A ground stress field inversion method and device based on bayesian optimization and a medium

Abstract

The application discloses a ground stress field inversion method and device based on Bayesian optimization and a medium, which can improve inversion efficiency and accuracy. The method comprises the following steps: obtaining parameters generated by a proxy model, wherein the parameters comprise boundary parameters and physical and mechanical parameters; calculating a prior probability of Bayesian model parameters according to the parameters; simulating to obtain a simulated stress according to the parameters and obtaining a likelihood probability of the Bayesian model parameters based on the simulated stress and corresponding measured stress; obtaining a target function based on the prior probability and the likelihood probability and adding the target function and corresponding parameters thereof into an optimization data set; adding the parameters and the target function into a sample set of the proxy model to update the proxy model, and performing a cycle after obtaining new parameters; and finally determining a minimum value of the target function in the optimization data set and simulating to obtain a ground stress field based on corresponding parameters of the target function.

Description

Technical Field

[0001] This invention belongs to the field of geostress inversion technology, specifically relating to a geostress field inversion method, apparatus and medium based on Bayesian optimization. Background Technology

[0002] Field testing of geostress is both expensive and time-consuming, and the number of tests is limited, making it difficult to grasp the geostress state of the study area based on a small amount of measured data. Therefore, numerical simulation and inverse analysis are currently common methods for obtaining geostress fields based on limited measurement data. Patent application number 202210216125.2 discloses an "accelerated optimization inversion method for initial geostress field under complex geological conditions." This inversion method specifically involves: establishing a three-dimensional geological model for stress field inversion calculation; determining the application method and range of tectonic stress boundaries, and then obtaining the stress calculation values ​​at measuring points under each stress boundary condition through numerical calculation; using the stress boundary conditions as network input and the stress calculation values ​​at measuring points as network output to establish a training sample for the surrogate model, and then inputting this training sample into the surrogate model for training; based on the trained surrogate model, using a genetic algorithm to quickly optimize within the trained sample range to obtain the optimal stress boundary conditions; and using the optimal stress boundary conditions to invert and calculate the initial geostress field within the region.

[0003] However, the existing methods have the following problems: 1. The existing inversion of the geostress field sets the physical and mechanical parameters of the rock mass as constants, and these settings are subjective and human-made, resulting in low accuracy of the inversion results.

[0004] 2. The inversion of the existing geostress field has low efficiency. Summary of the Invention

[0005] To address the problems of low accuracy and efficiency in existing geostress inversion methods due to the artificial setting of physical and mechanical parameters, this invention proposes a geostress field inversion method, device, and medium based on Bayesian optimization, which can improve inversion efficiency and accuracy.

[0006] The objective of this invention is achieved through the following technical solution: The first aspect of this invention discloses a Bayesian optimization-based method for inverting geostress fields, comprising the following steps: Step A: Obtain the parameters generated by the proxy model and initialize the number of loops. The parameters include boundary parameters and physical and mechanical parameters, including the elastic modulus. Step B: Calculate the prior probabilities of the Bayesian model parameters based on the parameters. Step C: Simulate the simulated stress according to the parameters, and obtain the likelihood probability of the Bayesian model parameters based on the simulated stress and the corresponding measured stress; Step D: Obtain the objective function based on the prior probability and likelihood probability, and add the objective function and its corresponding parameters to the optimization dataset; Step E: Update the loop count and determine if the loop count is greater than or equal to a threshold; Step F: In response to the number of iterations being less than a threshold, add the parameters and objective function to the sample set of the surrogate model to update the surrogate model, and then repeat step BE after obtaining the new parameters; Step G: In response to the number of iterations being greater than or equal to a threshold, determine the minimum value of the objective function in the optimized dataset and perform simulation based on the parameters corresponding to the objective function to obtain the geostress field.

