A method for predicting mountain landslide displacement 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 con

Description

This invention relates to the field of landslide displacement prediction technology, and specifically to a method for predicting mountain landslide displacement based on MI-GRA and improved PSO-LSTM. Background Art China has a vast mountainous area. Influenced by external factors such as earthquakes, rainfall, and floods, various types of landslide disasters, including landslides, collapses, and debris flows, occur frequently. Landslide displacement is a direct representation of landslide deformation. Grasping the laws of landslide displacement changes in mountainous areas is particularly important for the early prediction of landslide failure and the judgment of slope stability. In recent years, with the development of information technology, more and more artificial intelligence prediction methods have been applied to the field of landslide 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 landslide displacement, which restricts the improvement of prediction accuracy. Summary of the Invention The main objective of this invention is to provide a method for predicting mountain landslide displacement based on MI-GRA and improved PSO-LSTM to address the technical problem of existing prediction methods being unable to consider the historical information of landslide displacement, thus limiting the improvement of prediction accuracy. This invention provides a method for predicting mountain landslide displacement based on MI-GRAand improved PSO-LSTM, comprising the following steps: (1) Collecting and constructing the original data for landslide displacement prediction; (2) Based on the constructed original data for landslide displacement prediction, establishing a MI-GRA landslide displacement feature selection model; (3) Using the data after feature selection as the optimal feature set input for landslide displacement prediction, establishing an improved PSO-LSTM landslide displacement prediction model; (4) Conducting model prediction and testing using the established landslide prediction model. Further, step (1) includes:Collecting multi-source monitoring data of landslides;After obtaining the original landslide monitoring data, interpolating the missing data;Classifying the original data into displacement data and potential influencing factor data of displacement. Further, the missing data interpolation adopts the median interpolation method, and its formula is as follows: xt-i+xt+i xcb In this formula, xCb is the data after missing value interpolation, X(m) is the data at the time point before the interpolation point, and X(t+i) is the data at the time point after the interpolation point. Further, step (2) includes:Based on the displacement data, using the Ml algorithm to select the best historical displacement features;Based on the displacement data and potential influencing factor data of displacement, using the GRA algorithm to select the displacement influencing factor features;Combining the best historical displacement features and displacement influencing factor features to obtain the optimal feature set. Further, the use of the Ml algorithm to select the best historical displacement features includes the following steps: Normalizing the displacement data, the normalization formula is as follows: X Xmjn(-axjs=o) xstd = ---------—------- Amin(axis=O) Amax(axis=O) ^scaled = *std * (max - min) + min where x is the displacement data to be normalized, xmin(axis=o) is the row vector composed of the minimum values in each column, xmax(axis=o) is the row vector composed of the maximum values in each column, max is the maximum value of the target interval, default is 1, min is the minimum value of the target interval, default is 0, xstd is the standardized result, and Xscaied is the normalized result; Constructing the feature matrix Sinput and output sequence Soutput for each prediction day, The formulas for Sinput and Soutput are as follows: Sinput = [F1 F2 F3 F4 - F3(>] S(t)t S(t-l)i S(t-2)i S(t-3)i - S(t- 29)f S(t)n S(t—l)n S(t —2)n S(t —3)n - S(t-29)n. Soutput = [S(t+ 1)1 - S(t+l)n]T where Sinput is the feature matrix composed of historical displacement features, n is taken as 30, representing 30 historical displacement features, Fk (k=1,2...3O) corresponds to the k-th historical displacement feature, and Soutput is the output sequence composed of predicted displacement data; Calculating the mutual information evaluation index I(Sk; Soutput); Ranking and selecting historical displacement features. Further, calculating the mutual information evaluation index includes the following steps: Calculating information entropy: H(Fk) = -p(Sk(i))log2 f p(Sk(i))dSk(i) H(Soutput) = -f p(S(t + l)j)log2 p(S(t+ l)j)dS(t+ l)j H(Fk> Soutput) = — fJ Pjoint (Sk(0> S(t + l)j)log2 Pjoint (Sk(0»S(t+ l)j)dSk(i)dS(t + l)j where H(Fk) and H(Soutput) are the information entropy of the historical displacement feature sequence and the output sequence, respectively, used to measure their respective information content; H(Fk, Soutput) is the two-dimensional joint entropy of the historical displacement feature sequence and the output sequence, used to quantify the amount of shared information between variables, p is the marginal probability distribution of a single variable, and pjOint is the joint probability distribution between two variables; Calculating mutual information l(Sk! Soutput): l(Fk;Soutput) - H(Fk) + H(Soutput) - H(Fk,Soutput) rr / a Pioint (Sk(i)»S(t+l)j) = l)01og2^^^dSkffl where l(Fk; Soutput) is the mutual information between the historical displacement feature sequence and the output sequence. Further, using the GRA algorithm to select displacement influencing factor features includes the following steps: Determining the analytical series for landslide displacement feature selection: After averaging the displacement data and influencing factor data, let the displacement data be the reference sequence Yo, and the displacement influencing factor data be the comparison sequence X, denoted as: y0 - [yo(i),yo(2),-,y0(n)] rX^l) X1(2) - X^n)! v_ X2(l) X2(2) - X2(n) where n is the number of days, and m is the number of influencing factor indicators for landslide displacement; Calculating the correlation coefficient: minmm|Ax|+P maxmax| A x| € - 1 pX|+P„x;X| where Ax = yo(j) - Xi(j), p is the resolution coefficient, generally taken as 0.1 ~1.0, and in this paper, it is taken as 0.5; Calculating the degree of relevance: Y (Y0,Xj) = where y is the degree of relevance, Generally, when it is greater than 0.6, the sequences are considered to be strongly correlated, i = 1, 2, ..., m; j = 1, 2, ..., n Ranking displacement influencing factor features and determining the main influencing factors of displacement. Further, in step (3), establishing the improved PSO-LSTM landslide displacement prediction model includes the following steps: a. Obtaining time series data of mountain landslide displacement and main influencing factors of displacement and normalizing them, The normalization process and formula