A method for predicting landslide surface displacement intervals based on DBO-XGBoost and SMPSO optimized ABKDE

Abstract

This invention discloses a method for predicting landslide surface displacement intervals based on DBO-XGBoost and SMPSO-optimized ABKDE, comprising: acquiring cumulative landslide displacement monitoring data; preprocessing the cumulative landslide displacement monitoring data to obtain a cumulative landslide displacement time series; decomposing the cumulative landslide displacement time series using Local Mean Decomposition (LMD) to obtain multiple multiplicative inductors PF and a residual component R, calculating the sample entropy of the components, and reconstructing the displacement to obtain a trend term and a fluctuation term; performing polynomial fitting on the trend term to obtain a trend term displacement prediction result, and importing the fluctuation term into the DBO-XGBoost model to obtain a fluctuation term displacement prediction result; superimposing the trend term displacement prediction result and the fluctuation term displacement prediction result to obtain a cumulative displacement prediction result, which is used as a point prediction result; calculating an error sequence based on the point prediction result, and importing the obtained error displacement sequence into the SMPSO-optimized ABKDE for interval prediction to obtain the prediction interval; this invention can effectively predict landslide displacement and improve prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of geological disaster prediction and prevention technology, and in particular to a method for predicting landslide surface displacement intervals based on DBO-XGBoost and SMPSO optimized ABKDE. Background Technology

[0002] Landslides are a common natural disaster in mountainous areas of my country, often causing severe casualties and enormous property damage. Currently, landslide displacement prediction is an effective means of monitoring landslide hazards.

[0003] Traditional landslide displacement prediction methods include statistical and physical statistical methods. These methods are limited by their poor performance in handling nonlinear data and their inability to quantify uncertainties. In recent years, machine learning has rapidly developed in landslide displacement prediction. Extensive research has led to relatively mature landslide displacement point prediction technology. However, in practical engineering applications, a series of uncertainties still arise. Existing adaptive bandwidth kernel density estimation (ABKDE) is a non-parametric interval prediction method that adaptively adjusts the bandwidth parameter based on local data density. It can estimate the probability density function of the predicted value, but it suffers from difficulties in determining the optimal bandwidth and is prone to getting trapped in local optima, leading to inaccurate prediction results. Therefore, to improve upon the shortcomings of point prediction models and the large errors of traditional interval prediction, a novel DBO-XGBoost point prediction method and an SMPSO-optimized adaptive bandwidth kernel density estimation (ABKDE) interval prediction method are introduced, resulting in more reliable prediction results. Summary of the Invention

[0004] The purpose of this invention is to provide a landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO optimized ABKDE, so as to effectively predict landslide displacement, improve prediction accuracy and reliability of prediction interval.

[0005] This invention provides a method for predicting landslide surface displacement intervals based on DBO-XGBoost and SMPSO-optimized ABKDE, comprising:

[0006] Acquire cumulative landslide displacement monitoring data, which includes: cumulative landslide displacement, rainfall, and reservoir water level;

[0007] The landslide cumulative displacement monitoring data is preprocessed to obtain the landslide cumulative displacement time series;

[0008] The landslide cumulative displacement time series was decomposed using the Local Mean Decomposition (LMD) algorithm to obtain multiple multiplicative components PF and a residual component R. The sample entropy value of each component was calculated and reconstructed to obtain the fluctuation term and trend term.

[0009] The displacement prediction result of the trend term is obtained by predicting the trend term through polynomial fitting;

[0010] The original influencing factors are calculated based on the rainfall amount. The Pearson correlation coefficient is calculated based on the original influencing factors and the fluctuation term. Strongly correlated factors are selected as effective influencing factors.

[0011] The effective influencing factor and the fluctuation term are input into the pre-trained DBO-XGBoost model to predict the displacement of the fluctuation term.

[0012] The cumulative displacement prediction result is obtained by superimposing the trend term displacement prediction result and the fluctuation term displacement prediction result, and the cumulative displacement prediction result is used as the point prediction result.

