A landslide displacement prediction method based on multi-agent cooperative optimization and progressive optimization

Abstract

The application discloses a landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization, which comprises the following steps: obtaining and preprocessing landslide monitoring data to obtain displacement, rainfall and groundwater level sequences; taking a dynamic weighted composite function as a target, simultaneously optimizing a penalty factor and a decomposition layer number of a variational mode decomposition based on a multi-agent collaborative optimization algorithm, and outputting a candidate set; performing variational mode decomposition on each parameter combination in the candidate set to obtain intrinsic mode function components arranged in a low-to-high frequency order, taking a first component as a trend item, a second component as a periodic item, and the rest as a fluctuation item; constructing a combination prediction model for each candidate decomposition result, calculating a determination coefficient on a verification set, and selecting an optimal parameter combination; and performing landslide displacement prediction by using the optimal combination prediction model. The application makes the variational mode decomposition parameter selection directly serve the prediction accuracy through two-stage progressive optimization, and significantly improves the accuracy and generalization ability of landslide displacement prediction.

Description

Technical Field

[0001] This invention relates to the field of intelligent landslide disaster prediction technology, and more specifically, to a landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization. Background Technology

[0002] Landslide displacement prediction is an important research direction in the field of geological disaster prevention and control. Its core challenge lies in the nonlinearity, non-stationarity, and multi-scale evolution characteristics of landslide displacement sequences. Landslide displacement can usually be decomposed into a trend term (reflecting long-term creep), a periodic term (reflecting the influence of seasonal factors, such as rainfall), and a fluctuation term (reflecting short-term random disturbances). The current mainstream technical approach is to model and predict these three terms separately and then superimpose them.

[0003] Variational Mode Decomposition (VMD) is an effective method widely used in recent years for decomposing landslide displacement sequences. Compared with Empirical Mode Decomposition (EMD), VMD has a solid mathematical foundation and can effectively avoid mode aliasing and endpoint effects. The decomposition quality of VMD is highly dependent on the choice of the penalty factor α, while the number of decomposition layers K is usually preset to 3 based on the three evolutionary characteristics of landslide displacement (trend, period, and fluctuation) and does not need to participate in optimization. An unreasonable value of α can lead to mode aliasing or energy loss, directly affecting the accuracy of subsequent predictions.

[0004] In existing technologies, VMD parameters are often optimized through grid search or intelligent optimization algorithms, but the following main defects still exist: (1) Automated parameter optimization methods based on a single quality index: Existing optimization methods are often based on a single index, which makes it difficult to comprehensively evaluate the decomposition quality. For example, minimizing the envelope entropy may lead to over-decomposition; minimizing energy loss may not effectively separate the modal components. A single index cannot balance multiple needs at different optimization stages. (2) Existing optimization methods adopt a "one-step" single-level architecture, that is, outputting a single optimal parameter with the goal of optimizing the signal decomposition quality index. However, the relationship between the decomposition quality index and the prediction accuracy is not strictly monotonic: in the neighborhood of the optimal parameter, the decomposition quality corresponding to multiple different parameters is similar, but the subsequent modeling prediction accuracy may have significant differences. Therefore, outputting only a single optimal solution cannot support secondary optimization at the prediction accuracy level, and may miss parameters with higher prediction accuracy. In essence, existing technologies lack a hierarchical progressive architecture of "optimization based on decomposition quality" and "optimization based on prediction accuracy".

[0005] To address the aforementioned technical problems, this invention proposes a landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization. Summary of the Invention

[0006] The purpose of this invention is to provide a landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization. This method constructs a dynamic weighted composite function as the optimization objective and employs a two-stage decoupled architecture of "multi-agent optimization - prediction accuracy optimization": the first stage uses the dynamic weighted composite function as the objective and generates a diverse set of candidate penalty factors covering different regions of the search space based on a multi-agent collaborative optimization algorithm; the second stage selects the best candidate based on the actual prediction accuracy. This method allows the selection of VMD parameters to directly serve the landslide displacement prediction accuracy, avoiding the target bias caused by the direct selection of parameters based on the optimal decomposition quality index in traditional methods.