are the same as those in Ml feature selection; b. Dividing the dataset into training, validation, and test sets, and inputting the training and validation sets into the LSTM network model; c. Initially setting the parameters in the improved PSO algorithm and randomly initializing the hyperparameters to be optimized in the LSTM model; d. Calculating particle fitness (fit); e. Updating the individual best and the global best p|d, respectively; f. Updating the learning factors ci and C2, and the inertia factor w; g. Determining whether the number of iterations is greater than mmax, If the condition is met, the improved PSO algorithm optimization ends; otherwise, go to step 3 and repeat steps d, e, and f until the discriminant condition is met; h. Iteratively training the model based on the optimal network model configuration and saving the model. Further, the LSTM network model is a deep learning model, A forward calculation of an LSTM network model recurrent unit is: it - ° (Wj ■ [h^^xj +bs) ft = ° (Wf- [ht^xj +bf) where it is the input gate, ft is the forget gate, o is the sigmoid activation function, which can make the range of the gate between 0 and 1, xt is the input feature at the current time, represents the hidden state at the previous time, Wi and Wf are the weight matrices to be trained for the input gate and forget gate, respectively, and bi and bf are the bias terms to be trained for the input gate and forget gate, respectively. The candidate state represents the new knowledge to be stored in the cell state, which is a function of the current input features and the hidden state of the previous time, the cell state represents long-term memory, which is equal to the sum of the long-term memory of the previous time passing through the forget gate and the new knowledge induced at the current time passing through the input gate, the specific calculation process can be expressed as: Ct = tan^ (wc ■ L , xt] + bc) Ct — ft * Ct_i + it * Ct where ct is the candidate state, tanh is the activation function, Wc is the weight matrix to be trained, be is the bias term to be trained, Ct is the cell state at the current time, and C(t-i) is the cell state at the previous time; 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: ot = o (Wo ■ [ht-i.xj +bo) ht = ot * tanh(Ct) where Ot is the output gate, Wo and b0 are the weight matrix and bias term to be trained for the output gate, respectively, and h is the hidden state at the current time; The improved PSO algorithm is an optimization algorithm for the traditional PSO algorithm, including: Improved learning factor, the improved formula for the learning factor is as follows: / \ ., ( mcur V Ci - (cle - Clb) X I —---) + Clb (m \ L11cur \ ------I + C2b where mCUr is the current iteration number, rnmax is the maximum iteration number, cib, Cie, C2b, and C2e are the initial and final values of ci and C2, respectively; generally, the algorithm performs better when cib = 2.5, Cie = 0.5, C2b = 0.5, and C2e = 2.5. Improved inertia factor the larger the inertia factor w, the greater the particle flight speed, and the particle will perform a global search with a longer step length; the smaller the inertia factor w, the more it tends to fine local search; the improved formula is as follows: where Wmax represents the maximum value of oo, oomin represents the minimum value of oo, F represents the current objective function value, Favg represents the current average objective function value, and Fmin 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, the formula is as follows: N fit - mae = -Y |yt-yTI IN t=l where N represents the number of predicted samples, y(y1(y2,-,Yn) is the measured landslide displacement value in the validation set, and yCypy],-,W) is the predicted landslide displacement value on the validation set. Further, the step (4) of performing model prediction and testing with the established slope prediction model includes the following steps: calling the prediction model, where the called prediction model is the saved improved PSO-LSTM slope displacement prediction model after training; inputting the test set and performing prediction tests, where the prediction test method is rolling prediction; obtaining the prediction results and evaluating the model prediction accuracy; the model prediction accuracy evaluation adopts the coefficient of determination R2 and the mean absolute percentage error MAPE, and their formulas are as follows: r2 _ 1 ^i(yt-yt)2 2Xi(yt-y)2 N in these formulas, R2 is the coefficient of determination, and the larger its value, the higher the model accuracy; MAPE is the mean absolute percentage error, and the smaller its value, the smaller the prediction error; N is the number of predicted samples; yt is the measured displacement value in the test set; yt is the predicted displacement value on the test set; and y is the average of the measured values. The design idea of this invention, a mountainous landslide displacement prediction method based on MI-GRA and improved PSO-LSTM, is as follows: The change of landslide displacement is a dynamic process, and Long Short Term Memory (LSTM) has the function of memorizing historical information and has great advantages in processing long time series data. Therefore, it is theoretically feasible to apply the LSTM deep learning algorithm to mountainous landslide displacement prediction. Previous landslide displacement prediction only focused on the displacement itself, mining the change law of displacement time series through mathematical methods, and failed to incorporate displacement influencing factors into the prediction model, which is also an important reason for the poor prediction effect. Therefore, to accurately predict future landslide displacement changes, it is an important research direction to consider fusing multi-source heterogeneous influencing factors for collaborative prediction. There are many input features for landslide displacement prediction models. Inputting redundant and irrelevant features into the GRU prediction model may mask the role of important features and increase the difficulty of model training. Therefore, it is necessary to perform feature selection before establishing an accurate landslide displacement prediction model to mine and extract effective input features. In summary, it is necessary to combine feature selection algorithms and displacement prediction models to perform fusion and collaborative prediction of multi-source data of mountainous landslides. This method has better prediction accuracy and generalization ability, providing a new idea for early prediction of mountainous landslide failure and pre-judgment of landslide stability. The beneficial effects of this invention, a mountainous landslide displacement prediction method based on MI-GRA and improved PSO-LSTM, compared with the prior art are: This method solves the problems that previous prediction algorithms are static in nature and cannot consider the historical information of landslide displacement, thus limiting the improvement of prediction accuracy, and that previous landslide displacement