[0013] The error sequence is obtained by calculating the error between the predicted point and the actual value. The error sequence is then input into the SMPSO-ABKDE model to obtain the displacement prediction interval. The SMPSO-ABKDE model is obtained by optimizing the adaptive bandwidth kernel density estimation ABKDE model using the velocity-constrained multi-objective particle swarm optimization algorithm SMPSO.

[0014] Furthermore, the landslide cumulative displacement monitoring data is preprocessed to obtain a landslide cumulative displacement time series, including:

[0015] Outliers and noise were removed from the cumulative displacement monitoring data of the landslide.

[0016] Furthermore, the landslide cumulative displacement time series is decomposed using the Local Mean Decomposition (LMD) algorithm to obtain multiple multiplicative integrators PF and a residual component R. The sample entropy value of each component is calculated, and the data is reconstructed to obtain fluctuation and trend terms, including:

[0017] The landslide cumulative displacement time series was decomposed using the Local Mean Decomposition (LMD) algorithm to obtain the integral components PF1, PF2, PF3, and residual component R.

[0018] Calculate the sample entropy value for each component. Based on the calculated sample entropy value, reconstruct the fluctuation term by multiplying integrals PF1, PF2, and PF3, and reconstruct the trend term by the residual component R.

[0019] Furthermore, the original influencing factors include: cumulative rainfall Y1 within 15 days, cumulative rainfall Y2 within the previous 15 days, cumulative rainfall Y3 within 30 days, cumulative rainfall Y4 within the previous 30 days, reservoir water level change K1 within 15 days, reservoir water level change K2 within the previous 15 days, reservoir water level change K3 within 30 days, reservoir water level change K4 within the previous 30 days, cumulative displacement L1 within 15 days, cumulative displacement L2 within the previous 15 days, cumulative displacement L3 within 30 days, and cumulative displacement L4 within the previous 30 days.

[0020] The effective influencing factors include: the cumulative rainfall Y2 in the previous 15 days, the reservoir water level change K4 in the previous 30 days, the cumulative displacement L1 in the previous 15 days, and the reservoir water level change K3 in the previous 30 days.

[0021] Furthermore, the training of the DBO-XGBoost model includes:

[0022] The population size was set to 30, the maximum number of iterations to 50, and upper and lower limits for the parameters were set. The optimal parameters for the XGBoost model were obtained by using the Dung Beetle Optimization (DBO) algorithm to find the optimal maximum number of iterations, the optimal tree depth, and the optimal learning rate. The XGBoost model was then configured based on these optimal parameters.

[0023] Furthermore, the adaptive bandwidth kernel density estimation ABKDE model is optimized using the velocity-constrained multi-objective particle swarm optimization algorithm SMPSO, including:

[0024] S10. Construct an adaptive bandwidth kernel density function based on the Gaussian kernel function and adaptive bandwidth. The expression for the adaptive bandwidth kernel density function is:

[0025] ,

[0026] ,

[0027] ,

[0028] in, For local kernel density functions, For adaptive bandwidth kernel density function, It is the weight of the i-th kernel function. ; The bandwidth of the i-th kernel function is m; m is the total number of displacement data point samples. Represents the kernel function;

[0029] S20. Initialize the particle swarm: Based on the time displacement error data, randomly generate an initial particle swarm consisting of N particles, and assign a randomly initialized velocity vector to each particle; wherein, the initial position of each particle is... h is the global bandwidth parameter. The weights of the m-th kernel function;

[0030] S30. Construction of Multi-Objective Fitness Function: Integrating the risks of insufficient coverage and excessively wide intervals, a fitness function is constructed. The formula for quantifying the predicted interval performance is as follows: ,in, , These are the weighting coefficients, and ;

[0031] S40, Update Particles: Iteratively adjust the velocity and position of the particles;

[0032] S50, Polynomial Mutation and Archive Update: Apply mutation operation to 15% of the particles, update the non-dominated solution set, retain the parameter combination that takes into account the interval coverage PICP and the predicted interval average width PINAW, and calculate the crowding distance to preserve the diversity of the solution set.

[0033] Repeat steps S30-S50 for iterative optimization until a preset termination condition is met. The termination condition is: the maximum number of iterations reaches 200 or the change in the fitness function value is less than 10. -4 .