[0007] This invention is implemented as follows: The technical solution to achieve the purpose of this invention is: a landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization, comprising the following steps: S1. Acquire and preprocess historical online monitoring data of landslides to obtain displacement sequences, rainfall sequences and groundwater level sequences, and divide the data into training sets, validation sets and test sets according to preset ratios; S2. Using a dynamically weighted composite function as the objective, a multi-agent collaborative optimization algorithm is used to simultaneously optimize the penalty factor α and the number of decomposition layers K in variational mode decomposition, outputting a candidate set containing M sets of (α, K) values, where M is the number of intelligent individuals; the dynamically weighted composite function is composed of information entropy and energy loss terms weighted according to dynamically changing weights as the iteration progress; the multi-agent collaborative optimization algorithm consists of multiple intelligent individuals optimizing in parallel, and the historical optimal solution of each individual is included in the candidate set; S3. For each group (α, K) in the candidate set, perform variational mode decomposition on the displacement sequence to obtain K eigenmode function components arranged from low to high center frequency; among them, the first component is used as the trend term, the second component is used as the periodic term, and the third and subsequent components are combined as the fluctuation term. S4. For the decomposition results corresponding to each candidate (α, K), construct a combined prediction model and calculate the determination coefficient R² on the validation set. Select the model with the highest R² as the optimal parameter combination (α, K). S5. The combined prediction model corresponding to the optimal parameter combination is used to predict the landslide displacement at the time to be predicted.

[0008] Furthermore, in step S2, the multi-agent cooperative optimization algorithm specifically includes the following steps: S21: Initialization: Set the number of agents M, M≥2; within the search space, initialize M mutually distant initial positions X using Latin hypercube sampling. i , i is the agent index, i=1,...,M; initialize the velocity V of each agent. i=0; Initialize the individual historical best position P of each agent to 0. best,i =X i Initialize the taboo region set Φ to empty; the taboo region is the area around a converged agent where other agents are prohibited from entering. Set the maximum number of iterations T. max ; S22: Basic Fitness Evaluation: Calculate the basic fitness value for each agent, where the basic fitness value is the function value of a dynamically weighted composite function; the optimal position of the individual in the initial population is denoted as G. best ; S23: Calculate the post-penalty fitness value: Calculate the normalized distance d from each agent to the center of the m-th tabu zone. m : d m =[(KK m )² / (ΔK)²+(α-α m )² / (Δα)²] 1 / 2 ; Where K and α are the current position coordinates of the agent, K m and α m Let K be the coordinates of the center point of the m-th taboo zone, and ΔK and Δα be the search range widths of K and α, respectively. Calculate the fitness of each agent after penalty FP i : ; in, Q The total number of forbidden areas, R n The normalized tabu radius ranges from 0.12 to 0.18. λ This is the penalty coefficient, with a value ranging from 10 to 100; Update the individual historical best P of each agent based on the post-penalty fitness. best,i and the global historical best G best ; S24: Adaptive Parameter Calculation: Calculate the percentage p of each agent's current fitness among M agents. i Among them, the best one p i =0, worst performer p i =1; Calculate the individual cognitive coefficient c1 and the social sharing coefficient c2 using the following formulas: c1 = c 1max - (c 1max - c 1min ) × p i c2 = c 2min + (c 2max - c2min ) × p i ; Among them, c 1max The value range of c is 1.8~2.2. 1min The value range of c is 1.0~1.5. 2min The value range of c is 0.2~0.5. 2max The value of is in the range of 0.6 to 1.0, and satisfies c 1max > c 1min c 2max > c 2min ; S25: Velocity and Position Update: Each agent updates its velocity and position according to the following formula: V i (t+1)=ωV i (t)+c1×(P best,i -x i (t))+c2×β×(G best -x i (t)); x i (t+1)=x i (t)+V i (t+1); Among them, V i (t) and x i (t) represents the velocity and position of the i-th agent in the t-th iteration, respectively; ω is the inertia weight, with a value of 0.6~0.8; β=1-t / T max This represents the social learning attenuation coefficient. S26: Boundary handling and forbidden zone updates; The updated position is corrected for boundary constraints; if it exceeds the search range, it is mapped to the nearest boundary value. When the individual historical best position P of a certain agent best,i Continuous T stop If no change has occurred, the agent is determined to have converged, and P is set to... best,i When an agent is added to the taboo zone set Φ, it stops updating, ceases participation in subsequent iterations, and a normalized taboo radius of R is set around it. n Forbidden areas, R n The value range is 0.12 to 0.18; The T stop It is a preset integer, with a value range of 5 to 10.

