Hydropower high slope response updating method and device based on constraint bayesian inference

Abstract

The application relates to the technical field of slope engineering response updating, in particular to a hydropower high slope response updating method and device based on constraint Bayesian inference, which comprises the following steps: determining the prior distribution of key material parameters in an actual slope of a hydropower station, and constructing a monitoring data likelihood function by using slope monitoring data of the actual slope; constructing a constraint likelihood function according to a target constraint condition of the key material parameters; 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 samples of the key material parameters by using a slope response proxy model and a target sampling algorithm, updating the slope response of the hydropower station, and obtaining the hydropower high slope response updating result based on the constraint Bayesian inference. Therefore, the problem that the traditional Bayesian inference in the related art cannot effectively reduce the uncertainty of the geotechnical material parameters when the types and quantity of the monitoring data are limited is solved.

Description

Technical Field

[0001] This application relates to the field of slope engineering response update technology, and in particular to a method and apparatus for updating the response of hydropower high slopes based on constrained Bayesian inference. Background Technology

[0002] With the development of monitoring technology and the advent 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 anchorage stress. Utilizing monitoring data to compensate for the scarcity of measured data reduces the uncertainty of soil and rock parameters and improves the accuracy of slope response calculations. Therefore, various parameter inversion methods have been developed to reduce parameter uncertainty, such as neural networks, ensemble Kalman filtering, and Bayesian inference.

[0003] However, in related technologies, traditional Bayesian inference mainly relies on fusing monitoring data to invert soil and rock material parameters. However, the types and quantities of monitoring data for most geotechnical engineering projects are still very limited, and the collection is time-consuming and labor-intensive. Therefore, traditional Bayesian inference cannot effectively reduce the uncertainty of soil and rock material parameters and cannot obtain accurate slope responses, which urgently needs to be addressed. Summary of the Invention

[0004] This application is based on the inventor's understanding and insights into the following issues:

[0005] Rivers in Southwest China possess abundant hydropower resources due to their significant elevation differences. In recent years, hydropower development in the region has flourished, with a large number of high dams being constructed. During construction and operation, in addition to the stability of the dam itself, the stability of the reservoir slopes is a crucial factor in controlling the overall project safety. Slope instability can trigger a chain reaction of disasters—landslides, surges, dam failures, and floods—posing a serious threat to people's lives and property. Therefore, accurate slope response calculations are essential. However, due to the complex geological conditions and frequent geological activity in Southwest China, accurate slope response calculations are an extremely challenging task.

[0006] Furthermore, as natural materials, soil and rock masses exhibit significant uncertainties due to stress history, physicochemical processes, and other factors. In addition, in-situ and laboratory experiments are complex and time-consuming, resulting in a scarcity of measured data on soil and rock parameters for specific sites. Clearly, soil and rock parameter values ​​estimated from limited measured data do not represent their true values, leading to significant errors in numerical simulations for slope response calculations. Therefore, improving the accuracy of slope response calculations and reducing the uncertainty of soil and rock parameters is of paramount importance.

[0007] With the development of monitoring technology and the emergence 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 anchorage stress. Monitoring data is used to compensate for the scarcity of measured data, thereby reducing the uncertainty of soil and rock parameters and improving the accuracy of slope response calculation. In view of this, various parameter inversion methods have been developed to reduce parameter uncertainty, such as neural networks, ensemble Kalman filtering, and Bayesian inference. Bayesian inference has at least two advantages: (1) it integrates prior information and monitoring data into the posterior distribution, providing a reliable probability distribution of soil and rock parameters for slope response updates; (2) it can not only explicitly model the uncertainty of soil and rock parameters but also use monitoring data to reduce the uncertainty of soil and rock parameters, which makes Bayesian inference widely used in the probabilistic inversion of soil and rock parameters.

[0008] However, the complexity and special characteristics of geotechnical engineering mean that traditional Bayesian inference still has some shortcomings: (1) Traditional Bayesian inference mainly relies on the fusion of monitoring data to invert geotechnical material parameters. Although monitoring technology has made great strides in recent years, in most geotechnical engineering practices, the types and quantities of monitoring data are usually still very limited, which makes Bayesian inference not very effective in reducing the uncertainty of geotechnical material parameters; (2) Most geotechnical parameter inversion problems are unbalanced problems, which may result in some non-physical and inappropriate interpretations, which urgently need to be improved.