[0034] Furthermore, the error between the predicted point displacement and the actual value is calculated to obtain an error sequence. This error sequence is then input into the SMPSO-ABKDE model to obtain the displacement prediction interval, including:

[0035] The error sequence is generated by adaptive bandwidth kernel density estimation (ABKDE), and the displacement prediction interval at different confidence levels is obtained based on the probability density function and preset different confidence levels.

[0036] Furthermore, the Interval Coverage Rate (PICP), the Predicted Interval Average Width (PINAW), and the Comprehensive Index (CWC) were used as evaluation indicators to assess the effectiveness of displacement prediction intervals at different confidence levels.

[0037] The present invention has at least the following beneficial effects:

[0038] This invention decomposes the landslide cumulative displacement time series using the Local Mean Decomposition (LMD) algorithm, reducing computational load and adapting to different data. It also mitigates the adverse effects of volatility and randomness in the original data series, resulting in more accurate data and improved prediction interval precision. The Dung Beetle Optimization (DBO) algorithm is used to optimize the XGBoost model, significantly improving its prediction accuracy and stability, thus further enhancing prediction interval precision. Finally, the velocity-constrained Multi-Objective Particle Swarm Optimization (SMPSO) algorithm is used to optimize the Adaptive Bandwidth Kernel Density Estimation (ABKDE) model. This allows the ABKDE model to better fit the data distribution, easily determine the optimal bandwidth, and avoid getting trapped in local optima, further improving the accuracy and reliability of the prediction interval.

[0039] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of a landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO optimized ABKDE provided by the present invention;

[0041] Figure 2 This is a flowchart of a landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO optimized ABKDE provided by the present invention.

[0042] Figure 3 This is a schematic diagram of the multiplicative integral PF and residual component R after LMD decomposition provided by the present invention;

[0043] Figure 4 This is a schematic diagram of the fluctuation term and trend term provided by the present invention;

[0044] Figure 5 This is a schematic diagram of the trend term displacement prediction results provided by the present invention;

[0045] Figure 6 This is a schematic diagram of the displacement prediction results of the fluctuation term provided by the present invention;

[0046] Figure 7 This is a schematic diagram of the point displacement prediction results provided by the present invention;

[0047] Figure 8 This is a comparative diagram of the point prediction algorithms provided by this invention;

[0048] Figure 9 This is a schematic diagram of the SMPSO-ABKDE model optimization provided by the present invention;

[0049] Figure 10This is a comparative diagram of the optimized ABKDE and the unoptimized ABKDE provided by this invention;

[0050] Figure 11 This is a schematic diagram of the interval prediction results provided by the present invention. Detailed Implementation

[0051] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0052] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0053] Reference Figures 1-11 This invention provides a method for predicting landslide surface displacement intervals based on DBO-XGBoost and SMPSO-optimized ABKDE, comprising:

[0054] Acquire cumulative landslide displacement monitoring data, which includes: cumulative landslide displacement, rainfall, and reservoir water level;

[0055] In this invention, the cumulative displacement monitoring data of landslides collected from monitoring point ZG93 in a landslide early warning zone of a certain area for 192 periods are used as specific data.

[0056] The landslide cumulative displacement monitoring data is preprocessed to obtain the landslide cumulative displacement time series;

[0057] The landslide cumulative displacement time series was decomposed using the Local Mean Decomposition (LMD) algorithm to obtain multiple multiplicative components PF and a residual component R. The sample entropy value of each component was calculated and reconstructed to obtain the fluctuation term and trend term.

[0058] The Local Mean Decomposition (LMD) algorithm used in this invention is a classic nonlinear, non-stationary signal analysis method. It can automatically extract multiplicative components PF with different amplitude-frequency characteristics and a residual component R from the data. The residual component R is the final remaining part obtained by gradually subtracting the PF component from the original signal during the LMD decomposition process, and it is a signal that tends to be stationary. By decomposing the landslide cumulative displacement time series using the LMD algorithm, the amount of computation is reduced, and it can adapt to different data. It improves the modal confusion and endpoint effects that occur during decomposition, making the data more accurate and improving the accuracy of the data, thereby improving the accuracy of the prediction interval.

