Hydropower high slope response updating method and device based on constrained Bayesian reasoning

Abstract

The invention relates to the technical field of slope engineering response updating, in particular to a hydropower high slope response updating method and device based on constrained Bayesian reasoning, and the method comprises the steps: determining the prior distribution of key material parameters in an actual slope of a hydropower station, and constructing a monitoring data likelihood function through the slope monitoring data of the actual slope; constructing a constraint likelihood function according to the target constraint condition of the key material parameter; and combining the prior distribution, the monitoring data likelihood function and the constraint likelihood function by using the Bayesian theory to determine the posterior distribution of the key material parameters, thereby determining the equivalent sample of the key material parameters by using the slope response agent model and the target sampling algorithm to update the slope response of the hydropower station. And obtaining a hydropower high slope response updating result based on constrained Bayesian reasoning. Therefore, the problem that the uncertainty of geotechnical material parameters cannot be effectively reduced when the types and the number of monitoring data are limited by traditional Bayesian inference in the related technology is solved.

Description

Technical Field

[0001] The present application relates to the technical field of slope engineering response updating, and in particular to a method and device for updating the response of a hydropower high slope based on constrained Bayesian reasoning. Background Art

[0002] With the development of monitoring technology and the advent of automated monitoring instruments, in addition to limited measured data, slope engineering practice now also provides monitoring data, such as ground deformation, pile top displacement, and anchor stress. Leveraging monitoring data to compensate for the scarcity of measured data reduces the uncertainty of geotechnical parameters and improves the accuracy of slope response calculations. To address this, various parameter inversion methods have been developed, such as neural networks, ensemble Kalman filtering, and Bayesian inference.

[0003] However, in related technologies, traditional Bayesian reasoning mainly inverts geotechnical material parameters by fusing monitoring data. For most geotechnical engineering monitoring data, the types and quantities are still very limited, and collection is time-consuming and labor-intensive. Therefore, traditional Bayesian reasoning cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain accurate slope responses, which urgently needs to be solved. Summary of the Invention

[0004] This application is based on the following problems and understandings made by the inventors:

[0005] The rivers of southwest China, shaped by their dramatic elevation differences, possess abundant hydropower resources. In recent years, hydropower development has flourished in the region, with the construction of numerous high dams. During construction and operation, in addition to the stability of the dam itself, the stability of the reservoir slopes is a key factor in controlling overall project safety. Reservoir slope instability can trigger a cascade of landslides, surges, dam failures, and floods, posing a serious threat to life and property. Therefore, accurate slope response calculations are crucial. However, due to the complex geological conditions and frequent geological activity in southwest China, accurate slope response calculations are a challenging task.

[0006] Furthermore, as a natural material, geotechnical materials exhibit significant uncertainty due to stress histories and physical and chemical interactions. Furthermore, in-situ and laboratory experiments are complex and time-consuming, and measured data on geotechnical parameters for specific sites is often scarce. Obviously, geotechnical parameter values estimated from a small amount of measured data do not represent their true values, leading to significant errors in slope response calculations using numerical simulations. Reducing the uncertainty of geotechnical parameters is crucial to improving the accuracy of slope response calculations.

[0007] With the development of monitoring technology and the birth of automated monitoring instruments, in addition to limited measured data, slope engineering practice also has monitoring data, such as ground deformation, pile top displacement, and anchor stress. Monitoring data is used to make up for the scarcity of measured data, thereby reducing the uncertainty of geotechnical parameters and improving the accuracy of slope response calculation. In view of this, a variety of parameter inversion methods have been developed to reduce parameter uncertainty, such as neural networks, ensemble Kalman filtering, and Bayesian reasoning. Bayesian reasoning has at least the following two advantages: (1) It integrates prior information and monitoring data into the posterior distribution to provide a reliable probability distribution of geotechnical parameters for slope response updates; (2) It can not only explicitly model the uncertainty of geotechnical parameters, but also use monitoring data to reduce the uncertainty of geotechnical parameters, which makes Bayesian reasoning widely used in geotechnical engineering parameter probability inversion.

[0008] However, the complexity and particularity of geotechnical engineering lead to some deficiencies in traditional Bayesian reasoning: (1) Traditional Bayesian reasoning mainly inverts geotechnical material parameters by integrating monitoring data. Although monitoring technology has made great progress in recent years, the types and quantities of monitoring data are still very limited in most geotechnical engineering practices, which makes Bayesian reasoning not very effective in reducing the uncertainty of geotechnical material parameters; (2) Most geotechnical parameter inversion problems are ill-posed problems, and some non-physical solutions and incomprehensible solutions may be obtained through inversion, which urgently needs to be improved.

[0009] The present application provides a method and device for updating the response of a hydropower high slope based on constrained Bayesian reasoning to solve the problem in related technologies that traditional Bayesian reasoning mainly inverts geotechnical material parameters by fusing monitoring data. When the types and amount of monitoring data are limited, traditional Bayesian reasoning cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain accurate slope responses. The first aspect of the present application provides a method for updating the response of a high hydropower slope based on constrained Bayesian reasoning, comprising the following steps: determining the prior distribution of target key material parameters in the actual slope of a target hydropower station, and constructing a monitoring data likelihood function using the slope monitoring data of the actual slope; determining target constraints for the target key material parameters based on the target physical meaning of the geotechnical parameters in the actual slope, and constructing a target constraint likelihood function based on the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints according to the nature of the constraints, and into soft constraints and hard constraints according to the degree of constraints; combining the prior distribution, the monitoring data likelihood function and the target constraint likelihood function using Bayesian theory to determine the posterior distribution of the target key material parameters, and based on the posterior distribution, determining equivalent samples of the target key material parameters using a pre-constructed slope response proxy model and a target sampling algorithm, and using the equivalent samples to update the slope response of the target hydropower station to obtain a hydropower high slope response update result based on constrained Bayesian reasoning.

