mentioned optimization of the best historical displacement characteristics using the MI algorithm includes the following steps:

In order to ensure the computing speed and accuracy in the subsequent feature selection process, the mountainous slope displacement data are normalized and normalized to the range of [0,1]. The normalization process of the data is formula:

x _scaled ＝x _std *(max-min)+min (3)

In this formula, x is the displacement data to be normalized, x _{min (axis = 0)} is a row vector composed of the minimum value in each column of data, and x _{max (axis = 0)} is composed of the maximum value in each column of data. row vector, 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;

In order to analyze the information between the historical displacement characteristics and the displacement characteristics to be predicted, the characteristic matrix S _input and the output sequence S _output of each prediction day are constructed. The formulas of the characteristic matrix S _input and the output sequence S _output are as follows:

S _output =[S(t+1) ₁ … S(t+1) _n ] ^T (5)

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. F _k (k=1,2...30) corresponds to the kth historical displacement feature. , S _output is the output sequence, consisting of predicted displacement data;

Calculate the mutual information _evaluation index I(S _k ; S _output ), _which is the mutual information between the historical displacement feature sequence and the output sequence;

The sorting and optimization of historical displacement features. Specifically, the sorting and optimization of historical displacement features are used to sort each mutual information value from large to small, and finally the top five mutual information values are selected as the best historical displacement features.

Further, calculating the mutual information evaluation index includes the following steps:

Calculate information entropy:
H(F _k )＝-p(S _k (i))log ₂ ∫p(S _k (i))dS _k (i) (5)
H(S _output )＝-∫p(S(t+1) _j )log ₂ p(S(t+1) _j )dS(t+1) _j (6)
H(F _k ,S _output )＝-∫∫p _joint (S _k (i),S(t+1) _j )log ₂ p _joint (S _k (i),S(t+1) _j )dS _k (i)dS(t+1) _j (7)

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 content; H(F _k ,S _output ) is the historical displacement feature sequence and the two-dimensional joint entropy of the output sequence, 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;

Calculate 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.

Further, using the GRA algorithm to optimize the characteristics of displacement influencing factors includes the following steps:

Determine the slope displacement characteristics and select the analysis sequence:

After averaging the displacement data and influencing factor data, set the displacement data as the parent sequence Y ₀ and the displacement influencing factor data as the comparison sequence X, recorded as:
Y ₀ =[y ₀ (1),y ₀ (2),…,y ₀ (n)] (9)

In this formula, n is the number of days, m is the number of influencing factor indicators of slope displacement;

Calculate the correlation coefficient:

In this formula, Δx=y ₀ (j)-X _i (j), ρ is the resolution coefficient, generally 0.1 to 1.0, this article takes 0.5;

Calculate relevance:

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;

Characteristic ranking of displacement influencing factors and determination of main influencing factors of displacement.

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 saving. The establishment in step (3) The improved PSO-LSTM slope displacement prediction model includes the following steps:

a. Obtain the time series data of the mountainous slope displacement and the main influencing factors of the displacement and perform normalization processing on it. The normalization processing is consistent with the processing in MI feature selection and the formula adopted. The normalization processing The purpose 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; consistent with the processing in MI feature selection, the formula is also used:

b. Divide the data set into a training set, a verification set and a test set, and input the training set and verification set into the LSTM network model. Specifically, the training set and verification set are used to train the model and optimize the configuration, and the test set is used to predict. and test, divide the data set into a training set, a verification set and a test set according to the ratio of 6:2:2, and input the training set and verification set into the LSTM network model. The LSTM model is an improved version of RNN ( Variant), LSTM introduces memory cells based on RNN, and designs three thresholds, namely Input gate, forget gate, output gate. The flow and loss of information are controlled through the gate mechanism, which effectively solves the long-term dependence problem of RNN;

c. Preliminarily set the parameters in the improved PSO algorithm, and randomly initialize the hyperparameters to be optimized in the LSTM model. Preliminarily set the population number n, the maximum number of iterations m _max , the learning factors c ₁ and c ₂ , and the inertia factor in the improved PSO algorithm. 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. In order to ensure the prediction accuracy of the LSTM network model, the hyperparameters (learning The rate α and the number of neurons (Neuron) are optimized to achieve its adaptive determination;

