Bayesian-based landslide parameter back analysis and instability probability prediction method and device

Abstract

A landslide parameter back analysis and instability probability prediction method and device based on Bayes are provided in the application, the method comprising: establishing a numerical model according to the engineering information of the first sliding of the landslide, and determining random variables; determining the prior distribution of the random variables based on the current statistical information; updating the prior distribution based on the actual observation information of the first sliding of the landslide and the prediction information generated by the numerical model, obtaining the posterior distribution by combining the Bayes inference; statistically analyzing the posterior distribution by using the MCMC algorithm, obtaining the statistical characteristics of the random variables; and calculating the instability probability of the second sliding of the landslide by using the Monte Carlo method according to the statistical characteristics, and predicting the maximum critical sliding surface of the instability probability of the second sliding and analyzing the instability probability of the sliding surface. The application considers the uncertainty of the random variables and analyzes the stability of the landslide based on multiple observation information, thereby improving the reliability of the stability analysis.

Description

Technical Field

[0001] This application relates to the field of landslide stability and safety assessment in the railway and highway industries, and in particular to a Bayesian-based method and apparatus for landslide parameter back analysis and instability probability prediction. Background Technology

[0002] Landslide stability assessment is a crucial part of quantitative landslide risk assessment. Obtaining accurate physical and mechanical parameters is a fundamental prerequisite for conducting landslide stability assessment. Only on this basis can the stability state of landslides be effectively predicted, and the prediction of instability probability can provide important support for disaster prevention and mitigation.

[0003] In practical engineering, soil sampling is easily disturbed and damaged, making it difficult to obtain the true physical and mechanical parameters of undisturbed soil. Furthermore, due to the scale effect, there are errors between the indoor test results and the true physical and mechanical parameters of landslides. At the same time, in the probabilistic back analysis of landslide stability, the observation data is limited, and most of the time only the stability coefficient is used as the observation information, which leads to the unreliability of landslide stability analysis. Summary of the Invention

[0004] In view of the above problems, this application provides a Bayesian-based method and apparatus for inverse analysis of landslide parameters and prediction of instability probability, in order to overcome the above problems or at least partially solve them.

[0005] A first aspect of this application discloses a Bayesian-based method for landslide parameter inverse analysis and instability probability prediction, the method comprising:

[0006] A numerical model was established based on the engineering information of the first landslide, and random variables were determined.

[0007] Determine the prior distribution of the random variable based on the current statistical information;

[0008] Based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated by combining Bayesian inference to obtain the posterior distribution;

[0009] The MCMC algorithm is used to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variable;

[0010] Based on the statistical characteristics, the Monte Carlo method was used to calculate the probability of the second landslide instability, and to predict the maximum critical sliding surface and analyze the probability of instability of the sliding surface.

[0011] Optionally, based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated using Bayesian inference to obtain the posterior distribution, including:

[0012] Obtain m observation surface feature coordinate points for the first sliding of the landslide, and obtain observation data based on the m observation surface feature coordinate points and the stability coefficient, where m is an integer greater than 0;

[0013] Based on the numerical model, m predicted sliding surface feature coordinate points and predicted stability coefficients are obtained, and predicted data is obtained based on the m predicted sliding surface feature coordinate points and the predicted stability coefficients;

[0014] Based on the observed data and the predicted data, the probability density is calculated to obtain the conditional probability density of the random variable;

[0015] The posterior distribution is obtained based on the conditional probability density and the prior distribution.

[0016] Optionally, the method further includes:

[0017] A Kriging surrogate model is constructed using training samples. The Kriging surrogate model fits the relationship between the random variable and the landslide stability coefficient, and between the random variable and the deformation of all elements in the finite difference model.

[0018] Based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated using Bayesian inference to obtain the posterior distribution, including:

[0019] Based on the actual observation information of the first landslide and the prediction information generated by the Kriging surrogate model, the prior distribution is updated by combining Bayesian inference to obtain the posterior distribution.

[0020] Optionally, the MCMC algorithm is used to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variable, including:

[0021] The random variables are initialized based on their prior distribution to obtain η Markov chains, where η is equal to the number of random variables.

[0022] The posterior sample set is obtained by iterating over the η Markov chains respectively.

[0023] Statistical analysis is performed on the posterior sample set to obtain the statistical characteristics of the random variable, including the mean of the distribution, the variance of the distribution, and the type of distribution.

[0024] Optionally, the η Markov chains are iterated over to obtain a posterior sample set, including:

[0025] For each Markov chain, the i-th generation candidate sample value of the Markov chain is determined according to differential evolution;

[0026] Based on the crossover probability, determine whether to accept the i-th generation candidate sample value to obtain the i-th generation candidate sample;

[0027] Calculate the posterior probability density value of the i-th generation candidate sample, and if the posterior probability density value is greater than the probability density threshold, put the i-th generation candidate sample into the posterior sample set;

[0028] End the i-th iteration and remove isolated samples from the posterior sample set;

[0029] If convergence is not achieved, the above steps are followed for the (i+1)th iteration. If convergence is achieved, the posterior sample set is obtained.

[0030] Optionally, based on the statistical characteristics, the Monte Carlo method is used to calculate the instability probability of the second landslide, including:

[0031] Sample data for the random variable are generated based on the statistical characteristics.

[0032] The landslide stability functional response value is obtained based on the sample data.

[0033] According to the Monte Carlo method, the instability probability is calculated using the landslide stability functional response value to obtain the instability probability value of the second slide.