[0009] S27: Iteration termination judgment: Repeat steps S22 to S26 until the maximum number of iterations is reached; S28: Candidate Set Output: Outputs the individual historical best position P for each agent.best,i , as a set of candidate penalty factors.

[0010] Furthermore, in step S2, the calculation formula for the dynamically weighted composite function is: F(t) = w1 × H + w2 × L; The formula for calculating information entropy H is: H = -∑[p(x)×log(p(x))]; the formula for calculating energy loss coefficient L is: L = |E o -ΣE imf | / Eo; Where p(x) is the normalized probability distribution of each eigenmode function component; E o E represents the energy of the original displacement sequence. imf The energy of each intrinsic mode function component; The weighting functions are defined as follows: w1 = 0.5 × (1 - t)²; w2 = 1 - w1, where t is the normalized iteration progress, t ∈ [0, 1]; Furthermore, in step S4, the combined prediction model is constructed in the following way: the trend component is fitted with a quadratic polynomial, and the periodic component and fluctuation component are predicted by a gated cyclic unit network with rainfall data and groundwater level data as inputs, respectively. The three prediction results are superimposed to obtain the final displacement prediction value. The beneficial effects of this invention are as follows: First, by constructing a composite function composed of information entropy and energy loss dynamically weighted according to the iteration progress as the optimization objective, it overcomes the deficiency that a single index is difficult to comprehensively evaluate the quality of VMD decomposition and realizes progressive optimization evaluation. Second, it pioneers a two-level decoupled architecture of "multi-agent optimization - prediction accuracy selection". The first level outputs a diverse set of candidate penalty factors covering different regions of the search space, and the second level selects the best from the candidates based on the actual prediction accuracy, eliminating the target bias caused by the direct selection of parameters based on the optimal decomposition quality index in traditional methods. Third, it designs a multi-agent collaborative optimization algorithm with a taboo zone mechanism and adaptive parameters, effectively preventing the group from clustering in a single local optimum region and ensuring the diversity of the candidate set. Finally, it enables the selection of VMD parameters to directly serve the landslide displacement prediction accuracy, significantly improving prediction accuracy and model generalization ability compared with existing methods. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0012] Figure 1This is a flowchart of a landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization provided by an embodiment of the present invention. Figure 2 This is a flowchart of the multi-agent collaborative optimization algorithm provided in the embodiments of the present invention; Figure 3 This is a schematic diagram of monitoring data provided by an embodiment of the present invention; Figure 4 This is a comparison chart of the prediction errors of various comparative models provided in the embodiments of the present invention; Detailed Implementation

[0013] Example: A landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization, comprising the following steps: S1. Acquire and preprocess historical online monitoring data of landslides to obtain displacement sequences, rainfall sequences and groundwater level sequences, and divide the data into training sets, validation sets and test sets according to preset ratios; S2. Taking the dynamic weighted composite function as the objective, the penalty factor α and the number of decomposition layers K of the variational mode decomposition are simultaneously optimized based on the multi-agent collaborative optimization algorithm, and the output is a candidate set containing M groups of (α, K) values, where M is the number of intelligent individuals. The dynamic weighted composite function is composed of an information entropy term and an energy loss term weighted according to weights that change dynamically with the iteration progress; The multi-agent collaborative optimization algorithm consists of multiple intelligent agents that perform optimization in parallel, and the historical best solution of each agent is included in the candidate set. S3. For each group (α, K) in the candidate set, perform variational mode decomposition on the displacement sequence to obtain K eigenmode function components arranged from low to high center frequency; among them, the first component is used as the trend term, the second component is used as the periodic term, and the third and subsequent components are combined as the fluctuation term. S4. For the decomposition results corresponding to each candidate (α, K), construct a combined prediction model and calculate the determination coefficient R² on the validation set. Select the model with the highest R² as the optimal parameter combination (α, K). S5. The combined prediction model corresponding to the optimal parameter combination is used to predict the landslide displacement at the time to be predicted.