[0010] Optionally, in one embodiment of the present application, the constructing of the monitoring data likelihood function using the slope monitoring data of the actual slope includes: obtaining the slope monitoring data of the actual slope and determining the measurement error of the slope monitoring data; and constructing the monitoring data likelihood function based on the slope monitoring data and the measurement error.

[0011] Optionally, in one embodiment of the present application, the determining of the equivalent samples of the key material parameters using a pre-built slope response proxy model and a target sampling algorithm includes: based on the posterior distribution, determining the target posterior samples using the slope response proxy model and the target Markov chain Monte Carlo simulation MCMC algorithm; and determining the equivalent samples of the key material parameters based on the target posterior samples.

[0012] Optionally, in one embodiment of the present application, the target constraint likelihood function includes an equality soft constraint likelihood function, an inequality soft constraint likelihood function, and an inequality hard constraint likelihood function;

[0013] Among them, the equality soft constraint likelihood function is represented as:

[0014]

[0015] in, g l (θ)=0(l=1,2,...,N c ) is the lth constraint condition of θ; N c is the total number of constraints; σ l It is g l standard deviation of (θ);

[0016] The inequality soft constraint likelihood function is characterized as:

[0017]

[0018] Where a1 is a normalization constant that ensures that P(g(θ)≤0|θ) integrates to 1 within the possible range of parameters;

[0019] The inequality hard constraint likelihood function is characterized as:

[0020]

[0021] Among them, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ), a and b are the left and right boundaries of g(θ), and Φ is the standard normal cumulative distribution function.

[0022] Optionally, in one embodiment of the present application, the posterior distribution is expressed as:

[0023] P(θ|Z,G(θ))=a2P(Z|θ)P(G(θ)|θ)P(θ)

[0024] where P(θ) is the prior distribution, P(Z|θ) is the likelihood function of the monitored data, P(G(θ)|θ) is the constrained likelihood function, and a2 is a normalization constant that ensures that P(θ|Z,G(θ)) integrates to 1 over the possible range of parameters.

[0025] Optionally, in one embodiment of the present application, the hydropower high slope response update result is expressed as:

[0026]

[0027] Where Θ represents the equivalent sample and N represents the number of equivalent samples.

[0028] A second aspect of the present application provides a hydropower high slope response update device based on constrained Bayesian reasoning, including: a determination module for determining the prior distribution of target key material parameters in the actual slope of a target hydropower station, and constructing a monitoring data likelihood function using the slope monitoring data of the actual slope; a construction module for determining the target constraint conditions of the target key material parameters based on the target physical meaning of the geotechnical parameters in the actual slope, so as to construct a target constraint likelihood function based on the target constraint conditions, wherein the target constraint conditions are divided into equality constraints and inequality constraints according to the constraint properties, and are divided into soft constraints and hard constraints according to the constraint degree; an update module for combining the prior distribution, the monitoring data likelihood function and the target constraint likelihood function to determine the posterior distribution of the target key material parameters, and based on the posterior distribution, using a pre-constructed slope response proxy model and a target sampling algorithm to determine equivalent samples of the target key material parameters, and using the equivalent samples to update the slope response of the target hydropower station to obtain a hydropower high slope response update result based on constrained Bayesian reasoning.

[0029] Optionally, in one embodiment of the present application, the determination module includes: an acquisition unit for acquiring slope monitoring data of the actual slope and determining the measurement error of the slope monitoring data; and a construction unit for constructing the monitoring data likelihood function based on the slope monitoring data and the measurement error.

[0030] Optionally, in one embodiment of the present application, the update module includes: a first determination unit, used to determine the target posterior sample based on the posterior distribution using the slope response proxy model and the target Markov chain Monte Carlo simulation MCMC algorithm; a second determination unit, used to determine the equivalent sample of the key material parameter based on the target posterior sample.

[0031] Optionally, in one embodiment of the present application, the target constraint likelihood function includes an equality soft constraint likelihood function, an inequality soft constraint likelihood function, and an inequality hard constraint likelihood function;

[0032] Among them, the equality soft constraint likelihood function is represented as:

[0033]

[0034] in, g l (θ)=0(l=1,2,...,N c ) is the lth constraint condition of θ; N c is the total number of constraints; σ l It is g l standard deviation of (θ);

[0035] The inequality soft constraint likelihood function is characterized as:

[0036]

[0037] Where a1 is a normalization constant that ensures that P(g(θ)≤0|θ) integrates to 1 within the possible range of parameters;

[0038] The inequality hard constraint likelihood function is characterized as:

[0039]

[0040] Among them, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ), a and b are the left and right boundaries of g(θ), and Φ is the standard normal cumulative distribution function.

[0041] Optionally, in one embodiment of the present application, the posterior distribution is expressed as:

[0042] P(θ|Z,G(θ))=a2P(Z|θ)P(G(θ)|θ)P(θ)

[0043] where P(θ) is the prior distribution, P(Z|θ) is the likelihood function of the monitored data, P(G(θ)|θ) is the constrained likelihood function, and a2 is a normalization constant that ensures that P(θ|Z,G(θ)) integrates to 1 over the possible range of parameters.

[0044] Optionally, in one embodiment of the present application, the hydropower high slope response update result is expressed as:

[0045]

[0046] Where Θ represents the equivalent sample and N represents the number of equivalent samples.

[0047] A third aspect of the present application provides an electronic device, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the hydropower high slope response update method based on constrained Bayesian reasoning as described in the above embodiment.

[0048] A fourth aspect of the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for updating the high-slope response of hydropower stations based on constrained Bayesian reasoning.

[0049] The fifth aspect of the present application provides a computer program product, including a computer program, which, when executed, is used to implement the above-mentioned hydropower high slope response update method based on constrained Bayesian reasoning.