[0009] This application provides a method and apparatus for updating the response of hydropower high slopes based on constrained Bayesian inference, in order to solve the problem that in related technologies, traditional Bayesian inference mainly relies on the fusion of monitoring data to invert soil and rock material parameters. When the types and quantities of monitoring data are limited, traditional Bayesian inference cannot effectively reduce the uncertainty of soil and rock material parameters and cannot obtain accurate slope response. The first aspect of this application provides a method for updating the response of a hydropower high slope based on constrained Bayesian inference, comprising the following steps: determining the prior distribution of target key material parameters in the actual slope of the target hydropower station, and constructing a monitoring data likelihood function using slope monitoring data of the actual slope; determining the target constraints of the target key material parameters based on the target physical meaning of the soil and rock parameters in the actual slope, and constructing a target constraint likelihood function based on the target constraints, wherein the target constraints are classified into equality constraints and inequality constraints according to the constraint nature, and into soft constraints and hard constraints according to the constraint degree; 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 determining equivalent samples of the target key material parameters based on the posterior distribution using a pre-constructed slope response surrogate model and a target sampling algorithm, and updating the slope response of the target hydropower station using the equivalent samples to obtain the hydropower high slope response update result based on constrained Bayesian inference.

[0010] Optionally, in one embodiment of this application, the step of constructing a monitoring data likelihood function using the slope monitoring data of the actual slope includes: acquiring 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 this application, determining the equivalent samples of the key material parameters using a pre-built slope response surrogate model and a target sampling algorithm includes: determining target posterior samples based on the posterior distribution using the slope response surrogate 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 this 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] The soft-constraint likelihood function of the equation is characterized as follows:

[0014]

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

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

[0017]

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

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

[0020]

[0021] Where, μ g(θ) and σ g(θ) ...

[0022] Optionally, in one embodiment of this application, the posterior distribution is represented 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 monitoring data, P(G(θ)|θ) is the constraint likelihood function, and a2 is the normalization constant, which ensures that P(θ|Z,G(θ)) integrates to 1 within the possible range of parameters.

[0025] Optionally, in one embodiment of this application, the updated response result of the hydropower high slope is represented as:

[0026]

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

[0028] A second aspect of this application provides a hydropower high slope response update device based on constrained Bayesian inference, comprising: a determination module, used to determine the prior distribution of target key material parameters in the actual slope of the target hydropower station, and construct a monitoring data likelihood function using slope monitoring data of the actual slope; a construction module, used to determine the target constraints of the target key material parameters based on the target physical meaning of the soil and rock parameters in the actual slope, and construct a target constraint likelihood function based on the target constraints, wherein the target constraints are classified into equality constraints and inequality constraints according to the constraint nature, and into soft constraints and hard constraints according to the constraint degree; and an update module, 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-constructed slope response surrogate 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 a hydropower high slope response update result based on constrained Bayesian inference.

[0029] Optionally, in one embodiment of this application, the determining module includes: an acquisition unit, configured to acquire slope monitoring data of the actual slope and determine the measurement error of the slope monitoring data; and a construction unit, configured to construct the likelihood function of the monitoring data based on the slope monitoring data and the measurement error.

[0030] Optionally, in one embodiment of this application, the updating module includes: a first determining unit, configured to determine a target posterior sample based on the posterior distribution using the slope response surrogate model and the target Markov chain Monte Carlo simulation (MCMC) algorithm; and a second determining unit, configured to determine an equivalent sample of the key material parameters based on the target posterior sample.

[0031] Optionally, in one embodiment of this 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] The soft-constraint likelihood function of the equation is characterized as follows:

[0033]

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

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

[0036]

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

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

[0039]

[0040] Where, μ g(θ) and σ g(θ) ...

[0041] Optionally, in one embodiment of this application, the posterior distribution is represented 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 monitoring data, P(G(θ)|θ) is the constraint likelihood function, and a2 is the normalization constant, which ensures that P(θ|Z,G(θ)) integrates to 1 within the possible range of parameters.

[0044] Optionally, in one embodiment of this application, the updated response result of the hydropower high slope is represented as:

[0045]

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

[0047] A third aspect of this application provides an electronic device, including: 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 hydroelectric high slope response update method based on constrained Bayesian inference as described in the above embodiments.

[0048] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for updating the response of hydroelectric high slopes based on constrained Bayesian inference.

[0049] A fifth aspect of this application provides a computer program product, including a computer program that, when executed, is used to implement the above-described method for updating the response of hydroelectric high slopes based on constrained Bayesian inference.

[0050] This application's embodiments can determine the prior distribution of key material parameters in the actual slope of a hydropower station, construct a likelihood function for monitoring data and a constraint likelihood function, and then combine the prior distribution, monitoring data likelihood function, and constraint likelihood function using Bayesian theory to determine the posterior distribution of the key material parameters. This allows for the determination of equivalent samples of the key material parameters to update the slope response of the hydropower station, obtaining updated hydropower high slope response results based on constrained Bayesian inference. This effectively reduces the uncertainty of geotechnical material parameters and obtains an accurate slope response. Therefore, it solves the problem in related technologies where traditional Bayesian inference cannot effectively reduce the uncertainty of geotechnical material parameters and cannot obtain an accurate slope response when the types and quantities of monitoring data are limited.

