Landslide threshold estimation method based on adaptive hybrid copula model and osfoa algorithm
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUILIN UNIV OF ELECTRONIC TECH
- Filing Date
- 2026-01-30
- Publication Date
- 2026-05-29
Smart Images
Figure CN122113591A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of geological disaster early warning and risk assessment technology, and in particular relates to a landslide threshold estimation method based on an adaptive hybrid Copula model and OSFOA algorithm. Background Technology
[0002] Landslides, a frequent geological disaster, cause over 4,000 deaths and billions of dollars in economic losses globally each year, seriously threatening people's lives and property and regional ecological stability. Landslide risk threshold estimation is a core foundation of disaster early warning and prevention systems, and its accuracy directly determines the scientific validity and timeliness of disaster prevention and mitigation decisions. Traditional landslide risk assessment models (such as logistic regression and single random forest models) rely heavily on end-to-end training with raw monitoring data. This not only makes it difficult to characterize the complex nonlinear coupling relationships between geological parameters (rainfall, reservoir water level fluctuations, stratum displacement, etc.), but also fails to accurately quantify the tail dependence characteristics between variables, resulting in insufficient adaptability of the models to extreme conditions. Furthermore, traditional models lack adaptive optimization mechanisms in weight allocation, making it difficult to trace the contribution of individual factors to landslide disasters during the decision-making process, greatly restricting the precise deployment and implementation of prevention and control measures. Summary of the Invention
[0003] The purpose of this application is to provide a landslide threshold estimation method based on an adaptive hybrid Copula model and OSFOA algorithm. This method aims to address the problems of existing technologies, which are unable to characterize the complex nonlinear coupling relationship between geological parameters, and are unable to accurately quantify the tail dependence characteristics between variables, resulting in insufficient adaptability of the model to extreme conditions; as well as the lack of an adaptive optimization mechanism in weight allocation, making it difficult to trace the contribution of single factors to landslide disasters in the decision-making process, which greatly restricts the accurate deployment and implementation of prevention and control measures.
[0004] This application provides a landslide threshold estimation method based on an adaptive hybrid Copula model and the OSFOA algorithm, including the following steps: S101. Dynamically detect the optimal lag relationship between landslide displacement and influencing factors, and determine the optimal lag order by maximizing the log-likelihood value. The influencing factors include rainfall and reservoir water level fluctuation. S102. Based on the optimal lag order, align the landslide displacement, rainfall, and reservoir water level fluctuation. Use kernel density estimation to fit the marginal distribution of the landslide displacement, rainfall, and reservoir water level fluctuation respectively. Use empirical rank transformation to map the landslide displacement, rainfall, and reservoir water level fluctuation to the uniform distribution interval of [0,1] to obtain the standardized landslide displacement, rainfall, and reservoir water level fluctuation. S103. Based on the standardized landslide displacement, rainfall, and reservoir water level fluctuation, analyze the tail dependence characteristics of the landslide displacement and rainfall variable pairs and the landslide displacement and reservoir water level fluctuation variable pairs, respectively. Based on the tail dependence characteristics of the landslide displacement and rainfall variable pairs, adaptively select the components of the mixed Copula model for the landslide displacement and rainfall variable pairs to generate a mixed Copula model for landslide displacement and rainfall. Based on the tail dependence characteristics of the landslide displacement and reservoir water level fluctuation variable pairs, adaptively select the components of the mixed Copula model for the landslide displacement and reservoir water level fluctuation variable pairs to generate a mixed Copula model for landslide displacement and reservoir water level fluctuation. S104. The OSFOA algorithm is used to optimize the weight coefficients of the mixed Copula model of landslide displacement and rainfall and the mixed Copula model of landslide displacement and reservoir water level fluctuation, respectively, and the optimal mixed Copula model of landslide displacement and rainfall and the optimal mixed Copula model of landslide displacement and reservoir water level fluctuation are obtained by solving. S105. The early warning threshold is dynamically adjusted based on the optimal hybrid Copula model of landslide displacement and rainfall and the optimal hybrid Copula model of landslide displacement and reservoir water level fluctuation. The risk threshold under different confidence levels is calculated by combining the Value at Risk (VaR) and Conditional Value at Risk (CoVaR) theories. S106. Based on the risk threshold, establish a multi-level early warning threshold system, analyze parameter uncertainty through the Bootstrap resampling method, calculate the joint return period, and complete the landslide risk assessment.