[0007] The second aspect of the present invention discloses a geostress field inversion device based on Bayesian optimization, comprising a memory and a controller connected in series. The memory stores a computer program, and the controller is used to read the computer program and execute the geostress field inversion method based on Bayesian optimization described in the first aspect.

[0008] The third aspect of the present invention discloses a computer-readable storage medium storing instructions that, when executed on a computer, perform a Bayesian optimization-based geostress field inversion method as described in the first aspect and any possible design thereof.

[0009] The beneficial effects of this invention are: 1. By adopting the method of this scheme, physical and mechanical parameters are included in the optimization scope, and experimental information and engineering experience are incorporated in a priori form, which can improve the accuracy of geostress field inversion.

[0010] 2. The method adopted in this scheme is based on Bayesian optimization. During the iterative optimization process, historical data and prior information are used to guide the search process, which greatly improves the efficiency of geostress field inversion. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0014] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0015] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined with each other.

[0016] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0017] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are only used for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. In addition, the terms "first," "second," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0018] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0019] The first aspect of this invention discloses a Bayesian optimization-based method for inverting geostress fields. This method can be, but is not limited to, executed by a geostress field inversion device. The geostress field inversion device can be software, or a combination of software and hardware, and can be integrated into smart devices such as mobile terminals, tablets, and computers. Figure 1 As shown, the method includes steps A through G. It should be noted that the step identifiers in this scheme are only for the convenience of describing the method and do not constitute a limitation on the order of steps. The order of each step is based on its verbal description and the sequential connection of each signal.

[0020] Step A: Obtain the parameters generated by the proxy model and initialize the number of iterations. The parameters include boundary parameters and physical and mechanical parameters. The physical and mechanical parameters include the elastic modulus. The boundary parameters are stress boundary condition parameters or displacement boundary condition parameters.

[0021] The initial surrogate model is trained using an initial sample set, taking the parameters from the initial sample set as input and the objective function as output. The parameters in the initial sample set include boundary parameters and physical / mechanical parameters, which are extracted from the parameter search space using a random sampling algorithm. t 0 samples The FLAC3D numerical simulation was called sequentially to calculate the simulated stress. The objective function is then calculated. FLAC3D (Fast Lagrangian Analysis of Continua) is a simulation software developed by ITASC, Inc. in the United States.

[0022] use t 0 samples Once the initial surrogate model is trained, it can generate the next set of parameters.

[0023] The optimization parameters in this scheme include not only boundary parameters. X 1. It also includes physical and mechanical parameters. X 2. The entire inversion process does not require subjective setting of physical and mechanical parameters. Through continuous optimization, the accuracy of these parameters is improved, further enhancing the precision of the geostress field inversion. The physical and mechanical parameters include at least one of the following: elastic modulus, Poisson's ratio, cohesion, and angle of internal friction.

[0024] The more types of physical and mechanical parameters are added for optimization, the higher the accuracy of the geostress field inversion. However, the corresponding computational efficiency will be reduced. Therefore, while balancing accuracy and computational efficiency, when there is only one physical and mechanical parameter, the elastic modulus should be used first. When there are two physical and mechanical parameters, the physical and mechanical parameters include the elastic modulus and Poisson's ratio.

[0025] Step B: Calculate the prior probabilities of the Bayesian model parameters based on the parameters.

[0026] Parameter X includes boundary parameters X 1 and physical and mechanical parameters X 2. Boundary parameters are determined based on the researcher's subjective understanding of the regional geostress formation process and influencing factors. Generally, boundary parameters lack reference information and can only be roughly estimated in terms of their possible range. Therefore, weak information priors are assigned to the boundary parameters.

[0027] Assume boundary parameters any parameter x i The range of values ​​is N1 represents the number of boundary parameters, ai represents the lower boundary of the boundary parameters, bi represents the upper boundary of the boundary parameters, and T represents the transpose. The lower boundary of ai and the upper boundary of bi can be set empirically. Within the reference range, the parameters follow a uniform distribution; sampling beyond the parameter range is truncated. In summary, the probability density function of the boundary parameters can be expressed as: .