[0051] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

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

[0053] Figure 1 This is a flowchart of a hydroelectric high slope response update method based on constrained Bayesian inference provided in an embodiment of this application;

[0054] Figure 2 A logic diagram for updating the response of a hydroelectric high slope based on constrained Bayesian inference, according to a specific embodiment of this application;

[0055] Figure 3 This is a schematic diagram of the finite element model of the Nianshengken slope of the Liyuan Hydropower Station, a specific embodiment of this application;

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

[0057] Figure 5 The diagram shows the constraint likelihood function of the anchoring force of the anchor plate in a specific embodiment of this application.

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

[0059] Figure 7 This is a posterior probability distribution of the parameters after the first parameter inversion in a specific embodiment of this application.

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

[0061] Figure 9 This is a schematic diagram of a hydropower high slope response update device based on constrained Bayesian inference provided in an embodiment of this application;

[0062] Figure 10 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0063] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0064] The following describes, with reference to the accompanying drawings, a method and apparatus for updating the response of a hydropower high slope based on constrained Bayesian inference, according to embodiments of this application. Addressing the aforementioned issues in the background section regarding the solution of related technologies, traditional Bayesian inference primarily relies on fusing monitoring data to invert soil and rock material parameters. However, when the types and quantities of monitoring data are limited, traditional Bayesian inference cannot effectively reduce the uncertainty of soil and rock material parameters and cannot obtain accurate slope responses. This application provides a method for updating the response of a hydropower high slope based on constrained Bayesian inference. In this method, the prior distribution of key material parameters in the actual slope of the hydropower station can be determined, and a likelihood function of the monitoring data and a constraint likelihood function are constructed. Then, Bayesian theory is used to combine the prior distribution, the likelihood function of the monitoring data, and the constraint likelihood function to determine the posterior distribution of the key material parameters, thereby determining equivalent samples of the key material parameters to update the slope response of the hydropower station. This yields an updated response result for a hydropower high slope based on constrained Bayesian inference, effectively reducing the uncertainty of soil and rock material parameters and obtaining accurate slope responses. This solves the problem that traditional Bayesian inference, due to the limited types and quantities of monitoring data, cannot effectively reduce the uncertainty of soil and rock material parameters and cannot obtain accurate slope response.

[0065] Specifically, Figure 1 This is a flowchart illustrating a hydroelectric high slope response update method based on constrained Bayesian inference, provided in an embodiment of this application.

[0066] like Figure 1 As shown, the hydropower high slope response update method based on constrained Bayesian inference includes the following steps:

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

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

[0069] It is understood that, in this embodiment of the application, the rock and soil parameters that are difficult to measure or play a major role in slope stability and deformation can be selected as key material parameters θ for the actual slope of the hydropower station. Then, the key material parameters θ are treated as random variables, and the other rock and soil parameters are treated as constants. Finally, prior information on the key material parameters 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 parameters θ. In addition, this embodiment of the application can also collect slope monitoring data according to the specific project monitoring plan to construct the monitoring data likelihood function, which effectively improves the accuracy of slope behavior prediction.

[0070] Optionally, in one embodiment of this application, a monitoring data likelihood function is constructed using actual slope monitoring data, including: acquiring actual slope monitoring data and determining the 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, in this embodiment of the application, monitoring data Z can be collected 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] The likelihood function of the monitoring data is expressed as:

[0073]

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

[0075] In step S102, based on the target physical meaning of the soil and rock parameters in the actual slope, the target constraint conditions of the target key material parameters are determined, and the target constraint likelihood function is constructed according to the target constraint conditions. The target constraint conditions are divided into equality constraints and inequality constraints according to the constraint nature, and into soft constraints and hard constraints according to the constraint degree.

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

[0077] It is understood that, according to the physical meaning of the soil and rock parameters, the embodiments of this application can collect the possible constraints of each key material parameter under specific working conditions, such as the theoretical formulas of the physical and mechanical properties of soil and rock parameters, the interrelationships of empirical parameters, and the upper and lower limits of soil and rock parameters. Then, based on the collected constraints G(θ), a constraint likelihood function P(G(θ)|θ) is constructed, which effectively improves the accuracy of slope response updates.

[0078] In the embodiments of this application, constraints can be classified into equality constraints and inequality constraints according to their nature; and into soft constraints and hard constraints according to their degree of constraint; the target constraint likelihood function includes equality soft constraint likelihood function, inequality soft constraint likelihood function and inequality hard constraint likelihood function.