[0059] The displacement prediction result of the trend term is obtained by predicting the trend term through polynomial fitting;

[0060] The trend term displacement prediction results are as follows Figure 5 As shown, since the trend term is relatively flat and close to linear, we can directly use polynomial fitting to predict its displacement. The formula is: ,in, , , , These are the polynomial coefficients obtained through fitting, and x is the displacement value of the trend term.

[0061] Polynomial fitting was used to predict the trend term. It can be seen that the predicted displacement trend follows the original trend term changes well. The mean absolute error of the predicted displacement trend term is 1.258%, the root mean square error is 1.605 mm, and the coefficient of determination R² is 0.987. The results show that polynomial fitting has good applicability for predicting the displacement trend term.

[0062] The original influencing factors are calculated based on the rainfall amount. The Pearson correlation coefficient is calculated based on the original influencing factors and the fluctuation term. Strongly correlated factors are selected as effective influencing factors.

[0063] The following data were calculated as initial influencing factors: cumulative rainfall Y1 over 15 days, cumulative rainfall Y2 over the previous 15 days, cumulative rainfall Y3 over 30 days, cumulative rainfall Y4 over the previous 30 days, reservoir water level fluctuations K1, K2, K3, and K4 over the previous 15 days, and cumulative displacements L1, L2, L3, and L4 over the previous 30 days. Pearson correlation coefficients were calculated between these 12 initial influencing factors and the fluctuation term to establish the correlation between each initial influencing factor and the fluctuation term, as shown in Table 1.

[0064] Table 1. Pearson correlation coefficients between each influencing factor and the volatility term.

[0065]

[0066] As shown in Table 1, all 12 influencing factors are correlated with the fluctuation term. The closer the Pearson correlation coefficient is to 1, the stronger the correlation, and the closer it is to 0, the weaker the correlation. Therefore, in order to obtain more accurate prediction results, the cumulative rainfall Y2 in the first 15 days, the reservoir water level change K4 in the first 30 days, the cumulative displacement L1 in the first 15 days, and the reservoir water level change K3 in the first 30 days were selected as the final effective influencing factors.

[0067] The effective influencing factor and the fluctuation term are input into the pre-trained DBO-XGBoost model to predict the displacement of the fluctuation term.

[0068] The effective influencing factor and the fluctuation term are used as input parameters to a pre-trained DBO-XGBoost model to predict the fluctuation term displacement, resulting in the fluctuation term displacement prediction result. The fluctuation term displacement prediction result is as follows: Figure 6 As shown.

[0069] The cumulative displacement prediction result is obtained by superimposing the trend term displacement prediction result and the fluctuation term displacement prediction result, and the cumulative displacement prediction result is used as the point prediction result.

[0070] like Figure 7 As shown, by selecting the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²), 2 To evaluate the prediction results of the DBO-XGBoost model, the mean absolute error was calculated to be 1.380, the root mean square error was 1.781, and the coefficient of determination R0 was [value missing]. 2 The result is 0.996. The prediction results show that optimizing the XGBoost model by using the Dymplocant Optimization (DBO) algorithm significantly improves the prediction accuracy and stability of the DBO-XGBoost model, thereby improving the accuracy of the prediction interval.

[0071] like Figure 8 As shown, after preprocessing the cumulative displacement monitoring data of ZG93, it was imported into different models (LMD-XGBoost, LMD-SO-XGBoost, LMD-DBO-XGBoost) for prediction. Comparing the point displacement prediction results, the LMD-DBO-XGBoost model proposed in this invention is closer to the true value in point prediction results than the LMD-XGBoost and LMD-SO-XGBoost models, with stronger prediction ability, higher accuracy and better stability.

[0072] The error sequence is obtained by calculating the error between the predicted point displacement and the actual value. The error sequence is then input into the SMPSO-ABKDE model to obtain the displacement prediction interval. The SMPSO-ABKDE model is obtained by optimizing the adaptive bandwidth kernel density estimation ABKDE model using the velocity-constrained multi-objective particle swarm optimization algorithm SMPSO.

