Method and product for calibrating erosion parameters of landslide dam soil body using back-analysis method

Abstract

The present invention provides a method and product for calibrating the soil erosion parameters of a landslide dam using an inverse analysis method, which relates to the technical field of data processing. In the embodiments of the present invention, the average soil erosion parameters at different depths are characterized by the trend component function in the random field theory, and based on this, the calibration work of the soil erosion parameters of the landslide dam is carried out. According to the erosion parameter records at different depths in several landslide dam cases, a multi-criteria decision-making method is used to determine the best type of trend component function under the existing conditions. In addition, the embodiments of the present invention also use two complementary inverse analysis methods to calibrate the trend component function. One method is a deterministic inverse analysis based on multi-objective optimization to determine the best trend component function; the other method is a probabilistic inverse analysis based on Bayesian theory to quantify the uncertainty of the trend component function. The trend component function determined in the embodiments of the present invention can effectively describe this trend. The soil erosion parameters calibrated by the inverse analysis method can obtain good simulation results.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of data processing, and in particular, to a method and product for calibrating the erodibility parameters of landslide dam soil using an inverse analysis method. Background Art

[0002] A landslide dam is a natural sediment that blocks a river and forms a natural lake, which is widely distributed in mountainous areas worldwide. Landslide dams are at risk of breaching at any time, and the breach flood will cause huge losses to the downstream area. Among the many statistically recorded cases of breached landslide dams, overtopping failure accounts for 91%. Therefore, most studies have focused on quantifying the consequences of overtopping failure of landslide dams. The research results can generally be divided into two categories, namely empirical models and physical models. Empirical models are simple and practical. For a specific landslide dam, its dam body geometric parameters (such as dam height, dam width, upstream and downstream slopes, etc.) and the geometric parameters of the dammed lake (such as reservoir capacity, lake surface area, and water level relationship curve, etc.) are easy to determine. Therefore, researchers have established many empirical models based on these parameters to quickly predict the key physical quantities of landslide dam breach, such as the probability of landslide dam breach, peak outflow rate, final rupture size, and the lifespan of the landslide dam.

[0003] However, the overtopping failure process of landslide dams is a complex phenomenon, involving erosion, slope instability, and overtopping hydraulics, etc. It is difficult to achieve good prediction accuracy simply through empirical models because they ignore the erosion process and rarely consider the characteristics of landslide deposits. Therefore, at the present stage, physical models that consider the physical and mechanical mechanisms of the entire overturning process (including lake water overtopping, dam body erosion, and slope instability, etc.) have been vigorously developed. Some researchers have developed physical models using basic differential equations to simulate hydraulic conditions and erosion processes. However, this type of complex physical model usually has a large amount of calculation. Therefore, in the practical process, simplified physical models have been widely applied.

[0004] In the simplified physical model, the most crucial thing is to simulate the erosion process, in which the erodibility of the landslide dam soil is an important internal factor controlling the erosion process caused by overtopping of the landslide dam. The erodibility of the soil can be represented by the erodibility coefficient K d and the critical shear stress τ cCharacterization, these two parameters are crucial for accurately simulating the dam break process. In related technologies, these two parameters can be obtained through field tests, such as rotating cylinder tests, erosion function instrument tests, hole erosion tests, flume tests, and underwater jet tests. However, the limitations of field conditions mean that researchers can only obtain the soil erosivity of a few locations through experimental means, which cannot reflect the soil erosivity of the landslide dam as a whole. More importantly, almost all field tests are carried out after the dam break, and the test samples are collected in the residual area, which may not accurately represent the physical properties of the eroded soil. In addition, there are sampling interference and scale effects, which will reduce the reliability of field test results. Therefore, in order to more accurately understand the erosivity of landslide dam soil, and also to more reliably simulate the failure of landslide dams, it is necessary to calibrate these two erosivity parameters.

[0005] Similar to the characteristics of soil shear strength and seepage parameters considered in slope, embankment and foundation stability analysis, the properties of landslide sediments are also highly uncertain in space. Specifically, they include basic physical parameters such as dry density, average particle size and uniformity coefficient, and the erosivity of landslide dam soil is affected by these parameters (but not limited to these parameters). However, there is currently a lack of clear understanding of the actual variation of erosivity parameters of landslide dam soil, and its spatial variability needs to be characterized, which is an urgent problem to be solved. At the same time, it also brings great challenges to the calibration of soil erosivity parameters. Summary of the invention

[0006] The embodiment of the present invention provides a method and product for calibrating the erosivity parameters of soil in a landslide dam using a back-analysis method, which is intended to calibrate the erosivity parameters of soil in a landslide dam. The embodiment of the present invention, based on random field theory, adopts a trend component function to represent the erosivity parameters of soil in different spatial positions of a landslide dam, and calibrates the trend component function through two back-analysis methods. One is a deterministic back-analysis method based on a multi-objective optimization algorithm, and the other is a probabilistic back-analysis method based on Bayesian theory.

[0007] A first aspect of an embodiment of the present invention provides a method for calibrating soil erosivity parameters of a landslide dam using a back analysis method, the method comprising:

[0008] Collect historical landslide dam case data that record soil erosion parameters, and construct an alternative matrix of trend component functions t(z) of the landslide dam soil erosion coefficient; based on the historical landslide dam case data, obtain the curve fitting coefficients and modified R of the soil erosion coefficient of each landslide dam under each trend component function by curve fitting. 2 The erosibility coefficient of the landslide dam soil includes the erodibility coefficient K d and critical shear stress τ c ;

[0009] Determine the best trend component function from the alternative matrix, and use the coefficients of the best trend component function as the random coefficients θ to be calibrated;

[0010] Based on the curve fitting results, obtain the initial samples of the random coefficients θ of the best trend component function, generate prior samples through oversampling methods, and obtain the prior information and correlation coefficient matrix of θ;

[0011] Determine the observation information set Y for back analysis of the target landslide dam, and obtain the landslide dam breach simulation results corresponding to each random coefficient through the simplified physical model DABA;

[0012] Based on the deterministic back analysis method of multi-objective optimization, obtain the optimal coefficient θ optimal At the same time, obtain the posterior information of the random coefficient θ and the coefficient θ corresponding to the maximum probability density based on the probabilistic back analysis method max,post ;

[0013] According to θ optimal and θ max,post Obtain the calibrated change curve of soil erosion parameters and the corresponding landslide dam breach simulation results.

[0014] The second aspect of the embodiments of the present invention provides a device for calibrating soil erosion parameters of a landslide dam using a back analysis method. The device includes:

[0015] A construction module, configured to collect and record historical landslide dam case data of soil erosion parameters, and construct an alternative matrix of the trend component function t(z) of the landslide dam soil erosion coefficient;

[0016] A fitting module, configured to obtain the curve fitting coefficients and the corrected R 2 under each trend component function of each landslide dam soil erosion coefficient through curve fitting based on the historical landslide dam case data. The landslide dam soil erosion coefficients include the erodibility coefficient K d and the critical shear stress τ c ;

[0017] A best trend component function determination module, configured to determine the best trend component function from the alternative matrix, and use the coefficients of the best trend component function as the random coefficients θ to be calibrated;

[0018] A prior information determination module, configured to obtain the initial samples of the random coefficients θ of the best trend component function based on the curve fitting results, generate prior samples through oversampling methods, and obtain the prior information and correlation coefficient matrix of θ;

[0019] The simulation result determination module is used to determine the observation information set Y for back analysis of the target landslide dam, and obtain the landslide dam breach simulation results corresponding to each random coefficient through the simplified physical model DABA;

[0020] The back analysis module is used to obtain the optimal coefficient θ based on the deterministic back analysis method of multi-objective optimization optimal At the same time, based on the probabilistic back analysis method, the posterior information of the random coefficient θ and the coefficient θ corresponding to the maximum probability density are obtained max,post ;

[0021] The soil erosion parameter determination module is used to obtain the calibrated soil erosion parameters and the landslide dam breach simulation results according to θ optimal and θ max,post

[0022] The third aspect of the embodiments of the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes, the steps in the method described in the first aspect of the present invention are implemented.