[0005] In this application, by dynamically detecting the optimal hysteresis relationship between landslide displacement and influencing factors and using an adaptive hybrid Copula model, the model can automatically adapt to the complex time-delay response mechanism and variable tail-dependent characteristics of the landslide system, without requiring prior assumptions and exhibiting strong generalization ability. Furthermore, the introduction of the OSFOA algorithm to optimize the hybrid weights solves the challenges of high-dimensional and nonlinear optimization, improving model accuracy and stability. In addition, by combining VaR, CoVaR, dynamic threshold adjustment, Bootstrap uncertainty analysis, and joint return period calculation, a complete, rigorous, and operable risk early warning system is constructed, encompassing threshold calculation, risk measurement, and uncertainty assessment. Application in actual landslide cases has successfully output multi-level early warning thresholds with clear physical meaning and statistical confidence, validating the effectiveness and practicality of the method. Attached Figure Description
[0006] Figure 1 This is a flowchart of a landslide threshold estimation method based on an adaptive hybrid Copula model and OSFOA algorithm provided in an embodiment of this application.
[0007] Figure 2This is a hysteresis relationship analysis diagram of landslide displacement and influencing factors in one embodiment of this application.
[0008] Figure 3 This is a graph showing the estimated edge distribution kernel density of landslide displacement and influence factors in one embodiment of this application.
[0009] Figure 4 This is a comparison chart of tail dependence characteristics of landslide displacement and rainfall variables and Copula fitting in one embodiment of this application.
[0010] Figure 5 This is a tail-dependent feature analysis and Copula fitting comparison diagram of landslide displacement and reservoir water level fluctuation variables in one embodiment of this application. Detailed Implementation
[0011] To make the objectives, technical solutions, and beneficial effects of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0012] To illustrate the technical solution described in this application, specific embodiments are provided below.
[0013] Please see Figure 1 This is a flowchart of a landslide threshold estimation method based on an adaptive hybrid Copula model and OSFOA algorithm provided in an embodiment of this application. The landslide threshold estimation method based on an adaptive hybrid Copula model and OSFOA algorithm provided in an embodiment of this application includes the following steps: S101. Dynamically detect the optimal lag relationship between landslide displacement and influencing factors, and determine the optimal lag order by maximizing the log-likelihood value. The influencing factors include rainfall and reservoir water level fluctuation.
[0014] The impact of influencing factors on landslide displacement exhibits a certain lag. In one embodiment of this application, the data for influencing factors such as monthly landslide displacement rate, monthly rainfall, and monthly reservoir water level fluctuation are derived from long-term monitoring data, such as those from the National Glacier, Permafrost and Desert Science Data Center (http: / / www.ncdc.ac.cn), with a data time span of 108 months.
[0015] In one embodiment of this application, S101 specifically involves: traversing a preset range of lag orders, constructing variable pairs corresponding to different lag orders, wherein the variable pairs are landslide displacement and influencing factors, and determining the optimal lag order with the goal of maximizing the log-likelihood value of Gaussian Copula.
[0016] Gaussian Copula is a statistical tool that cleverly separates the marginal distributions of a set of random variables from the structure describing the dependencies between these variables. Its core idea is that regardless of the individual distribution of each variable, a method can be used to connect them into a multivariate joint distribution with a specific correlation structure.
[0017] In one embodiment of this application, S101 specifically includes the following steps: In the MATLAB environment, set the maximum lag order (for example, the maximum lag order is 3, which means detecting lags of 0, 1, 2, and 3 months). For each lag order (i.e. 0, 1, 2, 3), a corresponding variable pair is constructed, including the landslide displacement sequence and the lagged rainfall sequence, as well as the landslide displacement sequence and the lagged reservoir water level fluctuation sequence. The empirical rank transformation is performed on the two sets of variable pairs respectively to map the variable pairs to the uniform distribution interval [0,1], resulting in two sets of uniformly distributed samples [0,1]. For each lag order, a two-dimensional Gaussian Copula model is fitted according to the two sets of uniformly distributed samples in [0,1], and the sum of the log-likelihood values of the two two-dimensional Gaussian Copula models is calculated as an index to measure the goodness of fit of the joint distribution between variables under the lag relationship. After iterating through all lag orders, the lag order that maximizes the sum of log-likelihood values is selected as the optimal lag order, such as... Figure 2 As shown.
[0018] S102. Based on the optimal lag order, align the landslide displacement, rainfall, and reservoir water level fluctuations. Use kernel density estimation to fit the marginal distributions of the landslide displacement, rainfall, and reservoir water level fluctuations respectively. Through empirical rank transformation, map the landslide displacement, rainfall, and reservoir water level fluctuations to a uniform distribution interval of [0,1] to obtain standardized landslide displacement, rainfall, and reservoir water level fluctuations, eliminating dimensional interference. Figure 3 As shown.