[0073] The prediction error between the predicted point displacement and the actual value is calculated using the formula: Error = Actual value - Predicted value.

[0074] Based on the adaptive bandwidth kernel density estimation (ABKDE) model, a velocity-constrained multi-objective particle swarm optimization (SMPSO) algorithm is used to optimize the bandwidth parameter h and the weight ω in the mixture probability density function. The algorithm sets the minimum prediction interval width and the maximum prediction interval coverage. By iteratively updating the particle positions and velocities, an optimal set of bandwidth parameters is found, thus optimizing the ABKDE model. The optimized model is then used to generate a probability density function for the error sequence, obtaining displacement prediction intervals at different confidence levels. Optimizing the ABKDE model using SMPSO enables it to better fit the data distribution, facilitates the determination of the optimal bandwidth, and avoids getting trapped in local optima, thereby further improving the accuracy and reliability of the prediction interval.

[0075] Furthermore, the landslide cumulative displacement monitoring data is preprocessed to obtain a landslide cumulative displacement time series, including:

[0076] Outliers and noise were removed from the cumulative displacement monitoring data of the landslide.

[0077] Furthermore, the landslide cumulative displacement time series is decomposed using the Local Mean Decomposition (LMD) algorithm to obtain multiple multiplicative integrators PF and a residual component R. The sample entropy value of each component is calculated, and the data is reconstructed to obtain fluctuation and trend terms, including:

[0078] The landslide cumulative displacement time series was decomposed using the Local Mean Decomposition (LMD) algorithm to obtain the integral components PF1, PF2, PF3, and residual component R.

[0079] Calculate the sample entropy value for each component. Based on the calculated sample entropy value, reconstruct the fluctuation term by multiplying integrals PF1, PF2, and PF3, and reconstruct the trend term by the residual component R.

[0080] The landslide cumulative displacement time series was decomposed into integral components PF1, PF2, PF3 and residual component R using the LMD decomposition method. The sample entropy value of each component was calculated. Based on the sample entropy value, the subsequence was reconstructed into two sequences, which represent the trend term and the fluctuation term, respectively.

[0081] In this embodiment, the cumulative displacement time series of the ZG93 monitoring point in the landslide early warning area is decomposed using LMD. The decomposed integral components PF1, PF2, PF3, and residual component R are as follows: Figure 3 As shown in Table 2, the sample entropy values ​​of each component are calculated.

[0082] Table 2 Sample entropy values ​​of subsequences

[0083]

[0084] Table 2 shows that the entropy values ​​of subsequences PF1 to PF3 are all high, indicating high complexity and strong volatility. Therefore, these three subsequences are reconstructed and treated as volatility terms. The entropy value of subsequence R is relatively small. Figure 3 The sequence shows a relatively smooth surface with clear stationarity, which can be used as the trend term to represent the long-term deformation of the landslide. The reconstructed fluctuation and trend terms are as follows: Figure 4 As shown.

[0085] Furthermore, the original influencing factors include: cumulative rainfall Y1 within 15 days, cumulative rainfall Y2 within the previous 15 days, cumulative rainfall Y3 within 30 days, cumulative rainfall Y4 within the previous 30 days, reservoir water level change K1 within 15 days, reservoir water level change K2 within the previous 15 days, reservoir water level change K3 within 30 days, reservoir water level change K4 within the previous 30 days, cumulative displacement L1 within 15 days, cumulative displacement L2 within the previous 15 days, cumulative displacement L3 within 30 days, and cumulative displacement L4 within the previous 30 days.

[0086] The effective influencing factors include: the cumulative rainfall Y2 in the previous 15 days, the reservoir water level change K4 in the previous 30 days, the cumulative displacement L1 in the previous 15 days, and the reservoir water level change K3 in the previous 30 days.

[0087] Furthermore, the training of the DBO-XGBoost model includes:

[0088] The population size was set to 30, the maximum number of iterations to 50, and upper and lower limits for the parameters were set. The optimal parameters for the XGBoost model were obtained by using the Dung Beetle Optimization (DBO) algorithm to find the optimal maximum number of iterations, the optimal tree depth, and the optimal learning rate. The XGBoost model was then configured based on these optimal parameters.