[0034] Optionally, a second prediction of the critical slip surface with the maximum probability of slip instability and an analysis of the slip surface instability probability are performed, including:

[0035] The nearest point to the origin is determined on the limit state function surface, where the origin represents the actual sliding surface;

[0036] Extract the corresponding sliding surface based on the nearest point, and use it as the critical sliding surface with the maximum probability of the second sliding instability;

[0037] The slip surface instability probability is obtained based on the standard normal cumulative distribution function and the distance from the nearest point to the origin.

[0038] A second aspect of this application discloses a Bayesian-based landslide parameter inverse analysis and instability probability prediction device, the device comprising:

[0039] A module was established to build a numerical model based on engineering information from the first landslide and to determine random variables;

[0040] The distribution module is used to determine the prior distribution of the random variable based on the current statistical information;

[0041] The update module is used to update the prior distribution based on the actual observation information of the first landslide and the prediction information generated by the numerical model, combined with Bayesian inference, to obtain the posterior distribution;

[0042] The statistics module is used to perform statistical analysis on the posterior distribution using the MCMC algorithm to obtain the statistical characteristics of the random variable;

[0043] The analysis module is used to calculate the probability of a second landslide instability using the Monte Carlo method based on the statistical characteristics, and to predict the maximum critical sliding surface and analyze the probability of instability of the sliding surface.

[0044] A third aspect of this application discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the Bayesian-based landslide parameter back analysis and instability probability prediction method described in the first aspect of this application.

[0045] A fourth aspect of this application discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the Bayesian-based landslide parameter back analysis and instability probability prediction method described in the first aspect of this application.

[0046] The embodiments of this application have the following advantages:

[0047] In this embodiment, the uncertainty of random variables is considered, and landslide stability analysis is performed based on multiple observational information. First, a numerical model is established based on the engineering information of the first landslide, and random variables are determined. Simultaneously, the prior distribution of the random variables is determined based on current statistical information. Then, based on the actual observational information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated using Bayesian inference to obtain the posterior distribution. Next, the MCMC algorithm is used to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variables. Finally, based on the statistical characteristics, the Monte Carlo method is used to calculate the probability of the second landslide instability, and to predict the maximum critical sliding surface and analyze the probability of instability of the sliding surface during the second landslide.

[0048] Bayesian inverse analysis effectively reduces the standard deviation of random variables, thus reducing their uncertainty and improving the reliability of stability analysis. Furthermore, dynamic sampling simulation based on the MCMC algorithm can reduce the uncertainty of prior random variables based on observational information, further enhancing the reliability of stability analysis. This method provides a new approach for quantitative assessment of landslide risk, and the prediction of instability probability can provide important support for disaster prevention and mitigation. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart illustrating the steps of a Bayesian-based landslide parameter back analysis and instability probability prediction method provided in an embodiment of this application.

[0051] Figure 2 This is a schematic diagram of sliding surface position information and feature coordinate points provided in an embodiment of this application;

[0052] Figure 3 This is a schematic diagram of a Bayesian posterior distribution update process provided in an embodiment of this application;

[0053] Figure 4 This is a schematic diagram illustrating the principle of a Kriging proxy model provided in an embodiment of this application;

[0054] Figure 5 This application provides an elevation map of the Heifangtai area and a schematic diagram of the geographical location of the Dangchuan No. 2 landslide.

[0055] Figure 6 This is a longitudinal section view of the Dangchuan No. 2 landslide provided in an embodiment of this application;

[0056] Figure 7 This application provides an embodiment of a FLAC model of the Dangchuan No. 2 landslide after seepage.

[0057] Figure 8 This is a schematic diagram of the prior fitting distribution of four random variables for the Dangchuan No. 2 landslide provided in an embodiment of this application;

[0058] Figure 9 This is a fitting test result of the Kriging surrogate model for the Dangchuan No. 2 landslide provided in an embodiment of this application;

[0059] Figure 10 This application provides a sampling performance diagram of a Markov chain for four random variable parameters of the Dangchuan No. 2 landslide.

[0060] Figure 11 This application provides an embodiment of the probability of second and third rounds of instability and the maximum critical sliding surface of instability probability for the Dangchuan No. 2 landslide.

[0061] Figure 12This is a schematic diagram of a Bayesian-based landslide parameter back analysis and instability probability prediction device provided in an embodiment of this application.

[0062] Figure 13 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0063] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0064] Reference Figure 1 As shown, Figure 1 This is a flowchart illustrating the steps of a Bayesian-based landslide parameter back analysis and instability probability prediction method provided in an embodiment of this application. Figure 1 As shown in the embodiment of this application, a method for back analysis of landslide parameters and prediction of instability probability based on Bayesian methods includes steps S110 to S150:

[0065] Step S110: Establish a numerical model based on the engineering information of the first landslide and determine random variables.

[0066] In this embodiment, engineering information refers to the landslide's geographical location, lithology, and information about the first unstable sliding body (e.g., the length, width, and area of ​​the sliding body). Random variables refer to parameters related to landslide stability, such as the cohesion of each soil layer, effective internal friction angle, seepage coefficient and density, and landslide shear strength. In practice, engineering information about the first landslide is collected, and a data model is established using FLAC software. Simultaneously, the strength reduction method built into the finite difference software of FLAC is used for slope stability analysis.

[0067] Step S120: Determine the prior distribution of the random variable based on the current statistical information.