[0023] The fourth aspect of the embodiments of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, the steps in the method described in the first aspect of the present invention are implemented.

[0024] The fifth aspect of the embodiments of the present invention provides a computer program product, including a computer program / instructions. When the computer program / instructions are executed by a processor, the steps in the method described in the first aspect of the present invention are implemented.

[0025] In the embodiments of the present invention, for the soil erosion parameters with spatial variability characteristics, the trend component function in the random field theory can effectively unify the parameter values at different depths, thereby simplifying its calibration work. When facing rare samples, an optimal form of the trend component function can be effectively determined through curve fitting and multi-objective decision-making methods. In the embodiments of the present invention, the combined use of the deterministic back analysis method and the probabilistic back analysis method can achieve good application effects in parameter calibration work. The optimal parameter combination based on the deterministic back analysis method is highly similar to the maximum posterior probability density parameter combination based on the probabilistic back analysis method. At the same time, the probabilistic back analysis method can effectively quantify the uncertainty of the coefficients.

[0026] In the embodiments of the present invention, according to the calibrated soil erosion parameters, the top soil of the landslide dam shows the characteristics of high erosion and large variation with depth, while the middle and lower parts of the soil show the characteristics of small erosion and small variation with depth. The two forms of the trend component function determined in the embodiments of the present invention (that is, the power function for K d and the cThe exponential function) can better fit this changing trend.

[0027] The technical solution provided by the embodiment of the present invention can provide a reference for subsequent work such as the complete stochastic field characterization of the erosion parameters of the landslide dam soil body and the study of the factors causing the differences in the erosion properties of the landslide dam soil body. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solution of the embodiment of the present invention, the following will briefly introduce the drawings required to be used in the description of the embodiment of the present invention. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0029] Figure 1 shows the flowchart of the steps of the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method provided by the embodiment of the present invention;

[0030] Figure 2 shows the schematic diagram of the erosion evolution of three stages in the DABA model adopted in the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method provided by the embodiment of the present invention;

[0031] Figure 3 shows the schematic diagram of the implementation steps of an exemplary embodiment of the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method provided by the embodiment of the present invention;

[0032] Figure 4 shows the schematic diagram of the calibrated erosion parameter results of the landslide dam soil body obtained from an exemplary embodiment of the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method provided by the embodiment of the present invention;

[0033] Figure 5 shows the flow rate-time (Q b -t) curve and the soil erosion rate-time (E-t) curve during the breach process in an exemplary embodiment of the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method provided by the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0035] In the embodiment of the present invention, a method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method is provided, as Figure 1 shown. Figure 1The figure shows a flow chart of the steps of a method for calibrating the soil erosion parameters of a landslide dam using the back analysis method provided by an embodiment of the present invention. Specifically, the method includes the following steps:

[0036] S101, Collect and record the historical landslide dam case data of soil erosion parameters, and construct an alternative matrix of the trend component function t(z) of the soil erosion coefficient of the landslide dam; Based on the historical landslide dam case data, obtain the curve fitting coefficients and the corrected R of each landslide dam soil erosion coefficient under each trend component function through curve fitting 2 , The soil erosion coefficient of the landslide dam includes the erodibility coefficient K d and the critical shear stress τ c ;

[0037] S102, Determine the best trend component function from the alternative matrix, and use the coefficients of the best trend component function as the random coefficients θ to be calibrated;

[0038] S103, Based on the curve fitting results, obtain the initial sample of the random coefficient θ of the best trend component function, generate the prior sample through the oversampling method, and obtain the prior information and the correlation coefficient matrix of θ;

[0039] S104, Determine the observation information set Y for back analysis of the target landslide dam, and obtain the landslide dam breach simulation results corresponding to each random coefficient through the simplified physical model DABA;

[0040] S105, Based on the deterministic back analysis method of multi-objective optimization, obtain the optimal coefficient θ optimal , At the same time, obtain the posterior information of the random coefficient θ and the coefficient θ corresponding to the maximum probability density based on the probabilistic back analysis method max,post ;

[0041] S106, According to θ optimal and θ max,post Obtain the calibrated soil erosion parameter change curve and its corresponding landslide dam breach simulation result.

[0042] In the embodiment of the present invention, an erosion-based simplified physical model landslide dam breach simulation program DABA is used to quickly simulate the entire dam breach process. In this model, the cross-section and longitudinal section breaches of the landslide dam have experienced three stages of erosion evolution, as Figure 2 shown, and the specific description is as follows:

[0043] The first stage: On the cross-section (i.e., C-I), the width of the top of the breach does not change, but the depth of the breach, the width of the bottom, and the slope angle increase until the slope toe reaches the critical angle α c , and then with a fixed slope toe α cUniform expansion (i.e., the C-II stage). In the longitudinal section (i.e., the L-I stage), the water flow cuts the downstream slope angle to the critical angle β f , and only slight erosion occurs at the bottom of the breach. This stage belongs to the initial stage of the breach.

[0044] Second stage: The cross-section breach continues to expand uniformly at the fixed bank slope angle α c (i.e., the C-II stage). In the downstream of the longitudinal section, it erodes and retreats at the fixed slope angle β f , and significant longitudinal erosion occurs at the bottom of the breach. Eventually, the longitudinal shape of the dam body is triangular (i.e., the L-II stage). The end of the L-II stage is the end of the second stage, marking the transition of the breach from the initial stage to the development stage.

[0045] Third stage: After the end of the L-II stage, the bottom of the breach is rapidly eroded, the flow cross-section is significantly expanded, and the flow rate is significantly increased (i.e., the L-III stage). Eventually, when the water flow is not sufficient to cause continuous erosion of the riverbank, only vertical erosion (i.e., the C-III1 stage) or only horizontal erosion (i.e., the C-III2 stage) occurs in the cross-section.

[0046] Regarding the erosion rate of the soil mass under the action of water flow during the erosion process of the landslide dam, this model is described by the shear stress equation:

[0047] E = K d (τ - τ c ) (1)

[0048] In the formula, E is the soil erosion rate (mm 3 / m 2 -s); τ is the shear stress at the water-soil interface (Pa); K d is the erodibility coefficient (mm 3 / N-s); τ c is the critical shear stress (Pa). Among them, the shear stress acting at the water-soil interface is expressed as:

[0049] τ = γ w R h S (2)

[0050] In the formula, γ w is the unit weight of water (N / m 3 ); R h is the hydraulic radius (m); S is the hydraulic gradient. According to Figure 2 the cross-section shape of the breach, the hydraulic radius can be expressed as:

[0051]

[0052] In the formula, H is the water surface elevation (m); Z is the elevation of the bottom of the breach (m); B bwhere \(b\) is the width of the breach bottom (m); \(\alpha\) is the slope angle of the breach (°).