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

e. According to the principle of fitness minimization, update the individual optimal respectively and group optimal

f. Update the learning factors c ₁ and c ₂ and the inertia factor w, and nonlinearly update the learning factors c ₁ and c ₂ so that they evolve together with the number of iterations to avoid premature maturation; adaptively optimize the inertia factor w according to formula (21) , allowing it to co-evolve with the number of iterations, thereby avoiding premature maturation;

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 discrimination conditions are met;

h. Carry out iterative training of the model on the basis of obtaining the optimal network model configuration, and save the model. Carry out iterative training of the model on the basis of obtaining the optimal network model configuration. The number of iterations is usually set to between 100 and 200, and Save the model as .ckpt.

Further, 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)

In this formula, i _t is the input gate, f _t is the forgetting 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, and h _t-1 represents the previous The hidden state at the moment, W _i and W _f are the weight matrices to be trained of the input gate and the forget gate respectively, b _i and b _f are the bias terms to be trained of the input gate and the forget gate respectively;

The candidate state represents the new knowledge summarized 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 value of the long-term memory at the previous moment through the forgetting gate. and the sum of the new knowledge summarized at the current moment through the input gate. The specific calculation process can be expressed as:

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, and 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 ) (17)
h _t ＝o _t *tanh(C _t ) (18)

In this formula, o _t is the output gate, W _o and _bo are the weight matrix to be trained and the bias term of the output gate respectively, h _t is the hidden state at the current moment;

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

Improved learning factor, the improved formula of the improved learning factor is as follows:

In this formula, m _cur is the current number of iterations, m _max is the maximum number of iterations, c _1b , c _1e , c _2b and c _2e are the initial and final values of c ₁ and c ₂ respectively. Generally, c _1b = 2.5, The algorithm works better when c _1e =0.5, c _2b =0.5 and c _2e =2.5.

Improved inertia factor

The larger the inertia factor w is, the greater the particle flight speed is, and the particles will conduct a global search with a longer step size; the smaller the inertia factor w is, the more precise the local search will be. 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, and F _min represents the minimum value of the objective function;

The objective function uses the mean absolute error MAE on the verification set as the objective function, and its formula is as follows:

In this formula, N represents the number of predicted samples, y (y ₁ , y ₂ ,..., y _N ) is the measured slope displacement value in the verification set, is the predicted slope displacement value on the validation set.

Further, the step (4) of performing 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 saved after training in step (3). -LSTM slope displacement prediction model; the test set is input and the prediction test is performed. The test set is input into the improved PSO-LSTM slope displacement prediction model for rolling prediction; the prediction results are obtained and the model prediction accuracy is evaluated;

The model accuracy evaluation adopts the selection of goodness of fit R ² and mean absolute percentage error MAPE. The larger the value of R ² , the higher the model accuracy. The smaller the value of MAPE, the smaller the prediction error. The formula is as follows:

In this formula, R ² is the goodness of fit. The larger the value, the higher the accuracy of the model. MAPE is the average absolute percentage error. The smaller the value, the smaller the prediction error. N is the number of predicted samples, and y _t is the test set. The measured displacement value of is the predicted displacement value on the test set, is the average of the actual measured values.

The present invention will be further described below through specific examples.

The embodiments and implementation processes of the complete method according to the content of the present invention are as follows:

Collect and construct original data for slope displacement prediction

Relying on the slope work site in a mountainous area, inclinometers were deployed at different positions and depths of the slope to measure the displacement data of the slope. Rain gauge stations, hygrometers, water level observation holes, and pore water pressure gauges were also deployed to obtain data on potential influencing factors. By collecting multi-source slope monitoring data through wireless transmission, the overall sample length of the time series is 146. Part of the data is shown in Table 1 below;

After obtaining the original data from multi-source monitoring of mountainous slopes, the median interpolation method shown in formula (1) is used to interpolate the missing data to ensure the integrity of the original data and the quality of the data, and provide a basis for subsequent data analysis. provide assurance;

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, moisture content, slope gradient, slope top load, and earth pressure. (As shown in Table 1 below).