[0068] In this embodiment, the current statistical information refers to existing shear strength test results. These results can be used to determine the prior distribution of a random variable, which is represented by its prior probability density. Specifically, the probability distribution of a random variable can be obtained through regional data statistics, relevant experiments, and literature collection. In Bayesian inference, this distribution is called the prior distribution.

[0069] Step S130: Based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated by combining Bayesian inference to obtain the posterior distribution.

[0070] In this embodiment, Bayesian inference (Bayesian inverse analysis) effectively reduces the uncertainty of random variables by updating the prior distribution of random parameters to obtain a posterior distribution that better reflects reality, thereby improving the reliability of stability analysis. The actual observation information includes the observed slip surface position information and stability state (i.e., stability coefficients). Similarly, the prediction information generated by the numerical model includes the predicted slip surface position information and the predicted stability state. Updating the prior distribution through Bayesian inference means updating the distribution of the random variable by calculating the conditional probability of the random variable at a given measurement value.

[0071] Step S140: Use the MCMC algorithm to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variable.

[0072] In this embodiment, the MCMC algorithm (Markov Chain Monte Carlo) can efficiently estimate the posterior probability density function of parameters and is applicable to complex high-dimensional sampling problems. This algorithm can simultaneously perform a global search on multiple Markov chains and automatically adjust the proportion and size of the transition function during the calculation of the posterior distribution, exhibiting extremely high efficiency in complex, nonlinear, and multi-objective distribution problems. Furthermore, the MCMC algorithm is used to perform statistical analysis on the posterior distribution to quickly obtain the statistical characteristics of the random variable, including the mean, variance, and type of the distribution.

[0073] Step S150: Based on the statistical characteristics, the Monte Carlo method is used to calculate the probability of the second landslide instability, and to predict the maximum critical sliding surface and analyze the probability of instability of the sliding surface.

[0074] In this embodiment, the probability of a second landslide instability can provide important support for disaster prevention and mitigation. When the probability of a second landslide instability is greater than 50%, it indicates a high probability of landslide instability, and preventative measures should be taken. The prediction of the maximum critical sliding surface for the second landslide instability probability and the analysis of the sliding surface instability probability refer to analyzing the probability of multiple rounds of sliding surface instability and the corresponding critical sliding surface. In specific implementation, the mean and variance of random parameters are obtained based on statistical characteristics, such as the mean and standard deviation of soil cohesion and internal friction angle. The Monte Carlo method is then used to calculate the probability of a second landslide instability, which is one of the simplest and most direct methods in slope reliability analysis.

[0075] In this embodiment, the uncertainty of random variables is considered, and landslide stability analysis is performed based on multiple observational information. A method is proposed that utilizes Bayesian theory combined with Romålf chain Monte Carlo probabilistic inverse analysis to calibrate shear strength parameters, perform probabilistic parameter inverse analysis, evaluate instability probability, and predict the probabilistic critical slip surface. Since Bayesian inverse analysis can effectively reduce the standard deviation of random variables, i.e., reduce the uncertainty of random variables, it improves the reliability of stability analysis. Furthermore, dynamic sampling simulation based on the MCMC algorithm can reduce the uncertainty of prior random variables based on observational information, further improving the reliability of stability analysis. This method provides a new solution for quantitative landslide risk assessment, and the instability probability prediction can provide important support for disaster prevention and mitigation.

[0076] In an optional embodiment, step S130 updates the prior distribution based on the actual observation information of the first landslide and the prediction information generated by the numerical model, combined with Bayesian inference, to obtain the posterior distribution, including steps S130-1 to S130-4:

[0077] Step S130-1: Obtain m observation sliding surface feature coordinate points for the first sliding of the landslide, and obtain observation data based on the m observation sliding surface feature coordinate points and stability coefficient, where m is an integer greater than 0.

[0078] Specifically, based on the observation information of the sliding surface during the first landslide, the sliding surface is divided into m-1 equal segments in the x-direction (i.e., the horizontal direction), thus obtaining m characteristic coordinate points of the sliding surface. The leftmost characteristic coordinate point is the shear exit location, and the rightmost characteristic coordinate point is the location of the tensile crack at the rear edge. For example, using 5 characteristic coordinate points of the sliding surface... Figure 2 This diagram illustrates a sliding surface location information and characteristic coordinate points provided in an embodiment of this application. Furthermore, based on m observed characteristic coordinate points on the sliding surface, and combined with the landslide instability stability number FS = 1, 2m+1 observation values ​​are obtained. The observation data is represented as Y = [FS, a1, b1, ..., a m ,b m ], where (a1,b1) is the coordinate position of the first observed slip surface feature coordinate point, (a m ,b m ) represents the coordinates of the m-th observed slip surface feature point.

[0079] Step S130-2: Based on the numerical model, obtain m predicted sliding surface feature coordinate points and prediction stability coefficients, and obtain prediction data based on the m predicted sliding surface feature coordinate points and prediction stability coefficients.

[0080] Specifically, a stability analysis is performed on the numerical model, and then the m predicted characteristic coordinates of the sliding surface and the corresponding predicted stability coefficients FS(θ) are calculated. The predicted data can be represented as Y=[FS(θ),x1,y1,...,x m ,y m ], where (x1, y1) is the coordinate position of the first predicted sliding surface feature point, (x m ,y m ) represents the coordinates of the m-th predicted sliding surface feature point.