[0014] Furthermore, in step S2, the multi-agent cooperative optimization algorithm specifically includes the following steps: S21: Initialization: Set the number of agents M, M≥2; within the search space, initialize M mutually distant initial positions X using Latin hypercube sampling. i Let i be the agent index, i=1,...,M; initialize the velocity V of each agent. i =0; Initialize the individual historical best position P of each agent to 0.best,i =X i Initialize the taboo region set Φ to empty; the taboo region is the area around a converged agent where other agents are prohibited from entering. Set the maximum number of iterations T. max ; S22: Basic Fitness Evaluation: Calculate the basic fitness value for each agent, where the basic fitness value is the function value of a dynamically weighted composite function; the optimal position of the individual in the initial population is denoted as G. best ; S23: Calculate the post-penalty fitness value: Calculate the normalized distance d from each agent to the center of the m-th tabu zone. m : d m =[(KK m )² / (ΔK)²+(α-α m )² / (Δα)²] 1 / 2 ; Where K and α are the current position coordinates of the agent, K m and α m Let K be the coordinates of the center point of the m-th taboo zone, and ΔK and Δα be the search range widths of K and α, respectively. Calculate the fitness of each agent after penalty FP i : ; in, Q The total number of forbidden areas, R n The normalized tabu radius ranges from 0.12 to 0.18. λ This is the penalty coefficient, with a value ranging from 10 to 100; Update the individual historical best P of each agent based on the post-penalty fitness. best,i and the global historical best G best ; S24: Adaptive Parameter Calculation: Calculate the percentage p of each agent's current fitness among M agents. i Among them, the best one p i =0, worst performer p i =1; Calculate the individual cognitive coefficient c1 and the social sharing coefficient c2 using the following formulas: c1 = c 1max - (c 1max - c 1min ) × p i c2 = c 2min + (c 2max - c 2min ) × p i ; Among them, c 1max The value range of c is 1.8~2.2. 1min The value range of c is 1.0~1.5. 2min The value range of c is 0.2~0.5. 2max The value of is in the range of 0.6 to 1.0, and satisfies c 1max > c 1min c 2max > c 2min ; S25: Velocity and Position Update: Each agent updates its velocity and position according to the following formula: V i (t+1)=ωV i (t)+c1×(P best,i -x i (t))+c2×β×(G best -x i (t)); x i (t+1)=x i (t)+V i (t+1); Among them, V i (t) and x i (t) represents the velocity and position of the i-th agent in the t-th iteration, respectively; ω is the inertia weight, with a value of 0.6~0.8; β=1-t / T max This represents the social learning attenuation coefficient. S26: Boundary handling and forbidden zone update; The updated position is corrected for boundary constraints; if it exceeds the search range, it is mapped to the nearest boundary value. When the individual historical best position P of a certain agent best,i Continuous T stop If no change has occurred, the agent is determined to have converged, and P is set to... best,i When an agent is added to the taboo zone set Φ, it stops updating, ceases participation in subsequent iterations, and a normalized taboo radius of R is set around it. n Forbidden areas, R n The value range is 0.12 to 0.18; The T stop It is a preset integer, with a value range of 5 to 10.

[0015] S27: Iteration termination judgment: Repeat steps S22 to S26 until the maximum number of iterations is reached; S28: Candidate Set Output: Outputs the individual historical best position P for each agent. best,i , as a set of candidate penalty factors.

[0016] Furthermore, in step S2, the calculation formula for the dynamically weighted composite function is: F(t) = w1 × H + w2 × L; The formula for calculating information entropy H is: H = -∑[p(x)×log(p(x))]; the formula for calculating energy loss coefficient L is: L = |E o -ΣE imf | / Eo; Where p(x) is the normalized probability distribution of each eigenmode function component; E o E represents the energy of the original displacement sequence. imf The energy of each intrinsic mode function component; The weighting functions are defined as follows: w1 = 0.5 × (1 - t)²; w2 = 1 - w1, where t is the normalized iteration progress, t ∈ [0, 1]; Furthermore, in step S4, the combined prediction model is constructed in the following way: the trend component is fitted with a quadratic polynomial, and the periodic component and fluctuation component are predicted by a gated cyclic unit network with rainfall data and groundwater level data as inputs, respectively. The three prediction results are superimposed to obtain the final displacement prediction value. The method of the present invention will be described below using an example of online monitoring of a landslide.

[0017] The specific implementation process is as follows: like Figure 1 As shown, a landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization includes the following steps: S1. Acquire and preprocess historical online monitoring data of landslides to obtain displacement sequences, rainfall sequences and groundwater level sequences, and divide the data into training sets, validation sets and test sets according to preset ratios; In this embodiment, the experimental data came from online monitoring data of a tailings dam, with a total of 3000 sets of monitoring sample data collected, including displacement sequences, rainfall sequences, and groundwater level sequences. These were divided into a training set (2100 sets), a validation set (450 sets), and a test set (450 sets) in a 7:1.5:1.5 ratio. The Min-Max normalization method was used to map each sequence data to the [0,1] interval to eliminate the influence of dimensions.