Table 1 Multi-source monitoring data of slope

Establishing MI-GRA mountainous slope displacement feature selection model

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:

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

② Input the normalized data into the MI model, calculate the mutual information evaluation index I, and obtain the results as shown in Figure 7;

③ According to the calculation results, the displacement features are sorted, and the top five historical displacement features are S1(1.58)>S2(1.34)>S4(1.27)>S3(1.25)>S5(1.21), so S1~S5 are The five features are used as the best historical displacement features.

The mountain railway slope displacement data and displacement influencing factors 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:

①'In order to ensure the computing speed and accuracy in the subsequent feature selection process, the mountainous railway slope displacement data and displacement influencing factors data are averaged;

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

③' According to the calculation results, sorting the displacement characteristics, we get rainfall (0.82)>moisture content (0.76)>pore water pressure (0.70)>groundwater level (0.63)>slope slope (0.58)>earth pressure (0.54)>slope For the top load (0.53), the correlation between rainfall and displacement is the strongest, and the correlation degree reaches 0.82. Therefore, rainfall is regarded as the main controlling factor affecting slope displacement.

In summary, the historical displacement and rainfall characteristics of the first 5 days of the prediction day are selected as the optimal feature set and jointly input into the improved PSO-GRU prediction model;

Establishing an improved PSO-LSTM slope displacement prediction model in mountainous areas

Normalize the time series data of slope displacement and rainfall so that the input features are in the range of 0 to 1 to ensure the operation and convergence speed of the neural network.

Divide the data set into training set, verification set and test set according to the ratio of 6:2:2, and input the training set and verification set into the LSTM network model

Preliminarily set the population number n = 25, the maximum iteration number m _max = 50, the learning factors c ₁ = 2.5 and c ₂ , and the inertia factor w in the improved PSO algorithm, and randomly initialize the hyperparameters α and to be optimized in the LSTM model. Neuron.

In the improved PSO algorithm, the optimization range of the number of first and second hidden layer units is set to 0-200, and the values are randomly and uniformly taken on the linear axis; the optimization range of the learning rate is set to 10-4-100, using Search on a logarithmic scale; the loss function during model optimization and training is the mean absolute error function (MAE), the optimizer is the Adam algorithm, the number of iterations is set to 50, and the optimization results are shown in Figure 9. From this, the optimal network model configuration of LSTM is determined: the number of Neuron1 units in the first hidden layer is 80, the number of Neuron2 units in the second hidden layer is 100, and the learning rate α is 0.001.

On the basis of obtaining the optimal network model configuration, perform iterative training of the model. The number of iterations is usually set to 200, and the best model is saved in the form of .ckpt.

Carry out model prediction and testing on the established slope displacement prediction model.

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

Input the test set into the improved PSO-LSTM slope displacement prediction model for rolling prediction, and compare it with the single prediction value of the GRU model, support vector machine regression (SVR) model, and back propagation neural network (BP) model. In order to ensure the reliability of the comparison results, the improved PSO algorithm is also used for model optimization. The prediction results are shown in Figure 10. It can be seen that although the single prediction results of the GRU, SVR and BP models can reflect the general trend of displacement, the prediction effect is not good at the displacement mutation point, making it difficult to cope with some external emergencies. Displacement changes lead to low overall prediction accuracy, and the prediction results of the LSTM collaborative prediction model have the highest consistency with the actual values.

