Transformer substation grounding grid structure parameter identification and reliability evaluation method based on variable dimension Bayesian

Abstract

The invention relates to a transformer substation grounding grid structure parameter identification and reliability evaluation method based on variable dimension Bayesian, and belongs to the field of parameter identification, and the method comprises the following steps: S1, initializing an electromagnetic model of a transformer substation grounding grid; s2, sampling based on reversible jump Markov chain Monte Carlo (RJMCMC), and generating a parameter sample; s3, performing statistical analysis on the recognition result based on posterior probability distribution, and outputting a reliability range and a credible interval of the parameters so as to judge whether convergence occurs or not; and S4, after a sampling convergence condition is reached, outputting a posterior probability density function of the parameter and a grounding grid structure parameter. The method has a reliable quantification capability, reduces the dependence of an initial model, and enhances the adaptability of the model.

Description

Technical Field

[0001] This invention belongs to the field of parameter identification and relates to a method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods. Background Technology

[0002] In the field of substation grounding grid parameter identification, traditional methods typically rely on deterministic algorithms, such as least squares gradient descent. While these methods can obtain approximate structural parameters under specific conditions, they generally depend on pre-defined simplified models. For complex situations in actual grounding grids, such as irregular structures and uneven conductor distribution, it is difficult to construct a grounding grid structure model that truly matches the actual situation. Furthermore, these methods are highly sensitive to the initial model; obtaining near-realistic initial parameters in real-world scenarios is often extremely difficult, easily leading to the solution getting trapped in local optima and thus failing to accurately identify key parameters.

[0003] Traditional methods only provide a single "optimal solution" and lack the ability to quantitatively analyze the reliability, uncertainty, and error range of the solution. In practical applications, this method is difficult to provide sufficient basis for subsequent design and evaluation. Once affected by noise or model bias, it will directly affect parameter judgment and safety redundancy design, resulting in high engineering risks. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods. This method quantifies the confidence interval of model parameters by establishing a probabilistic parameter identification framework, uses the nonlinear parameter identification results as the initial model, and proposes a dual-factor (adaptive step size adjustment factor and convergence acceleration factor) control strategy to enable the sampling process to cover the high-probability region of the parameter space, thereby providing a relatively efficient parameter reliability estimation strategy for electromagnetic data detected by substation grounding grids.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for identifying structural parameters and assessing the reliability of substation grounding grids based on variable-dimensional Bayesian methods includes the following steps:

[0007] S1: Initialize the electromagnetic model of the substation grounding grid;

[0008] S2: Generate parameter samples based on Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampling;

[0009] S3: Perform statistical analysis on the recognition results based on the posterior probability distribution, output the reliability range and confidence interval of the parameters, and thus determine whether convergence has occurred;

[0010] S4: After the sampling convergence condition is met, output the posterior probability density function of the parameters and the grounding grid structure parameters.

[0011] Furthermore, in this method, in order to base the observation data d obs To estimate the model parameters m that best reflect the actual condition of the grounding grid, a Bayesian framework is introduced, and the formula is shown below:

[0012]

[0013] Within the Bayesian framework, the solution for the geoelectric model parameter m follows Bayes' theorem, which involves estimating the posterior probability distribution P(m|d) of the model given the observed data d. P(m|d) represents the posterior probability distribution, i.e., the probability of each possible geoelectric model m after measuring the electromagnetic data d; P(d|m) is the likelihood function, describing the probability of observing electromagnetic data d given the geoelectric model m, i.e., the degree of fit between the model and the observed data; P(m) is the prior distribution, reflecting the expectation of the model parameters before incorporating the observed data; and P(d) is the marginal likelihood function, serving as a normalization factor to ensure the normalization of the posterior probability density. Its value is calculated by comprehensively considering the contributions of all possible geoelectric models to the data d.

[0014] Furthermore, the initialization of the electromagnetic model of the substation grounding grid in step S1 includes:

[0015] Input initial parameters, prior information, and electromagnetic data; model parameters include resistivity, number of layers, interface depth, and noise impact parameters;

[0016] The initial model m(0) is generated based on the Snow Ablation Optimizer (SAO) algorithm; the likelihood function p(d|m(0)) is generated.