[0081] Furthermore, the predicted data can also be represented as:

[0082] Y = F(θ) + E

[0083] in, c1, c represents the cohesion and internal friction angle of the first soil layer under the Mohr-Coulomb criterion, respectively. z , Let represent the cohesion and internal friction angle of the z-th soil layer under the Mohr-Coulomb criterion, respectively; F(θ) is the response function that predicts the critical slip surface location and stability coefficient; E = [εFS, εx1, εy1, ..., εx m ,εy m ] represents the error vector between the observed data and the predicted data.

[0084] Step S130-3: Calculate the probability density based on the observed data and the predicted data to obtain the conditional probability density of the random variable.

[0085] For example, the conditional probability density function of a random variable is expressed as:

[0086]

[0087] Where φ is the probability density function of the optimal fitting distribution of the random variable θ, and is the stability coefficient obtained from numerical simulation; FS(·) is the stability coefficient obtained from numerical simulation; σ1 is the standard deviation of the stability coefficient error; σ2 is the standard deviation of the coordinate values ​​of the sliding surface feature points; u1 is the mean error of the stability coefficient; μ2 is the mean displacement error; (x i ,y i (a) represents the coordinates of the characteristic points of the sliding surface; i ,b i () represents the coordinates of the observed slip surface features.

[0088] Step S130-4: Based on the conditional probability density and the prior distribution, obtain the posterior distribution.

[0089] For example, in Bayesian inference, the posterior distribution f post (θY) is represented as:

[0090] f post (θ|Y)∝L(θ|Y)f prior (θ)

[0091] Among them, f prior (θ) is the prior probability density function (i.e., prior distribution) of the random variable θ.

[0092] Then, based on the stability information of the slip surface and the observation information and numerical model of the first landslide, the prior distribution is updated to obtain the posterior distribution. For example, Figure 3 This is a schematic diagram of a Bayesian posterior distribution update process provided in an embodiment of this application.

[0093] In an optional embodiment, to efficiently obtain the posterior distribution of the random variable, the method includes:

[0094] A Kriging surrogate model is constructed using training samples. The Kriging surrogate model fits the relationship between the random variable and the landslide stability coefficient, and between the random variable and the deformation of all elements in the finite difference model.

[0095] Based on the actual observation information of the first landslide and the prediction information generated by the Kriging surrogate model, the prior distribution is updated by combining Bayesian inference to obtain the posterior distribution.

[0096] In this embodiment of the application, considering that Bayesian inference requires repeated numerical simulations, directly using the numerical model would significantly increase the computational cost of probabilistic analysis, resulting in an unacceptable computational burden. Therefore, a Kriging surrogate model equivalent to the numerical model is constructed for computation, thereby reducing computational costs. For example, Figure 4 This is a schematic diagram illustrating the principle of a Kriging surrogate model provided in this application embodiment. It utilizes a limited number of training samples to fit the relationships between random variables and landslide stability coefficients, and between random variables and the deformation quantities of all units in a finite difference model, ultimately obtaining the Kriging surrogate model. This model is then used to generate corresponding predicted slip surface feature coordinate points to calculate the posterior distribution. This application embodiment achieves more efficient computation by replacing numerical models with Kriging surrogate models, reducing computation time, and the test results based on the Kriging surrogate model have high accuracy.

[0097] In an optional embodiment, step S140 uses the MCMC algorithm to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variable, including steps S140-1 to S140-3:

[0098] Step S140-1: Initialize according to the prior distribution of the random variables to obtain η Markov chains, where η is equal to the number of random variables.

[0099] Step S140-2: Iterate over the η Markov chains respectively to obtain the posterior sample set.

[0100] Step S140-3: Perform statistical analysis on the posterior sample set to obtain the statistical characteristics of the random variable, including: the mean of the distribution, the variance of the distribution, and the type of distribution.

[0101] In this embodiment, the posterior sample includes posterior sample data for each random variable. For example, if there are 10 random variables, the posterior sample contains posterior sample data for all 10 random variables. Then, by analyzing the posterior sample data for each random variable in the posterior sample set, the statistical characteristics of each random sample are obtained. For example, for the random variable of effective cohesion of the soil layer, after statistical analysis, the distribution type (such as normal distribution), mean, and variance of the effective cohesion of the soil layer are obtained. Subsequently, in subsequent steps, sampling is performed based on the statistical characteristics to conduct further analysis based on the sampling results.

[0102] Furthermore, each Markov chain represents a random variable, and all Markov chains are iterated over to obtain the posterior sample set after iteration. Specifically, the η Markov chains are iterated over to obtain the posterior sample set, including steps A1 and A5:

[0103] Step A1: For each Markov chain, determine the i-th generation candidate sample value of the Markov chain according to differential evolution.

[0104] Wherein, the i-th generation candidate sample value Represented as:

[0105]

[0106] In the formula, θ η,i For the i-th generation sample of the η-th Markov chain; I N ψ is an N-order identity matrix; i and λ i Let ψ be a randomly generated minimal number, and ψ i (i = 1, 2, 3, ..., n) follow a uniform distribution λ i(i = 1, 2, 3, ..., n) follow a normal distribution Z z and t z γ is a user-defined minimum value; v is the number of parallel chain pairs used to generate candidate samples; γ(v,d) is a scaling factor; r1(m′) and r2(m′) are randomly selected parallel chain numbers, and r1(m′) ≠ r2(m′).