[0053] In this model, the soil erodibility parameters at different depths are defined based on the basic soil parameters in the field test results, and can be specifically expressed by the following empirical formula:

[0054]

[0055] In the formula, \(e\) is the void ratio; \(C\) u is the coefficient of uniformity; \(PI\) is the plasticity index; \(P\) is the fine-grained content (\(<0.063\) mm); \(g\) is the acceleration due to gravity (N / kg); \(\rho\) s is the soil mass density (kg / m 3 ³); \(\rho_w\) w is the mass density of water (kg / m 3 ³); \(\varphi\) is the friction angle; \(d\) 50 is the average particle size (m). However, in actual landslide dam-break prediction, it is very complex to determine the two key parameters (\(K\) d and \(\tau\) c ) using so many basic soil parameters. Therefore, in the embodiments of the present invention, the focus is placed on the direct characterization of the two soil erodibility parameters (i.e., determining the direct relationship between the soil erodibility parameters and the depth), and the interval of each depth is set to 1 m.

[0056] In the embodiments of the present invention, the random field theory is used to describe the spatial variability of the soil. According to the random field theory, the spatial variability of soil properties consists of two parts: the trend part and the random fluctuation part. The model can be expressed as:

[0057] \(g(z)=t(z)+\omega(z)\) (6)

[0058] In the formula, \(g(z)\) represents the soil parameter at the position \(z\), which represents the soil erodibility parameter of the landslide dam (i.e., \(K\) d and \(\tau\) c ) in the embodiments of the present invention; \(z\) is the spatial position, which represents the depth (m) from a certain position to the top of the landslide dam in the embodiments of the present invention; \(t(z)\) is the trend component; \(\omega(z)\) is the random fluctuation component.

[0059] The random fluctuation component \(\omega(z)\) describes the variability of the soil parameter at a certain spatial position and is usually characterized as a specific distribution. However, currently, only the soil erodibility parameters at several depths of several landslide dams have been obtained from limited field tests, which is not sufficient to support the research on the random fluctuation component. Therefore, in the embodiments of the present invention, only the trend component function \(t(z)\) in the one-dimensional direction (i.e., the depth direction) is concerned.

[0060] The trend component function t(z) describes the spatial variation characteristics of soil parameters and is related to the absolute spatial position. When considered as a constant term, t(z) can be simplified to the mean value of soil parameters. However, the on-site test results show that the two key parameters (i.e., K d and τ c ) that describe the erodibility of the landslide dam soil have an obvious trend of varying with depth. At the same time, when calibrating the soil erodibility parameters, it is inevitable to consider their values at different depths.

[0061] Therefore, in the embodiments of the present invention, the trend component function in the random field theory is used to characterize the soil erodibility parameters at different depths of the landslide dam. It should be noted that the soil erodibility parameters characterized in the embodiments of the present invention are not the soil erodibility parameters at a specific spatial position, but the average soil erodibility parameters of the landslide dam at this depth. Thus, the calibration of the soil erodibility parameters in the embodiments of the present invention is transformed into the calibration of the trend component function that takes into account the spatial variation characteristics of the soil erodibility parameters.

[0062] The trend component function t(z) is usually an empirical formula established based on data, and different selections of the trend component function may lead to significant differences in results. Therefore, in the embodiments of the present invention, it is necessary to first determine the type of trend component function applicable to the soil erodibility parameters of the landslide dam, and the specific description is as follows:

[0063] K d = t1(z, ζ1, ζ2, …, ζ p ) (7)

[0064] τ c = t2(z, ξ1, ξ2, …, ξ q ) (8)

[0065] where t1 and t2 respectively represent the types of trend component functions applicable to K d and τ c ; ζ = [ζ1, ζ2, …, ζ p represents the vector of t1 coefficients; ξ = [ξ1, ξ2, …, ξ q represents the vector of t2 coefficients. Next, it is necessary to calibrate the coefficients of these functions (i.e., ζ and ξ).

[0066] In the embodiments of the present invention, in step S101, based on the historical landslide dam case data collected, the type of trend component function that may be applicable to the soil erodibility parameters of the landslide dam can be determined, and based on this, an alternative matrix of the trend component function t(z) regarding the soil erodibility coefficients of the landslide dam is constructed.

[0067] In the embodiments of the present invention, a multi-criteria decision-making method (MCDM) is required to select the most suitable type of trend component function. Specifically, in the embodiments of the present invention, a simple and general method, TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), is adopted to determine the optimal solution. The TOPSIS method evaluates alternative solutions by measuring the distances between the alternative solutions and the "positive" and "negative" ideal solutions.

[0068] Specifically, in an alternative embodiment, the step S102 includes:

[0069] Step S1021, constructing a decision matrix according to the alternative solution matrix and the judgment indicators:

[0070]

[0071] where, A = [A1, A2,..., A i ,..., A u T represents the alternative solution matrix, u is the number of alternative solutions; C = [C1, C2,..., C j ,..., C v is the judgment indicator, v is the number of judgment criteria; x ij is the value corresponding to each alternative solution under each judgment indicator; in the embodiments of the present invention, the judgment indicator is the modified R 2 .

[0072] Step S1022, constructing a weighted normalized decision matrix:

[0073] where, v ij is the weighted normalized x ij ; w j is the element of the weight matrix w, representing the weight of each judgment indicator, w = [w1, w2,..., w v . In the embodiments of the present invention, when the judgment indicator is the modified R 2 , the weight of this judgment indicator is 1.

[0074] Step S1023, calculating the positive ideal solution PIS and the negative ideal solution NIS:

[0075]

[0076] where, if the jth criterion is beneficial, then otherwise, then

[0077] ​Step S1024, calculate the distances from each alternative to the positive and negative ideal solutions:

[0078]

[0079] In the formula, is the distance from the i-th solution to the positive ideal solution, is the distance from the i-th solution to the negative ideal solution;

[0080] Step S1025, calculate the relative distance R i between the positive and negative ideal solutions of each alternative and the normalized score S i :

[0081] Determine the alternative with the maximum normalized score as the best trend component function.

[0082] Inverse analysis refers to inversely calculating the input coefficients that best fit the known observation results. In this process, a set of objective functions needs to be defined first. In the embodiments of the present invention, let θ = [ζ, ξ] represent the coefficients of the trend function of the soil erosion parameter to be calibrated; let Y = [Y1, Y2,..., Y k ,..., Y s represent the observation results based on the observation information, where s represents the number of observation information; let y(θ) = [y1, y2,..., y k ,..., y s represent the simulation results corresponding to the observation results calculated based on the physical model (DABA is used in the embodiments of the present invention) corresponding to the coefficient θ.

[0083] In the embodiments of the present invention, based on the deterministic inverse analysis method of multi-objective optimization, the optimal coefficient θ optimal is obtained, specifically including:

[0084] Construct an optimization objective function for the error between the observation results and the simulation results:

[0085] G k (θ|Y) = |y k (θ) / Y k - 1| (14)

[0086] For different combinations of coefficients θ, the same simulation results may be obtained, and theoretically, there will be an infinite number of solutions that minimize G i (θY), but some of these coefficients may have exceeded their reasonable existence range. To avoid this phenomenon, in the embodiments of the present invention, prior information based on field tests is introduced. Theoretically, the optimal θ should be within its prior information range and relatively close to its prior mean. Therefore, the objective function considering the reasonable existence range of the coefficients can be expressed as:

[0087]

[0088] Among them, T represents the transpose of the matrix; l = 1, 2, …, n, where n is the number of coefficients and n = p + q; μ l,prior and σ l,prior are the prior mean and standard deviation of the l-th coefficient.