[0019] S103. Based on the standardized landslide displacement, rainfall, and reservoir water level fluctuation, analyze the tail dependency characteristics of the landslide displacement and rainfall variable pairs and the landslide displacement and reservoir water level fluctuation variable pairs, respectively. Based on the tail dependency characteristics of the landslide displacement and rainfall variable pairs, adaptively select the components of the mixed Copula model for the landslide displacement and rainfall variable pairs, and generate a mixed Copula model for landslide displacement and reservoir water level fluctuation, ensuring that the model adapts to the data dependency structure.
[0020] The Copula model is a function used to model the joint distribution of multidimensional random variables. It flexibly handles complex correlations by decoupling the dependency structure and marginal distributions between variables. Its core principle is Sklar's theorem: any joint distribution can be decomposed into a combination of marginal distributions and a Copula function. In one embodiment of this application, S103 specifically includes the following steps: S1031. Based on the standardized landslide displacement, rainfall, and reservoir water level fluctuation, calculate the empirical tail dependence coefficients of the landslide displacement and rainfall variables and the landslide displacement and reservoir water level fluctuation variables, respectively, i.e., Kendall τ.
[0021] Kendall's τ is a nonparametric statistic used to measure the degree of rank correlation between two variables. Its core characteristic is reflecting whether the ranking trends of the two variables are consistent, and its value ranges from -1 to 1. It does not depend on the specific distribution of the variables, is insensitive to outliers, and is particularly suitable for characterizing nonlinear but monotonic correlations. It is also a core indicator in Copula models describing the dependency structure of variables.
[0022] S1032. Based on Kendall's τ, fit Gumbel Copula, Clayton Copula, and Frank Copula to the variables of landslide displacement versus rainfall and landslide displacement versus reservoir water level fluctuation, respectively, and calculate the upper tail dependence coefficients of Gumbel Copula, Clayton Copula, and Frank Copula. and lower tail dependency coefficient .
[0023] Gumbel Copula, Clayton Copula, and Frank Copula are three of the most commonly used Archimedes Copula functions. Their core commonality is that they are constructed through a single generating function, have few parameters, and have clear physical meanings. The differences lie in their tail correlation characteristics and applicable dependency structures. They are core tools for characterizing nonlinear and asymmetric dependencies of multidimensional variables.
[0024] S1033. For the variables of landslide displacement and rainfall, and landslide displacement and reservoir water level fluctuation, respectively, based on the upper tail dependence coefficients of Gumbel Copula, Clayton Copula, and Frank Copula. and lower tail dependency coefficient Calculate the average tail characteristic index, including the average upper tail dependence coefficient. Average lower tail dependence coefficient and tail asymmetry index .
[0025] S1034, Based on the average upper tail dependency coefficient Average lower tail dependence coefficient and tail asymmetry index Based on preset thresholds, the components of the hybrid Copula model are adaptively selected for the landslide displacement and rainfall variable pairs and the landslide displacement and reservoir water level fluctuation variable pairs, respectively: if the tail features are obvious, the corresponding Archimedean Copula is added to the elliptic Copula family; if the tail features are not obvious, only the elliptic Copula family is used for mixing, and finally, the hybrid Copula model of landslide displacement and rainfall and the hybrid Copula model of landslide displacement and reservoir water level fluctuation are generated.
[0026] Archimedean Copula is a class of parameterized Copula functions constructed using generating functions.
[0027] In one embodiment of this application, the preset threshold includes an upper tail strength threshold. =0.3, lower tail strength threshold =0.3, tail asymmetry threshold =0.2.
[0028] In one embodiment of this application, the adaptive selection of the components of the hybrid Copula model in conjunction with a preset threshold can specifically be as follows: like > or > or > If the tail features are obvious, Archimedesian Copula needs to be added to the elliptic family Copula. like > 1.5× Then, Gumbel Copula is added to the elliptic family Copula; like > 1.5× Then, Clayton Copula is added to the elliptic family Copula. Otherwise, choose to add Frank Copula to the elliptic family Copula; If the tail features are not obvious, then only the elliptic family of Copula is used for mixing, such as... Figure 4 and Figure 5 As shown.
[0029] In one embodiment of this application, the dependency parameters of Gumbel Copula and Clayton Copula are determined by Kendall correlation coefficient, corresponding to upper tail dependency and lower tail dependency features, respectively; the parameters of Frank Copula are determined by numerical solution, and there is no obvious tail dependency.
[0030] S104. The OSFOA algorithm is used to optimize the weight coefficients of the mixed Copula model of landslide displacement and rainfall and the mixed Copula model of landslide displacement and reservoir water level fluctuation, respectively. The optimal mixed Copula model of landslide displacement and rainfall and the optimal mixed Copula model of landslide displacement and reservoir water level fluctuation are obtained by solving the problem, thereby improving the model fitting accuracy.