[0079] The soft-constraint likelihood function of the equation is characterized as follows:

[0080]

[0081] in, g l (θ)=0(l=1,2,...,N c ) is the l-th constraint condition of θ; N c It 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:

[0083]

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

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

[0086]

[0087] Where, μ g(θ) and σ g(θ) ...

[0088] In step S103, Bayesian theory is used to combine the prior distribution, the likelihood function of the monitoring data, and the target constraint likelihood function to determine the posterior distribution of the target key material parameters. Based on the posterior distribution, a pre-built slope response surrogate model and a target sampling algorithm are used to determine the equivalent samples of the target key material parameters. The equivalent samples are then used to update the slope response of the target hydropower station to obtain the hydropower high slope response update results based on constrained Bayesian inference.

[0089] In this embodiment of the application, the method for constructing a surrogate model of slope response is as follows: First, 1000 sets of samples are generated from the prior distribution of random variable θ using Latin hypercube, wherein the ratio of training samples to test samples is 7:3. Then, the slope response corresponding to the training and test samples is calculated using the finite element method. Finally, the surrogate model of slope response is trained using the LightGBM algorithm to approximate the physical numerical model of slope response, so as to construct a surrogate model of slope response.

[0090] In one embodiment of this application, the slope response proxy model is represented as follows:

[0091] H j (θ)=LM j (θ)

[0092] Here, LM(θ) represents the proxy model constructed using LightGBM with θ as input and H(θ) as input.

[0093] It is understood that the embodiments of this application employ Bayesian theory, combining the prior distribution P(θ), the likelihood function P(Z|θ) of the monitoring data, and the constraint 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. Based on the posterior distribution P(θ|Z,G(θ)), an equivalent sample Θ of the key material parameter θ is extracted using a slope response surrogate model and a sampling algorithm. The equivalent sample Θ is then used to update the slope response of the hydropower station, thereby obtaining the updated hydropower high slope response based on constrained Bayesian inference. This effectively reduces the uncertainty of geotechnical material parameters and can obtain an accurate slope response.

[0094] The posterior distribution P(θ|Z,G(θ)) is characterized as follows:

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

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

[0097] Optionally, in one embodiment of this application, determining equivalent samples of key material parameters using a pre-built slope response surrogate model and a target sampling algorithm includes: determining target posterior samples based on the posterior distribution using the slope response surrogate 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 practical implementation, the embodiments of this application can extract equivalent samples Θ of key material parameters based on the slope response surrogate model and MCMC simulation. Specifically, firstly, the slope response surrogate model is 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 equivalent posterior distribution sample Θ=[θ1,...,θ k ,...,θ N ] T Finally, the posterior probability density function (PDF) of key material parameters is determined based on N equivalent samples. The determination of N needs to meet the requirements of both the stability of the Markov chain and the high accuracy and low variability of the slope response update.

[0099] Furthermore, the average of the slope responses 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 this application can effectively solve the problem that traditional Bayesian inference only uses monitoring data, and under the condition of scarce monitoring data, the effect of reducing parameter uncertainty through parameter probability inversion is not significant, resulting in a large error in slope response calculation.

[0103] The constrained Bayesian inference in this embodiment integrates known constraints, such as theoretical formulas for the physical and mechanical properties of soil and rock parameters, empirical parameter relationships, and upper and lower limits of soil and rock material parameters, into the traditional Bayesian update process to form constrained Bayesian inference. Compared with traditional Bayesian inference, the posterior probability density function of key material parameters obtained by parameter inversion using constrained Bayesian inference has less uncertainty, thus obtaining a more accurate slope response in subsequent updates. Furthermore, constrained Bayesian inference adds additional constraints during the parameter probability inversion process, thereby avoiding some non-physical and unreasonable solutions.

[0104] For example, such as Figure 2 As shown, the working principle of the embodiments of this application will be described in detail below with a specific example.

[0105] The Liyuan Hydropower Station is located at the border of Yulong County (right bank) and Shangri-La County (left bank) in Yunnan Province, China. It is the third of eight cascade hydropower stations on the middle reaches of the Jinsha River, adjacent to the Liangjiaren Hydropower Station upstream and the Ahai Hydropower Station downstream. The Nianshengken Slope is situated in a wide, gentle gully on the right bank in front of the reservoir of the Liyuan Hydropower Station, at an elevation between 1500 and 1850 meters. It is a mixed deposit of Quaternary alluvial, colluvial, colluvial, colluvial, and landslide deposits, with a total volume of approximately 2000 × 10⁻⁶ m³. 4 m 3 The underlying bedrock of the deposit is mainly basaltic extrusive rocks of the Upper Permian Dongba Formation (P2d).