[0050] The embodiment of the present application can determine the prior distribution of key material parameters in the actual slope of the hydropower station, and construct a monitoring data likelihood function and a constrained likelihood function. Then, the prior distribution, the monitoring data likelihood function and the constrained likelihood function are combined using Bayesian theory to determine the posterior distribution of the key material parameters, thereby determining the equivalent samples of the key material parameters to update the slope response of the hydropower station, obtain the updated result of the hydropower high slope response based on constrained Bayesian reasoning, effectively reduce the uncertainty of geotechnical material parameters, and obtain accurate slope response. Thus, it solves the problem in the related art that when the types and quantity of monitoring data are limited, traditional Bayesian reasoning cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain accurate slope response.

[0051] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0053] Figure 1 A flowchart of a method for updating a hydropower high slope response based on constrained Bayesian reasoning according to an embodiment of the present application;

[0054] Figure 2 A logic diagram for updating the response of a hydropower high slope based on constrained Bayesian reasoning according to a specific embodiment of the present application;

[0055] Figure 3 This is a schematic diagram of a finite element model of the Niansheng Reclamation Slope of the Liyuan Hydropower Station, a specific embodiment of the present application;

[0056] Figure 4 This is a relationship diagram between the slope angle and friction angle of 12 engineering landslides in a specific embodiment of this application;

[0057] Figure 5 This is a diagram of the constraint likelihood function of the anchoring force of the anchor plate according to a specific embodiment of the present application.

[0058] Figure 6 A comparison chart of response values calculated by a proxy model and a finite element model according to a specific embodiment of the present application;

[0059] Figure 7 This is a posterior probability distribution diagram of parameters after the first parameter inversion of a specific embodiment of the present application;

[0060] Figure 8This is a schematic diagram of the response PDF of the anchoring force after the second update of a specific embodiment of the present application;

[0061] Figure 9 This is a schematic structural diagram of a hydropower high slope response updating device based on constrained Bayesian reasoning according to an embodiment of the present application;

[0062] Figure 10 A schematic diagram of the structure of an electronic device provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0063] The following describes in detail embodiments of the present application, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0064] The following describes a method and device for updating the response of a high hydropower slope based on constrained Bayesian reasoning in accordance with an embodiment of the present application with reference to the accompanying drawings. In view of the problem that, in the above-mentioned background technology center, traditional Bayesian reasoning mainly inverts geotechnical material parameters by fusing monitoring data, when the types and quantities of monitoring data are limited, traditional Bayesian reasoning cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain accurate slope responses, the present application provides a method for updating the response of a high hydropower slope based on constrained Bayesian reasoning, in which the prior distribution of key material parameters in the actual slope of the hydropower station can be determined, and a monitoring data likelihood function and a constrained likelihood function can be constructed. Then, the prior distribution, the monitoring data likelihood function and the constrained likelihood function are combined using Bayesian theory to determine the posterior distribution of the key material parameters, thereby determining an equivalent sample of the key material parameters to update the slope response of the hydropower station, obtain an updated result of the response of a high hydropower slope based on constrained Bayesian reasoning, effectively reduce the uncertainty of the geotechnical material parameters, and obtain an accurate slope response. This solves the problem in related technologies that traditional Bayesian reasoning cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain accurate slope responses due to the limited types and quantities of monitoring data.

[0065] Specifically, Figure 1 A flowchart of a method for updating a hydropower high slope response based on constrained Bayesian reasoning provided in an embodiment of the present application.

[0066] like Figure 1 As shown in FIG, the hydropower high slope response updating method based on constrained Bayesian reasoning includes the following steps:

[0067] In step S101 , the prior distribution of target key material parameters in the actual slope of the target hydropower station is determined, and the slope monitoring data of the actual slope is used to construct a monitoring data likelihood function.

[0068] In the embodiment of the present application, the target hydropower station is the hydropower station currently being monitored; the target key material parameters are rock and soil parameters that are difficult to measure or play a major role in slope stability and deformation.

[0069] It can be understood that the embodiment of the present application can first select rock and soil parameters that are difficult to measure or play a major role in slope stability and deformation as key material parameters θ for the actual slope of the hydropower station; then, the key material parameter θ is regarded as a random variable, and the remaining rock and soil parameters are regarded as constants; finally, prior information of the key material parameter θ can be collected based on in-situ experiments, laboratory experiments, relevant literature and engineering experience, so as to determine the prior distribution P(θ) of the key material parameter θ. In addition, the embodiment of the present application can also collect slope monitoring data according to a specific project monitoring plan to construct a likelihood function of the monitoring data, thereby effectively improving the accuracy of slope behavior prediction.

[0070] Optionally, in one embodiment of the present application, a monitoring data likelihood function is constructed using slope monitoring data of an actual slope, including: obtaining slope monitoring data of the actual slope and determining a measurement error of the slope monitoring data; and constructing a monitoring data likelihood function based on the slope monitoring data and the measurement error.

[0071] For example, the embodiment of the present application can collect monitoring data Z according to a specific project monitoring plan, such as various slope response data such as ground deformation, pile top displacement and anchoring force. Then, the measurement error can be given according to the accuracy of the monitoring instrument and the level of monitoring technology. Finally, the monitoring data likelihood function P(Z|θ) is constructed based on the monitoring data Z and the measurement error, which effectively improves the accuracy of the data.

[0072] Among them, the monitoring data likelihood function is expressed as:

[0073]

[0074] Where Z=[Y1,...,Y j ,...,Y m ] T Indicates multiple types of monitoring data; m indicates the number of monitoring data types; Y j represents the jth monitoring data; H j (θ) represents the relationship with Y j The response value of the corresponding numerical model; ε j represents the measurement error of the j-th type of monitoring data, where ε j =Y j -H j(θ); Σ εj Represents the covariance matrix of measurement errors.