[0089] In the embodiments of the present invention, theoretically, the objective function value vector G obtained from all coefficient combinations θ will take 0 as the ideal solution. However, there may be conflicts in minimizing all objective functions simultaneously, which means that when one objective function approaches the ideal solution, other objective functions may be moving away. However, a set of optimal solutions can be found through multi-objective optimization methods to make all objective functions as small as possible.

[0090] The Pareto optimal solution (also known as the Pareto optimal front) is a set of equilibrium solutions obtained based on the dominance and non-dominance relationships between objective function solutions, and is defined as a solution that cannot improve one objective function solution without weakening at least one other objective function solution. In the embodiments of the present invention, the Pareto optimal front of the objective function in the embodiments of the present invention is searched through the NSGA-II algorithm.

[0091] Based on the prior statistical information of each random coefficient and the physical model DABA, a plurality of random coefficients and their corresponding objective function values y k (θ) are generated for the initial population;

[0092] The Pareto optimal front of the initial population is identified through the NSGA-II algorithm to generate the next generation of dominant population, and the Pareto optimal front of the dominant population is identified through the NSGA-II algorithm to further generate the next generation of dominant population based on this dominant population; after 20 iterations, the optimal solution θ of the final Pareto optimal front is obtained optimal ;

[0093] Based on θ optimal , the trend component function of the calibrated soil erosion parameters is determined.

[0094] In the embodiments of the present invention, NSGA-II (Non-dominated Sorting Genetic Algorithm II) is a genetic algorithm for solving multi-objective optimization problems. It is an improved algorithm based on the first-generation non-dominated sorting genetic algorithm (NSGA), aiming to find a series of solution sets that perform well on multiple objectives, and these solution sets constitute an approximation of the Pareto optimal solution set.

[0095] The NSGA-II algorithm adopts methods such as fast non-dominated sorting, crowding degree calculation, and dominant solution selection, and has high computational efficiency and good convergence. When using the NSGA-II algorithm, the algorithm will continuously search for the non-dominated solution set through iteration. The average Euclidean distance (D i,w ) This index can be used to evaluate the diversity of solutions and the distribution of the population. When D i,w decreases, it means that the diversity of solutions decreases, the population tends to converge, and the algorithm may have found a better solution. Therefore, the number of iterations can be judged according to the node where D i,w tends to be stable. Then, the TOPSIS method is used to select the optimal solution θ optimal from the Pareto optimal front.

[0096] In the embodiment of the present invention, based on the probabilistic inverse analysis method, the posterior information of the random coefficient θ and the coefficient θ max,post corresponding to the maximum probability density are obtained, specifically including:

[0097] S1, taking the standard deviation σ ε of the model deviation factor ε as a random coefficient to participate in the Bayesian inverse analysis process.

[0098] In the embodiment of the present invention, when using the Bayesian inverse analysis method to calibrate the coefficient θ, a model deviation factor ε = [ε1, ε2,..., ε k ,..., ε s needs to be defined to characterize the error between the calculation result and the observed information. Similar to the deterministic inverse analysis process, these errors are unified through the quotient, and each model deviation factor can be expressed as:

[0099] ε k (θ) = y k (θ) / Y k (16)

[0100] Generally speaking, the smaller the deviation, the greater the possibility, that is, the closer ε k (θ) is to 1, the closer the coefficient θ is to the ideal value. Since the dimensionless processing of the errors of different observed information has been carried out, the embodiment of the present invention assumes that all deviations follow a normal distribution with a mean of 1 and a standard deviation of σ e . If the deviations of different observed information are statistically independent, the likelihood function L(θ|Y) reflecting the consistency between the model calculation result and the observed result can be expressed as:

[0101]

[0102] In the formula, since the deviation standard deviation σ eThere is no clear research record, so it is used as a random coefficient in the Bayesian back-analysis process to participate in the update process. According to Bayesian theory, the posterior probability of the random coefficient can be expressed as:

[0103] f post (θY) = K·L(θY)·f prior (θ) (18)

[0104] In the formula, K is a normalization constant used to verify the probability density function; f prior (θ) is the prior joint probability of the random coefficient θ.

[0105] S2. The Nataf transformation is used to determine the correlation of each coefficient.

[0106] In the embodiments of the present invention, the Nataf transformation (Iso-Probabilistic Marginal Transformation) is used to transform multiple correlated random variables into a series of independent standard normal distribution random variables for statistical analysis and reliability assessment.

[0107] S3. The formula (18) is solved by the DREAM (Differential Evolution Adaptive Metropolis) method for sampling to obtain a preset number of groups of posterior samples.

[0108] S4. According to the posterior samples, the posterior correlation and posterior information statistical characteristics between various parameters are obtained; the most suitable posterior distribution of each random coefficient is obtained through the K-S test, and the coefficient θ with the maximum probability density is obtained max,post ;

[0109] S5. According to θ max,post , the trend component function of the calibrated soil erodibility parameter is determined.

[0110] For easy understanding, an exemplary embodiment is also proposed in the embodiments of the present invention, Figure 3 showing the implementation step flow diagram of this exemplary embodiment.

[0111] In this embodiment, the specific situation of the research case in this exemplary embodiment is as follows: On October 10 and November 3, 2018, two consecutive landslides occurred in a certain place in the Jinsha River Basin, completely blocking the Jinsha River. The volume of the first landslide was about 2.26×10 7 m 3 (where the volume of the sliding source area was 1.96×10 7 m 3 , and the volume of the scraping area was 2.4×10 6 m 3)。Finally, a landslide dam with a minimum dam crest height of 61 m, a length along the river of 1200 m, and a volume of approximately 2.4×10 7 m 3 was formed. The maximum storage capacity of the barrier lake formed by the landslide dam is approximately 2.9×10 8 m 3 . The lifespan of the landslide dam formed by the first landslide is only 2.7 days. The lake water began to overflow naturally at 17:30 on October 12 and reached the peak outflow rate at 6:00 on October 13, approximately 10000 m 3 / s, and returned to the base flow of 1680 m 3 / s at 14:00 on October 14. After the first breach in this area, the depth of the breach is approximately 32 m.

[0112] On November 3, a second landslide occurred at the same location. The total volume of the landslide source area and the scraping area is approximately 8.5×10 6 m 3 of landslide materials (the volume of the landslide source area is 3.68×10 6 m 3 , and the volume of the scraping area is 4.82×10 6 m 3 ). Based on the residual materials eroded by the breach of the first landslide dam, a landslide dam with a minimum dam crest height of 96 m, a length along the river of 1000 m, and a volume of approximately 3.02×10 7 m 3 was formed. To reduce the risk, a diversion channel with a length of 220 m, a depth of 15 m, a top width of 42 m, and a bottom width of 3 m was excavated at the top of the landslide dam formed by the second landslide, reducing the maximum capacity of the barrier lake from 7.5×10 8 m 3 to 5×10 8 m 3 . The lifespan of the landslide dam formed by the second landslide is 10.6 days. The lake water began to flow through the diversion channel at 4:45 on November 12 and reached the peak outflow rate at 18:20 on November 13, approximately 33900 m 3 / s, and returned to the base flow of 800 m 3 / s at 8:00 on November 14. In addition, in the embodiments of the present invention, some observation information on key physical quantities during the two breaches in this area was collected, as shown in Table 1.