Use formulas (23) and (24) to evaluate the model prediction accuracy. The results are shown in Table 2. It can be seen that the prediction results of the GRU collaborative prediction model have the highest consistency with the actual values, and the goodness of fit R ² is 0.928. The prediction The error MAPE is 0.496%, which is higher than the prediction accuracy evaluation results of each univariate prediction model (the goodness-of-fit ^R2 of the GRU model is 0.528, and the MAPE is 0.696%, which are both better than the 0.267 and 1.283% of the BP model and the SVR model. 0.284, 1.229%), this is because the collaborative prediction model considers the influence of rainfall, the main controlling factor, on the displacement of mountainous slopes, and can better reflect the displacement changes of mountainous slopes caused by external induced factors. In summary, the slope displacement prediction method based on MI-GRA and improved PSO-LSTM proposed in this article introduces the main displacement control factors, which has certain advantages in prediction accuracy and generalization ability, and can well support mountainous areas. Slope displacement prediction.

Table 2 Prediction accuracy evaluation results

The relevant contents of the present invention have been described above. A person of ordinary skill in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by those of ordinary skill in the art without any creative work should fall within the scope of protection of the present invention.

Claims (4)

1. A mountainous slope displacement prediction method based on MI-GRA and improved PSO-LSTM is characterized by including the following steps:

   (1) Collect and construct original data for slope displacement prediction;

   (2) Based on the constructed original data for slope displacement prediction, establish the MI-GRA slope displacement feature selection model;

   (3) Use the feature-selected data as the optimal feature set input for slope displacement prediction, and establish an improved PSO-LSTM slope displacement prediction model;

   (4) Carry out model prediction and testing on the established slope prediction model;

   The step (2) includes: on the basis of the displacement data, using the MI algorithm to select the best historical displacement characteristics; on the basis of the displacement and displacement potential influencing factors data, using the GRA algorithm to select the displacement influencing factor characteristics; comprehensively analyzing the best historical displacement characteristics. Displacement characteristics and displacement influencing factor characteristics are used to obtain the optimal feature set;

   The use of MI algorithm to optimize the best historical displacement characteristics includes the following steps:

   The displacement data is normalized using the following formula:
   
   x _scaled = x _std *(max-min)+min

   In this formula, x is the displacement data to be normalized, x _{min (axis = 0)} is a row vector composed of the minimum value in each column of data, and x _{max (axis = 0)} is composed of the maximum value in each column of data. row vector, 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;

   Construct the feature matrix S _input and the output sequence S _output of each prediction day. The formulas of the feature matrix S _input and the output sequence S _output are as follows:
   
   S _output =[S(t+1) ₁ …S(t+1) _n ] ^T

   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. F _k (k=1,2...30) corresponds to the kth historical displacement feature. , S _output is the output sequence, consisting of predicted displacement data;

   Calculate the mutual information evaluation index I(S _k ; S _output );

   Sorting and optimizing historical displacement features;

   Calculating the mutual information evaluation index includes the following steps:

   Calculate information entropy:
   H(F _k )＝-p(S _k (i))log ₂ ∫p(S _k (i))dS _k (i)
   H(S _output )＝-∫p(S(t+1) _j )log ₂ p(S(t+1) _j )dS(t+1) _j
   H(F _k ,S _output )＝-∫∫p _joint (S _k (i),S(t+1) _j )log ₂ 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, which are used to measure their respective information content; H(F _k ,S _output ) is the historical displacement feature sequence and the two-dimensional joint entropy of the output sequence, 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;

   Calculate 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;

   Using the GRA algorithm to optimize the characteristics of displacement influencing factors includes the following steps:

   Determine the slope displacement characteristics and select the analysis sequence:

   After averaging the displacement data and influencing factor data, set the displacement data as the parent sequence Y ₀ and the displacement influencing factor data as the comparison sequence X, recorded as:
   Y ₀ =[y ₀ (1),y ₀ (2),…,y ₀ (n)]
   

   In this formula, n is the number of days, m is the number of influencing factor indicators of slope displacement;

   Calculate the correlation coefficient:
   

   In this formula, Δx=y ₀ (j)-X _i (j), ρ is the resolution coefficient, generally 0.1 to 1.0, this article takes 0.5;

   Calculate relevance:
   

   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;

   Characteristic ranking of displacement influencing factors and determination of main influencing factors of displacement;