[0017] The parameters constraining resistivity, number of layers, interface depth, and noise influence are expressed as follows:

[0018] p(m)=p(k)·p(z|k)·p(ρ|k)·p(dn)

[0019] Where p(m) is the probability of model m, k represents the number of underground layers, p(k) is the probability of the kth layer, p(z|k) is the probability of the thickness of each layer based on the kth layer, p(p|k) is the probability of the resistivity of each layer based on the kth layer, and p(dn) is the probability of noise occurring.

[0020] Furthermore, in step S2, a two-factor controlled iterative method is used to control the weight of prior information and the sampling step size, thereby constructing a complete electromagnetic data distribution model.

[0021] In the proposed distribution sampling phase, candidate models are built based on resistivity, interface depth, and the number of model layers. There are two methods for generating candidate models: RJMCMC uses a birth-death mechanism to adjust the number of layers and the interface depth; after determining the number of layers and the interface, the resistivity of each layer is adjusted. The proposed distribution function q(m′|m) in the RJMCMC sampling process consists of the following three parts:

[0022] q(m′|m)=q(k′|k)·q(z′|k′,z)·q(ρ′|k′,z′,ρ)

[0023] Where q(k′|k) represents the change of the number of layers controlled by the Birth / Death mechanism; q(z′|k′,z) controls the adjustment of the interface depth after the number of layers is determined; q(ρ′|k′,z′,ρ) controls the adjustment of resistivity; the update method of the resistivity parameter is determined by the proposed distribution and follows a Gaussian distribution, that is, the new resistivity value is randomly sampled from the Gaussian distribution, and the mean of this Gaussian distribution is the resistivity value of the current model. Therefore, excluding the grounding grid layer, the expression is:

[0024]

[0025] Where, ρ k′ Resistivity and mean vector of the candidate model ω is the current model resistivity, and both are logarithmic in the calculation process; the physical meaning of ω is to balance the weight between model constraints and data fitting; the sampling step size is controlled by the posterior covariance matrix, and a scaling factor c is introduced as a scale factor to dynamically adjust the step size; It is the posterior covariance matrix;

[0026]

[0027] Where c is the trigonometric function learning factor, and c is the sum of c1 and c2.

[0028] Furthermore, RJMCMC updates the model in the following four ways:

[0029] 1. Birth Move: At this point, k′ = k + 1, based on the minimum depth z in the prior information. min and maximum depth z max Choose a random position between the given points as the new interface. This interface will conform to U(z) min ,z maxThe resistivity of a new stratum is formed by a uniform distribution of ρ and σ, and the resistivity of this stratum follows a normal distribution N(ρ,σ). birth 2 ), where ρ is the resistivity of the current interface;

[0030] 2. Layer Removal (Death Move): At this point, k′ = k-1. In the geoelectric model, one layer is randomly selected and removed.

[0031] 3. Layer Perturbation Move: In this case, k′=k. Under the condition that the number of interfaces remains unchanged, a layer interface is randomly selected to change position, and the change step size follows N(0,σ). move 2 )normal distribution;

[0032] 4. Resistivity Change: At this point, k′=k, z′=z, the number of layers and the interface position remain unchanged, only the resistivity is changed, and the change step size follows N(ρ,σ) change 2 The resistivity of the interface is to be changed according to the normal distribution.

[0033] Set the sampling probability of the first three perturbation types (Birth, Death, Perturbation) to 1 / 6, and increase the probability of resistivity change to 1 / 2.

[0034] Furthermore, whenever a model is generated, a receive-reject parameter is set to determine whether the model is accepted. Based on the Metropolis-Hastings sampling principle, the acceptance probability α(m'|m) is obtained using the following formula:

[0035]

[0036] In the formula, matrix J is the Jacobian matrix for transforming model m to model m′. When the transformation involves a jump between dimensions, the Jacobian matrix can normalize the volume difference between two spaces of different dimensions. The determinant of the Jacobian matrix is ​​|J|=1; p(d|m') / p(d|m), p(m') / p(m), and q(m|m') / q(m'|m) are the likelihood ratio, prior probability ratio, and proposal probability ratio of the new and old models, respectively.