prediction only focused on the displacement itself, failing to incorporate displacement influencing factors into the prediction model, resulting in poor prediction effects. In the era of information technology, combining deep learning algorithms and feature selection algorithms, feature selection is performed before establishing an accurate landslide displacement prediction model to mine and extract effective input features, obtaining the optimal feature set for landslide displacement prediction. Then, using metaheuristic algorithms and deep learning algorithms, an improved PSO-GRU collaborative prediction model based on dominant factors is established to perform fusion and collaborative prediction of multi-source data of mountainous landslides. Based on the in-situ test results of mountainous landslide monitoring, the results show that under the effect of this mountainous landslide displacement prediction method based on MI-GRA and improved PSO-LSTM, the average mutual information of the historical displacement features of the previous 5 days is 1.33, which is much higher than the average mutual information of the latter 25 days, which is 0.86. The correlation between rainfall and displacement is the largest (0.82), indicating that external rainfall is the dominant factor affecting mountainous landslide displacement. The historical displacement and rainfall features of the previous 5 days of the prediction day are selected as the optimal feature set. The improved PSO-GRU prediction model based on rainfall as the dominant factor has high prediction accuracy at the displacement mutation point, with a coefficient of determination RA2 of 0.928. This method has good prediction accuracy and generalization ability, providing a new idea for early prediction of mountainous landslide failure and pre-judgment of landslide stability. The invention will be further illustrated 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 become apparent from the description, or may be learned by practice of the invention. Brief Description of the Drawings The drawings forming part of this invention are included to further facilitate the understanding of the invention. The content provided in the drawings and the related descriptions in this invention can be used to explain the invention, but do not constitute an undue limitation to the invention. In the drawings: Figure 1: Flowchart of the mountain landslide displacement prediction method based on MI-GRA and improved PSO-LSTM. Figure 2: Flowchart of collecting and constructing original data. Figure 3: Flowchart of building the MI-GRA mountain landslide displacement feature selection model. Figure 4: Flowchart of establishing the improved PSO-LSTM mountain landslide displacement prediction model. Figure 5: Optimization process diagram of the improved PSO algorithm. Figure 6: Evolution diagram of RNN and LSTM. Figure 7: Analysis result diagram of the Ml algorithm. Figure 8: Correlation analysis result of GRA. Figure 9: Optimization result of the improved PSO. Figure 10: Results of collaborative prediction and single prediction. Detailed Implementation Method The invention will be clearly and completely described below with reference to the accompanying drawings. A person skilled in the art will be able to implement the invention based on these descriptions. Before describing the invention in conjunction with the drawings, it should be particularly pointed out that: The technical solutions and technical features provided in various parts of this invention, including the following description, can be combined with each other without conflict. Furthermore, the embodiments of the invention involved in the following description are generally only some embodiments of the invention, and not all embodiments. Therefore, based on the embodiments in this invention, all other embodiments obtained by a person skilled in the art without creative effort shall fall within the protection scope of this invention. Regarding the terms and units in this invention, the terms "comprising," "having," and any variations thereof in the description, claims, and related parts of this invention are intended to cover non-exclusive inclusions. This invention provides a method for predicting mountain landslide displacement based on MI-GRAand improved PSO-LSTM, comprising the following steps: (1) Collecting and constructing the original data for landslide displacement prediction; (2) Based on the constructed original data for landslide displacement prediction, establishing a MI-GRA landslide displacement feature selection model; (3) Using the data after feature selection as the optimal feature set input for landslide displacement prediction, establishing an improved PSO-LSTM landslide displacement prediction model; (4) Conducting model prediction and testing using the established landslide prediction model. Furthermore, step (1), collecting and constructing the original data for landslide displacement prediction, is mainly divided into three steps, including: Collection of multi-source monitoring data of landslides: Specifically, multi-source data of landslides are acquired in real-time through intelligent sensors at the landslide monitoring site in mountainous areas, and collected through wireless transmission methods. Interpolation of missing data: Specifically, after obtaining the original multi-source monitoring data of the mountainous landslides, the median interpolation method is used to interpolate the missing data to ensure the integrity and quality of the original data, providing a guarantee for subsequent data analysis. Classification of original data: Specifically, the original data are classified into displacement data and potential influencing factor data of displacement. The potential influencing factor data of displacement can include rainfall, groundwater level, pore water pressure, moisture content, slope gradient, slope top surcharge, earth pressure, crack width, and other 12 possible influencing factors. Further, the missing data interpolation adopts the median interpolation method, and its formula is as follows: _ Xt-1 + Xt+1 Z4 \ xcb — 2 ' ' In this formula, xCb is the data after missing value interpolation, X(t-i) is the data at the time point before the interpolation point, and X(t+i) is the data at the time point after the interpolation point. Furthermore, in the aforementioned step (2): The establishment of the MI-GRA mountain landslide displacement feature selection model mainly refers to landslide displacement prediction features, which can be divided into displacement itself and displacement influencing features. That is, historical displacement features may overshadow other features, so historical displacement and displacement influencing factors are considered separately. The Ml algorithm and the GRA algorithm are used to optimize the two different types of features, respectively. This process is mainly divided into three steps: Optimizing the best historical displacement features based on the Ml algorithm: Based on the mountain landslide displacement data, the Mutual Information (Ml) algorithm is used to select the optimal historical displacement features. Optimizing the displacement influencing factor features based on the GRA algorithm: Based on the mountain landslide displacement data and potential influencing factor data, the Grey Relational Analysis (GRA) algorithm is used to select the optimal displacement influencing factors. Obtaining the optimal feature set: The optimal historical displacement features and displacement influencing factor features are combined to obtain the optimal feature set. The process of optimizing the best historical displacement features using the Ml algorithm includes the following steps: To ensure the computational speed and accuracy in the subsequent feature selection process, the mountain landslide displacement data is normalized to the range of [0,1]. The normalization of the data uses the following formula: _ x-xmin(axis=0) / n\ ^■std — / xmin(axis=0)—xmax(axis=0) Scaled = xstd * (max - min) + min (3) where x is the displacement data to be normalized, xmin(axis=o) is the row vector composed of the minimum values in each column, Xmax(axis=0) is the row vector composed of the maximum values in each column, max is the maximum value of the target interval, default is 1, min is the minimum value of the target interval, default is 0, xstd is the standardized result, and Xscaied is the normalized result. To analyze the information between historical displacement features and the displacement feature to be predicted, a feature matrix Sinput and an output sequence Soutput are constructed for each prediction day. The formulas for the feature matrix Sinput and the output sequence Soutput are as follows: Sinput = [F1 F2 F3 F4 - F30] -S(t)t S(t- l)i S(t- 2)t S(t —3)i - S(t —29)t' S(t)n S(t-l)n S(t - 2)n S(t-3)n S(t - 29)n (4) Soutput = [S(t+ lh -- S(t+l)n]T where Sinput is the feature matrix composed of historical displacement features, n is taken as 30, representing 30 historical displacement features, Fk (k=1,2...3O) corresponds to the k-th historical displacement feature, and Soutput is the output sequence composed of predicted displacement data. Calculating the mutual information evaluation index l(Sk! Soutput), the mutual information evaluation index l(Sk; Soutput) represents the mutual information between the historical displacement feature sequence and the output sequence. Historical displacement feature ranking and selection, Specifically, the historical displacement features are ranked and selected by sorting the mutual information values in 14 descending order. 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: Calculating information entropy: H(Fk) = —p(Sk(i))log2 f p(Sk(i)) dSk(i) (5) H(Soutput) = -f p(S(t + l)j)log2 p(S(t + l)j)dS(t + l)j (6) H(Fk, Soutput) = - ff pjoint (Sk(i), S(t + l)j)log2 pjoint (Sk(i), S(t + l)j)dSk(i)dS(t + 1), (7) where H(Fk) and H(Soutput) are the information entropy of the historical displacement feature sequence and the output sequence, respectively, used to measure their respective information content; H(Fk, Soutput) is the two-dimensional joint entropy of the historical displacement feature sequence and the output sequence, used to quantify the amount of shared information between variables, p is the marginal probability distribution of a single variable, and pjoint is the joint probability distribution between two variables. Calculating mutual information l(Sk; Soutput): l(Fk; Soutput) — H(Fk) + H(Soutput) — H(Fk, Soutput) — ff PjOjnt (Sk(i), S(t + l)j)10g2 Pjo.nt(Sk(i),S(t+l)j) dSk(i)dS(t + 1),. (8) 82 p(Sk(i))p(S(t+l)j) } V \ / where l(Fk; Soutput) is the mutual information between the historical displacement feature sequence and the output sequence. Further, using the GRA algorithm to select displacement influencing factor features includes the following steps: Determining the analytical series for landslide displacement feature selection. After averaging the displacement data and influencing factor data, let the displacement data be the reference sequence Yo, and the displacement influencing factor data be the comparison sequence X, denoted as: Yo = [yo(iXyo (2),-,y0(n)] (9) rX^l) Xt(2) - X^n)! x= X2(l) X2(2) - X2(n) *m(l) Xm(2) - Xm(n). where n is the number of days, and m is the number of influencing factor indicators for landslide displacement. Calculating the correlation coefficient: mjnmin| A x|+ p maxmax| A x| C (yoO-XjQ)) = —;1।----- (11) | Ax|+P m.axmax| Ax| V ' where Ax = yo(j) - XiQ), p is the resolution coefficient, generally taken as 0.1 ~1.0, and in this paper, it is taken as 0.5. Calculating the degree of relevance: YfYo.XO^i^i €(yo(j),Xia)) (12) where y is the degree of relevance, Generally, when it is greater than 0.6, the sequences are considered to be strongly correlated, i = 1, 2, ..., m; j = 1, 2, ..., n. Ranking displacement influencing factor features and determining the main influencing factors of displacement. Furthermore, step (3), improving the PSO-LSTM landslide displacement prediction model, is mainly divided into three aspects: dataset construction, improved PSO-GRU neural network architecture construction, model training, and saving. Step (3), establishing the improved PSO-LSTM landslide displacement prediction model, includes the following steps: a. Data Preprocessing: Obtain the time-series data of mountain landslide displacement and its main influencing factors and normalize them. The normalization process is consistent with that in Ml feature selection, using the same formula: The purpose of normalization is to ensure that the input features are within the range of 0-1, guaranteeing the computational efficiency and convergence speed of the neural network. b. Dataset Splitting: Divide the dataset into training, validation, and test sets. The training and validation sets are input into the LSTM network model. Specifically, the training and validation sets are used for model training and configuration optimization, while the test set is used for prediction and testing. The dataset is divided into training, validation, and test sets according to a 6:2:2 ratio. The LSTM model is an improved version (variant) of RNN. LSTM introduces a memory cell based on RNN and designs three gates: input gate, forget gate, and output gate. Through the gate mechanism, the flow and loss of information are controlled, which effectively solves the long-term dependency problem of RNN. c. Parameter Initialization: Initially set the parameters in the improved PSO algorithm and randomly initialize the hyperparameters to be optimized in the LSTM model. Initially set parameters such as population size n, maximum number of iterations mmax, learning factors ci and C2, and inertia factor w in the improved PSO algorithm. Randomly initialize the hyperparameters a (learning rate) and Neuron (number of neurons) to be optimized in the LSTM model. The improved PSO algorithm is a metaheuristic algorithm. To ensure the prediction accuracy of the LSTM network model, the hyperparameters (learning rate a and the number of neurons Neuron) of the LSTM network model are optimized to achieve their adaptive