[0089] Furthermore, the adaptive bandwidth kernel density estimation ABKDE model is optimized using the velocity-constrained multi-objective particle swarm optimization algorithm SMPSO, including:

[0090] S10. Construct an adaptive bandwidth kernel density function based on the Gaussian kernel function and adaptive bandwidth. The expression for the adaptive bandwidth kernel density function is:

[0091] ,

[0092] ,

[0093] ,

[0094] in, For local kernel density functions, For adaptive bandwidth kernel density function, It is the weight of the i-th kernel function. ; The bandwidth of the i-th kernel function is m; m is the total number of displacement data point samples. Represents the kernel function;

[0095] S20. Initialize the particle swarm: Based on the time displacement error data, randomly generate an initial particle swarm consisting of N particles, and assign a randomly initialized velocity vector to each particle; wherein, the initial position of each particle is... h is the global bandwidth parameter. The weights of the m-th kernel function;

[0096] S30. Construction of Multi-Objective Fitness Function: Integrating the risks of insufficient coverage and excessively wide intervals, a fitness function is constructed. The formula for quantifying the predicted interval performance is as follows: ,in, , These are the weighting coefficients, and ;

[0097] S40, Update Particles: Iteratively adjust the velocity and position of the particles;

[0098] S50, Polynomial Mutation and Archive Update: Apply mutation operation to 15% of the particles, update the non-dominated solution set, retain the parameter combination that takes into account the interval coverage PICP and the predicted interval average width PINAW, and calculate the crowding distance to preserve the diversity of the solution set.

[0099] Repeat steps S30-S50 for iterative optimization until a preset termination condition is met. The termination condition is: the maximum number of iterations reaches 200 or the change in the fitness function value is less than 10. -4 .

[0100] In this invention, the Gaussian kernel function is selected as the basic kernel function for kernel density estimation, and an adaptive bandwidth parameter is used to replace the fixed bandwidth to obtain an adaptive bandwidth kernel density function based on the Gaussian kernel function. , Adaptive bandwidth kernel density function of Gaussian kernel function , The expression is:

[0101] ,

[0102] ,

[0103] ,

[0104] in, For local kernel density functions, For adaptive bandwidth kernel density function, It is the weight of the i-th kernel function. ; The bandwidth of the i-th kernel function is m; m is the total number of displacement data point samples. Represents the kernel function;

[0105] Based on ABKDE, SMPSO is used to optimize the bandwidth parameter h and the weights in the mixing probability density function. The process involves setting the minimum prediction interval width and the maximum prediction interval coverage, and finding an optimal set of bandwidth parameters by iteratively updating the particle position and velocity. This includes the following steps:

[0106] ① An initial particle swarm consisting of N particles is randomly generated based on the time displacement error data. The initial position of each particle is: Initial position This represents a set of parameters to be optimized; where h is the global bandwidth parameter. The weights of the m-th kernel function are used; at the same time, each particle is assigned a randomly initialized velocity vector.

[0107] ② Define the fitness function This is used to quantify the performance of the prediction interval, integrate the risks of insufficient coverage and excessively wide intervals, and construct a fitness function. for:

[0108] ;

[0109] in, , These are the weighting coefficients, and .

[0110] ③ Iteratively adjust the velocity and position of the particles and update the particles.

[0111] ④ Apply mutation operations to 15% of the particles to enhance global exploration capabilities and update the non-dominated solution set (Pareto optimal solution set), retain the excellent parameter combination that balances interval coverage (PICP) and predicted interval average width (PINAW), and preserve solution set diversity by calculating crowding distance.

[0112] ⑤ When the pre-set termination condition is met (i.e., the maximum number of iterations reaches 200, or the change in the fitness function value is less than 10), -4 When the condition is met, the optimization process terminates.

[0113] Through the above SMPSO optimization process, the bandwidth parameters and weights are repeatedly adjusted based on the time displacement error data to achieve the goal of minimizing the loss function, thereby improving the performance of the adaptive bandwidth hybrid probability density function for predicting the time displacement error interval.