[0037] During the RJMCMC sampling process, the above formula generates a number ξ randomly in the interval between 0 and 1, compares the size of ξ with α(m'|m), and if ξ < α(m'|m), the candidate model is accepted; otherwise, it is rejected, and sampling continues to generate a new proposed model until the model converges or reaches the maximum sampling threshold.

[0038] Furthermore, in step S3, during Bayesian structural parameter identification, the likelihood function is the core of posterior probability calculation, and its expression is written as:

[0039]

[0040] Prior variance matrix C d The diagonal elements represent the reliability of the measurement data, i.e., the variance, and it is assumed by default that the data errors are mutually exclusive. C d The larger the determinant, the greater the measurement error. In this case, the influence of the prior factor should be increased during sampling. Therefore, a weighting factor ω2 is added to control the influence of prior information on sample generation. N d The likelihood function is a measure of the goodness of fit between the forward response data of a certain model structure parameters and the actual observed data, where is the number of observation data.

[0041] The sampling convergence condition is defined as follows: the model's confidence interval and the standard deviation of its error are both sufficiently stable during the sampling iteration process. The stability condition for the model's confidence interval and the standard deviation of its error are set as follows:

[0042]

[0043] Where CR(x) is the boundary value of the confidence interval in the x-th sampling, S i This represents the current cumulative sampling count, excluding the sampling count during the Burn-in phase. S0 is the preset interval sampling count. When the Sth... i When the fluctuation of the confidence interval of the model in the second sampling is less than k1% compared with the confidence interval of the model in the previous S0 sampling, it is considered that the stability condition of the model confidence interval has been reached.

[0044] The stability condition for the standard deviation of the error is that the system calculates the statistical characteristics of the model fitting error every certain number of iterations N_refresh, and maintains a sliding window N_end during the sampling process to record the root mean square error σ in each of the most recent N iterations. std When σ std When the value is less than the preset threshold σ, the sampling process is considered to have entered a stable phase, which is regarded as a signal of "sampling end". An upper limit is set for the number of consecutive rejected models. Once triggered, the sampling process will be automatically interrupted to avoid wasting computing resources.

[0045] The beneficial effects of this invention are as follows:

[0046] (1) Possesses reliability quantification capability

[0047] This method performs statistical analysis on the recognition results based on the posterior probability distribution, and can output the reliability range and confidence interval of the parameters, thereby realizing the reliability assessment of the recognition results.

[0048] (2) Reduce the dependence on the initial model

[0049] The RJMCMC algorithm is used for global sampling search to avoid getting trapped in local optima, thus improving the stability and robustness of the algorithm in the presence of measurement errors or structural nonlinearity.

[0050] (3) The adaptability of the model

[0051] This method is applicable to grounding grid parameter identification tasks in different environments, and has good versatility and scalability. It can also be extended to electromagnetic detection tasks such as tower grounding electrode detection and urban underground equipment detection.

[0052] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0053] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0054] Figure 1 Flowchart of structural parameter identification method;

[0055] Figure 2 This is a graph showing the change of the learning factor with the number of iterations.

[0056] Figure 3 The diagram illustrates four states of the new RJMCMC sampling model: (a) layer increase, (b) layer deletion, (c) layer perturbation, and (d) resistivity update.