determination. d. Fitness Calculation: Calculate the particle fitness (fit). The mean absolute error (MAE) on the validation set is used as the objective function to calculate the particle fitness (fit). e. Update Individual and Global Best: Update the individual best and the global best Pgd according to the principle of fitness minimization. f. Update Learning Factors and Inertia Factor: Update the learning factors ci and C2 and the inertia factor w. Non-linearly update the learning factors ci and C2 so that they co-evolve with the number of iterations to avoid premature convergence. Adaptively optimize the inertia factor w according to formula (21) so that it co-evolves with the number of iterations to avoid premature convergence. (Please provide formula 21 for a complete translation). g. Termination Condition: Determine whether the number of iterations is greater than mmax. If the condition is met, the improved PSO algorithm optimization ends. Otherwise, go to step d and repeat steps d, e, and f until the termination condition is met. h. Model Training and Saving: Perform iterative training of the model based on the optimal network model configuration and save the model. The number of iterations is typically set between 100 and 200. Save the model in the .ckpt format. Further, the LSTM network model is a deep learning model, A forward calculation of an LSTM network model recurrent unit is: it = O (Wj ■ xt +bj) (13) ft - 0 (Wf- ^t l,xt +bf) (14) where it is the input gate, ft is the forget gate, a is the sigmoid activation function, which can make the range of the gate between 0 and 1, xt is the input feature at the current time, h _ represents the hidden state at the previous time, Wi and Wf are the weight matrices to be trained for the input gate and forget gate, respectively, and bi and bf are the bias terms to be trained for the input gate and forget gate, respectively. The candidate state represents the new knowledge to be stored in the cell state, which is a function of the current input features and the hidden state of the previous time, the cell state represents long-term memory, which is equal to the sum of the long-term memory of the previous time passing through the forget gate and the new knowledge induced at the current time passing through the input gate, the specific calculation process can be expressed as: Ct = tan4 (wc • pt l, xt] + bc) (15) Ct = ft * Ct_t + it * ct (16) where ct is the candidate state, tan^ is the activation function, Wc is the weight matrix to be trained, be is the bias term to be trained, Ct is the cell state at the current time, and C(t-i) is the cell state at the previous time. 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: Ot = O (wo ■ ptl, xt] + bo) (17) — ot * tan4(Ct) (18) where Ot is the output gate, Wo and b0 are the weight matrix and bias term to be trained for the output gate, respectively, and h is the hidden state at the current time. The improved PSO algorithm is an optimization algorithm for the traditional PSO algorithm, including: Improved learning factor, the improved formula for the learning factor is as follows: z , 3 Cl = (cle - clb) X + clb (1 9) z , 3 c2 - (c2e _ c2b) x + c2b (20) vmmax / where mCUr is the current iteration number, mmax is the maximum iteration number, cw, Cie, C2b, and C2e are the initial and final values of ci and C2, respectively; generally, the algorithm performs better when cib = 2.5, Cie = 0.5, C2b = 0.5, and C2e = 2.5. Improved inertia factor the larger the inertia factor w, the greater the particle flight speed, and the particle will perform a global search with a longer step length; the smaller the inertia factor w, the more it tends to fine local search; the improved formula is as follows: CO ----- CO p Foxxrr max dV& where Umax represents the maximum value of oo, oomin represents the minimum value of oo, F represents the current objective function value, Favg represents the current average objective function value, and Fmin 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, the formula is as follows: fit = MAE = i^=1|yt — y^| (22) where N represents the number of predicted samples, y(yi,y2,-,yN) is the measured landslide displacement value in the validation set, and y(yl,71,-,Tn) is the predicted landslide displacement value on the validation set. Further, the step (4) of performing model prediction and testing with the established slope prediction model includes the following steps: Calling the prediction model, where the called prediction model is the saved improved PSO-LSTM slope displacement prediction model after training. Inputting the test set and performing prediction tests, where the prediction test method is rolling prediction. Obtaining the prediction results and evaluating the model prediction accuracy. The model prediction accuracy evaluation adopts the coefficient of determination R2 and the mean absolute percentage error MAPE, and their formulas are as follows: in these formulas, R2 is the coefficient of determination, and the larger its value, the higher the model accuracy; MAPE is the mean absolute percentage error, and the smaller its value, the smaller the prediction error; N is the number of predicted samples; yt is the measured displacement value in the test set; yt is the predicted displacement value on the test set; and y is the average of the measured values. The following specific examples further illustrate the present invention: The examples and their implementation processes according to the complete method of the present invention are as follows: Collection and Construction of Original Data for Landslide Displacement Prediction: Based on a mountainous landslide site, inclinometers are installed at different locations and depths of the slope to measure displacement data. Simultaneously, rainfall stations, humidity meters, water level observation holes, and pore water pressure gauges are deployed to obtain data on potential influencing factors. Multi-source monitoring data of the slope is collected through wireless transmission, resulting in a total time-series sample length of 146 records. Part of the data is shown in Table 1 below (please provide Table 1 for a complete translation). After obtaining the original multi-source monitoring data of the mountain landslide, the median interpolation method shown in formula (1) (please provide formula 1 for a complete translation) is used to interpolate the missing data, ensuring the integrity and quality of the original data and providing a guarantee for subsequent data analysis. The original data is classified into displacement data and potential displacement influencing factor data. The potential displacement influencing factor data includes rainfall, groundwater level, pore water pressure, moisture content, slope gradient, crest surcharge, and earth pressure (as shown in Table 1 below). Table 1 Multi-source Monitoring Data of Landslide Horizontal Displacement Rainfall Ground water Level Pore Water Pressure Moisture Content Slope Gradient Crest Surcharge Earth Pressure 0.00 0.12 7.6 0 55.864 33.69 200.00 0 0.39 0.56 7.6 0 55.71 33.69 200.00 0 0.52 