[0028] Based on basic geological understanding, it is assumed that the boundary parameters are independently distributed; therefore, the parameter set... The joint probability density function can be expressed as: .

[0029] Physical and mechanical parameters X The priors for 2 are specified based on physical and mechanical experiments, engineering analogies, or experience. For this parameter set... any parameter in x j Assuming it follows a Gaussian distribution Physical and mechanical parameters x j mean μ j and variance Based on empirical information, its probability density function is determined as follows: .

[0030] Assuming that the physical and mechanical parameters of each rock mass are independent, the parameter set The joint probability density function can be expressed as: .

[0031] In the formula, N 1+1 is the number of the first physical and mechanical parameter; N is the total number of boundary parameters and physical and mechanical parameters.

[0032] Parameter setX 1. Follows a uniform distribution, parameter set X 2. They follow a Gaussian distribution and are independent events. Therefore, the parameter set for geostress field inversion is... X The joint probability density distribution can be expressed as: .

[0033] The prior probability P(of the Bayesian model parameters can then be obtained.) X ).

[0034] Step C: Simulate the stress according to the parameters, and obtain the likelihood probability of the Bayesian model parameters based on the simulated stress and the corresponding measured stress. .

[0035] Assuming that the geostress measurement error follows a zero-mean normal distribution, the likelihood function is defined in the form of a Gaussian probability density function: , in, and They are the first i The simulated stress, measured stress, and standard deviation are parameters, with the standard deviation set according to the confidence level of the simulation error.

[0036] Step D: Obtain the objective function based on the prior probability and likelihood probability, and add the objective function and its corresponding parameters to the optimization dataset.

[0037] make for k One field test value of geostress, Optimize parameters. According to Bayes' theorem, model parameters... The posterior probability can be expressed as: .

[0038] According to Bayes' theorem, to maximize the posterior probability Solving parameters in this way X This is to achieve the inversion of the geostress field. That is: .

[0039] Combining the prior and posterior probability formulas, to adhere to the optimization principle and ensure numerical stability, the negative logarithm of maximizing the posterior probability is taken as the objective function for model optimization: .

[0040] The objective function is: in, β i ,β j For constant coefficients, C It is a constant.

[0041] Step E: Update the loop count and determine if the loop count is greater than or equal to a threshold.

[0042] The threshold for the number of iterations can be set according to the specific circumstances.

[0043] Step F: In response to the number of iterations being less than a threshold, the parameters and objective function are added to the sample set of the surrogate model to update the surrogate model. After obtaining the new parameters, step BE is repeated until the number of iterations is greater than or equal to a threshold.

[0044] Step G: In response to the number of iterations being greater than or equal to a threshold, determine the minimum value of the objective function in the optimized dataset and perform simulation based on the parameters corresponding to the objective function to obtain the geostress field.

[0045] Specifically, after determining the parameters corresponding to the minimum value of the objective function in this step, FLAC3D is called to perform forward calculations to obtain the optimal geostress field.

[0046] By incorporating physical and mechanical parameters into the optimization process and integrating experimental information and engineering experience in a priori form, the accuracy of geostress field inversion can be improved.

[0047] The method adopted in this scheme is based on Bayesian optimization. During the iterative optimization process, historical data and prior information are used to guide the search process, which greatly improves the efficiency of geostress field inversion.

[0048] The second aspect of this invention discloses a Bayesian optimization-based geostress field inversion device, comprising a memory and a controller connected in series. The memory stores a computer program, and the controller reads the computer program and executes the Bayesian optimization-based geostress field inversion method described in the first aspect. Specifically, the memory may include, but is not limited to, random-access memory (RAM), read-only memory (ROM), flash memory, first-in-first-out (FIFO) memory, and / or first-in-last-out (FILO) memory, etc.; the controller may not be limited to using a microcontroller of the STM32F105 series. Furthermore, the computer device may also include, but is not limited to, a power supply unit, a display screen, and other necessary components.