[0031] OSFOA (Improved Starfish Optimization Algorithm) is an improved version of SFOA (Starfish Optimization Algorithm). The OSFOA algorithm integrates three core technologies to solve the problems of slow convergence and susceptibility to local optima in the original SFOA, demonstrating excellent performance in fields such as engineering optimization, parameter optimization, and path planning.
[0032] In one embodiment of this application, S104 specifically includes the following steps: S1041. Construct the matrices of a hybrid Copula model of landslide displacement and rainfall and a hybrid Copula model of landslide displacement and reservoir water level fluctuation, respectively. The Copula model, which combines landslide displacement and rainfall, takes the following form: The density function of the Copula model, which combines landslide displacement and reservoir water level fluctuation, is: in, Let be the weight vector, satisfying , This represents the cumulative distribution function value of the landslide displacement after kernel density estimation and probability integral transformation; This represents the cumulative distribution function value of rainfall after kernel density estimation and probability integral transformation; This represents the cumulative distribution function value of the reservoir water level fluctuation after kernel density estimation and probability integral transformation; its value ranges from [0,1]. , and , representing the probability density functions of Gumbel Copula, t-Copula, and Frank Copula, respectively. Gumbel is used to characterize the upper tail dependency between variables, t-Copula is used to characterize the two-tailed features, and Frank Copula is used to characterize the symmetric correlation. , and These are the dependency parameters for each individual Copula model. The correlation coefficient of Gumbel Copula. For the degrees of freedom of the t-Copula, The correlation strength of the Frank Copula structure; S1042. Define the objective function. For empirical Copula values The root mean square error between the predicted values and those of the mixture model. The objective function formula is: , in, This represents the fitness function of the hybrid Copula model. Its physical meaning is the root mean square error between the model's fitted value and the empirical value. It is the criterion for the OSFOA algorithm to find the best fit. This represents the total number of observed samples (e.g., 108 monthly monitoring data points in this example). This represents the empirical Copula value calculated based on measured monitoring data, which serves as a benchmark for model fitting. This represents the theoretical prediction value in the current hybrid Copula model; This represents the cumulative distribution function value of the landslide displacement after kernel density estimation and probability integral transformation; This represents the cumulative distribution function value of the influence factor after kernel density estimation and probability integral transformation; S1043. Initialize OSFOA algorithm parameters; S1044. The weight vector w is iteratively optimized using the OSFOA algorithm. In each iteration, the fitness (i.e., the objective function value) of each individual in the population is calculated, and the global optimum is updated. The weights are constrained by the softmax function to ensure that their sum is 1.
[0033] S1045. After reaching the maximum number of iterations, output the optimal weight coefficients of the mixed Copula model of landslide displacement and rainfall and the mixed Copula model of landslide displacement and reservoir water level fluctuation, respectively, to obtain the optimal mixed Copula model of landslide displacement and rainfall and the optimal mixed Copula model of landslide displacement and reservoir water level fluctuation.
[0034] S105. The optimal hybrid Copula model based on landslide displacement and rainfall and the optimal hybrid Copula model based on landslide displacement and reservoir water level fluctuation are used to dynamically adjust the early warning threshold. The risk threshold under different confidence levels is calculated by combining Value at Risk (VaR) and Conditional Value at Risk (CoVaR) theories, thereby enhancing the rationality and adaptability of the risk threshold.
[0035] In one embodiment of this application, the dynamic adjustment of the early warning threshold includes: calculating an initial VaR threshold based on sample quantiles; and adjusting the threshold according to the dependence parameter of Gumbel Copula, which reflects upper tail correlation. The dependency parameter of Clayton Copula reflecting lower tail correlation The initial VaR threshold is adjusted proportionally; if the optimal hybrid Copula model includes Archimedes Copula, then the average upper tail dependency coefficient calculated in S1033 is used. Average lower tail dependence coefficient and tail asymmetry index Further fine-tuning.
[0036] In one embodiment of this application, S105 specifically includes the following steps: S1051. Based on the optimal hybrid Copula model of landslide displacement and rainfall and the optimal hybrid Copula model of landslide displacement and reservoir water level fluctuation, a large number of simulated samples conforming to the joint distribution are generated through hybrid sampling technology.
[0037] S1052, Calculate the landslide displacements respectively. Rainfall Reservoir water level fluctuation At four confidence levels VaR at the following confidence level The values are 0.95, 0.90, 0.85, and 0.80, respectively, to define the risk probability boundaries of different levels, and the calculated VaR is defined as the key risk threshold for landslide early warning.