[0113] Table 1: Observation information during the two landslide dam breaches

[0114] Observation information First time Second time <![CDATA[Peak flow rate, Q p (m 3 / s)]]> 10000.0 33900.0 <![CDATA[Time of breach development, T b (h)]]> 12.5 37.6 <![CDATA[Breaching start time, T i (h)]]> 6.5 33.3 Final breach depth, D (m) 32.0 61.0 <![CDATA[Time to peak flow, T p (h)]]> 14.5 17.9 <![CDATA[Final top width of the breach, W t (m)]]> 180.0 300.0 <![CDATA[Final bottom width of the breach, W b (m)]]> 80.0 90.0

[0115] In the embodiments of the present invention, first, six cases (Baige first, Baige second, Jiala, Tangjiashan, Xiaogangjian, Hongshihe) with records of erosion parameters varying along the soil depth and including two landslide dams in this area were collected. The results are shown in Table 2. Based on this data, it can be obtained that the erodibility coefficient K d is negatively correlated with the critical shear stress τ c , and the correlation coefficient (ρ) is -0.277.

[0116] Based on the fact that the trend component function should satisfy its own as simple as possible linear characteristics, the embodiments of the present invention selected three common function types, namely linear type, exponential type, and power-law type, to characterize the trend characteristics of the variation of soil erosion parameters in space. At the same time, considering the large difference between the maximum and minimum values of the soil erosion parameters in Table 2, the soil erosion parameters after logarithmic transformation were added. Therefore, for each erosion parameter, the embodiments of the present invention provide six trend function types, as shown in Table 3 specifically.

[0117] In addition, since the trend component function should make the residual after its fitting as small as possible, the embodiments of the present invention selected the corrected R 2 (R 2 adj ) of the curve fitting of each landslide dam case under each alternative as the judgment criterion. So far, in the embodiments of the present invention, for two erosion parameters, a decision matrix including six alternatives (i.e., six trend component function types) and six judgment criteria (i.e., the R 2 adj after fitting the six landslide dam cases in Table 2 respectively) was constructed. Through the TOPSIS method described by formulas (9) to (13), the embodiments of the present invention can obtain the normalized score (S) of each alternative, and the results are shown in Table 4. Therefore, in the embodiments of the present invention, the optimal function of the trend component of the spatial variability of the landslide dam soil erosion parameters is expressed as:

[0118] K d = 10 a ·z -b (z > 0) (19)

[0119] τ c = c·e d·z (z > 0) (20)

[0120] In the formula, a, b, c, and d are the coefficients to be calibrated in the embodiments of the present invention.

[0121] Table 2: Erosion parameters of each landslide dam soil along the depth direction

[0122]

[0123]

[0124] Note: The soil erosion parameters of the first white grid are obtained based on the field test results of the second white grid.

[0125] Table 3: Alternative schemes for characterizing the spatial variation trend characteristics of soil erosion parameters of landslide dams

[0126]

[0127] Among them, a, b, c, and d represent the coefficients of the trend component function.

[0128] Table 4: Normalized scores of each alternative scheme

[0129]

[0130] Based on the curve coefficients and fitting determination coefficients of the two erosion parameters in each landslide dam case under each alternative scheme, in the embodiments of the present invention, the initial samples of the four coefficients in Equation (18) can be obtained, as shown in Table 5. In the embodiments of the present invention, the SMOTE oversampling method is used to expand the small samples (i.e., the initial samples) into large samples (i.e., prior samples), and then the most suitable distribution type of each coefficient is determined through the K-S test. The K-S test shows that for the four random coefficients a, b, c, and d, their most suitable distributions are lognormal distribution, lognormal distribution, lognormal distribution, and normal distribution, respectively. The statistical characteristics (mean, standard deviation) and correlation coefficients (ρ) of each random coefficient are shown in Table 6. For the standard deviation σ of the model deviation factor ε ε , in the embodiments of the present invention, it is assumed that its prior distribution follows a uniform distribution with σ ε ∈ [0, 2].

[0131] Table 5: Prior information of each coefficient

[0132]

[0133] Table 6: Correlation coefficients and prior statistical characteristics of random coefficients a, b, c, and d

[0134]

[0135] The deterministic inverse analysis aims to determine the optimal coefficients of the first white grid landslide dam and the second white grid landslide dam, respectively. In the multi-objective optimization process, in the embodiments of the present invention, the peak outflow rate (Q p ) and the peak outflow rate arrival time (T p ) in Table 1 are selected, and the breach formation time (T i), and four representative observation information items, namely the maximum discharge (Q), the time to peak discharge (T), the time to peak discharge (T), and the final breach depth (D), are used to construct the optimization objective function (i.e., formula (14)) based on the error between the observation results and the simulation results in the embodiments of the present invention. At the same time, an optimization objective function based on prior information (i.e., formula (14)) is constructed according to the prior statistical eigenvalue of each random coefficient in Table 6. Where s = 4, θ = [a, b, c, d], Y = [Q p , T p , T i , D], and y k (θ) is the calculated value corresponding to the kth observation value, which is obtained based on the DABA model. At the same time, an objective function based on prior information (i.e., formula (15)) is constructed according to the prior statistical information in Table 6, where n = 4. So far, a total of five objective functions have been constructed in the embodiments of the present invention.

[0136] First, according to the prior statistical information of each random coefficient and the physical model DABA, an initial population containing 1000 groups of θ and their corresponding objective function values y k (θ) is generated. Then, the NSGA-II algorithm is applied to identify the Pareto optimal front of the initial population and generate the next generation of dominant population. Then, the NSGA-II algorithm is used to identify the Pareto optimal front of the dominant population and further generate the next generation of dominant population based on this dominant population. The evolution result of the average Euclidean distance D i,w between the two Baige landslide dam breaches during the iteration process shows that 20 iterations are sufficient to ensure convergence. Finally, the optimal solution (i.e., θ optimal ) of the final Pareto optimal front is obtained through the TOPSIS method, and the results are shown in Table 7. According to θ optimal , the trend component function t(z) of the calibrated soil erosion parameter can be expressed as:

[0137] Baige first time:

[0138] Baige second time:

[0139] Table 7: Optimal solutions for multi-objective optimization of two Baige landslide dam breaches

[0140]

[0141] In the Bayesian-based probabilistic back-analysis process, the embodiments of the present invention select the same observation information as in the multi-objective optimization process. The difference is that in this process, the standard deviation σ ε of the model deviation factor ε in the embodiments of the present invention is used as a new random coefficient to participate in the update process, that is, θ * = [a, b, c, d, σ εAccording to the prior distributions of the random coefficients, the embodiments of the present invention use the Nataf transformation to consider the correlations of the coefficients in Table 6. Subsequently, sampling is performed by solving Equation (18) using the DREAM method to obtain 20,000 sets of posterior samples θ * Based on these samples, the posterior correlations of a, b, c, and d are shown in Table 8, and their posterior information statistical characteristics are shown in Table 9. The most appropriate posterior distribution of each random coefficient is obtained through the K-S test, and the values of a, b, c, and d corresponding to the maximum probability density (i.e., θ max,post ) are: 3.795, 1.729, 0.983, 0.113 (the first white grid); 2.868, 0.602, 1.005, 0.112 (the second white grid). According to θ max,post , the calibration trend component function t(z) of the soil erodibility parameter can be expressed as:

[0142] The first white grid:

[0143] The second white grid:

[0144] Comparing the prior and posterior correlation matrices of the random coefficients in Table 9, it can be seen that in the two research cases, the posterior correlations between the random coefficients a and b, c and d are significantly enhanced; the posterior correlations between the random coefficients a and c, a and d are significantly weakened; the correlations between other random coefficients change little. Such changes are reasonable because a and b jointly define the same soil erodibility coefficient, K d (as shown in Equation (19)); similarly, c and d jointly define τ c (as shown in Equation (20)). At the same time, according to Equations (4) and (5), it can be seen that K d and τ c are determined by different basic soil parameters, which means that the coefficients defining different soil erodibility parameters (such as a and c, a and d, etc.) have no necessary connection, so they do not show obvious correlations. In addition, the obvious prior correlations between the random coefficients a and c, a and d are because the prior information covers too large a range and is not accurate enough.