[0018] S2. Taking the dynamic weighted composite function as the objective, the penalty factor α and the number of decomposition layers K of the variational mode decomposition are simultaneously optimized based on the multi-agent collaborative optimization algorithm, and the output is a candidate set containing M groups of (α, K) values, where M is the number of intelligent individuals. The dynamic weighted composite function is composed of an information entropy term and an energy loss term weighted according to weights that change dynamically with the iteration progress; The multi-agent collaborative optimization algorithm consists of multiple intelligent agents that perform optimization in parallel, and the historical best solutions of each agent are included in the candidate set; the multi-agent collaborative optimization algorithm process is as follows: Figure 2 As shown; In this embodiment, the number of agents is set to M=5, the search space is: α∈[500,5000], K∈[2,5], and the maximum number of iterations T_max=50. The specific parameter settings of the multi-agent collaborative optimization algorithm are as follows: R n =0.15; λ=100; inertial weight ω=0.7; c 1max =2.0, c 1min =1.2; c 2max =0.8, c 2min =0.3; Convergence threshold T stop =8; α∈[500,5000], K∈[2,5] and rounded down.

[0019] S3. For each group (α, K) in the candidate set, perform variational mode decomposition on the displacement sequence to obtain K eigenmode function components arranged from low to high center frequency; among them, the first component is used as the trend term, the second component is used as the periodic term, and the third and subsequent components are combined as the fluctuation term. S4. For the decomposition results corresponding to each candidate (α, K), construct a combined prediction model and calculate the coefficient of determination R² on the validation set. Select the model with the highest R² as the optimal parameter combination (α, K).

[0020] The parameters of the gated recurrent unit network structure are as follows: input layer time step = 30, number of GRU layer units = 32, output dimension of fully connected layer = 1, optimizer = Adam, learning rate = 0.01, batch size = 64, training epochs = 30.

[0021] S5. The combined prediction model corresponding to the optimal parameter combination is used to predict the landslide displacement at the time to be predicted.

[0022] To verify the advantages of the method of this invention, a comparative experiment was conducted on ordinary VMD decomposition, PSO-VMD decomposition, and the method of this invention. In the ordinary VMD decomposition, K=3 and α=2000 were set. The optimization range of PSO-VMD decomposition was the same as that of the method of this invention. The mean absolute error (MAE) / root mean square error (RMSE) / R... 2 The results are shown in Table 1: Table 1 Comparative Experimental Results

[0023] Experimental results show that the MAE and RMSE of the method of the present invention are lower than those of the comparative method, and the R² is higher than that of the comparative method, which verifies the superiority of the method of the present invention.

Claims

1. A landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization, characterized in that, Includes the following steps: S1. Acquire and preprocess historical online monitoring data of landslides to obtain displacement sequences, rainfall sequences and groundwater level sequences, and divide the data into training sets, validation sets and test sets according to preset ratios; S2. Using a dynamically weighted composite function as the objective, a multi-agent collaborative optimization algorithm is used to simultaneously optimize the penalty factor α and the number of decomposition layers K in variational mode decomposition, outputting a candidate set containing M sets of (α, K) values, where M is the number of intelligent individuals; the dynamically weighted composite function is composed of information entropy and energy loss terms weighted according to dynamically changing weights as the iteration progress; the multi-agent collaborative optimization algorithm consists of multiple intelligent individuals optimizing in parallel, and the historical optimal solution of each individual is included in the candidate set; S3. For each group (α, K) in the candidate set, perform variational mode decomposition on the displacement sequence to obtain K eigenmode function components arranged from low to high center frequency; among them, the first component is used as the trend term, the second component is used as the periodic term, and the third and subsequent components are combined as the fluctuation term. S4. For the decomposition results corresponding to each candidate (α, K), construct a combined prediction model and calculate the determination coefficient R² on the validation set. Select the model with the highest R² as the optimal parameter combination (α, K). S5. The combined prediction model corresponding to the optimal parameter combination is used to predict the landslide displacement at the time to be predicted.