[0075] In step S102, based on the target physical meaning of the geotechnical parameters in the actual slope, the target constraints of the target key material parameters are determined to construct a target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints according to the nature of the constraints, and are divided into soft constraints and hard constraints according to the degree of constraints.

[0076] In the embodiment of the present application, the target physical meaning may be the theoretical formula of the physical and mechanical properties of the rock and soil parameters, the relationship between the empirical parameters, and the upper and lower limits of the rock and soil parameters.

[0077] It can be understood that the embodiments of the present application can collect the possible constraints of various key material parameters under specific working conditions based on the physical meaning of the rock and soil parameters, such as the theoretical formulas of the physical and mechanical properties of the rock and soil parameters, the relationship between empirical parameters, and the upper and lower limits of the rock and soil parameters, etc., and then construct the constrained likelihood function P(G(θ)|θ) based on the collected constraints G(θ), which effectively improves the accuracy of slope response update.

[0078] In the embodiment of the present application, the constraints can be divided into equality constraints and inequality constraints according to their nature; they can be divided into soft constraints and hard constraints according to the degree of constraint; the target constraint likelihood function includes the equality soft constraint likelihood function, the inequality soft constraint likelihood function and the inequality hard constraint likelihood function;

[0079] Among them, the equality soft constraint likelihood function is represented as:

[0080]

[0081] in, g l (θ)=0(l=1,2,...,N c ) is the lth constraint condition of θ; N c is the total number of constraints; σ l It is g l The standard deviation of (θ).

[0082] The likelihood function of the inequality soft constraint (taking g(θ)≤0 as an example) is characterized as follows:

[0083]

[0084] Where a1 is a normalization constant that ensures that P(g(θ)≤0|θ) integrates to 1 within the possible range of parameters; g(θ) is a constraint on θ. It should be noted that when g(θ)≥0, simply change “max” to “min” in the formula.

[0085] The likelihood function of the inequality hard constraint (taking g(θ)≤0 as an example) is characterized as follows:

[0086]

[0087] Among them, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ), respectively; a and b are the left and right boundaries of g(θ), respectively; when g(θ)≤0, a=-inf, b=0; when g(θ)≥0, a=0, b=inf; Φ is the standard normal cumulative distribution function.

[0088] In step S103, the prior distribution, the monitoring data likelihood function and the target constraint likelihood function are combined using Bayesian theory to determine the posterior distribution of the target key material parameters. Based on the posterior distribution, the pre-built slope response proxy model and the target sampling algorithm are used to determine the equivalent samples of the target key material parameters, and the equivalent samples are used to update the slope response of the target hydropower station to obtain the updated result of the hydropower high slope response based on constrained Bayesian reasoning.

[0089] In an embodiment of the present application, a method for constructing a proxy model of slope response is as follows: first, Latin hypercube is used to generate 1000 groups of samples from the prior distribution of the random variable θ, where the ratio of training samples to test samples is 7:3; then, the finite element method is used to calculate the slope responses corresponding to the training and test samples; finally, the LightGBM algorithm is used to train the proxy model of slope response to approximate the physical numerical model of slope response, so as to construct a proxy model of slope response.

[0090] In one embodiment of the present application, the slope response proxy model is expressed as:

[0091] H j (θ)=LM j (θ)

[0092] Among them, LM(θ) represents the proxy model constructed for H(θ) through LightGBM with θ as input.

[0093] It can be understood that the embodiment of the present application adopts Bayesian theory to combine the prior distribution P(θ), the monitoring data likelihood function P(Z|θ) and the constrained likelihood function P(G(θ)|θ) in the above steps to obtain the posterior distribution P(θ|Z,G(θ)) of the key material parameter θ, and based on the posterior distribution P(θ|Z,G(θ)), the slope response proxy model and the sampling algorithm are used to extract the equivalent sample Θ of the key material parameter θ, and the equivalent sample Θ is used to update the slope response of the hydropower station to obtain the updated result of the hydropower high slope response based on constrained Bayesian reasoning, which effectively reduces the uncertainty of the geotechnical material parameters and obtains accurate slope response.

[0094] Among them, the posterior distribution P(θ|Z,G(θ)) is represented as:

[0095] P(θ|Z,G(θ))=a2P(Z|θ)P(G(θ)|θ)P(θ)

[0096] where a2 is a normalization constant that ensures that P(θ|Z,G(θ)) integrates to 1 over the possible range of parameters.

[0097] Optionally, in one embodiment of the present application, equivalent samples of key material parameters are determined using a pre-constructed slope response proxy model and a target sampling algorithm, including: based on the posterior distribution, determining target posterior samples using the slope response proxy model and the target Markov chain Monte Carlo simulation MCMC algorithm; and determining equivalent samples of key material parameters based on the target posterior samples.

[0098] In the actual implementation process, the embodiment of the present application can extract equivalent samples Θ of key material parameters based on the slope response proxy model and MCMC simulation. Specifically, the slope response proxy model is first used to quickly calculate the posterior distribution probability, and then an improved MCMC simulation method such as the DREAM algorithm is used to generate 2N posterior samples, and the last 50% of the samples are taken as the posterior distribution equivalent samples Θ = [θ1, ..., θ k ,...,θ N ] T Finally, the posterior probability density function (PDF) of the key material parameters is determined based on N equivalent samples, where the determination of N needs to meet the requirements of Markov chain stability and high precision and low variability of slope response update.

[0099] Furthermore, the average value of the slope response calculated from N equivalent samples can be taken as the updated hydropower high slope response H(Θ), that is:

[0100]

[0101] Where Θ represents the equivalent sample and N represents the number of equivalent samples.

[0102] Therefore, the embodiments of the present application can effectively solve the problem that traditional Bayesian reasoning only uses monitoring data. Under the condition of scarce monitoring data, the effect of reducing parameter uncertainty through parameter probability inversion is not significant, which leads to large errors in slope response calculation.