[0057] Figure 4 Flowchart for identifying structural parameters of substation grounding grid. Detailed Implementation

[0058] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0059] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0060] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0061] Example 1:

[0062] This invention belongs to the field of parameter identification technology for substation grounding networks. It proposes a variable-dimensional Bayesian algorithm based on Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampling to achieve structural parameter identification and reliability assessment of substation grounding networks. This invention aims to solve the problems of inaccurate identification of substation grounding network structural parameters and the lack of reliability assessment. Given that grounding networks are often buried underground and structural parameters (such as burial depth and topology) are difficult to obtain directly, traditional identification methods often suffer from insufficient accuracy when dealing with complex structures. Furthermore, existing methods typically only provide a single optimal solution and cannot effectively model and quantify the uncertainty of parameter identification results, lacking reliability assessment capabilities. Therefore, this patent proposes a variable-dimensional Bayesian algorithm based on RJMCMC sampling, which can achieve adaptive identification of structural parameters even when the parameter dimension is uncertain, and quantitatively assess the reliability and robustness of the identification results through posterior probability distribution.

[0063] In the field of substation grounding grid parameter identification, traditional methods typically rely on deterministic algorithms, such as least squares gradient descent. While these methods can obtain approximate structural parameters under specific conditions, they still suffer from the following two key shortcomings:

[0064] 1. Parameters are difficult to identify accurately.

[0065] Traditional parameter identification methods generally rely on pre-set simplified models, making it difficult to construct a grounding grid structure model that truly matches the complexities of actual grounding grids, such as irregular structures and uneven conductor distribution. Furthermore, these methods are highly sensitive to the initial model; obtaining near-realistic initial parameters in real-world scenarios is often extremely difficult, easily leading to the solution getting trapped in local optima and thus failing to accurately identify key parameters.

[0066] 2. Lack of reliability assessment mechanism

[0067] Traditional methods only provide a single "optimal solution" and lack the ability to quantitatively analyze the reliability, uncertainty, and error range of the solution. In practical applications, this method is difficult to provide sufficient basis for subsequent design and evaluation. Once affected by noise or model bias, it will directly affect parameter judgment and safety redundancy design, resulting in high engineering risks.

[0068] To address the non-uniqueness problem in substation grounding grid parameter identification and the limitation of traditional parameter identification methods that can only provide a single optimal solution, a variable-dimensional Bayesian probabilistic parameter identification method is proposed. This method quantifies the reliability interval of model parameters by establishing a probabilistic parameter identification framework, uses the nonlinear parameter identification results as the initial model, and proposes a dual-factor control strategy (adaptive step size adjustment factor and convergence acceleration factor) to ensure that the sampling process covers the high-probability region of the parameter space. This provides a relatively efficient parameter reliability estimation strategy for electromagnetic data from substation grounding grid detection.

[0069] The process for identifying the structural parameters of a substation grounding grid is as follows: Figure 1 and Figure 4 As shown, the key steps in applying the Bayesian method to identify the structural parameters of a substation grounding grid include structural parameter initialization and sample generation, posterior probability estimation, and model convergence assessment. Based on these steps, the posterior probability distribution of the substation grounding grid structural parameters can be effectively estimated. Given observation data, the reliability of each parameter can be quantified, thereby identifying the grounding grid parameters that best match the observation information.

[0070] The purpose of parameter identification is to identify parameters based on the observed data d. obsThe model parameters *m* that best represent the actual grounding grid are estimated. However, due to the unreliability of observation data, parameter identification often faces challenges such as non-uniqueness and data errors caused by noise. Even with the same observation data, multiple reasonable underground structure models may correspond. To more reasonably characterize the unreliability of parameter identification results and fully utilize existing geological information, a Bayesian framework is introduced, as shown in the following formula:

[0071]

[0072] Within the Bayesian framework, the solution for the geoelectric model parameter m follows Bayes' theorem, which involves estimating the posterior probability distribution P(m|d) of the model given the observed data d. Here, P(m|d) represents the posterior probability distribution, which assesses the probability of each possible geoelectric model m after measuring the electromagnetic data d—the primary objective of Bayesian inference. P(d|m) is the likelihood function, describing the probability of observing electromagnetic data d given the geoelectric model m, i.e., the degree of fit between the model and the observed data. P(m) is the prior distribution, reflecting the expectation of the model parameters before incorporating the observed data; in this embodiment, the prior information is constrained based on relevant standards and field measurement information. P(d) is the marginal likelihood function, serving as a normalization factor to ensure the normalization of the posterior probability density; its value is calculated by comprehensively considering the contributions of all possible geoelectric models to the data d.