[0114] The optimized adaptive bandwidth kernel density estimation is used to generate a probability density function for the error sequence, thereby obtaining the displacement prediction interval at different confidence levels.

[0115] An adaptive kernel density estimation method based on velocity-constrained multi-objective particle swarm optimization is used to obtain the probability density function and cumulative distribution function of the cumulative displacement prediction error. Taking a 95% confidence level as an example, this model is compared with the unoptimized fixed-bandwidth kernel density estimation curve. The comparison results are as follows: Figure 10 As shown in the figure. The results indicate that the optimized adaptive bandwidth kernel density estimation curve is more concentrated near the true value, better matches the actual distribution, and has less fluctuation in prediction error, thus significantly improving the model's prediction performance.

[0116] Based on the probability density function of the predicted data, the displacement prediction intervals at different confidence levels are obtained, as shown in the following figures. Figure 11 As shown in Table 3, the model performance was analyzed using PICP, PINAW, and CWC as evaluation metrics for the prediction interval.

[0117] Table 3 Evaluation parameters of the interval prediction model

[0118]

[0119] As shown in Table 3, the values ​​of Interval Coverage Rate (PICP), Average Width of Predicted Interval (PINAW), and Composite Index (CWC) decrease as the confidence interval decreases. The SMPSO-ABKDE model can provide a wider prediction interval at high confidence intervals (e.g., 99%) to ensure a high coverage probability, while providing a narrower prediction interval at low confidence intervals (e.g., 90%) to reduce prediction uncertainty, while maintaining a good coverage probability, demonstrating good interval prediction performance.

[0120] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Terms such as "first," "second," etc., are used to denote names and do not indicate any particular order. The invention and its embodiments have been described above illustratively, and this description is not restrictive. The invention can be implemented in other specific forms without departing from its spirit or essential characteristics. The accompanying drawings are only one embodiment of the invention, and the actual structure is not limited thereto. No reference numerals in the claims should limit the scope of the claims. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the scope of protection of this invention.

Claims

1. A landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO optimized ABKDE, characterized in that, The method comprises the following steps: obtaining landslide cumulative displacement monitoring data, wherein the landslide cumulative displacement monitoring data comprises landslide cumulative displacement, rainfall and reservoir water level; preprocessing the landslide cumulative displacement monitoring data to obtain a landslide cumulative displacement time sequence; decomposing the landslide cumulative displacement time sequence by using a local mean decomposition algorithm (LMD) to obtain a plurality of product components (PF) and a residual component (R), calculating sample entropy values of each component, and reconstructing to obtain a fluctuation term and a trend term; predicting the trend term by polynomial fitting to obtain a trend term displacement prediction result; calculating the rainfall to obtain an original influence factor, calculating a Pearson correlation coefficient according to the original influence factor and the fluctuation term, and screening a strong correlation factor as an effective influence factor; inputting the effective influence factor and the fluctuation term into a pre-trained DBO-XGBoost model to obtain a fluctuation term displacement prediction result; superimposing the trend term displacement prediction result and the fluctuation term displacement prediction result to obtain a cumulative displacement prediction result, and taking the cumulative displacement prediction result as a point prediction result; calculating an error sequence between the point prediction result and an actual value, and inputting the error sequence into an SMPSO-ABKDE model to obtain a displacement prediction interval, wherein the SMPSO-ABKDE model is obtained by optimizing an adaptive bandwidth kernel density estimation (ABKDE) model by using a speed-constrained multi-objective particle swarm optimization (SMPSO) algorithm.

2. The landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO optimized ABKDE according to claim 1, characterized in that, The method further comprises the following steps of preprocessing the landslide cumulative displacement monitoring data to obtain a landslide cumulative displacement time sequence: removing outliers and noise in the landslide cumulative displacement monitoring data.