[0145] Comparing the prior and posterior information in Table 6 and Table 10, for the first white cell, the standard deviation of the random coefficient a decreases from 1.682 to 0.311, and the standard deviation of the random coefficient b decreases from 1.270 to 0.421; for the second white cell, the standard deviation of the random coefficient a decreases from 1.682 to 0.469, and the standard deviation of the random coefficient b decreases from 1.270 to 0.458; in the posterior results of the two research cases, the standard deviations of the random coefficients c and d change very little. Corresponding to the prior and posterior distributions of each random coefficient, it can be seen that in the two target cases, the updating effects of the random coefficients a and b are significant, and the uncertainty is significantly reduced, while the updating effects of c and d are not significant. This indicates that compared with the erodibility coefficient K determined by a and b d compared with the critical shear stress τ determined by c and d c does not play a decisive role in the simulation results. Therefore, the updating effect of Bayesian back-analysis is mainly reflected in a and b. In addition, the standard deviation σ of the model deviation factor ε has been significantly updated, and the values corresponding to the maximum probability density are 0.184 and 0.122 respectively. This result can provide a reference for subsequent research.

[0146] Table 8: Posterior correlation matrix of random coefficients a, b, c, and d

[0147]

[0148] Posterior correlation matrix (first white cell)

[0149] Random coefficient a b c d a 1 0.818 -0.068 -0.026 b 0.818 1 0.148 0.022 c -0.068 0.148 1 -0.107 d -0.026 0.022 -0.107 1

[0150] Posterior correlation matrix (second white cell)

[0151] Random coefficient a b c d a 1 0.715 -0.008 -0.021 b 0.715 1 0.022 0.039 c -0.008 0.022 1 -0.146 d -0.021 0.039 -0.146 1

[0152] Table 9: Posterior information statistical values

[0153]

[0154]

[0155] According to formulas (21) to (24), the calibrated landslide dam soil erodibility parameters can be obtained, and the results are as Figure 4 shown, where the blue line is the result obtained by random sampling within the 95% confidence interval of the posterior distribution of each random coefficient in Table 10 (to ensure both high confidence and sample accuracy). It can be seen that the two back-analysis methods obtain almost the same calibrated soil erodibility parameters. Among them, for the first white cell, τ obtained by the probabilistic back-analysis method c is slightly smaller; for the second white cell, K obtained by the probabilistic back-analysis method dSlightly smaller, and these trend component curves obtained by random sampling show clear envelopes, successfully covering the field test results, indicating that both methods have been successfully applied.

[0156] In addition, there are obvious differences between the calibrated soil erosion parameters and the test results. For the first time at Baige, the K at the top of the calibrated landslide dam d is much larger than the test result, and the K in the middle and lower parts d is slightly smaller than the test result; while the calibrated τ c are all smaller than the test results. This shows that the first Baige landslide dam has higher soil erodibility than the test results, and this result is in line with expectations. Because the on-site test of the first Baige was carried out after the second Baige breach, which means that the soil has been severely disturbed. The moving materials of the second landslide accumulated on the residual soil of the first landslide dam, and the huge impact force produced a compaction effect on the residual soil. According to formulas (4) and (5), the decrease in porosity leads to a decrease in the erodibility coefficient at the beginning of soil erosion and an increase in the critical shear stress, thus showing lower erodibility. For the second time at Baige, the K at the lower part of the calibrated landslide dam d is greater than the test result, while the τ c are all greater than the test results, indicating that there are differences in soil erodibility between the residual area and the erosion area.

[0157] Based on the calibrated soil erosion parameters of the landslide dam, the process of landslide dam breach is re-simulated. Figure 5 Shows the discharge-time (Q b -t) curve and the soil erosion rate-time (E-t) curve of the breach process; Table 10 shows the 4 simulation results corresponding to the observed information Y, and the errors between the simulation results calculated based on formula (14) and the observed results. It can be seen that for the first Baige, the simulation results obtained based on θ optimal and θ max,post are highly similar. For the second Baige, the simulation results obtained by θ optimal have a greater erosion rate before the peak discharge arrival time, so the breach initiation stage (i.e., smaller T i ) is completed faster and the peak discharge (i.e., smaller T p ) is reached. At the same time, the higher soil erodibility makes the simulation results obtained by θ optimal have a greater final breach depth D and peak discharge Q p .

[0158] The main differences between the simulation results and the observed results are the T p and T i of the first Baige, and the D of the two breaches at Baige. Their errors are greater than 0.1; the errors of other observed items are all less than 0.1. For the first Baige, the larger Ti With a smaller T p This indicates that the soil erosion at the top of the calibrated landslide dam is less, while the soil erosion in the middle is greater. In addition, in the two landslide dam cases, the error in the simulation results of the final breach depth D is acceptable because it is itself in a large range of variation. According to the report of Zhang et al., the final breach depth of the second white grid was 38 to 94 m, so the average depth (i.e., 61 m) was used as the observation result in the back analysis process. The simulation results in the embodiment of the present invention are 76.6 m and 77.3 m, which are acceptable, and the same is true for the first white grid.

[0159] Table 10: Re-simulation results and errors based on calibrated soil erosivity parameters

[0160]

[0161] In the embodiment of the present invention, the trend component function in the random field theory is used to unify the soil erosion parameters of different depths of the landslide dam, and the uncertainty of the spatial variation of the soil erosion parameters is characterized by the uncertainty of the trend component function coefficient. At the same time, two back analysis methods are used in the embodiment of the present invention. A set of optimal coefficients can be obtained by the deterministic back analysis method, and the probability back analysis method quantifies the uncertainty of each random coefficient, making up for the defects of the results of the deterministic back analysis method; and the two methods obtain highly similar results, which further illustrates the feasibility of the method.

[0162] In the embodiment of the present invention, based on the multi-criteria decision-making method, the trend component function form (i.e., equations (19) and (20)) for describing the spatial variation trend of the soil erosivity parameters of the landslide dam was determined from six landslide dam cases, and the back analysis results also proved its applicability. In addition, according to the results of the calibrated soil erosivity parameters of the landslide dam in the embodiment of the present invention, it is shown that the soil erosivity is extremely high at the top of the landslide dam, and the soil erosivity decreases rapidly with increasing depth; in the middle and lower parts of the landslide dam, the soil erosivity is relatively small, and does not change much with increasing depth.