   The establishment of an improved PSO-LSTM slope displacement prediction model in the step (3) includes the following steps: a. Obtain the time series data of the mountainous slope displacement and the main influencing factors of the displacement and normalize it. The normalization process The processing is consistent with that in MI feature selection and the formula used is consistent; b. Divide the data set into a training set, a verification set and a test set, and input the training set and verification set into the LSTM network model; c. Preliminary settings to improve PSO parameters in the algorithm, and randomly initialize the hyperparameters to be optimized in the LSTM model; d. Calculate particle fitness (fit); e. Update the individual optimal respectively and group optimal f. Update the learning factors c ₁ and c ₂ and the 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 Satisfy the discriminant conditions; h. Carry out iterative training of the model on the basis of obtaining the optimal network model configuration, and save the model;

   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 )

   In this formula, i _t is the input gate, f _t is the forgetting 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, and h _t-1 represents the previous The hidden state at the moment, W _i and W _f are the weight matrices to be trained of the input gate and the forget gate respectively, b _i and b _f are the bias terms to be trained of the input gate and the forget gate respectively;

   The candidate state represents the new knowledge summarized 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 value of the long-term memory at the previous moment through the forgetting gate. and the sum of the new knowledge summarized at the current moment through the input gate. The specific calculation process can be expressed as:
   
   

   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, and 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, W _o and _bo are the weight matrix to be trained and the bias term of the output gate respectively, h _t is the hidden state at the current moment;

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

   Improved learning factor, the improved formula of the improved learning factor is as follows:

   
   

   In this formula, m _cur is the current number of iterations, m _max is the maximum number of iterations, c _1b , c _1e , c _2b and c _2e are the initial and final values of c ₁ and c ₂ respectively. Generally, c _1b = 2.5, The algorithm works better when c _1e =0.5, c _2b =0.5 and c _2e =2.5;

   Improved inertia factor

   The larger the inertia factor w, the greater the particle flight speed, and the particles will conduct a global search with a longer step size; the smaller the inertia factor w, the more precise the local search will be. 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, and F _min represents the minimum value of the objective function;

   The objective function uses the mean absolute error MAE on the verification set as the objective function, and its formula is as follows:
   

   In this formula, N represents the number of predicted samples, y (y ₁ , y ₂ ,..., y _N ) is the measured slope displacement value in the verification set, is the predicted slope displacement value on the validation set.
2. A method for predicting slope displacement in mountainous areas based on MI-GRA and improved PSO-LSTM as claimed in claim 1, characterized in that step (1) includes: collecting slope multi-source monitoring data; After collecting the original data, interpolate the missing data; classify the original data into displacement data and data of potential influencing factors of displacement.
3. A mountainous slope displacement prediction method based on MI-GRA and improved PSO-LSTM as claimed in claim 2, characterized in that the interpolation of missing data adopts the method of median interpolation, and the formula is as follows;
   

   In this formula, x _cb is the data after missing value interpolation, x _t-1 is the data at the time before the point to be interpolated, and x _t+1 is the data at the time after the point to be interpolated.
4. A mountain slope displacement prediction method based on MI-GRA and improved PSO-LSTM as claimed in claim 1, characterized in that: the step (4) of performing model prediction and testing on the established slope prediction model includes: The following steps: call the prediction model, and the called prediction model is the improved PSO-LSTM slope displacement prediction model saved after training; input the test set, and perform prediction testing, and the prediction testing method is rolling prediction; obtain the prediction As a result, the model prediction accuracy is evaluated;

   The prediction accuracy of the model is evaluated by selecting the goodness of fit ^R2 and the mean absolute percentage error MAPE, whose formula is as follows:
   
   

   In this formula, R ² is the goodness of fit. The larger the value, the higher the accuracy of the model. MAPE is the average absolute percentage error. The smaller the value, the smaller the prediction error. N is the number of predicted samples, and y _t is the test set. The measured displacement value of is the predicted displacement value on the test set, is the average of the actual measured values.