[0073] (1) Model initialization

[0074] In the electromagnetic model of a substation grounding grid, key model parameters mainly include resistivity, number of layers, and interface depth. Within a Bayesian framework, these parameters are perturbed and updated using the RJMCMC algorithm. Before parameter identification, an optimization strategy is introduced to construct a near-optimal initial model to accelerate the convergence process during the preheating phase. It is important to emphasize that this initial model is only used to optimize sampling efficiency and is not used as the final solution. Inspired by the "snow melting" mechanism in the Snow ablation optimizer (SAO), which exhibits a good balance between global search and local exploration (ENE), it can be used to generate an initial solution that more closely approximates the actual model distribution, thereby improving the overall efficiency of the RJMCMC sampling process. Furthermore, during model parameter setting, parameter thresholds need to be set based on prior information. The resistivity search range is typically set based on known geological information, as different substation grounding grid soil environments have different resistivity ranges. The constraints are mainly on resistivity, number of layers, interface depth, and noise impact parameters, as shown in the following expression:

[0075] p(m)=p(k)·p(z|k)·p(ρ|k)·p(dn) (2)

[0076] Where p(m) is the probability of model m, k represents the number of underground layers, p(k) is the probability of the kth layer, p(z|k) is the probability of the thickness of each layer based on the kth layer, p(p|k) is the probability of the resistivity of each layer based on the kth layer, and p(dn) is the probability of noise occurring.

[0077] (2) Parameter sample generation based on RJMCMC

[0078] The primary objective of RJMCMC sampling is to find an optimal set of subsurface electrical models that best fits the observed data. However, due to the non-uniqueness of geophysical inversion, multiple possible models can often explain the same data. Furthermore, due to the implicit natural parsimony criterion in Bayesian rules, models tend to favor those with fewer layers during generation, resulting in incomplete sampling. Therefore, the goal of sample generation is not to find a unique solution, but rather to sample all possible models and ultimately select the set of models that best fits the observed data.

[0079] The basic process of RJMCMC is the same as MCMC: candidate models are generated from the proposal distribution, and the acceptance probability determines whether to accept a candidate model. RJMCMC introduces a variable-dimensional mechanism, allowing the model to freely jump between different dimensional model spaces, thus enabling more flexible search for the optimal solution. Furthermore, to improve sampling accuracy and efficiency, it introduces an ω-c two-factor method to enhance resistivity resolution and dynamically controls the sampling step size.

[0080] Based on the horizontal layered model of the substation grounding network, an iterative method using two-factor control (ω-c) is proposed, which controls the weight of prior information and the sampling step size, respectively, to construct a complete electromagnetic data distribution model. In the proposed distribution sampling stage, candidate models are built for the three main parameters of parameter identification (resistivity, interface depth, and number of model layers). There are two main methods for generating candidate models: RJMCMC uses a Birth-Death mechanism to adjust the number of layers and the interface depth; after determining the number of layers and the interface, the resistivity of each layer is adjusted. Therefore, the proposed distribution function q(m′|m) in the RJMCMC sampling process consists of the following three parts:

[0081] q(m′|m)=q(k′|k)·q(z′|k′,z)·q(ρ′|k′,z′,ρ) (3)

[0082] Where q(k′|k) represents the change of the number of layers controlled by the Birth / Death mechanism; q(z′|k′,z) controls the adjustment of the interface depth after the number of layers is determined; and q(ρ′|k′,z′,ρ) controls the adjustment of resistivity. The update method for the resistivity parameter is determined by the proposed distribution and follows a Gaussian distribution. That is, the new resistivity value is randomly sampled from the Gaussian distribution, and the mean of this Gaussian distribution is the resistivity value of the current model. Therefore, excluding the grounding grid layer, the expression is:

[0083]

[0084] Where, ρ k ′ represents the resistivity and mean vector of the candidate model. This refers to the current model resistivity; both are calculated using logarithms. ω is used to balance the weights between model constraints and data fitting. The sampling step size is controlled by the posterior covariance matrix, and a scaling factor c is introduced as a scaling factor to dynamically adjust the step size. It is the posterior covariance matrix.