[0038] S1053. Calculate CoVaR: For a given influencing factor (such as rainfall)... ), for four confidence levels First, we define rainfall at a confidence level. The value at risk is Satisfying P( > ) This value is calculated by S1052. It is calculated when the user is in a high-risk state (i.e., ...). ≥ Under the condition of ), landslide displacement The risk threshold is denoted as Its definition is: That is, when the rainfall exceeds its confidence level Under the condition of VaR value below, the landslide displacement exceeds The probability does not exceed Similarly, the reservoir water level fluctuation can be defined and calculated. At confidence level Value at Risk and the corresponding conditional risk thresholds .
[0039] S1054, Dynamic Threshold Adjustment: The variables calculated using S1052 at the confidence level... The VaR value below is used as the initial VaR warning threshold, based on the Gumbel Copula parameter, which reflects the upper tail correlation. and the Clayton Copula parameter, which reflects the lower tail correlation. and average upper tail dependence coefficient or average lower tail dependence coefficient The initial VaR warning threshold is adjusted proportionally; the adjustment rules are as follows: like A value > 2.0 indicates extremely strong upper-tail correlation, and the warning threshold should be raised by 20%. like > 1.5, warning threshold increased by 10%; If the tail characteristics are obvious (i.e., the average upper tail dependence coefficient) or average lower tail dependence coefficient (greater than 0.3), adjusted using an adjustment factor, the adjusted warning threshold. The formula for calculating the adjustment factor is: ,in The upward displacement ratio is based on the Gumbel parameter. For tail feature-based fine-tuning factors, Defined as: the probability that a variable exceeds this value does not exceed [a certain value]. ,Right now .
[0040] S106. Based on the risk threshold, establish a multi-level early warning threshold system, analyze parameter uncertainty through the Bootstrap resampling method, calculate the joint return period, and complete the landslide risk assessment.
[0041] In one embodiment of this application, S106 specifically involves: generating simulated samples based on the optimal hybrid Copula model, establishing four warning levels according to different confidence levels, calculating the joint return period, and obtaining the VaR value confidence interval through the Bootstrap method to complete the parameter uncertainty analysis.
[0042] In one embodiment of this application, the four-level early warning threshold system corresponds to four confidence levels: =0.80 (blue), 0.85 (yellow), 0.90 (orange), 0.95 (red), each level provides VaR and CoVaR for landslide displacement, rainfall, and reservoir water level fluctuations.
[0043] In one embodiment of this application, S106 specifically includes the following steps: S1061. Based on the VaR and CoVaR values obtained in S105 at different confidence levels, a four-level early warning threshold system is established, corresponding to... =0.80, 0.85, 0.90, 0.95. Each warning level provides independent thresholds and conditional thresholds for landslide displacement, rainfall, and reservoir water level fluctuations.
[0044] S1062. Uncertainty analysis is performed on the parameter estimation of the critical risk threshold using the Bootstrap resampling method. Specifically, the critical risk threshold (e.g., 95% VaR) calculated in S1052 is resampled B=100 times. The estimation error is quantified by simulating the sampling distribution of the parameters, and the 95% confidence interval is estimated. The Bootstrap confidence interval calculation formula is: in, This represents a confidence interval with a confidence level of 1-β. When β=0.05, it is a 95% confidence interval, which quantifies the uncertainty of the parameter estimation. Here is the parameter to be estimated (e.g., VaR); B is the number of Bootstrap resampling attempts; β = 0.05; ; This represents the Bootstrap estimate that is the kth value after the estimated values obtained from B resamplings are sorted in ascending order.
[0045] S1063. Based on the joint simulation samples generated by the optimal hybrid Copula model of landslide displacement and rainfall and the optimal hybrid Copula model of landslide displacement and reservoir water level fluctuation, risk events are defined, and the OR-type joint return period is calculated. The average interval between landslide displacements or any event exceeding a certain threshold for a given influencing factor is calculated using the following formula: Calculate the AND-type joint return period The average interval between events in which landslide displacement and a certain influencing factor simultaneously exceed their respective thresholds is calculated using the following formula: in, For landslide displacement X The marginal distribution function at the threshold x The value at that location, i.e. P ( X ≤ x The result is obtained by fitting the kernel density estimation method in S102; Influencing factors (rainfall or reservoir water level fluctuations) Y The marginal distribution function at the threshold y The value at that location, i.e. P ( Y ≤ y ), obtained by fitting S102; For the optimal hybrid Copula model at point The value at this point indicates that the landslide displacement does not exceed the threshold. x And the impact factor does not exceed the threshold. y joint probability P ( X ≤ x , Y ≤ y ).