[0163] Based on the same inventive concept, an embodiment of the present invention provides a device for calibrating soil erosivity parameters of a landslide dam using a back analysis method, the device comprising:

[0164] A construction module is used to collect historical landslide dam case data recording soil erosivity parameters and construct an alternative scheme matrix of the trend component function t(z) of the soil erosivity coefficient of the landslide dam;

[0165] The fitting module is used to obtain the curve fitting coefficient and the modified R of the soil erosivity coefficient of each landslide dam under each trend component function through curve fitting based on the historical landslide dam case data. 2, the landslide dam soil erosion coefficient includes the erodibility coefficient K d and the critical shear stress τ c ;

[0166] The optimal trend component function determination module is used to determine the optimal trend component function from the alternative matrix and use the coefficients of the optimal trend component function as the random coefficients θ to be calibrated;

[0167] The prior information determination module is used to obtain the initial sample of the random coefficient θ of the optimal trend component function based on the curve fitting result, generate prior samples through oversampling methods, and obtain the prior information and correlation coefficient matrix about θ;

[0168] The simulation result determination module is used to determine the observation information set Y for back analysis of the target landslide dam, and obtain the landslide dam breach simulation results corresponding to each random coefficient through the simplified physical model DABA;

[0169] The back analysis module is used to obtain the optimal coefficient θ based on the deterministic back analysis method of multi-objective optimization optimal , and at the same time, obtain the posterior information of the random coefficient θ and the coefficient θ corresponding to the maximum probability density based on the probabilistic back analysis method max,post ;

[0170] The soil erosion parameter determination module is used to obtain the calibrated soil erosion parameter change curve and its corresponding landslide dam breach simulation result according to θ optimal and θ max,post ;

[0171] Optionally, the optimal trend component function determination module is specifically used for:

[0172] Construct a decision matrix according to the alternative matrix and judgment indicators:

[0173] where A = [A1, A2, …, A i , …, A u T represents the alternative matrix, u is the number of alternative plans; C = [C1, C2, …, C j , …, C v is the judgment indicator, v is the number of judgment criteria; x ij is the value corresponding to each alternative plan under each judgment indicator; the judgment indicator is the modified R 2 ;

[0174] Construct a weighted normalized decision matrix:

[0175] where v ij is the weighted normalized x​ij ; w j is an element of the weight matrix w, representing the weight of each judgment index;

[0176] Calculate the positive ideal solution PIS and the negative ideal solution NIS:

[0177]

[0178] Among them, if the jth criterion is beneficial, then Otherwise, then

[0179] Calculate the distance of each alternative to the positive and negative ideal solutions:

[0180]

[0181] In the formula, is the distance from the ith alternative to the positive ideal solution, is the distance from the ith alternative to the negative ideal solution;

[0182] Calculate the relative distance R between the positive and negative ideal solutions of each alternative i and the normalized score S i :

[0183] Determine the alternative with the largest normalized score as the best trend component function.

[0184] Optionally, the simulation result determination module is specifically used for:

[0185] Let θ = [ζ, ξ] represent the coefficients of the trend function of the soil erosion parameter to be calibrated;

[0186] Let Y = [Y1, Y2, …, Y k , …, Y s represent the observation results based on the observation information, where s represents the number of observation information; Let y(θ) = [y1, y2, …, y k , …, y s represent the simulation results corresponding to the observation results calculated based on the physical model DABA corresponding to the coefficients θ.

[0187] Optionally, the back-analysis module is specifically used for:

[0188] Construct an optimization objective function for the error between the observation result and the simulation result:

[0189] G k (θ|Y) = |y k (θ) / Y k - 1|;

[0190] Construct an optimization objective function based on prior information according to the prior statistical eigenvalues of each random coefficient:

[0191] where T represents the transpose of a matrix; l = 1, 2, …, n, and n is the number of coefficients; μ l,prior and σ l,prior are the prior mean and standard deviation of the l-th coefficient;

[0192] Generate an initial population of multiple random coefficients and their corresponding objective function values y k (θ) according to the prior statistical information of each random coefficient and the physical model DABA;

[0193] Identify the Pareto optimal front of the initial population through the NSGA-II algorithm and generate the next generation of dominant population. Identify the Pareto optimal front of the dominant population through the NSGA-II algorithm and further generate the next generation of dominant population based on this dominant population; after 20 iterations, obtain the optimal solution θ of the final Pareto optimal front optimal；

[0194] According to θ optimal , determine the trend component function of the calibrated soil erosion parameters.

[0195] Optionally, the inverse analysis module is specifically used for:

[0196] Take the standard deviation σ ε of the model deviation factor ε as a random coefficient to participate in the Bayesian inverse analysis process;

[0197] Adopt the Nataf transformation to consider the correlation of each coefficient;

[0198] Solve the following formula through the DREAM method for sampling to obtain a preset number of groups of posterior samples: f post (θ|Y) = K · L(θ|Y) · f prior (θ), where f post (θ|Y) represents the posterior probability of the random coefficient, and K is a normalization constant used to verify the probability density function; f prior (θ) is the prior joint probability of the random coefficient θ;

[0199] ε k (θ) = y k (θ) / Y k ;

[0200] According to the posterior samples, obtain the posterior correlation and posterior information statistical characteristics between each parameter; obtain the most suitable posterior distribution of each random coefficient through the K-S test, and obtain the coefficient θ with the maximum probability density max,post ;

[0201] According to θ max,post , determine the trend component function of the calibrated soil erodibility parameter.

[0202] Based on the same inventive concept, an embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps in the method for calibrating the soil erodibility parameter of a landslide dam using the back-analysis method described in any one of the above embodiments are implemented.

[0203] Based on the same inventive concept, an embodiment of the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes, the steps in the method for calibrating the soil erodibility parameter of a landslide dam using the back-analysis method described in any one of the above embodiments are implemented.

[0204] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other.

[0205] Although the preferred embodiments of the embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they know the basic creative concept. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

[0206] Finally, it should also be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or terminal device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or terminal device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article or terminal device including the element.

[0207] The above has introduced in detail a method for calibrating the erosion parameters of landslide dam soil using the back-analysis method. In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. At the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation on the present invention.

Claims

1. A method for calibrating the erosion parameters of landslide dam soil using the back-analysis method, characterized in that The method includes: Collecting and recording historical landslide dam case data of soil erosion parameters, and constructing an alternative matrix of the trend component function t(z) of the soil erosion coefficient of the landslide dam; the trend component function t(z) characterizes the soil erosion parameters at different depths of the landslide dam, is used to describe the spatial variation characteristics of soil parameters, and is related to the absolute spatial position; The curve fitting coefficients and the corrected R of the soil erosion parameters of each landslide dam under each trend component function are obtained by curve fitting based on the historical landslide dam case data 2 , and the soil erosion coefficient of the landslide dam includes the erodibility coefficient K d and the critical shear stress τ c ; Determining the best trend component function from the alternative matrix, and taking the coefficients of the best trend component function as the random coefficients θ to be calibrated; Based on the curve fitting results, obtaining the initial samples of the random coefficients θ of the best trend component function, generating prior samples through oversampling methods, and obtaining the prior information and correlation coefficient matrix about θ; Determining the observation information set Y for back analysis of the target landslide dam, and obtaining the breach simulation results corresponding to each combination of random coefficients through the simplified physical model DABA; the physical model DABA is a simplified physical model landslide dam breach simulation program based on erosion; Deterministic inverse analysis method based on multi-objective optimization to obtain the optimal coefficient θ optimal , meanwhile, posterior information of the random coefficient θ and the coefficient θ corresponding to the maximum probability density are obtained based on the probabilistic inverse analysis method max,post ; According to θ optimal and θ max,post Obtain the calibrated change curve of soil erosion parameters and its corresponding landslide dam breach simulation results.