0.78 7.5 0 55.968 33.69 200.00 1 1.02 0.56 7.4 2 55.761 33.69 500.00 2 1.88 9.12 7.4 0 55.916 33.69 500.00 2 1.84 0.56 7.4 0 55.813 33.69 500.00 3 1.95 0.43 7.3 0 55.813 33.69 500.00 3 1.54 0.55 7.4 1.00 55.146 33.69 500.00 3 Establishing the MI-GRA Mountainous Landslide Displacement Feature Selection Model: The mountainous railway landslide displacement data obtained from step 1) is input into the Ml model, and the Ml algorithm is used to select the best historical displacement features. The detailed process is as follows: (T) Normalization: To ensure the computational speed and accuracy in the subsequent feature selection process, the mountainous landslide displacement data is normalized to the range of [0, 1]. (2) Ml Calculation: The normalized data is input into the Ml model, and the mutual information evaluation index I is calculated. The results are shown in Figure 7 (please provide Figure 7 for a complete translation). (3) Feature Ranking: Based on the calculation results, the displacement features are ranked. The top five historical displacement features are S1 (1.58) >S2 (1.34) >S4 (1.27) >S3 (1.25) >S5 (1.21). Therefore, these five features, S1 to S5, are selected as the best historical displacement features. The mountainous railway landslide displacement data and displacement influencing factor data obtained from step 1) are input into the GRA model, and the GRA algorithm is used to select the best historical displacement features. The detailed process is as follows: (T)’ Averaging: To ensure the computational speed and accuracy in the subsequent feature selection process, the mountainous railway landslide displacement data and displacement influencing factor data are averaged. (2)’ GRA Calculation: The averaged data is input into the GRA model, and the degree of correlation between each influencing factor and landslide displacement is calculated. The results are shown in Figure 8 (please provide Figure 8 for a complete translation). (3)’ Feature Ranking: Based on the calculation results, the displacement features are ranked: Rainfall (0.82) >Moisture Content (0.76) >Pore Water Pressure (0.70) >Groundwater Level (0.63) >Slope Gradient (0.58) >Earth Pressure (0.54) >Crest Surcharge (0.53). Rainfall has the strongest correlation with displacement, with a correlation degree of 0.82. Therefore, rainfall is selected as the main controlling factor affecting landslide displacement. In summary, the historical displacement of the previous 5 days and the rainfall feature are selected as the optimal feature set and input into the improved PSO-GRU prediction model. Establishing the Improved PSO-LSTM Mountainous Landslide Displacement Prediction Model: Normalization: The time-series data of landslide displacement and rainfall are normalized to ensure that the input features are within the range of 0~1, guaranteeing the computational efficiency and convergence speed of the neural network. Dataset Splitting: The dataset is divided into training, validation, and test sets according to a 6:2:2 ratio. The training and validation sets are input into the LSTM network model. Parameter Initialization: Initially set the parameters in the improved PSO algorithm: population size n=25, maximum number of iterations m_max=50, learning factors ci=2.5 and C2 (value for C2 is missing), and inertia factor w. Randomly initialize the hyperparameters a and Neuron in the LSTM model. PSO Optimization: In the improved PSO algorithm, the search range for the number of units in the first and second hidden layers is set to 0-200, randomly and uniformly sampled on a linear scale. The search range for the learning rate is set to 10-4 - 100, using a logarithmic scale for searching. The loss function for both model optimization and training is the Mean Absolute Error (MAE) function. The optimizer is the Adam algorithm, and the number of iterations is set to 50. The optimization results are shown in Figure 9 (please provide Figure 9 for a complete translation). The optimal network model configuration for LSTM is determined as follows: the number of units in the first hidden layer (Neuron 1) is 80, the number of units in the second hidden layer (Neuron2) is 100, and the learning rate (a) is 0.001. Model Training and Saving: Based on the optimal network model configuration, iterative training of the model is performed. The number of iterations is typically set to 200. The best model is saved in the .ckpt format. Model Prediction and Testing: Model Loading: Call the saved improved PSO-LSTM landslide displacement prediction model from step 3. Rolling Prediction: Input the test set into the improved PSO-LSTM landslide displacement prediction model for rolling prediction. Compare the results with the single prediction values of the GRU model, Support Vector Regression (SVR) model, and Back Propagation Neural Network (BP) model. 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 (please provide Figure 10 for a complete translation). 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 at the displacement mutation points is not good, and it is difficult to cope with displacement changes caused by some external emergencies, resulting in low overall prediction accuracy. The prediction results of the LSTM collaborative prediction model have the highest degree of agreement with the actual values. Model Evaluation: Use formulas (23) and (24) (please provide formulas 23 and 24 for a complete translation) to evaluate the model prediction accuracy. The results are shown in Table 2 (please provide Table 2 for a complete translation). It can be seen that the prediction results of the GRU collaborative prediction model have the highest degree of agreement with the actual values. The goodness of fit RA2 is 0.928, and 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 RA2 of the GRU model is 0.528, and the MAPE is 0.696%, both better than the BP model's 0.267, 1.283% and the SVR model's 0.284, 1.229%). This is because the collaborative prediction model considers the influence of rainfall, the main controlling factor, on mountainous landslide displacement and can better reflect the displacement changes caused by external inducing factors. In summary, the landslide displacement prediction method based on MI-GRAand improved PSO-LSTM proposed in this paper introduces the main controlling factor of displacement, which has certain advantages in prediction accuracy and generalization ability and can well support landslide displacement prediction in mountainous areas. Table 2 Prediction Accuracy Evaluation Results Model Type R2 MAPE BP Univariate Prediction 0.267 1.283% SVR Univariate Prediction 0.284 1.229% GRU Univariate Prediction 0.484 1.062% GRU Collaborative Prediction 0.928 0.496% The foregoing description sets forth the features of the present invention. A person of ordinary skill in the art, having the benefit of this disclosure, will be able to implement the invention. Based on the foregoing, all other embodiments obtainable by persons skilled in the art without undue experimentation or inventive effort are within the intended scope of the invention.