[0046] In this application, by dynamically detecting the optimal hysteresis relationship between landslide displacement and influencing factors and using an adaptive hybrid Copula model, the model can automatically adapt to the complex time-delay response mechanism and variable tail-dependent characteristics of the landslide system, without requiring prior assumptions and exhibiting strong generalization ability. Furthermore, the introduction of the OSFOA algorithm to optimize the hybrid weights solves the challenges of high-dimensional and nonlinear optimization, improving model accuracy and stability. In addition, by combining VaR, CoVaR, dynamic threshold adjustment, Bootstrap uncertainty analysis, and joint return period calculation, a complete, rigorous, and operable risk early warning system is constructed, encompassing threshold calculation, risk measurement, and uncertainty assessment. Application in actual landslide cases has successfully output multi-level early warning thresholds with clear physical meaning and statistical confidence, validating the effectiveness and practicality of the method.
[0047] It should be understood that the steps in the various embodiments of this application are not necessarily executed sequentially according to the order indicated by the step numbers. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in each embodiment may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.
[0048] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.
[0049] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0050] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.
Claims
1. A landslide threshold estimation method based on an adaptive hybrid Copula model and the OSFOA algorithm, characterized in that, Includes the following steps: S101. Dynamically detect the optimal lag relationship between landslide displacement and influencing factors, and determine the optimal lag order by maximizing the log-likelihood value. The influencing factors include rainfall and reservoir water level fluctuation. S102. Based on the optimal lag order, align the landslide displacement, rainfall, and reservoir water level fluctuation. Use kernel density estimation to fit the marginal distribution of the landslide displacement, rainfall, and reservoir water level fluctuation respectively. Use empirical rank transformation to map the landslide displacement, rainfall, and reservoir water level fluctuation to the uniform distribution interval of [0,1] to obtain the standardized landslide displacement, rainfall, and reservoir water level fluctuation. S103. Based on the standardized landslide displacement, rainfall, and reservoir water level fluctuation, analyze the tail dependence characteristics of the landslide displacement and rainfall variable pairs and the landslide displacement and reservoir water level fluctuation variable pairs, respectively. Based on the tail dependence characteristics of the landslide displacement and rainfall variable pairs, adaptively select the components of the mixed Copula model for the landslide displacement and rainfall variable pairs to generate a mixed Copula model for landslide displacement and rainfall. Based on the tail dependence characteristics of the landslide displacement and reservoir water level fluctuation variable pairs, adaptively select the components of the mixed Copula model for the landslide displacement and reservoir water level fluctuation variable pairs to generate a mixed Copula model for landslide displacement and reservoir water level fluctuation. S104. The OSFOA algorithm is used to optimize the weight coefficients of the mixed Copula model of landslide displacement and rainfall and the mixed Copula model of landslide displacement and reservoir water level fluctuation, respectively, and the optimal mixed Copula model of landslide displacement and rainfall and the optimal mixed Copula model of landslide displacement and reservoir water level fluctuation are obtained by solving. S105. The early warning threshold is dynamically adjusted based on the optimal hybrid Copula model of landslide displacement and rainfall and the optimal hybrid Copula model of landslide displacement and reservoir water level fluctuation. The risk threshold under different confidence levels is calculated by combining the Value at Risk (VaR) and Conditional Value at Risk (CoVaR) theories. S106. Based on the risk threshold, establish a multi-level early warning threshold system, analyze parameter uncertainty through the Bootstrap resampling method, calculate the joint return period, and complete the landslide risk assessment.
2. The method as described in claim 1, characterized in that, S101 specifically involves: traversing the preset lag order range, constructing variable pairs corresponding to different lag orders, wherein the variable pairs are landslide displacement and influencing factors, and determining the optimal lag order with the goal of maximizing the log-likelihood value of Gaussian Copula.
3. The method as described in claim 2, characterized in that, S101 specifically includes the following steps: In the MATLAB environment, set the maximum lag order; For each lag order, a corresponding variable pair is constructed, including the landslide displacement sequence and the lagged rainfall sequence, as well as the landslide displacement sequence and the lagged reservoir water level fluctuation sequence. The empirical rank transformation is performed on the two sets of variable pairs respectively to map the variable pairs to the uniform distribution interval of [0,1], resulting in two sets of uniformly distributed samples of [0,1]. For each lag order, a two-dimensional Gaussian Copula model is fitted according to the two sets of uniformly distributed samples in [0,1], and the sum of the log-likelihood values of the two two-dimensional Gaussian Copula models is calculated as an index to measure the goodness of fit of the joint distribution between variables under the lag relationship. After iterating through all lag orders, the lag order that maximizes the sum of log-likelihood values is selected as the optimal lag order.