[0103] The constrained Bayesian reasoning in the embodiments of this application integrates known constraints, such as theoretical formulas for the physical and mechanical properties of geotechnical parameters, empirical parameter relationships, and upper and lower limits of geotechnical material parameters, into traditional Bayesian updating as additional constraints. Compared with traditional Bayesian reasoning, the posterior probability density function of key material parameters obtained through parameter inversion using constrained Bayesian reasoning has less uncertainty, resulting in more accurate slope responses in subsequent updates. Furthermore, constrained Bayesian reasoning incorporates additional constraints into the parameter probability inversion process, thereby avoiding some unphysical and unreasonable solutions.

[0104] For example, if Figure 2 As shown, the working principle of the embodiment of the present application is described in detail below with a specific embodiment.

[0105] The Liyuan Hydropower Station is located at the junction of Yulong County (right bank) and Shangri-La County (left bank) in Yunnan Province, China. The station is the third of eight cascade hydropower stations in the middle reaches of the Jinsha River, adjacent to the Liangjiaren Hydropower Station upstream and the Ahai Hydropower Station downstream. The Niansheng Reclamation Slope is located in a wide, gentle gully in front of the reservoir on the right bank of the Liyuan Hydropower Station, at an altitude of between 1,500 and 1,850 meters. It is a Quaternary deposit composed of a mixture of alluvial, flood deposits, slope deposits, colluvial deposits, and landslide deposits, with a total volume of approximately 2,000 × 10 4 m 3 The underlying bedrock of the accumulation body is mainly basaltic eruptive rocks of the Dongba Formation (P2d) of the Upper Permian System.

[0106] Under natural conditions, the slope of Nianshengken has no obvious signs of deformation except for a slight collapse at the front edge caused by river erosion. However, based on the data from 25 boreholes, it is inferred that the accumulation body has undergone slip deformation toward the Jinsha River during or after its formation. There is a slip deformation zone composed of multiple levels of potential slip surfaces inside and at the bottom of the accumulation body. The lower interface of this zone is the soil-rock interface between the residual layer and the strongly weathered layer, with a depth of about 50m to 68m and an inclination of 10° to 18°. The slope of Nianshengken consists of two layers of soil and three layers of rock, namely, from top to bottom, the accumulation body, the residual layer, the strongly weathered layer, the moderately weathered layer and the slightly weathered layer, as shown in the following example. Figure 3 shown.

[0107] It can be seen that the slope stability is mainly controlled by the two soil layers, so the material parameters of the three rock layers are considered constants. For the two soil layers, the bulk density (γ) and Poisson's ratio (ν) are considered constants because of their small variability. On the other hand, the elastic modulus (E) and shear strength parameters (cohesion c and friction angle ) has a large variability, so it is regarded as a random variable. Therefore, a total of 6 material parameters are regarded as random variables, namely Among them, the subscripts 1 and 2 represent the accumulation body and residual layer respectively. The specific values of the parameters are shown in Table 1. Table 1 is the prior value table of material parameters for two layers of soil and three layers of rock. The specific Table 1 is as follows:

[0108] Table 1

[0109]

[0110] In addition, in the embodiment of the present application, it is assumed that the six random variables all obey the lognormal distribution, thereby determining Figure 2 Prior distributions of key material parameters in .

[0111] Then, under the excavation conditions: the slope of Niansheng Reclamation began to deform locally and gradually developed into overall deformation, and the deformation rate tended to increase. There are three main factors causing the slope deformation: First, the excavation of the diversion channel formed a deep ditch with a length of 350 meters and a bottom width of 90 meters in the north-south direction at the front edge of the slope, which caused the anti-sliding force that the slope could provide to be significantly reduced. (2) The excavation of the access road and the construction access road seriously damaged the integrity of the accumulation body. (3) The accumulation of waste slag increased the sliding force of the slope, and a total of 45×10 4 m 3 Waste is accumulated on the slope. When the slope is about to fail, the safety factor FS can be used to be approximately equal to 1 for parameter inversion. Therefore, it is assumed here that FS obeys the mean μ FS =1, coefficient of variation COV FS = 0.05 is used as the likelihood function of the monitoring data of the excavation condition for the first parameter inversion.

[0112] Under the reinforcement condition: It is obvious that if the reinforcement is not carried out, the slope of Nianshengken will become unstable, so the slope is reinforced. The reinforcement plan is: two rows of anti-slide piles are buried in the middle and lower part of the slope of Nianshengken and anchor plates are set at three locations on the slope of Nianshengken for reinforcement. The anchor cables are 2000kN grade pressure-distributed prestressed anchor cables. The specific reinforcement locations are shown in Figure 3 .

[0113] After the Nianshengken slope reinforcement project was completed, relevant departments conducted comprehensive monitoring of the slope, including ground deformation, pile top displacement, and anchorage force. The selected two-dimensional profile shows three ground deformation monitoring points (numbered, from bottom to top, NSKTP18, NSKTP14, and NSKIN01), two pile top displacement monitoring points (numbered Z48TP01 and ZS23TP01), and three anchorage force monitoring points (numbered NSKPR36, NSKPR06, and NSKPR02), for a total of eight monitoring points. The monitoring data for each monitoring point are shown in the third column of Table 2. It can be assumed that the ground deformation monitoring data follow a normal distribution with a coefficient of variation (COV) of 0.15, while the pile top displacement and anchorage force monitoring data follow a normal distribution with a coefficient of variation (COV) of 0.1. This constructs the likelihood functions for the three monitoring data under the reinforcement conditions.