3. The landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO-optimized ABKDE according to claim 2, wherein the method further comprises the following steps of decomposing the landslide cumulative displacement time sequence by using the LMD to obtain a plurality of product components (PF) and a residual component (R), calculating sample entropy values of each component, and reconstructing to obtain a fluctuation term and a trend term: decomposing the landslide cumulative displacement time sequence by using the LMD to obtain a product component PF1, a product component PF2, a product component PF3 and a residual component R; calculating sample entropy values of each component, and reconstructing the product component PF1, the product component PF2 and the product component PF3 based on the calculated sample entropy values to obtain a fluctuation term, and reconstructing the residual component R to obtain a trend term.

4. The landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO-optimized ABKDE according to claim 3, wherein the method further comprises the following steps of ​ The original influence factors include: cumulative rainfall Y1 in 15 days, cumulative rainfall Y2 in the previous 15 days, cumulative rainfall Y3 in 30 days, cumulative rainfall Y4 in the previous 30 days, reservoir water level variation value K1 in 15 days, reservoir water level variation value K2 in the previous 15 days, reservoir water level variation value K3 in 30 days, reservoir water level variation value K4 in the previous 30 days, cumulative displacement L1 in 15 days, cumulative displacement L2 in the previous 15 days, cumulative displacement L3 in 30 days, and cumulative displacement L4 in the previous 30 days. The effective influence factors include: cumulative rainfall Y2 in the previous 15 days, reservoir water level variation value K4 in the previous 30 days, cumulative displacement L1 in 15 days, and reservoir water level variation value K3 in 30 days.

5. The landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO optimized ABKDE according to claim 4, characterized in that, The training of the DBO-XGBoost model includes: Setting the population number to 30, the maximum number of iterations to 50, setting the upper and lower limits of the parameters, and optimizing the best maximum number of iterations, the best tree depth and the best learning rate in the XGBoost model by the DBO optimization algorithm to obtain the optimal parameters, and configuring the parameters of the XGBoost model based on the optimal parameters.

6. The landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO-optimized ABKDE according to claim 5, wherein a speed-constrained multi-objective particle swarm optimization algorithm SMPSO is used to optimize an adaptive bandwidth kernel density estimation ABKDE model, including: S10, constructing an adaptive bandwidth kernel density function based on a Gaussian kernel function and an adaptive bandwidth, and the adaptive bandwidth kernel density function expression is: S40, updating the particles: iteratively adjusting the speed and position of the particles; ， ， ， wherein, is a local kernel density function, is an adaptive bandwidth kernel density function, is a weight of the i-th kernel function, ; is a bandwidth of the i-th kernel function; m is a total number of displacement data points, denotes a kernel function; S20, initializing a particle swarm: an initial particle swarm composed of N particles is randomly generated based on the time displacement error data, and each particle is given a randomly initialized velocity vector; wherein the initial position of each particle is h is a global bandwidth parameter, is the weight of the mth kernel function; S30, multi-objective fitness function construction: fusion of coverage risk and interval risk, construction of fitness function To quantify the performance of the prediction interval, the formula is: Wherein, , is a weight coefficient, and ; S50, polynomial mutation and archive update: applying a mutation operation to 15% of the particles, updating the non-dominated solution set, retaining the parameter combination considering the interval coverage rate PICP and the prediction interval average width PINAW, and calculating the crowded distance to retain the solution set diversity; 7. The landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO-optimized ABKDE according to claim 6, wherein the error sequence is obtained by calculating the error between the point displacement prediction result and the actual value, and the displacement prediction interval is obtained by inputting the error sequence into the SMPSO-ABKDE model, including: The iteration optimization is repeated by steps S30-S50 until a preset termination condition is met, the termination condition being that the maximum iteration number reaches 200 or the change of the fitness function value is less than 10 -4 . Generating a probability density function for the error sequence by adaptive bandwidth kernel density estimation ABKDE, and obtaining the displacement prediction interval under different confidence levels based on the probability density function and the different preset confidence levels.

8. The landslide surface displacement interval prediction method based on DBO-XGBoost and SMPSO-optimized ABKDE according to claim 7, wherein the interval coverage rate PICP, the prediction interval average width PINAW and the comprehensive index CWC are used as the prediction interval evaluation indexes to evaluate the effect of the displacement prediction interval under different confidence levels. ​ ​ ​

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