2. The method for calibrating the soil erosion parameters of a landslide dam using the back-analysis method according to claim 1, characterized in that, Determining the best trend component functions t1 and t2 from the alternative matrix, including: Construct a decision matrix based on the alternative matrix and judgment criteria: Among them, A = [A1, A2, …, A i , …, A u T represents the alternative matrix, where u is the number of alternatives; C = [C1, C2, …, C j , …, C v is the judgment index, and v is the number of judgment criteria; x ij is the value corresponding to each alternative under each judgment index; the judgment index is the modified R 2 ;​ Constructing a weighted normalized decision matrix: Among them, v ij is the weighted and normalized x ij ; w j is an element of the weight matrix w, representing the weight of each judgment index; Calculating the positive ideal solution PIS and the negative ideal solution NIS: wherein, if the j-th criterion is beneficial, then otherwise, Calculating the distances from each alternative to the positive and negative ideal solutions: In the formula, is the distance from the $i$-th solution to the positive ideal solution, is the distance from the $i$-th solution to the negative ideal solution; Calculate the relative distance R between the positive and negative ideal solutions for each alternative i and the normalized score S i : Determining the alternative with the maximum normalized score as the best trend component function.

3. The method for calibrating the soil erosion parameters of a landslide dam using the back-analysis method according to claim 1, characterized in that Determining the observation information set Y for back analysis of the target landslide dam, and obtaining the breach simulation results corresponding to each combination of random coefficients through the simplified physical model DABA, including: Letting θ = [ζ, ξ] represent the coefficients of the best trend component function to be calibrated; Let \(Y = [Y_1, Y_2, \ldots, Y k , \ldots, Y s \) represent the observation results based on the observation information, where \(s\) represents the number of observation information; let \(y(\theta)=[y_1, y_2, \ldots, y k , \ldots, y s \) represent the simulation results corresponding to the observation results calculated based on the physical model DABA corresponding to the coefficient \(\theta\).

4. The method for calibrating the soil erosion parameters of a landslide dam using the inverse analysis method according to claim 3, characterized in that, Deterministic inverse analysis method based on multi-objective optimization to obtain the optimal coefficient θ optimal , including: Constructing an optimization objective function for the error between the observation results and the simulation results: G k (θ|Y) = |y k (θ) / Y k -1|; Constructing an optimization objective function based on prior information according to the prior statistical eigenvalue of each random coefficient: where \(T\) represents the transpose of a matrix; \(l = 1, 2, \ldots, n\), and \(n\) is the number of coefficients; \(\mu\) l,prior and \(\sigma\) l,prior are the prior mean and standard deviation of the \(l\)-th coefficient, respectively; Generate a plurality of random coefficients and their corresponding objective function values y according to the prior statistical information of each random coefficient and the physical model DABA. k (θ) initial population; Identify the Pareto optimal front of the initial population through the NSGA-II algorithm and generate the next generation of dominant populations. Identify the Pareto optimal front of the dominant population through the NSGA-II algorithm and further generate the next generation of dominant populations based on this dominant population. After 20 iterations, obtain the optimal solution θ of the final Pareto optimal front optimal； According to θ optimal , determine the trend component function of the calibrated soil erodibility parameter.

5. The method for calibrating the soil erosion parameters of a landslide dam using the back-analysis method according to claim 3, characterized in that, Obtain the posterior information of the random coefficient θ and the coefficient θ corresponding to the maximum probability density based on the probabilistic inverse analysis method max,post , including: The standard deviation σ of the model deviation factor ε ε is involved in the Bayesian back-analysis process as a random coefficient; Adopting the Nataf transformation to consider the correlation of each coefficient; Sampling is performed by solving the following equation through the DREAM method to obtain a preset number of groups of posterior samples: f post p(θ|Y) = K · L(θ|Y) · f prior (θ), where f post p(θ|Y) represents the posterior probability of the random coefficient, and K is a normalization constant used to verify the probability density function; f prior (θ) is the prior joint probability of the random coefficient θ; ε k (θ) = y k (θ) / Y k ; Based on the posterior samples, obtain the posterior correlation and posterior information statistical characteristics among various parameters; through the K-S test, obtain the most suitable posterior distribution for each random coefficient, and obtain the coefficient θ with the maximum probability density. max,post； According to θ max,post , determine the trend component function of the calibrated soil erodibility parameter.

6. Device for calibrating erosion parameters of landslide dam soil using back-analysis method, characterized in that, The device includes: A construction module for collecting and recording historical landslide dam case data of soil erosion parameters, and constructing an alternative matrix of the trend component function t(z) of the soil erosion coefficient of the landslide dam; the trend component function t(z) characterizes the soil erosion parameters at different depths of the landslide dam, is used to describe the spatial variation characteristics of soil parameters, and is related to the absolute spatial position; A fitting module, configured to obtain curve fitting coefficients and corrected R of each landslide dam soil erosion coefficient under each trend component function through curve fitting based on the historical landslide dam case data 2 , where the landslide dam soil erosion coefficient includes the erodibility coefficient K d and the critical shear stress τ c ; A best trend component function determination module for determining the best trend component function from the alternative matrix, and taking the coefficients of the best trend component function as the random coefficients θ to be calibrated; A prior information determination module for obtaining the initial samples of the random coefficients θ of the best trend component function based on the curve fitting results, generating prior samples through oversampling methods, and obtaining the prior information and correlation coefficient matrix about θ; A simulation result determination module for determining the observation information set Y for back analysis of the target landslide dam, and obtaining the landslide dam breach simulation results corresponding to each random coefficient through the simplified physical model DABA; the physical model DABA is a simplified physical model landslide dam breach simulation program based on erosion; An inverse analysis module, which is used to obtain the optimal coefficient θ based on the deterministic inverse analysis method of multi-objective optimization optimal , and at the same time, obtain the posterior information of the random coefficient θ and the coefficient θ corresponding to the maximum probability density based on the probabilistic inverse analysis method max,post ; Soil erosion parameter determination module, which is used to obtain the calibrated change curve of soil erosion parameters and the corresponding landslide dam breach simulation results according to θ optimal and θ max,post ​ 7. The device for calibrating the soil erosion parameters of a landslide dam using the back-analysis method according to claim 6, characterized in that The best trend component function determination module is specifically used for: Construct a decision matrix based on the alternative matrix and judgment indicators: Among them, A = [A1, A2, …, A i , …, A u T represents the alternative matrix, where u is the number of alternatives; C = [C1, C2, …, C j , …, C v is the judgment index, and v is the number of judgment criteria; x ij is the value corresponding to each alternative under each judgment index; the judgment index is the modified R 2 ;​ Construct a weighted normalized decision matrix: Among them, v ij is the weighted and normalized x ij ; w j is an element of the weight matrix w, representing the weight of each judgment index; Calculating the positive ideal solution PIS and the negative ideal solution NIS: wherein, if the j-th criterion is beneficial, then otherwise, Calculating the distances from each alternative to the positive and negative ideal solutions: wherein, is the distance from the i-th solution to the positive ideal solution, is the distance from the i-th solution to the negative ideal solution; Calculate the relative distance R between the positive and negative ideal solutions for each alternative i and the normalized score S i : Determine the alternative solution with the maximum normalized score as the optimal trend component function.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When executed, the processor implements the steps in the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method as described in any one of claims 1-5.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the computer program implements the steps in the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method as described in any one of claims 1-5.

10. A computer program product comprising a computer program / instructions, characterized in that, When executed by the processor, the computer program / instructions implement the steps in the method for calibrating the erosion parameters of the landslide dam soil body using the back-analysis method as described in any one of claims 1-5.

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