[0114] Secondly, the relevant technical personnel of Yunnan Provincial Geological Engineering conducted a regression analysis on the shear strength parameters of the sliding zone soil and the corresponding slope angles of 12 engineering landslides in Yunnan, China, and found that the friction angle There is a linear relationship between it and the slope angle (α) (correlation coefficient ρ = 0.986):

[0115]

[0116] in, Figure 4 The relationship between the sliding zone soil slope angle and friction angle of the 12 engineering landslides is given. Combined with the slope of this project, the above formula can be regarded as The soft constraint of the equation is incorporated into the parameter inversion under the excavation condition. Since the inclination of the sliding deformation zone of the Nianshengken slope is between 10° and 18°, the average value of 14° is taken and substituted into the formula to obtain Therefore, assuming The normal distribution with mean μ = 12.45° and standard deviation σ = 2° is used as the constraint likelihood function of the excavation condition.

[0117] In the reinforcement condition, since the anchor cables used in the anchor plates are all 2000kN grade and can operate stably after reinforcement, the anchoring force of the anchor cables (NSKPR36, NSKPR06 and NSKPR02) should not exceed 2000kN during the inversion process. However, since structural design generally includes a certain safety reserve, it is assumed that the anchoring force T of the anchor cables follows σ T =100kN inequality soft constraint (i.e. T≤2000kN, σ T =100kN). Set T≤2000kN and σ T = 100kN Substituting into the inequality soft constraint, we can get the constraint likelihood function under the reinforcement condition, see Figure 5 .

[0118] Again, as Figure 2As shown in Figure 2, the Bayesian theory is used to combine the prior distribution P(θ) of rock and soil parameters, the likelihood function P(Z|θ) of monitoring data, and the constraint likelihood function P(G(θ)|θ) to obtain the posterior distribution P(θ|Z,G(θ)). The specific expression is:

[0119] P(θ|Z,G(θ))=a2P(Z|θ)P(G(θ)|θ)P(θ)

[0120] where a2 is a normalization constant that ensures that P(θ|Z,G(θ)) integrates to 1 over the possible range of parameters.

[0121] Since the slope can be divided into three working conditions: natural, excavation and reinforcement, and the monitoring data and constraints of the excavation and reinforcement conditions were collected, two constrained Bayesian inferences (two parameter inversions) were performed, and the slope response was updated twice accordingly. According to the strength reduction method, FS has nothing to do with the elastic modulus E, so the first parameter inversion only involves four random variables. The second parameter inversion involves all random variables

[0122] Among them, LightGBM is used to establish a proxy model of the response values of 8 monitoring points. The accuracy of the proxy model is usually related to the number and quality of training samples. In this embodiment of the application, Latin hypercube sampling is first used to generate 1000 groups of samples from the prior distribution of the random variable θ, where the ratio of training samples to test samples is 7:3. Then, the finite element method is used to calculate the slope response corresponding to the training and test samples. Finally, the LightGBM algorithm is used to train the proxy model of the slope response. Among them, as Figure 6 As shown, the finite element model corresponding to 300 test samples and the calculated results of the LightGBM proxy model are shown. Figure 6 (a) Ground deformation, Figure 6 (b) Pile top displacement and Figure 6 (c) Response values of the eight monitoring points in the anchoring force. Obviously, the coefficient of determination R of all proxy models is 2 Both are greater than 0.95. It can be seen that the proxy model trained by LightGBM has good performance in predicting the response of slope monitoring points.

[0123] The embodiment of the present application can first use the slope response proxy model to quickly calculate the posterior distribution probability, then use the DREAM algorithm to generate 2N posterior samples, and take the last 50% of the samples as the posterior distribution equivalent samples Θ = [θ1, ..., θ k ,...,θ N ] TFinally, the posterior probability density function (PDF) of the key material parameters is determined based on N equivalent samples. The posterior PDF of the parameters obtained by the first inversion is as follows: Figure 7 shown.

[0124] It can be seen that after the first parameter inversion, c1, The posterior distribution of and c2 is not much different from the prior distribution, while The uncertainty of the posterior distribution of is significantly reduced. This is because It plays a decisive role in the stability and response of the slope, and its sensitivity is significantly greater than c1. and c2. It can be seen that the use of traditional Bayesian reasoning and constrained Bayesian reasoning for parameter inversion can significantly reduce the uncertainty of sensitive parameters. In addition, the The COV of the posterior distribution is 0.103, while the COV obtained using traditional Bayesian inference is 0.180. This is because constrained Bayesian inference makes full use of It can be seen that compared with traditional Bayesian reasoning, constrained Bayesian reasoning has significant advantages in reducing parameter uncertainty.

[0125] Finally, the average value of the slope response calculated by N equivalent samples is taken as the updated slope response H(Θ), which is calculated as follows:

[0126]

[0127] Table 2 is a comparison table of the prior response values and the first updated response values of the eight monitoring points. The specific table 2 is as follows:

[0128] Table 2

[0129]

[0130] Table 2 compares the prior response values for the eight monitoring points from the first parameter inversion with the updated response values from the first update. It can be seen that the average error of the response values for the eight monitoring points obtained using the prior distribution is as high as 43.7%, while the average errors obtained using traditional Bayesian reasoning and constrained Bayesian reasoning are 19.8% and 14.2%, respectively. While traditional Bayesian reasoning improves the accuracy of slope response assessment, constrained Bayesian reasoning further improves accuracy by incorporating additional constraints. Thus, constrained Bayesian reasoning outperforms traditional Bayesian reasoning in slope response assessment.

[0131] like Figure 8Figure 2 shows the response PDFs of the anchoring forces of the three anchor plates obtained after the second update. It can be seen that a large portion of the anchoring forces obtained using traditional Bayesian inference are significantly greater than 2000 kN or even 3000 kN, which is inconsistent with the ultimate anchoring force of 2000 kN for the anchor cable. However, constrained Bayesian inference effectively filters out these unphysical values after adding the ultimate anchoring force constraint. This shows that constrained Bayesian inference can avoid these unreasonable inversion results.