[0106] Under natural conditions, the Nianshengken slope shows no obvious signs of deformation except for slight subsidence at its leading edge caused by river erosion. However, data from 25 boreholes suggest that the deposit underwent sliding deformation towards the Jinsha River during or after its formation. Within and at the bottom of the deposit, there is a sliding deformation zone composed of multiple potential sliding surfaces. The lower interface of this zone is the soil-rock interface between the residual layer and the strongly weathered layer, with a depth of approximately 50m to 68m and a dip angle of 10° to 18°. The Nianshengken slope consists of two soil layers and three rock layers, namely, from top to bottom: deposit, residual layer, strongly weathered layer, moderately weathered layer, and slightly weathered layer, as detailed below. Figure 3 As shown.

[0107] Therefore, slope stability is mainly controlled by two soil layers. Thus, the material parameters of all three rock layers are considered constants. For the two soil layers, since the variability of unit weight (γ) and Poisson's ratio (ν) is relatively small, they are also considered constants. On the other hand, the elastic modulus (E) and shear strength parameters (cohesion c and friction angle) are also considered constants. The variability of the material parameters is relatively large, therefore they are treated as random variables. Thus, a total of six material parameters are considered random variables. In this table, subscripts 1 and 2 represent the deposited body and residual layer, respectively. The specific values ​​of the parameters are shown in Table 1. Table 1 is a priori value table of material parameters for two soil layers and three rock layers. The specific values ​​of Table 1 are as follows:

[0108] Table 1

[0109]

[0110] Furthermore, in this embodiment, it is assumed that these six random variables all follow a log-normal distribution, thereby determining... Figure 2 The prior distribution of key material parameters in the material.

[0111] Next, under the excavation conditions: the Nianshengken slope began to show local deformation and gradually developed into overall deformation, and the deformation rate showed an increasing trend. There are three main factors that caused the slope deformation: First, the excavation of the diversion channel formed a deep ditch with a near north-south orientation, a length of 350 meters and a bottom width of 90 meters at the front edge of the slope, which led to a significant decrease in the slope's anti-sliding force. (2) The excavation of the access road and construction access road seriously damaged the integrity of the stockpile. (3) The stockpiling of waste increased the slope's sliding force, with a total of 45×10 4 m 3 Waste material is piled up on the slope. When the slope is about to become unstable, the safety factor FS can be approximated as 1 for parameter inversion. Therefore, it is assumed here that FS follows the mean μ. FS =1, coefficient of variation COV FS The first parameter inversion was performed using the likelihood function of the monitoring data with a normal distribution of 0.05 as the basis for the excavation condition.

[0112] Under reinforced conditions: Clearly, without reinforcement, the Nianshengken slope would become unstable; therefore, slope reinforcement was implemented. The reinforcement scheme involved embedding two rows of anti-slide piles in the lower and middle sections of the Nianshengken slope and installing anchor plates at three locations on the slope. The anchor cables were 2000kN pressure-dispersing prestressed anchor cables. Specific reinforcement locations are detailed below. Figure 3 .

[0113] After reinforcing and treating the Nianshengken slope, relevant departments conducted comprehensive monitoring of the slope, including ground deformation, pile top displacement, and anchorage force. In the selected two-dimensional profile, there are 3 ground deformation monitoring points (numbered NSKTP18, NSKTP14, and NSKIN01 from bottom to top), 2 pile top displacement monitoring points (numbered Z48TP01 and ZS23TP01), and 3 anchorage force monitoring points (numbered NSKPR36, NSKPR06, and NSKPR02), for a total of 8 monitoring points. The monitoring data for each point are shown in column 3 of Table 2. It can be assumed that the ground deformation monitoring data follows 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 COV of 0.1. This allows for the construction of likelihood functions for the three monitoring data under the reinforcement condition.

[0114] Secondly, relevant technical personnel from Yunnan Province conducted regression analysis on the shear strength parameters of the slip 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 the slope angle (α) and the slope angle (correlation coefficient ρ = 0.986):

[0115]

[0116] in, Figure 4 The relationship between the slip zone slope angle and friction angle for these 12 engineering landslides is given. In conjunction with the slope of this project, the above formula can be considered as... The equation-based soft constraints are incorporated into the parameter inversion under excavation conditions. Since the dip angle of the sliding deformation zone of the Nianshengken slope is between 10° and 18°, taking an average of 14°, substituting it into the formula yields the result. Therefore, it is assumed The constraint likelihood function for the excavation condition follows a normal distribution with mean μ = 12.45° and standard deviation σ = 2°.