[0107] Step A2: Determine whether to accept the i-th generation candidate sample value based on the crossover probability, and obtain the i-th generation candidate sample.

[0108] Specifically, the judgment method is expressed as follows:

[0109]

[0110] Where CR is the crossover probability, and U is a random number generated according to the uniform distribution [0,1]. When U≤1-CR, the i-th generation candidate sample value is not accepted. In this case, the i-th generation candidate sample value is equal to the (i-1)-th generation candidate sample value. Otherwise, accept the value of the i-th generation candidate sample.

[0111] Step A3: Calculate the posterior probability density value of the i-th generation candidate sample. If the posterior probability density value is greater than the probability density threshold, put the i-th generation candidate sample into the posterior sample set.

[0112] Wherein, the posterior probability density value of the i-th generation candidate sample Represented as:

[0113]

[0114] exist If the condition is met, the i-th generation candidate sample is added to the posterior sample set; otherwise, the (i-1)-th generation candidate sample is added to the posterior sample set as the i-th generation candidate sample.

[0115] Step A4: End the i-th iteration and remove isolated samples from the posterior sample set;

[0116] Specifically, isolated samples in the posterior sample set are removed based on the difference between the 75th and 25th percentiles (interquartile range, or IQR).

[0117] Step A5: If convergence is not satisfied, perform the (i+1)th iteration according to the above steps. If convergence is satisfied, the posterior sample set is obtained.

[0118] Specifically, the Rstat value is calculated. If Rstat is less than the termination threshold, the convergence condition is met; otherwise, the number of iterations is increased to continue the iteration. Rshat is a convergence diagnostic method for the MCMC algorithm. It compares the parameter estimates of each Markov chain. If the chain has converged and the mixing is good, then the Rshat value is close to 1.

[0119] In one optional embodiment, the Monte Carlo method is used to calculate the instability probability of the second landslide, including: generating sample data of the random variable based on the statistical characteristics; obtaining the landslide stability function response value based on the sample data; and calculating the instability probability using the landslide stability function response value according to the Monte Carlo method to obtain the instability probability value of the second landslide.

[0120] Specifically, the landslide stability functional response value f′(θ) is expressed as:

[0121] f′(θ)=FS(θ)-1

[0122] Therefore, the probability of instability P during the second sliding is... f,s Represented as:

[0123]

[0124] Where G represents the number of samples where the landslide stability function response value f′(θ) is less than 0, and I represents the total number of samplings.

[0125] In one optional embodiment, the second slip instability probability maximum critical slip surface prediction and slip surface instability probability analysis are performed, including: determining the nearest point to the origin on the limit state function surface, where the origin represents the actual slip surface; extracting the corresponding slip surface based on the nearest point as the second slip instability probability maximum critical slip surface; and obtaining the slip surface instability probability based on the standard normal cumulative distribution function and the distance from the nearest point to the origin.

[0126] In this embodiment, the verification point (i.e., the closest point) is determined based on the finite difference strength reduction method, and the slip surface with the highest instability probability is identified based on this. The slip surface instability probability can be expressed as:

[0127] P f =Φ(-β)=1-Φ(β)

[0128] Among them, P f Φ(·) represents the probability of slip surface instability along the slip surface of a landslide, Φ(·) represents the standard normal cumulative distribution function, and β represents the distance from the nearest point to the origin in the standard normal space.

[0129] In this embodiment, the uncertainty of random variables is considered, and landslide stability analysis is performed based on multiple observational information. First, a numerical model is established based on the engineering information of the first landslide, and random variables are determined. Simultaneously, the prior distribution of the random variables is determined based on current statistical information. Then, based on the actual observational information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated using Bayesian inference to obtain the posterior distribution. Next, the MCMC algorithm is used to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variables. Finally, based on the statistical characteristics, the Monte Carlo method is used to calculate the probability of the second landslide instability, and to predict the maximum critical sliding surface and analyze the probability of instability of the sliding surface. Since Bayesian inverse analysis can effectively reduce the standard deviation of random variables, i.e., reduce the uncertainty of random variables, it improves the reliability of stability analysis. Furthermore, dynamic sampling simulation based on the MCMC algorithm can reduce the uncertainty of prior random variables based on observational information, further improving the reliability of stability analysis. This method provides a new solution for quantitative assessment of landslide risk, and the instability probability prediction can provide important support for disaster prevention and mitigation.

[0130] Furthermore, taking the Heifangtai Dangchuan No. 2 landslide as an example, the Bayesian-based landslide parameter back analysis and instability probability prediction method of this application embodiment is described in detail.

[0131] (1) Establish a numerical model.

[0132] like Figure 5 As shown, Figure 5 This application provides an elevation map of the Heifangtai area and a geographical location diagram of the Dangchuan No. 2 landslide, as illustrated in an embodiment. Heifangtai is located on the north bank of the Yellow River in Yongjing County, Gansu Province, downstream of the Yangguoxia Reservoir, 45 km from Lanzhou City and 20 km from Yongjing County. The Heifangtai plateau covers an area of ​​approximately 11.5 km², divided into two parts by the longest gully, the Hulanggou Gully. The highest point of Heifangtai is located in the northwest of the plateau, at an elevation of 1855.46 m, while the lowest point is located at the confluence of the Yellow River and the Huangshui River, at an elevation of approximately 1510.41 m. The smaller western part is Fangtai, approximately 1.5 km², while the larger eastern part is Heitai, approximately 9 km². Figure 6 This is a longitudinal profile of the Dangchuan No. 2 landslide provided in an embodiment of this application. It can be seen that the lithology of the landslide strata, from top to bottom, is as follows: loess, approximately 20-50m thick; silty clay, approximately 4-20m thick; gravel layer, approximately 1-8m thick; mudstone and sandy mudstone, with a dip of 135°∠11°. On April 29, 2015, the Dangchuan No. 2 landslide experienced two static liquefaction-type instability failures. The first instability involved a sliding mass approximately 20m long, with an average width of approximately 115m and an area of ​​approximately 8396m². The second instability included three rounds of sliding, with a total area of ​​approximately 27422m².