[0132] Therefore, the constrained Bayesian reasoning (CBR) in the embodiments of this application integrates some known constraints as additional constraints into traditional Bayesian reasoning to form constrained Bayesian reasoning. Compared with traditional Bayesian reasoning, the posterior probability density function of key material parameters obtained through parameter inversion using constrained Bayesian reasoning has less uncertainty, thereby obtaining more accurate slope responses in subsequent updates. Furthermore, constrained Bayesian reasoning also incorporates additional constraints during the parameter probability inversion process, thus avoiding some unphysical and unreasonable solutions.

[0133] According to the method for updating the response of a high hydropower slope based on constrained Bayesian reasoning proposed in the embodiment of the present application, the prior distribution of key material parameters in the actual slope of the hydropower station can be determined, and a monitoring data likelihood function and a constrained likelihood function can be constructed. Then, the prior distribution, the monitoring data likelihood function and the constrained likelihood function are combined using Bayesian theory to determine the posterior distribution of the key material parameters, thereby determining an equivalent sample of the key material parameters to update the slope response of the hydropower station, obtain the updated result of the response of the high hydropower slope based on constrained Bayesian reasoning, effectively reduce the uncertainty of geotechnical material parameters, and obtain an accurate slope response. Thus, the problem that the traditional Bayesian in the related art cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain an accurate slope response due to the limited types and quantity of monitoring data is solved.

[0134] Next, a hydropower high slope response updating device based on constrained Bayesian reasoning proposed in accordance with an embodiment of the present application will be described with reference to the accompanying drawings.

[0135] Figure 9 It is a block diagram of a hydropower high slope response updating device based on constrained Bayesian reasoning in an embodiment of the present application.

[0136] like Figure 9 As shown, the hydropower high slope response updating device 10 based on constrained Bayesian reasoning includes: a determination module 100, a construction module 200 and an update module 300.

[0137] Specifically, the determination module 100 is used to determine the prior distribution of target key material parameters in the actual slope of the target hydropower station, and to construct a monitoring data likelihood function using the slope monitoring data of the actual slope.

[0138] Construction module 200 is used to determine the target constraints of the target key material parameters based on the target physical meaning of the geotechnical parameters in the actual slope, so as to construct the target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints according to the constraint properties, and are divided into soft constraints and hard constraints according to the constraint degree.

[0139] The updating module 300 is used to combine the prior distribution, the monitoring data likelihood function and the target constraint likelihood function to determine the posterior distribution of the target key material parameters, and based on the posterior distribution, use the pre-built slope response proxy model and the target sampling algorithm to determine the equivalent samples of the target key material parameters, and use the equivalent samples to update the slope response of the target hydropower station to obtain the updated result of the hydropower high slope response based on constrained Bayesian reasoning.

[0140] Optionally, in one embodiment of the present application, the determination module 100 includes: an acquisition unit and a construction unit.

[0141] The acquisition unit is used to acquire slope monitoring data of an actual slope and determine a measurement error of the slope monitoring data.

[0142] The construction unit is used to construct a monitoring data likelihood function based on the slope monitoring data and measurement errors.

[0143] Optionally, in one embodiment of the present application, the updating module 300 includes: a first determining unit and a second determining unit.

[0144] The first determination unit is configured to determine a target posterior sample based on the posterior distribution by using the slope response proxy model and the target Markov Chain Monte Carlo simulation MCMC algorithm.

[0145] The second determining unit is used to determine an equivalent sample of the key material parameter based on the target posterior sample.

[0146] Optionally, in one embodiment of the present application, the target constraint likelihood function includes an equality soft constraint likelihood function, an inequality soft constraint likelihood function, and an inequality hard constraint likelihood function;

[0147] Among them, the equality soft constraint likelihood function is represented as:

[0148]

[0149] in, g l (θ)=0(l=1,2,...,N c ) is the lth constraint condition of θ; N c is the total number of constraints; σ l It is gl standard deviation of (θ);

[0150] The inequality soft constraint likelihood function is characterized as:

[0151]

[0152] Where a1 is a normalization constant that ensures that P(g(θ)≤0|θ) integrates to 1 within the possible range of parameters;

[0153] The inequality hard constraint likelihood function is characterized as:

[0154]

[0155] Among them, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ), a and b are the left and right boundaries of g(θ), and Φ is the standard normal cumulative distribution function.

[0156] Optionally, in one embodiment of the present application, the posterior distribution is expressed as:

[0157] P(θ|Z,G(θ))=a2P(Z|θ)P(G(θ)|θ)P(θ)

[0158] where P(θ) is the prior distribution, P(Z|θ) is the likelihood function of the monitored data, P(G(θ)|θ) is the constrained likelihood function, and a2 is a normalization constant that ensures that P(θ|Z,G(θ)) integrates to 1 over the possible range of parameters.

[0159] Optionally, in one embodiment of the present application, the hydropower high slope response update result is expressed as:

[0160]

[0161] Where Θ represents the equivalent sample and N represents the number of equivalent samples.

[0162] It should be noted that the above explanation of the embodiment of the hydropower high slope response updating method based on constrained Bayesian reasoning is also applicable to the hydropower high slope response updating device based on constrained Bayesian reasoning in this embodiment, and will not be repeated here.

[0163] According to the hydropower high slope response update device based on constrained Bayesian reasoning proposed in the embodiment of the present application, the prior distribution of key material parameters in the actual slope of the hydropower station can be determined, and the monitoring data likelihood function and the constrained likelihood function can be constructed. Then, the prior distribution, the monitoring data likelihood function and the constrained likelihood function are combined using Bayesian theory to determine the posterior distribution of the key material parameters, thereby determining the equivalent samples of the key material parameters to update the slope response of the hydropower station, obtain the hydropower high slope response update result based on constrained Bayesian reasoning, effectively reduce the uncertainty of geotechnical material parameters, and obtain accurate slope response. Thus, the problem that traditional Bayesian reasoning in the related art cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain accurate slope response due to the limited types and quantity of monitoring data is solved.