[0117] In the reinforcement process, since the anchor cables used in the anchor plates are all of the 2000kN class 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 designs generally include a certain safety margin, 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). For T≤2000kN and σ T Substituting 100kN into the inequality for the soft constraint yields the constraint likelihood function under the reinforced condition, see [link / reference]. Figure 5 .

[0118] Again, such as Figure 2As shown, Bayesian theory is used to combine the prior distribution P(θ) of soil and rock 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)), which is specifically expressed as:

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

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

[0121] Since the slope can be divided into three working conditions: natural, excavated, and reinforced, and monitoring data and constraints for both excavated and reinforced conditions were collected, two constrained Bayesian inferences (two parameter inversions) were performed, resulting in two updates to the slope response. The first parameter inversion used monitoring data from the FS under the excavated condition and... According to the strength reduction method, the constraints FS are independent of the elastic modulus E. Therefore, the first parameter inversion involves only four random variables. The second parameter inversion involves all random variables.

[0122] In this application, LightGBM is used to establish a surrogate model for the response values ​​of eight monitoring points. The accuracy of the surrogate model is usually related to the quantity and quality of the training samples. This embodiment first uses Latin hypercube sampling to generate 1000 sets of samples from the prior distribution of the random variable θ, with a training sample to test sample ratio of 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 surrogate model of the slope response. For example... Figure 6 As shown, the results calculated by the finite element model and the LightGBM proxy model corresponding to 300 test samples are presented. Figure 6 (a) Ground deformation, Figure 6 (b) Pile top displacement and Figure 6 (c) The response values ​​at the eight monitoring points in the anchoring force clearly show that the coefficient of determination R for all surrogate models is... 2 All values ​​are greater than 0.95. This demonstrates that the surrogate model trained with LightGBM exhibits good performance in predicting the response of slope monitoring points.

[0123] In this embodiment, a slope response surrogate model is first used to quickly calculate the posterior distribution probability. Then, the DREAM algorithm is used to generate 2N posterior samples, and the latter 50% of the samples are taken as the equivalent posterior distribution samples Θ=[θ1,...,θ k ,...,θ N ] TFinally, based on N equivalent samples, the posterior probability density function (PDF) of the key material parameters is determined. The posterior PDF of the parameters obtained in the first inversion is as follows: Figure 7 As shown.

[0124] It can be seen that after the first parameter inversion, c1 is obtained using both traditional Bayesian inference and constrained Bayesian inference. The posterior distribution of c2 is not much different from the prior distribution, while The uncertainty of the posterior distribution 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 that of c1. And c2. It is evident that using traditional Bayesian inference and constrained Bayesian inference for parameter inversion can significantly reduce the uncertainty of sensitive parameters. Furthermore, the results obtained using constrained Bayesian inference... 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 fully utilizes... The constraints are thus demonstrated. Therefore, compared to traditional Bayesian inference, constrained Bayesian inference has a significant advantage in reducing parameter uncertainty.

[0125] Finally, the average of the slope responses calculated from N equivalent samples is taken as the updated slope response H(Θ), and the calculation formula is as follows:

[0126]

[0127] Table 2 compares the prior response values ​​with the first updated response values ​​for the eight monitoring points. The details of Table 2 are as follows:

[0128] Table 2

[0129]

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

[0131] like Figure 8As shown, the response PDFs of the three anchoring forces obtained after the second update are presented. It can be seen that a large portion of the anchoring forces obtained using traditional Bayesian inference are significantly greater than 2000kN or even 3000kN, which is inconsistent with the ultimate anchoring force of the anchor cable being 2000kN. Constrained Bayesian inference, by adding the ultimate anchoring force constraint, effectively filters out these non-physical values. Therefore, constrained Bayesian inference can avoid these unreasonable inversion results.

[0132] Therefore, the constrained Bayesian inference in this embodiment integrates some known constraints as additional constraints into traditional Bayesian inference to form constrained Bayesian inference. Compared with traditional Bayesian inference, the posterior probability density function of the key material parameters obtained by parameter inversion using constrained Bayesian inference has less uncertainty, thus obtaining a more accurate slope response in subsequent updates. In addition, constrained Bayesian inference also adds additional constraints during the parameter probability inversion process, thereby avoiding some non-physical and unreasonable solutions.