[0133] Investigation revealed that the landslide instability primarily occurred within the loess layer, with some silty clay layers scraped away during the movement. Therefore, for computational simplicity, a FLAC model was established using both the loess layer and a portion of the silty clay layer. The model is 50m high, 260m wide at the top, and 300m wide at the bottom, employing a constant head boundary. To avoid complex seepage mechanisms, only dominant seepage was considered for simplicity. In the GWflow mode of FLAC, a partially saturated fast steady-state flow (Fastwb) method was used to rapidly saturate the bottom loess, simulating high irrigation flow through dominant channels and fissures in the loess layer to quickly reach the bottom. A seepage flow inflow and outflow determination program was written using FLAC's built-in FISH language to determine if the seepage had reached a stable state. The seepage simulation showed that the seepage flow exited from the interface between the loess and silty clay layers, consistent with reality, confirming that the layer below the waterline is saturated loess. The final model is as follows. Figure 7 As shown.

[0134] (2) Obtain and update the prior distribution of model parameters.

[0135] To obtain statistical information (i.e., random variables) on the shear strength parameters of loess in the Heifangtai area, a large number of experimental research results on the slip zone soil of the Heifangtai landslide were collected. Specifically, the shear strength parameters of loess in the Heifangtai area are shown in Tables 1 and 2. Prior estimation of the Heifangtai loess experimental parameters was then performed. Figure 8 The prior probability density histograms of four random variables are presented, and four commonly used probability distribution models are used for fitting: normal distribution, log-normal distribution, Gamma distribution, and Weibull distribution. The Kolmogorov-Smirnov (KS) test shows that the normal distribution is the best-fit distribution type.

[0136] Table 1 Shear strength parameters of unsaturated loess in Heifangtai

[0137]

[0138] Table 2 Shear strength parameters of saturated loess in Heifangtai

[0139]

[0140] (3) The posterior distribution is obtained quickly based on the Kriging surrogate model.

[0141] A Kriging surrogate model is constructed to approximate the calculation results of the finite-difference numerical simulation, thereby reducing the computational cost of Bayesian inverse analysis. Surrogate models are constructed using 400 initial sample points, relating the loess shear strength random variable to the landslide stability coefficient and the loess shear strength random variable to the deformation of all elements in the finite-difference model. The accuracy of the surrogate model predictions is evaluated using the coefficient of determination (R²). The Kriging fit of the deformation of one feature point element is presented, where the output feature point element deformation is combined with the feature point coordinates before sliding to derive the post-slide feature point coordinates. Figure 9 The deterministic coefficient R² of the stability coefficient surrogate model is 0.986, the deterministic coefficient R² of the x-direction coordinate surrogate model of the sliding surface feature point coordinate unit is 0.990, and the R² of the y-direction coordinate is 0.991. The three fitted R² values ​​are of high accuracy and can be used for probabilistic inverse analysis.

[0142] (4) The MCMC algorithm is used to perform statistical analysis on the posterior sample to obtain the statistical characteristics of the random variable.

[0143] We set 30,000 random samples, discarded the first 100,000 samples, and used the last 200,000 samples as the posterior samples for statistical analysis. Furthermore, the stability of the Markov chain is also crucial; a stationary or slowly shifting Markov chain will affect the accuracy of the posterior distribution. Figure 10 The sampling performance of the Markov chain is shown in the figure. The graph reveals that the Markov chain moves actively during posterior calculation, demonstrating its excellent sampling performance. Statistical analysis of the posterior samples of these parameters yielded their means and standard deviations, as shown in Table 3.

[0144] Table 3 Comparison of mean and standard deviation of random variable parameters

[0145]

[0146] Comparative analysis shows that the posterior mean of the shear strength parameter of the unsaturated loess layer varies significantly, while the posterior mean of the shear strength parameter of the saturated loess layer does not vary significantly. The posterior standard deviations of the four random variables all decreased, indicating that Bayesian updates can effectively reduce the uncertainty of random variables.

[0147] (5) Calculation of the probability of the second sliding instability.

[0148] In this embodiment of the application, a total of 100,000 samples were taken, i.e., I = 100,000. Using the posterior information of random variables, the system instability probability of the second sliding of the Dangchuan No. 2 landslide was calculated to be 57.79%, which exceeds 50%, indicating that the probability of landslide instability is very high. In actual observation, the landslide experienced three large-scale sliding events in the second phase, which is consistent with the calculation results.

[0149] (6) Prediction of the critical sliding surface with the highest probability of the second sliding instability and analysis of the probability of sliding surface instability.

[0150] Using the method described in step S150 above, the instability probabilities of the second three-wheeled sliding surface were calculated to be 42.70%, 40.97%, and 28.30%, respectively; the corresponding critical sliding surface with the maximum instability probability is shown below. Figure 11 As shown, the calculated instability probability and critical slip surface results are in good agreement with the actual observation results.