Claims

1. A method for predicting mountain landslide displacement based on MI-GRA and improved PSO-LSTM, characterized by the following steps:(1) Collecting and constructing raw data for landslide displacement prediction;(2) Based on the constructed raw data, establishing a MI-GRA landslide displacement feature selection model;(3) Using the data after feature selection as the optimal feature set input for landslide displacement prediction, establishing an improved PSO-LSTM landslide displacement prediction model;(4) Performing model prediction and testing with the established landslide prediction model; Step (2) includes: Based on the displacement data, using the Ml algorithm to select the best historical displacement features; based on the displacement and potential displacement influencing factor data, using the GRA algorithm to select the displacement influencing factor features; combining the best historical displacement features and displacement influencing factor features to obtain the optimal feature set;Using the Ml algorithm to select the best historical displacement features includes the following steps:Normalizing the displacement data, the normalization formula is as follows:^min(axis=0)^min(axis=0) — ^max(axis=0)^scaled = *std * (max - min) + minwhere x is the displacement data to be normalized, xmin(axis=o) is the row vector composed of the minimum values in each column, Xmax(axis=O) is the row vector composed of the maximum values in each column, max is the maximum value of the target interval, default is 1, min is the minimum value of the target interval, default is 0, xstd is the standardized result, and Xscaied is the normalized result;Constructing the feature matrix Sinput and output sequence Soutput for each prediction day, The formulas for Sinput and Soutput are as follows:Sinput = [Fi F2 F3 F4 - F30]Xt)t SCt-1), S(t —2)4 S(t—3)4 - S(t-29)fS(t)„ S(t-l)n S(t —2)n S(t-3)n - S(t—29)n.Soutput = [S(t+ 1)1 - S(t+l)n]Twhere Sinput is the feature matrix composed of historical displacement features, n is taken as 30, representing 30 historical displacement features, Fk (k=1,2...30) corresponds to the k-th historical displacement feature, and Soutput is the output sequence composed of predicted displacement data;Calculating the mutual information evaluation index l(Sk! Soutput);Ranking and selecting historical displacement features;Calculating the mutual information evaluation index includes the following steps: Calculating information entropy:H(Fk) = -p(sk(i))log2 f p(Sk(0)dSk(i) H(S0Utput) = -f p(S(t+ l)j)log2 p(S(t+ l)j)dS(t+ l)jH(Fk, Soutput) - -ff pJoint (Sk(i), S(t + 1)j)log2 pJoint (Sk(i), S(t + 1 )j)dSk(i)dS(t + 1), where H(Fk) and H(SOutPut) are the information entropy of the historical displacement feature sequence and the output sequence, respectively, used to measure their respective information content; H(Fk, Soutput) is the two-dimensional joint entropy of the historical displacement feature sequence and the output sequence, used to quantify the amount of shared information between variables, p is the marginal probability distribution of a single variable, and pjoint is the joint probability distribution between two variables;Calculating mutual information l(Sk! Soutput):l(Fk; Soutput) = H(Fk) + H(Soutput) - H(^k' ^output)rr / x Pjoint (Sk(0> S(t + 1).-)= / / p,o,„, (skG). set + D,)^ i),where l(Fk; S„„tPut) is the mutual information between the historical displacement feature sequence and the output sequence;Using the GRA algorithm to select displacement influencing factor features includes the following steps:Determining the analytical series for landslide displacement feature selection:After averaging the displacement data and influencing factor data, let the displacement data be the reference sequence Yo, and the displacement influencing factor data be the comparison sequence X, denoted as:y0 = [yo(i),yo(2), -,y0(n)]rXt(l) Xt(2) - Xt(n)ix= x’w xfJ -Xm(l) Xm(2) - Xm(n).where n is the number of days, and m is the number of influencing factor indicators forlandslide displacement;Calculating the correlation coefficient:minmin| Ax| + p maxmax| Ax|€ (yoCD-w) = 1 pX|+p„x;X|where Ax = yo(j) - Xi(j), P is the resolution coefficient, generally taken as 0.1 ~1.0, and in this paper, it is taken as 0.5;Calculating the degree of relevance:where y is the degree of relevance, Generally, when it is greater than 0.6, the sequences are considered to be strongly correlated, i = 1, 2, ..., m; j = 1, 2, ..., n;Ranking displacement influencing factor features and determining the main influencing factors of displacement;In step (3), establishing the improved PSO-LSTM landslide displacement prediction model includes the following steps: a. Obtaining time series data of mountain landslide displacement and main influencing factors of displacement and normalizing them, The normalization process and formula are the same as those in Ml feature selection; b. Dividing the dataset into training, validation, and test sets, and inputting the training and validation sets into the LSTM network model; c. Initially setting the parameters in the improved PSO algorithm and randomly initializing the hyperparameters to be optimized in the LSTM model; d. Calculating particle fitness (fit); e. Updating the individual best and the global best p^d, respectively; f. Updating the learning factors ci and C2, and the inertia factor w; g. Determining whether the number of iterations is greater