[0133] The hydropower high slope response update method based on constrained Bayesian inference proposed in this application can determine the prior distribution of key material parameters in the actual slope of a hydropower station, construct a likelihood function of monitoring data and a constraint likelihood function, and then combine the prior distribution, the likelihood function of monitoring data, and the constraint likelihood function using Bayesian theory to determine the posterior distribution of key material parameters. This determines equivalent samples of key material parameters to update the slope response of the hydropower station, obtaining the hydropower high slope response update result based on constrained Bayesian inference. This effectively reduces the uncertainty of soil and rock material parameters and obtains an accurate slope response. Therefore, it solves the problem in related technologies where traditional Bayesian methods cannot effectively reduce the uncertainty of soil and rock material parameters and cannot obtain an accurate slope response due to the limited types and quantities of monitoring data.

[0134] Next, referring to the accompanying drawings, a hydroelectric high slope response update device based on constrained Bayesian inference, according to an embodiment of this application, is described.

[0135] Figure 9 This is a block diagram of a hydropower high slope response update device based on constrained Bayesian inference, according to an embodiment of this application.

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

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

[0138] Module 200 is used to determine the target constraints of key material parameters based on the target physical meaning of the soil and rock parameters in the actual slope, so as to construct the target constraint likelihood function according to the target constraint conditions. The target constraints are divided into equality constraints and inequality constraints according to the constraint nature, and into soft constraints and hard constraints according to the constraint degree.

[0139] The update module 300 is used to combine the prior distribution, the likelihood function of the monitoring data, and the target constraint likelihood function to determine the posterior distribution of the target key material parameters. Based on the posterior distribution, it uses a pre-built slope response surrogate model and a target sampling algorithm to determine the equivalent samples of the target key material parameters. The equivalent samples are then used to update the slope response of the target hydropower station to obtain the hydropower high slope response update results based on constrained Bayesian inference.

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

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

[0142] The building block is used to construct the likelihood function of the monitoring data based on the slope monitoring data and measurement errors.

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

[0144] The first determining unit is 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.

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

[0146] Optionally, in one embodiment of this 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] The soft-constraint likelihood function of the equation is characterized as follows:

[0148]

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

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

[0151]

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

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

[0154]

[0155] Where, μ g(θ) and σ g(θ) ...

[0156] Optionally, in one embodiment of this application, the posterior distribution is represented 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 monitoring data, P(G(θ)|θ) is the constraint likelihood function, and a2 is the normalization constant, which ensures that P(θ|Z,G(θ)) integrates to 1 within the possible range of parameters.

[0159] Optionally, in one embodiment of this application, the updated response result of the hydropower high slope is represented as follows:

[0160]

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

[0162] It should be noted that the foregoing explanation of the embodiment of the hydropower high slope response update method based on constrained Bayesian inference also applies to the hydropower high slope response update device based on constrained Bayesian inference in this embodiment, and will not be repeated here.

[0163] The hydropower high slope response update device based on constrained Bayesian inference proposed in this application can determine the prior distribution of key material parameters in the actual slope of a hydropower station, construct a likelihood function of monitoring data and a constraint likelihood function, and then combine the prior distribution, the likelihood function of monitoring data, and the constraint likelihood function using Bayesian theory to determine the posterior distribution of key material parameters. This determines equivalent samples of key material parameters to update the slope response of the hydropower station, obtaining the hydropower high slope response update result based on constrained Bayesian inference. This effectively reduces the uncertainty of soil and rock material parameters and obtains an accurate slope response. Therefore, it solves the problem in related technologies where traditional Bayesian inference cannot effectively reduce the uncertainty of soil and rock material parameters and cannot obtain an accurate slope response due to the limited types and quantities of monitoring data.

[0164] Figure 10 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:

[0165] The memory 1001, the processor 1002, and the computer program stored on the memory 1001 and capable of running on the processor 1002.

[0166] When the processor 1002 executes the program, it implements the hydropower high slope response update method based on constrained Bayesian inference provided in the above embodiments.

[0167] Furthermore, electronic devices also include:

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

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

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

[0171] If the memory 1001, processor 1002, and communication interface 1003 are implemented independently, then the communication interface 1003, memory 1001, and processor 1002 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be divided into address buses, data buses, control buses, etc. For ease of representation, Figure 10 The bus is represented by a single thick line, 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, processor 1002, and communication interface 1003 are integrated on a single chip, then the memory 1001, processor 1002, and 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 this application.

[0174] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described hydropower high slope response update method based on constrained Bayesian inference.

[0175] This embodiment also provides a computer program product, including a computer program that, when executed, is used to implement the above-described method for updating the response of hydropower high slopes based on constrained Bayesian inference.