4. The method as described in claim 3, characterized in that, S103 specifically includes the following steps: S1031. Based on the standardized landslide displacement, rainfall, and reservoir water level fluctuation, calculate the empirical tail dependence coefficients of the landslide displacement and rainfall variables and the landslide displacement and reservoir water level fluctuation variables, i.e., Kendall τ. S1032. Based on Kendall's τ, fit Gumbel Copula, Clayton Copula, and Frank Copula to the variables of landslide displacement versus rainfall and landslide displacement versus reservoir water level fluctuation, respectively, and calculate the upper tail dependence coefficients of Gumbel Copula, Clayton Copula, and Frank Copula. and lower tail dependency coefficient ; S1033. For the variables of landslide displacement and rainfall, and landslide displacement and reservoir water level fluctuation, respectively, based on the upper tail dependence coefficients of Gumbel Copula, Clayton Copula, and Frank Copula. and lower tail dependency coefficient Calculate the average tail characteristic index, including the average upper tail dependence coefficient. Average lower tail dependence coefficient and tail asymmetry index ; S1034, Based on the average upper tail dependency coefficient Average lower tail dependence coefficient and tail asymmetry index Based on preset thresholds, the components of the hybrid Copula model are adaptively selected for the landslide displacement and rainfall variable pairs and the landslide displacement and reservoir water level fluctuation variable pairs, respectively: if the tail features are obvious, the corresponding Archimedean Copula is added to the elliptic Copula family; if the tail features are not obvious, only the elliptic Copula family is used for mixing, and finally, the hybrid Copula model of landslide displacement and rainfall and the hybrid Copula model of landslide displacement and reservoir water level fluctuation are generated.
5. The method as described in claim 4, characterized in that, The preset threshold includes the upper tail strength threshold. =0.3, lower tail strength threshold =0.3, tail asymmetry threshold =0.2; The adaptive selection of components of the hybrid Copula model, based on a preset threshold, specifically involves: like > or > or > If the tail features are obvious, Archimedesian Copula needs to be added to the elliptic family Copula. like > 1.5× Then, Gumbel Copula is added to the elliptic family Copula; like > 1.5× Then, Clayton Copula is added to the elliptic family Copula. Otherwise, choose to add Frank Copula to the elliptic family Copula; If the tail features are not obvious, then only the elliptic family Copula is used for mixing.
6. The method as described in claim 5, characterized in that, S104 specifically includes the following steps: S1041. Construct the matrices of a hybrid Copula model of landslide displacement and rainfall and a hybrid Copula model of landslide displacement and reservoir water level fluctuation, respectively. The Copula model, which combines landslide displacement and rainfall, takes the following form: The density function of the Copula model, which combines landslide displacement and reservoir water level fluctuation, is: in, Let be the weight vector, satisfying , This represents the cumulative distribution function value of the landslide displacement after kernel density estimation and probability integral transformation; This represents the cumulative distribution function value of rainfall after kernel density estimation and probability integral transformation; This represents the cumulative distribution function value of the reservoir water level fluctuation after kernel density estimation and probability integral transformation; its value ranges from [0,1]. , and , representing the probability density functions of Gumbel Copula, t-Copula, and Frank Copula, respectively. Gumbel is used to characterize the upper tail dependency between variables, t-Copula is used to characterize the two-tailed features, and Frank Copula is used to characterize the symmetric correlation. , and These are the dependency parameters for each individual Copula model. The correlation coefficient of Gumbel Copula. For the degrees of freedom of the t-Copula, The correlation strength of the Frank Copula structure; S1042. Define the objective function. For empirical Copula values The root mean square error between the predicted values and the mixed model is expressed by the objective function formula: ， in, This represents the fitness function of the hybrid Copula model. Its physical meaning is the root mean square error between the model's fitted value and the empirical value. It is the criterion for the OSFOA algorithm to find the best fit. This represents the total number of observed samples; This represents the empirical Copula value calculated based on measured monitoring data, which serves as a benchmark for model fitting. This represents the theoretical prediction value in the current hybrid Copula model; This represents the cumulative distribution function value of the landslide displacement after kernel density estimation and probability integral transformation; This represents the cumulative distribution function value of the influence factor after kernel density estimation and probability integral transformation; S1043. Initialize OSFOA algorithm parameters; S1044. The weight vector w is iteratively optimized using the OSFOA algorithm. In each iteration, the fitness of the individuals in the population is calculated, and the global optimal solution is updated. The weights are constrained by the softmax function to ensure that their sum is 1. S1045. After reaching the maximum number of iterations, output the optimal weight coefficients of the mixed Copula model of landslide displacement and rainfall and the mixed Copula model of landslide displacement and reservoir water level fluctuation, respectively, to obtain the optimal mixed Copula model of landslide displacement and rainfall and the optimal mixed Copula model of landslide displacement and reservoir water level fluctuation.
7. The method as described in claim 6, characterized in that, The dynamic adjustment of the early warning threshold includes: calculating the initial VaR threshold based on sample quantiles; and adjusting the dependence parameter reflecting upper tail correlation based on Gumbel Copula. The dependency parameter of Clayton Copula, reflecting the lower tail correlation. The initial VaR threshold is adjusted proportionally; if the optimal mixture Copula model includes Archimedes Copula, then the average upper tail dependency coefficient is incorporated. Average lower tail dependence coefficient and tail asymmetry index Further fine-tuning.