[0151] This application also provides a Bayesian-based landslide parameter inverse analysis and instability probability prediction device, referring to... Figure 12 As shown, Figure 12 This is a schematic diagram of a Bayesian-based landslide parameter back analysis and instability probability prediction device provided in an embodiment of this application. The device includes:

[0152] Module 1210 is established to build a numerical model based on the engineering information of the first landslide and to determine random variables;

[0153] Distribution module 1220 is used to determine the prior distribution of the random variable based on current statistical information;

[0154] The update module 1230 is used to update the prior distribution based on the actual observation information of the first landslide and the prediction information generated by the numerical model, combined with Bayesian inference, to obtain the posterior distribution;

[0155] The statistics module 1240 is used to perform statistical analysis on the posterior distribution using the MCMC algorithm to obtain the statistical characteristics of the random variable;

[0156] The analysis module 1250 is used to calculate the probability of the second landslide instability using the Monte Carlo method based on the statistical characteristics, and to predict the maximum critical sliding surface and analyze the probability of the sliding surface instability.

[0157] In one optional embodiment, the update module includes:

[0158] The first update submodule is used to obtain m observation sliding surface feature coordinate points of the landslide during its first sliding, and to obtain observation data based on the m observation sliding surface feature coordinate points and the stability coefficient, where m is an integer greater than 0;

[0159] The second update submodule is used to obtain m predicted sliding surface feature coordinate points and predicted stability coefficients based on the numerical model, and to obtain predicted data based on the m predicted sliding surface feature coordinate points and the predicted stability coefficients.

[0160] The third update submodule is used to perform probability density calculation based on the observed data and the predicted data to obtain the conditional probability density of the random variable;

[0161] The fourth update submodule is used to obtain the posterior distribution based on the conditional probability density and the prior distribution.

[0162] In an optional embodiment, the device further includes:

[0163] The surrogate model construction module is used to construct a Kriging surrogate model using training samples. The Kriging surrogate model fits the relationship between the random variable and the landslide stability coefficient, and between the random variable and the deformation of all units in the finite difference model.

[0164] The posterior module is used to update the prior distribution based on the actual observation information of the first landslide and the prediction information generated by the Kriging surrogate model, combined with Bayesian inference, to obtain the posterior distribution.

[0165] In an optional embodiment, the statistics module includes:

[0166] An initialization module is used to initialize the random variables according to their prior distribution, thereby obtaining η Markov chains, where η is equal to the number of random variables.

[0167] An iteration module is used to iterate over the η Markov chains respectively to obtain the posterior sample set;

[0168] The feature module is used to perform statistical analysis on the posterior sample set to obtain the statistical features of the random variable, including: the mean of the distribution, the variance of the distribution, and the type of distribution.

[0169] In one alternative embodiment, the iteration module includes:

[0170] The first iterative submodule is used to determine the i-th generation candidate sample value of each Markov chain based on differential evolution.

[0171] The second iteration submodule is used to determine whether to accept the i-th generation candidate sample value based on the crossover probability, and to obtain the i-th generation candidate sample.

[0172] The third iteration submodule is used to calculate the posterior probability density value of the i-th generation candidate sample, and if the posterior probability density value is greater than the probability density threshold, the i-th generation candidate sample is put into the posterior sample set.

[0173] The fourth iteration submodule is used to end the i-th iteration and remove isolated samples from the posterior sample set;

[0174] The fifth iteration submodule is used to perform the (i+1)th iteration according to the above steps if convergence is not satisfied, and to obtain the posterior sample set if convergence is satisfied.

[0175] In one optional embodiment, the analysis module includes:

[0176] The first analysis submodule is used to generate sample data of the random variable based on the statistical characteristics;

[0177] The second analysis submodule is used to obtain the landslide stability functional response value based on the sample data;

[0178] The third analysis submodule is used to calculate the instability probability of the second slide by using the landslide stability function response value according to the Monte Carlo method.

[0179] In one optional embodiment, the analysis module includes:

[0180] The fourth analysis submodule is used to determine the nearest point of the origin on the limit state function surface, where the origin represents the actual sliding surface;

[0181] The fifth analysis submodule is used to extract the corresponding sliding surface based on the nearest point, as the critical sliding surface with the maximum probability of the second sliding instability.

[0182] The sixth analysis submodule is used to obtain the slip surface instability probability based on the standard normal cumulative distribution function and the distance from the nearest point to the origin.

[0183] This application also provides an electronic device, see embodiments thereof. Figure 13 , Figure 13 This is a schematic diagram of an electronic device structure provided in an embodiment of this application. For example... Figure 13 As shown, the electronic device 1300 includes a memory 1310 and a processor 1320. The memory 1310 and the processor 1320 are connected via a bus for communication. The memory 1310 stores a computer program that can run on the processor 1320 to implement the steps of the Bayesian-based landslide parameter back analysis and instability probability prediction method described in the embodiments of this application.

[0184] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the Bayesian-based landslide parameter back analysis and instability probability prediction method described in this application.

[0185] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0186] This application describes embodiments of methods, apparatus, and devices according to embodiments of this application with reference to flowchart illustrations and / or block diagrams. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0187] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0188] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0189] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0190] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device 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 terminal device. 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 terminal device that includes said element.