[0176] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

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

[0178] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0179] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing 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 (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs 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: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0180] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0181] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

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

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

Claims

1. A method for updating the response of hydroelectric high slopes based on constrained Bayesian inference, characterized in that, Includes the following steps: Determine the prior distribution of key material parameters of the target hydropower station in the actual slope, and construct the monitoring data likelihood function using the slope monitoring data of the actual slope; Based on the target physical meaning of the soil and rock parameters in the actual slope, the target constraints for the key material parameters are determined. A target constraint likelihood function is then constructed based on these constraints. These constraints are categorized into equality constraints and inequality constraints based on their nature, and into soft constraints and hard constraints based on their degree of constraint. The target constraint likelihood function includes equality soft constraint likelihood functions, inequality soft constraint likelihood functions, and inequality hard constraint likelihood functions. The equality soft constraint likelihood function is characterized as follows: in, ; ( l = 1, 2, ..., N c )yes θ The l One constraint condition; N c It is the total number of constraints; yes Standard deviation; The inequality soft-constraint likelihood function is characterized as follows: in, It is a normalization constant, ensuring The integral is 1 within the possible range of parameters; The inequality hard constraint likelihood function is characterized as follows: in, μ g(θ) and σ g(θ) They are g ( θ The mean and standard deviation of (). a and b They are g ( θ The left and right boundaries of ); Φ is the standard normal cumulative distribution function; By combining the prior distribution, the likelihood function of the monitoring data, and the target constraint likelihood function using Bayesian theory, the posterior distribution of the target key material parameters is determined. Based on the posterior distribution, an equivalent sample of the target key material parameters is determined using a pre-constructed slope response surrogate model and a target sampling algorithm. The slope response of the target hydropower station is then updated using the equivalent sample to obtain the hydropower high slope response update result based on constrained Bayesian inference. The posterior distribution is expressed as: in, P ( θ ) is the prior distribution. P ( Z | θ ) is the likelihood function of the monitoring data. P ( G ( θ )| θ ) is the constraint likelihood function. It is a normalization constant, ensuring P ( θ | Z , G ( θ The integral is 1 within the possible range of parameters.

2. The method according to claim 1, characterized in that, The construction of the monitoring data likelihood function using the actual slope monitoring data includes: Obtain slope monitoring data of the actual slope and determine the measurement error of the slope monitoring data; Based on the slope monitoring data and the measurement error, a likelihood function for the monitoring data is constructed.

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

4. The method according to claim 1, characterized in that, The updated response results for the hydropower high slope are expressed as follows: in, Θ Indicates equivalent samples, N Indicates the number of equivalent samples.

5. A hydropower high slope response update device based on constrained Bayesian inference, characterized in that, include: The determination module is used to determine the prior distribution of key material parameters of the target in the actual slope of the target hydropower station, and to construct the monitoring data likelihood function using the slope monitoring data of the actual slope. A construction module is used to determine the target constraints of the target key material parameters based on the target physical meaning of the soil and rock parameters in the actual slope, and to construct a target constraint likelihood function based on the target constraints. The target constraints are classified into equality constraints and inequality constraints according to their nature, and into soft constraints and hard constraints according to their degree. The target constraint likelihood function includes equality soft constraint likelihood functions, inequality soft constraint likelihood functions, and inequality hard constraint likelihood functions. The equality soft constraint likelihood function is characterized as follows: in, ; ( l = 1, 2, ..., N c )yes θ The l One constraint condition; N c It is the total number of constraints; yes Standard deviation; The inequality soft-constraint likelihood function is characterized as follows: in, It is a normalization constant, ensuring The integral is 1 within the possible range of parameters; The inequality hard constraint likelihood function is characterized as follows: in, μ g(θ) and σ g(θ) They are g ( θ The mean and standard deviation of (). a and b They are g ( θ The left and right boundaries of ); Φ is the standard normal cumulative distribution function; The update module is used to combine the prior distribution, the likelihood function of the monitoring data, and the target constraint likelihood function to determine the posterior distribution of the target key material parameters. Based on the posterior distribution, it uses a pre-built slope response surrogate model and a target sampling algorithm to determine equivalent samples of the target key material parameters, and uses the equivalent samples to update the slope response of the target hydropower station to obtain the hydropower high slope response update result based on constrained Bayesian inference. The posterior distribution is expressed as: in, P ( θ ) is the prior distribution. P ( Z | θ ) is the likelihood function of the monitoring data. P ( G ( θ )| θ ) is the constraint likelihood function. It is a normalization constant, ensuring P ( θ | Z , G ( θ The integral is 1 within the possible range of parameters.

6. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the program to implement the hydroelectric high slope response update method based on constrained Bayesian inference as described in any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the hydroelectric high slope response update method based on constrained Bayesian inference as described in any one of claims 1-4.

8. A computer program product, comprising a computer program, characterized in that, The computer program is executed by a processor to implement the hydroelectric high slope response update method based on constrained Bayesian inference as described in any one of claims 1-4.

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