[0085]

[0086] Here, c is the trigonometric function learning factor, and c2 is the sum of c1 and c2. Introducing the trigonometric function learning factor balances the weights of the early global search phase with those of the later convergence phase, making the formula non-linear and thus exhibiting faster convergence speed and higher accuracy in most optimization functions. Furthermore, the values ​​of c1 and c2 remain between 0.5 and 2.5, and their trends over time are as follows: Figure 2 As shown.

[0087] At this point, RJMCMC updates the model in the following four ways:

[0088] 1. Birth Move: At this point, k′ = k + 1, based on the minimum depth z in the prior information. min and maximum depth z max Choose a random position between the given points as the new interface. This interface will conform to U(z) min ,z max The resistivity of a new stratum is formed by a uniform distribution of ρ and σ, and the resistivity of this stratum follows a normal distribution N(ρ,σ). birth 2 ), where ρ is the resistivity of the current interface.

[0089] 2. Layer Deletion (Death Move): At this time, k′=k-1, and a layer is randomly selected to be removed in the geoelectric model.

[0090] 3. Layer Perturbation Move: In this case, k′=k. Under the condition that the number of interfaces remains unchanged, a layer interface is randomly selected to change position, and the change step size follows N(0,σ). move 2 )normal distribution.

[0091] 4. Resistivity Change: At this point, k′=k, z′=z, the number of layers and the interface position remain unchanged, only the resistivity is changed, and the change step size follows N(ρ,σ) change 2 The resistivity of the interface is to be changed according to the normal distribution.

[0092] It should be noted that since the thickness and resistivity of the grounding grid are much smaller than those of the generated model, parameter identification will first determine whether the layer thickness is greater than or equal to 0.1 and whether the resistivity is greater than 0 (using logarithmic form in the calculation) when updating the model.

[0093] Because changes in the number of layers and interface depth have a significant impact on the model, excessively frequent adjustments to the number of layers during sampling make RJMCMC sampling difficult to converge, and excessive interface perturbations may lead to model instability. Therefore, the sampling probability of the first three perturbation types (Birth, Death, Perturbation) is set to 1 / 6 to prevent excessively frequent layer adjustments. The probability of resistivity change is also increased to 1 / 2, allowing the model to fully optimize the resistivity distribution with a fixed number of layers. The state changes are obtained as follows: Figure 3 As shown.

[0094] Figure 3 This paper demonstrates four possible states for generating new models through RJMCMC sampling: (a) increasing the number of layers, (b) deleting layers, (c) perturbing the number of layers, and (d) updating the resistivity. However, not all generated models are suitable for the sampled data. Therefore, during the sampling process, the generated models need to be evaluated using a probabilistic model to determine their applicability. This process ensures that the model can reasonably fit the observed data and improves the stability and reliability of the parameter identification results.

[0095] Whenever a model is generated, an accept / reject parameter needs to be set to determine whether the model is accepted. Based on the Metropolis-Hastings sampling principle, the acceptance probability α(m'|m) is obtained using the following formula:

[0096]

[0097] In the formula, matrix J is the Jacobian matrix for transforming model m to model m′. When the transformation involves a jump between dimensions, the Jacobian matrix can normalize the volume difference between two spaces of different dimensions. In the RJMCMC sampling method proposed in this invention, the determinant of the Jacobian matrix is ​​|J|=1, ensuring that the transformation between different dimensions meets the invertibility requirement. In the formula, p(d|m') / p(d|m), p(m') / p(m), and q(m|m') / q(m'|m) are the likelihood ratio, prior probability ratio, and proposal probability ratio of the new and old models, respectively.