[0164] Figure 10 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

[0165] A memory 1001 , a processor 1002 , and a computer program stored in the memory 1001 and executable on the processor 1002 .

[0166] When the processor 1002 executes the program, the hydropower high slope response updating method based on constrained Bayesian reasoning provided in the above embodiment is implemented.

[0167] Furthermore, the electronic device further includes:

[0168] The communication interface 1003 is used for communication between the memory 1001 and the processor 1002 .

[0169] The memory 1001 is used to store computer programs that can be run on the processor 1002 .

[0170] The memory 1001 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0171] If the memory 1001, the processor 1002, and the communication interface 1003 are implemented independently, the communication interface 1003, the memory 1001, and the processor 1002 can be connected to each other via a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 10 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0172] Optionally, in a specific implementation, if the memory 1001, the processor 1002 and the communication interface 1003 are integrated on a chip, the memory 1001, the processor 1002 and the communication interface 1003 can communicate with each other through an internal interface.

[0173] The processor 1002 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0174] This embodiment also provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the method for updating the response of a hydropower high slope based on constrained Bayesian reasoning is implemented.

[0175] This embodiment also provides a computer program product, including a computer program. When the computer program is executed, it is used to implement the above-mentioned hydropower high slope response update method based on constrained Bayesian reasoning.

[0176] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0177] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of this application, "N" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0178] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing a custom logical function or process step, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed in a different order than shown or discussed, including performing functions in a substantially simultaneous manner or in a reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application pertain.

[0179] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or N wires (electronic devices), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program can be obtained electronically by optically scanning the paper or other medium and then editing, interpreting or processing it in other suitable ways as necessary, and then storing it in a computer memory.

[0180] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, it can be implemented using any one or a combination of the following technologies known in the art: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0181] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0182] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0183] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. A method for updating the response of hydropower high slopes based on constrained Bayesian reasoning, characterized in that: The following steps are involved: Determining a priori distribution of target key material parameters in an actual slope of a target hydropower station, and constructing a monitoring data likelihood function using slope monitoring data of the actual slope; Based on the target physical meaning of the rock and soil parameters in the actual slope, target constraints of the target key material parameters are determined to construct a target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints according to the constraint nature, and are divided into soft constraints and hard constraints according to the constraint degree; The prior distribution, the monitoring data likelihood function and the target constraint likelihood function are combined using Bayesian theory to determine the posterior distribution of the target key material parameters. Based on the posterior distribution, a pre-built slope response proxy model and a target sampling algorithm are used to determine equivalent samples of the target key material parameters. The equivalent samples are used to update the slope response of the target hydropower station to obtain an updated result of the hydropower high slope response based on constrained Bayesian reasoning.

2. The method according to claim 1, characterized in that The constructing of a monitoring data likelihood function using the slope monitoring data of the actual slope includes: Obtaining slope monitoring data of the actual slope and determining a measurement error of the slope monitoring data; The monitoring data likelihood function is constructed based on the slope monitoring data and the measurement error.

3. The method according to claim 1, characterized in that The method of determining equivalent samples of the key material parameters using a pre-built slope response proxy model and a target sampling algorithm includes: Based on the posterior distribution, determining a target posterior sample using the slope response proxy model and the target Markov chain Monte Carlo simulation MCMC algorithm; Based on the target a posteriori samples, equivalent samples of the key material parameters are determined.

4. The method according to claim 1, wherein The target constraint likelihood function includes an equality soft constraint likelihood function, an inequality soft constraint likelihood function and an inequality hard constraint likelihood function; Among them, the equality soft constraint likelihood function is represented as: in, g l (θ)=0(l=1,2,...,N c ) is the lth constraint condition of θ; N c is the total number of constraints; σ l It is g l standard deviation of (θ); The inequality soft constraint likelihood function is characterized as: Where a1 is a normalization constant that ensures that P(g(θ)≤0|θ) integrates to 1 within the possible range of parameters; The inequality hard constraint likelihood function is characterized as: Among them, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ), a and b are the left and right boundaries of g(θ), and Φ is the standard normal cumulative distribution function.

5. The method according to claim 1, wherein The posterior distribution is expressed as: P(θ|Z,G(θ))=a2P(Z|θ)P(G(θ)|θ)P(θ) where P(θ) is the prior distribution, P(Z|θ) is the likelihood function of the monitored data, P(G(θ)|θ) is the constrained likelihood function, and a2 is a normalization constant that ensures that P(θ|Z,G(θ)) integrates to 1 over the possible range of parameters.

6. The method according to claim 1, characterized in that The updated result of the hydropower high slope response is expressed as: Where Θ represents the equivalent sample and N represents the number of equivalent samples.

7. A hydropower high slope response update device based on constrained Bayesian reasoning, characterized in that: include: a determination module for determining a priori distribution of target key material parameters in an actual slope of a target hydropower station and constructing a monitoring data likelihood function using slope monitoring data of the actual slope; a construction module, configured to determine target constraints of the target key material parameters based on the target physical meanings of the rock and soil parameters in the actual slope, and to construct a target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints according to the constraint properties, and are divided into soft constraints and hard constraints according to the constraint degrees; An updating module is used to combine the prior distribution, the monitoring data likelihood function and the target constraint likelihood function to determine the posterior distribution of the target key material parameters, and based on the posterior distribution, use a pre-built slope response proxy model and a target sampling algorithm to determine equivalent samples of the target key material parameters, and use the equivalent samples to update the slope response of the target hydropower station to obtain an updated result of the hydropower high slope response based on constrained Bayesian reasoning.

8. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the hydropower high slope response updating method based on constrained Bayesian reasoning as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the hydropower high slope response updating method based on constrained Bayesian reasoning as described in any one of claims 1 to 6.

10. A computer program product comprising a computer program, characterized in that The computer program is executed by a processor to implement the hydropower high slope response updating method based on constrained Bayesian reasoning as described in any one of claims 1 to 6.

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