8. The method as described in claim 7, characterized in that, S105 specifically includes the following steps: S1051. Based on the optimal hybrid Copula model of landslide displacement and rainfall and the optimal hybrid Copula model of landslide displacement and reservoir water level fluctuation, a large number of simulated samples conforming to the joint distribution are generated through hybrid sampling technology. S1052, Calculate the landslide displacements respectively. Rainfall Reservoir water level fluctuation At four confidence levels The VaR is used to define the risk probability boundary of different levels and the calculated VaR is defined as the key risk threshold for landslide early warning. S1053. Calculate CoVaR: For a given impact factor, at four confidence levels... First, we define rainfall at a confidence level. The value at risk is Satisfying P( > ) This value is calculated by S1052; the calculation is performed when the device is in a high-risk state, i.e. ≥ Under these conditions, landslide displacement The risk threshold is denoted as Its definition is: That is, when the rainfall exceeds its confidence level Under the condition of VaR value below, the landslide displacement exceeds The probability does not exceed Similarly, define and calculate the reservoir water level fluctuation. At confidence level Value at Risk and the corresponding conditional risk thresholds ; S1054, Dynamic Threshold Adjustment: The variables calculated using S1052 at the confidence level... The VaR value below is used as the initial VaR warning threshold, based on the Gumbel Copula parameter, which reflects the upper tail correlation. and the Clayton-Copula parameter reflecting the lower tail correlation and average upper tail dependence coefficient Or the average lower tail dependence coefficient The initial VaR warning threshold is adjusted proportionally; the adjustment rules are as follows: like A value > 2.0 indicates extremely strong upper-tail correlation, and the warning threshold should be raised by 20%. like > 1.5, warning threshold increased by 10%; If the tail characteristics are obvious, i.e., the average upper tail dependence coefficient Or the average lower tail dependence coefficient If the value is greater than 0.3, adjust it using an adjustment factor. The adjusted warning threshold is then determined. Adjustment factor, the formula for calculating the adjustment factor is: Adjustment factor ,in The upward displacement ratio is based on the Gumbel parameter. For tail feature-based fine-tuning factors, Defined as: the probability that a variable exceeds this value does not exceed [a certain value]. ,Right now .
9. The method as described in claim 8, characterized in that, Specifically, S106 involves generating simulated samples based on the optimal hybrid Copula model, establishing four warning levels according to different confidence levels, calculating the joint return period, and obtaining the VaR confidence interval through the Bootstrap method to complete the parameter uncertainty analysis.
10. The method as described in claim 9, characterized in that, S106 specifically includes the following steps: S1061. Based on VaR and CoVaR values at different confidence levels, a four-level early warning threshold system is established, with each early warning level providing independent thresholds and conditional thresholds for landslide displacement, rainfall, and reservoir water level fluctuations. S1062. Uncertainty analysis is performed on the parameter estimation of the critical risk threshold using the Bootstrap resampling method. Specifically, the calculated critical risk threshold is resampled B times. The estimation error is quantified by simulating the sampling distribution of the parameters, and its 95% confidence interval is estimated. The Bootstrap confidence interval calculation formula is as follows: in, This represents a confidence interval with a confidence level of 1-β. When β=0.05, it is a 95% confidence interval, which quantifies the uncertainty of the parameter estimation. is the parameter to be estimated; B is the number of Bootstrap resampling times; β=0.05; ; This represents the Bootstrap estimate that is the kth value after sorting the estimates obtained from B resamplings in ascending order. S1063. Based on the joint simulation samples generated by the optimal hybrid Copula model of landslide displacement and rainfall and the optimal hybrid Copula model of landslide displacement and reservoir water level fluctuation, risk events are defined, and the OR-type joint return period is calculated. The average interval between landslide displacements or any event exceeding a certain threshold for a given influencing factor is calculated using the following formula: Calculate the AND-type joint return period The average interval between events in which landslide displacement and a certain influencing factor simultaneously exceed their respective thresholds is calculated using the following formula: in, For landslide displacement X The marginal distribution function at the threshold x The value at that location, i.e. P ( X ≤ x The result was obtained by fitting the kernel density estimation method. Impact Factor Y The marginal distribution function at the threshold y The value at that location, i.e. P ( Y ≤ y ), obtained by fitting S102; For the optimal hybrid Copula model at point The value at this point indicates that the landslide displacement does not exceed the threshold. x And the impact factor does not exceed the threshold. y joint probability P ( X ≤ x , Y ≤ y ).