[0098] During the RJMCMC sampling process, equation (6) generates a random number ξ in the interval between 0 and 1, compares ξ with α(m'|m). If ξ < α(m'|m), the candidate model is accepted; otherwise, it is rejected, and sampling continues to generate new proposed models until the model converges or reaches the maximum sampling threshold. This sampling mechanism ensures that the sampling density in high-probability regions of the model space is higher than that in low-probability regions, improving sampling efficiency and the convergence of the posterior distribution. Finally, after the sampling process is completed, statistical methods can be used to extract the probability density distribution of the posterior resistivity, enabling reliability analysis of underground medium parameters.

[0099] (3) Posterior generalization estimation and reliability assessment methods

[0100] In Bayesian structural parameter identification, the likelihood function is the core of posterior probability calculation, and its main function is to evaluate the data d generated by the candidate model m. model The likelihood function measures the degree of fit between the model and the actual observed data d. A high likelihood value indicates that the model fits the observed data well. After electromagnetic data denoising, the errors caused by measurement and previous signal processing can be considered to conform to a Gaussian model. Therefore, the expression for the likelihood function can be written as:

[0101]

[0102] In equation (7), the prior variance matrix C d The diagonal elements represent the reliability of the measurement data, i.e., the variance, and it is assumed by default that the data errors are mutually exclusive. C d The larger the determinant, the greater the measurement error. In this case, the influence of the prior factor should be increased during sampling. Therefore, a weighting factor ω2 is added to control the influence of prior information on sample generation. N d The likelihood function is a measure of the goodness of fit between the forward response data of a model's structural parameters and the actual observed data, where is the number of observation data.

[0103] Based on the characteristics of RJMCMC sampling, when the model converges, both the model's confidence interval and the fluctuations in error statistics tend to stabilize. To avoid consuming excessive computational resources, we define a convergence condition as achieved when both the model's confidence interval and the standard deviation of the error are sufficiently stable during the sampling iterations. The stability condition for the model's confidence interval and the standard deviation of the error are set as follows:

[0104]

[0105] Where CR(x) is the boundary value of the confidence interval in the x-th sampling, S i This represents the current cumulative sampling count, excluding the sampling count during the Burn-in phase. S0 is the preset interval sampling count. When the Sth... i When the fluctuation of the model confidence interval range of the second sampling is less than k1% compared with the model confidence interval of the previous S0 samplings, it can be considered that the stability condition of the model confidence interval has been reached.

[0106] The stability condition for the standard deviation of the error specifically involves the system calculating the statistical characteristics of the model fitting error every certain number of iterations N_refresh, and maintaining a sliding window N_end during the sampling process to record the root mean square error for each of the most recent N iterations. When this σ... std When the value is less than a preset threshold σ, the sampling process is considered to have entered a stable phase, which is regarded as a signal that "sampling has ended". In addition, to prevent sampling from getting stuck in the low a posteriori region and causing long-term invalid sampling, the system sets an upper limit on the number of consecutively rejected models. Once triggered, the sampling process is automatically interrupted to avoid wasting computational resources.

[0107] Example 2:

[0108] An electronic device, comprising a memory and a processor;

[0109] The memory is used to store computer programs;

[0110] The processor is configured to implement the method described in Embodiment 1 when executing the computer program.

[0111] Example 3:

[0112] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0113] Example 4:

[0114] A computer program product includes a computer program that, when executed by a processor, implements the method described in Example 1.

[0115] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily refer to the same embodiment.

[0116] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0117] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0118] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0119] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0120] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0121] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0122] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying structural parameters and assessing the reliability of substation grounding grids based on variable-dimensional Bayesian methods, characterized in that: Includes the following steps: S1: Initialize the electromagnetic model of the substation grounding grid; S2: Generate parameter samples based on Monte Carlo RJMCMC sampling of reversible jumping Markov chains; S3: Perform statistical analysis on the recognition results based on the posterior probability distribution, output the reliability range and confidence interval of the parameters, and thus determine whether convergence has occurred; S4: After the sampling convergence condition is met, output the posterior probability density function of the parameters and the grounding grid structure parameters.