[0191] The foregoing provides a detailed description of the Bayesian-based landslide parameter back analysis and instability probability prediction method and apparatus provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A Bayesian-based method for inverse analysis of landslide parameters and prediction of instability probability, characterized in that, The method includes: A numerical model was established based on the engineering information of the first landslide, and random variables were determined. Determine the prior distribution of the random variable based on the current statistical information; Based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated by combining Bayesian inference to obtain the posterior distribution; The MCMC algorithm is used to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variable; Based on the statistical characteristics, the Monte Carlo method was used to calculate the probability of the second landslide instability, and to predict the maximum critical sliding surface and analyze the probability of the sliding surface instability. Specifically, based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated using Bayesian inference to obtain the posterior distribution, including: Obtain the first sliding of the landslide Each observed slip surface feature coordinate point, according to the... By observing the coordinates of the characteristic points of the slip surface and the stability coefficient, observation data is obtained. It is an integer greater than 0; Based on the numerical model, we obtain Each predicted slip surface feature coordinate point and predicted stability coefficient, based on the... The predicted data is obtained by using the predicted surface feature coordinates and the predicted stability coefficient; Based on the observed data and the predicted data, the probability density is calculated to obtain the conditional probability density of the random variable; The posterior distribution is obtained based on the conditional probability density and the prior distribution.

2. The method according to claim 1, characterized in that, The method further includes: A Kriging surrogate model is constructed using training samples. The Kriging surrogate model fits the relationship between the random variable and the landslide stability coefficient, and between the random variable and the deformation of all elements in the finite difference model. Based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated using Bayesian inference to obtain the posterior distribution, including: Based on the actual observation information of the first landslide and the prediction information generated by the Kriging surrogate model, the prior distribution is updated by combining Bayesian inference to obtain the posterior distribution.

3. The method according to claim 1, characterized in that, The MCMC algorithm is used to perform statistical analysis on the posterior distribution to obtain the statistical characteristics of the random variable, including: Initialize based on the prior distribution of the random variable to obtain A Markov chain, It equals the number of the random variables; For the above The Markov chain is iterated to obtain the posterior sample set; Statistical analysis is performed on the posterior sample set to obtain the statistical characteristics of the random variable, including the mean of the distribution, the variance of the distribution, and the type of distribution.

4. The method according to claim 3, characterized in that, For the above The Markov chain is iterated to obtain the posterior sample set, including: For each Markov chain, the first step of the Markov chain is determined by differential evolution. Replace candidate sample values; Whether to accept the first [probability] is determined based on the crossover probability. Substitute candidate sample values ​​to obtain the first Alternate candidate samples; Calculate the first The posterior probability density value of the candidate sample is used. If the posterior probability density value is greater than the probability density threshold, the first... The candidate samples are placed into the posterior sample set; End of the first The next iteration removes isolated samples from the posterior sample set. If convergence is not satisfied, proceed with the steps outlined above. In the next iteration, if convergence is satisfied, the posterior sample set is obtained.

5. The method according to claim 1, characterized in that, Based on the aforementioned statistical characteristics, the Monte Carlo method is used to calculate the instability probability of the landslide's second sliding, including: Sample data for the random variable are generated based on the statistical characteristics. The landslide stability functional response value is obtained based on the sample data. According to the Monte Carlo method, the instability probability is calculated using the landslide stability functional response value to obtain the instability probability value of the second slide.

6. The method according to claim 1, characterized in that, The second prediction of the critical slip surface with the highest probability of slip instability and the analysis of slip surface instability probability are carried out, including: The nearest point to the origin is determined on the limit state function surface, where the origin represents the actual sliding surface; Extract the corresponding sliding surface based on the nearest point, and use it as the critical sliding surface with the maximum probability of the second sliding instability; The slip surface instability probability is obtained based on the standard normal cumulative distribution function and the distance from the nearest point to the origin.

7. A Bayesian-based landslide parameter inverse analysis and instability probability prediction device, characterized in that, The device includes: A module was established to build a numerical model based on engineering information from the first landslide and to determine random variables; The distribution module is used to determine the prior distribution of the random variable based on the current statistical information; The update module is used to update the prior distribution based on the actual observation information of the first landslide and the prediction information generated by the numerical model, combined with Bayesian inference, to obtain the posterior distribution; The statistics module is used to perform statistical analysis on the posterior distribution using the MCMC algorithm to obtain the statistical characteristics of the random variable; The analysis module is used to calculate the probability of the second landslide instability using the Monte Carlo method based on the statistical characteristics, and to predict the maximum critical sliding surface and analyze the probability of the sliding surface instability. Specifically, based on the actual observation information of the first landslide and the prediction information generated by the numerical model, the prior distribution is updated using Bayesian inference to obtain the posterior distribution, including: Obtain the first sliding of the landslide Each observed slip surface feature coordinate point, according to the... By observing the coordinates of the characteristic points of the slip surface and the stability coefficient, observation data is obtained. It is an integer greater than 0; Based on the numerical model, we obtain Each predicted slip surface feature coordinate point and predicted stability coefficient, based on the... The predicted data is obtained by using the predicted surface feature coordinates and the predicted stability coefficient; Based on the observed data and the predicted data, the probability density is calculated to obtain the conditional probability density of the random variable; The posterior distribution is obtained based on the conditional probability density and the prior distribution.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the Bayesian-based landslide parameter inverse analysis and instability probability prediction method as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the Bayesian-based landslide parameter inverse analysis and instability probability prediction method as described in any one of claims 1-6.

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