[0049] The third aspect of the present invention discloses a computer-readable storage medium storing instructions that, when executed on a computer, perform a Bayesian optimization-based geostress field inversion method as described in the first aspect and any possible design thereof.

[0050] The operating principles of the apparatus and medium disclosed in the second and third aspects of this invention are detailed in the first aspect and will not be repeated here.

[0051] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for inverting geostress fields based on Bayesian optimization, characterized in that, Includes the following steps: Step A: Obtain the parameters generated by the proxy model and initialize the number of iterations. The parameters include boundary parameters and physical and mechanical parameters. The physical and mechanical parameters include the elastic modulus. The boundary parameters are stress boundary condition parameters or displacement boundary condition parameters. Step B: Calculate the prior probabilities of the Bayesian model parameters based on the parameters. Step C: Simulate the simulated stress according to the parameters, and obtain the likelihood probability of the Bayesian model parameters based on the simulated stress and the corresponding measured stress; Step D: Obtain the objective function based on the prior probability and likelihood probability, and add the objective function and its corresponding parameters to the optimization dataset; Step E: Update the loop count and determine if the loop count is greater than or equal to a threshold; Step F: In response to the number of iterations being less than a threshold, add the parameters and objective function to the sample set of the surrogate model to update the surrogate model, and then repeat step BE after obtaining the new parameters; Step G: In response to the number of iterations being greater than or equal to a threshold, determine the minimum value of the objective function in the optimized dataset and perform simulation based on the parameters corresponding to the objective function to obtain the geostress field; The surrogate model is trained from the initial sample set, taking the parameters in the initial sample set as input and the objective function as output. The parameters in the initial sample set include boundary parameters and physical and mechanical parameters. A random sampling algorithm is used to draw t0 sets of samples X from the parameter set search space. t0 The FLAC3D numerical simulation was called sequentially to calculate the simulated stress. Then the objective function is calculated. The prior probabilities of the Bayesian model parameters calculated based on the parameters are: Calculate the boundary parameter x based on the lower boundary, upper boundary, and number of boundary parameters. i The joint probability density function P(X1). ， ， In the formula, a i The lower boundary is the boundary parameter. b i For the upper boundary of the boundary parameters, N 1 represents the number of boundary parameters; Calculate physical and mechanical parameters x j The joint probability density function P(X2), ， In the formula, µ j Physical and mechanical parameters x j The mean, σ 2 j Physical and mechanical parameters x j The variance; 𝑁1+1 is the number of the first physical mechanical parameter; N is the total number of boundary parameters and physical mechanical parameters; According to the boundary parameters x i The joint probability density function P(X1) and physical and mechanical parameters x j The prior probability P(X) of the Bayesian model parameters is obtained by calculating the joint probability density function P(X2). ； The simulated stress is obtained based on the parameters, and the likelihood probability of the Bayesian model parameters is obtained based on the simulated stress and the corresponding measured stress: ， In the formula, For the likelihood probability of the Bayesian model parameters, and They are the first i Simulated stress, measured stress, and standard deviation of each parameter; The objective function obtained based on the prior probability and the likelihood probability is: ， In the formula, M(X) is the objective function. β i , β j Here, is a constant coefficient, and C is a constant.

2. The geostress field inversion method based on Bayesian optimization according to claim 1, characterized in that, The physical and mechanical parameters also include at least one of Poisson's ratio, cohesion, and internal friction angle.

3. A Bayesian optimization-based geostress field inversion device, comprising a memory and a controller connected in series, wherein the memory stores a computer program, and the controller is used to read the computer program and execute the Bayesian optimization-based geostress field inversion method according to any one of claims 1-2.

4. A computer-readable storage medium storing instructions thereon, characterized in that: When the instructions are executed on a computer, the geostress field inversion method based on Bayesian optimization as described in any one of claims 1-2 is performed.

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