2. The landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization as described in claim 1, characterized in that, In step S2, the multi-agent cooperative optimization algorithm specifically includes the following steps: S21: Initialization: Set the number of agents M, M≥2; within the search space, initialize M mutually distant initial positions X using Latin hypercube sampling. i Let i be the agent index, i=1,...,M; initialize the velocity V of each agent. i =0; Initialize the individual historical best position P of each agent to 0. best,i =X i Initialize the taboo region set Φ to empty; the taboo region is the area around a converged agent where other agents are prohibited from entering. Set the maximum number of iterations T. max ; S22: Basic Fitness Assessment: Calculate the basic fitness value for each agent. F i The basic fitness value is the function value of the dynamic weighted composite function; the optimal individual position in the initial population is denoted as G. best ; S23: Calculate the post-penalty fitness value: Calculate the normalized distance d from each agent to the center of the m-th tabu zone. m : d m =[(KK m )² / (ΔK)²+(α-α m )² / (Da)²] 1 / 2 ; Where K and α are the current position coordinates of the agent, K m and α m Let K be the coordinates of the center point of the m-th taboo zone, and ΔK and Δα be the search range widths of K and α, respectively. Calculate the fitness of each agent after penalty FP i : ； in, Q The total number of forbidden areas, R n The normalized tabu radius ranges from 0.12 to 0.

18. λ This is the penalty coefficient, with a value ranging from 10 to 100; Update the individual historical best P of each agent based on the post-penalty fitness. best,i and the global historical best G best ; S24: Adaptive parameter calculation: Calculate the percentage of each agent's current fitness among M agents, p. i Among them, the best one p i =0, worst player p i =1; Calculate the individual cognitive coefficient c1 and the social sharing coefficient c2 using the following formulas: c1 = c 1max - (c 1max - c 1min ) × p i ; c2 = c 2min + (c 2max - c 2min ) × p i ; Among them, c 1max The value range of c is 1.8~2.

2. 1min The value range of c is 1.0~1.

5. 2min The value range of c is 0.2~0.

5. 2max The value of is in the range of 0.6 to 1.0, and satisfies c 1max > c 1min c 2max > c 2min ; S25: Velocity and Position Update: Each agent updates its velocity and position according to the following formula: V i (t+1)=ωV i (t)+c1×(P best,i -x i (t))+c2×β×(G best -x i (t)); x i (t+1)=x i (t)+V i (t+1); Among them, V i (t) and x i (t) represents the velocity and position of the i-th agent in the t-th iteration, respectively; ω is the inertia weight, with a value of 0.6~0.8; β=1-t / T max This represents the social learning attenuation coefficient. S26: Boundary Handling and Taboo Zone Update: The updated position is corrected for boundary constraints; if it exceeds the search range, it is mapped to the nearest boundary value; when an agent's individual historical best position P... best,i Continuous T stop If no change has occurred, the agent is determined to have converged, and P is set to... best,i When an agent is added to the taboo zone set Φ, it stops updating, no longer participates in subsequent iterations, and a normalized taboo radius of R is set around it. n Forbidden areas, R n The value range of T is 0.12~0.18; stop The value is a preset integer, ranging from 5 to 10; S27: Iteration termination judgment: Repeat steps S22 to S26 until the maximum number of iterations is reached; S28: Candidate Set Output: Outputs the individual historical best position P for each agent. best,i , as a set of candidate penalty factors.

3. The landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization as described in claim 1, characterized in that, In step S2, the formula for calculating the dynamic weighted composite function is: F(t) = w1 × H + w2 × L; The formula for calculating information entropy H is: H = -∑[p(x)×log(p(x))]; the formula for calculating energy loss coefficient L is: L = |E o -ΣE imf | / E o ; Where p(x) is the normalized probability distribution of each eigenmode function component; E o E represents the energy of the original displacement sequence. imf The energy of each intrinsic mode function component; The weight functions are defined as follows: w1=0.5×(1-t)²; w2=1-w1, where t is the normalized iteration progress, t∈[0,1].

4. The landslide displacement prediction method based on multi-agent collaborative optimization and progressive optimization as described in claim 1, characterized in that, In step S4, the combined prediction model is constructed in the following way: the trend component is fitted with a quadratic polynomial, and the periodic component and fluctuation component are predicted by a gated cyclic unit network with rainfall data and groundwater level data as inputs, respectively. The three prediction results are superimposed to obtain the final displacement prediction value.

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