than mmax, If the condition is met, the improved PSO algorithm optimization ends; otherwise, go to step 3 and repeat steps d, e, and f until the discriminant condition is met; h. Iteratively training the model based on the optimal network model configuration and saving the model;The LSTM network model is a deep learning model, A forward calculation of an LSTM network model recurrent unit is:it = o (Wj ■ [ht_t,xt] +bj) ft = o (Wf [ht-t.Xt] +bf)where it is the input gate, ft is the forget gate, o is the sigmoid activation function, which can make the range of the gate between 0 and 1, xt is the input feature at the current time, ht_x represents the hidden state at the previous time, Wi and Wf are the weight matrices to be trained for the input gate and forget gate, respectively, and bi and bf are the bias terms to betrained for the input gate and forget gate, respectively;The candidate state represents the new knowledge to be stored in the cell state, which is a function of the current input features and the hidden state of the previous time, the cell state represents long-term memory, which is equal to the sum of the long-term memory of the previous time passing through the forget gate and the new knowledge induced at the current time passing through the input gate, the specific calculation process can be expressed as:Ct = tan^ (wc ■ pt l, xt] + bc)Ct = ft * Ct_t + it *Ctwhere ct is the candidate state, tanh is the activation function, Wc is the weight matrix to be trained, be is the bias term to be trained, Ct is the cell state at the current time, and C(t-i) is the cell state at the previous time;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:ot — o (Wo- [ht-^Xt] + b0)ht = ot * tanh(Ct)where ot is the output gate, Wo and b0 are the weight matrix and bias term to be trained for the output gate, respectively, and is the hidden state at the current time;The improved PSO algorithm is an optimization algorithm for the traditional PSO algorithm, including:Improved learning factor, the improved formula for the learning factor is as follows:Cl = fee - Clb) XmCur ^maxwhere mCUr is the current iteration number, mmax is the maximum iteration number, cw, Cie, C2b, and C2e are the initial and final values of ci and C2, respectively; generally, the algorithm performs better when cib = 2.5, Cie = 0.5, C2b = 0.5, and C2e = 2.5;Improved inertia factor: the larger the inertia factor w, the greater the particle flight speed, and the particle will perform a global search with a longer step length; the smaller the inertia factor w, the more it tends to fine local search; the improved formula is as follows:+ clb3+ c2bC2 = fee - C2b) Xwhere Wmax represents the maximum value of w, cumin represents the minimumvalue of w, F represents the current objective function value, Favg represents the current average objective function value, and Fmin represents the minimum value ofthe objective function;The objective function uses the mean absolute error (MAE) on the validation set as the objective function, the formula is as follows:fit = MAE = —^|yt — jT| t=lwhere N represents the number of predicted samples, y(yi,y2,-,yN) is the measured landslide displacement value in the validation set, and y(yl,yl,-,yjO is the predicted landslide displacement value on the validation set.

2. A method for predicting mountain landslide displacement based on MI-GRA and improved PSO-LSTM, as claimed in claim 1, is characterized by step (1) including: collecting multi-source monitoring data of the slope; interpolating missing data after obtaining the original monitoring data of the slope; and classifying the original data into displacement data and displacement potential influencing factor data.

3. A method for predicting mountain landslide displacement based on MI-GRA and improved PSO-LSTM, as claimed in claim 2, is characterized in that the missing data interpolation adopts the median interpolation method, and its formula is as follows:in this formula, xcb is the data after missing value interpolation, x (t-i) is the data at the time before the interpolation point, and x (t+i) is the data at the time after the interpolation point.

4. A method for predicting mountain landslide displacement based on MI-GRA and improved PSO-LSTM, as claimed in claim 1, is characterized in that the step (4) of performing model prediction and testing with the established slope prediction model includes the following steps: calling the prediction model, where the called prediction modelis the saved improved PSO-LSTM slope displacement prediction model after training;inputting the test set and performing prediction tests, where the prediction test method isrolling prediction; obtaining the prediction results and evaluating the model predictionaccuracy; the model prediction accuracy evaluation adopts the coefficient of determinationR2 and the mean absolute percentage error MAPE, and their formulas are as follows:R2 = 1—ZtN=i (yt - yt)2SU (yt-y)2MAPE =N 100% y |yt — yt[N ZI yt I t=lin these formulas, R2 is the coefficient of determination, and the larger its value, the higherthe model accuracy; MAPE is the mean absolute percentage error, and the smaller its value,the smaller the prediction error; N is the number of predicted samples; yt is the measureddisplacement value in the test set; yt is the predicted displacement value on the test set; and y is the average of the measured values.

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