2. The method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods according to claim 1, characterized in that: In this method, in order to base the observation data d obs To estimate the model parameters m that best reflect the actual condition of the grounding grid, a Bayesian framework is introduced, and the formula is shown below: Within the Bayesian framework, the solution for the geoelectric model parameter m follows Bayes' theorem, which involves estimating the posterior probability distribution P(m|d) of the model given the observed data d. P(m|d) represents the posterior probability distribution, i.e., the probability of each possible geoelectric model m after measuring the electromagnetic data d; P(d|m) is the likelihood function, describing the probability of observing electromagnetic data d given the geoelectric model m, i.e., the degree of fit between the model and the observed data; P(m) is the prior distribution, reflecting the expectation of the model parameters before incorporating the observed data; and P(d) is the marginal likelihood function, serving as a normalization factor to ensure the normalization of the posterior probability density. Its value is calculated by comprehensively considering the contributions of all possible geoelectric models to the data d.

3. The method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods according to claim 1, characterized in that: Step S1, which initializes the electromagnetic model of the substation grounding grid, includes: Input initial parameters, prior information, and electromagnetic data; model parameters include resistivity, number of layers, interface depth, and noise impact parameters; The initial model m(0) is generated based on the snowmelt optimizer SAO algorithm; the likelihood function p(d|m(0)) is generated. The parameters constraining resistivity, number of layers, interface depth, and noise influence are expressed as follows: p(m)=p(k)·p(z|k)·p(ρ|k)·p(dn) Where p(m) is the probability of model m, k represents the number of underground layers, p(k) is the probability of the kth layer, p(z|k) is the probability of the thickness of each layer based on the kth layer, p(p|k) is the probability of the resistivity of each layer based on the kth layer, and p(dn) is the probability of noise occurring.

4. The method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods according to claim 1, characterized in that: In step S2, a two-factor controlled iterative method is used to control the weight of prior information and the sampling step size, thereby constructing a complete electromagnetic data distribution model. In the proposed distribution sampling phase, candidate models are built based on resistivity, interface depth, and the number of model layers. There are two methods for generating candidate models: RJMCMC uses a birth-death mechanism to adjust the number of layers and the interface depth; after determining the number of layers and the interface, the resistivity of each layer is adjusted. The proposed distribution function q(m′|m) in the RJMCMC sampling process consists of the following three parts: q(m′|m)=q(k′|k)·q(z′|k′,z)·q(ρ′|k′,z′,ρ) Where q(k′|k) represents the change of the number of layers controlled by the Birth / Death mechanism; q(z′|k′,z) controls the adjustment of the interface depth after the number of layers is determined; q(ρ′|k′,z′,ρ) controls the adjustment of resistivity; the update method of the resistivity parameter is determined by the proposed distribution and follows a Gaussian distribution, that is, the new resistivity value is randomly sampled from the Gaussian distribution, and the mean of this Gaussian distribution is the resistivity value of the current model. Therefore, excluding the grounding grid layer, the expression is: Where, ρ k′ Resistivity representing the candidate model, mean vector ω is the current model resistivity, and both are logarithmic in the calculation process; the physical meaning of ω is to balance the weight between model constraints and data fitting; the sampling step size is controlled by the posterior covariance matrix, and a scaling factor c is introduced as a scale factor to dynamically adjust the step size; It is the posterior covariance matrix; Where c is the trigonometric function learning factor, and c is the sum of c1 and c2.

5. The method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods according to claim 1, characterized in that: RJMCMC updates the model in the following four ways:

1. Increase the number of layers: Birth Move: At this time, k′=k+1, based on the minimum depth z in the prior information. min and maximum depth z max Choose a random position between the given points as the new interface. This interface will conform to U(z) min ,z max The resistivity of a new stratum is formed by a uniform distribution of ρ and σ, and the resistivity of this stratum follows a normal distribution N(ρ,σ). birth 2 ), where ρ is the resistivity of the current interface; 2. Layer Removal (Death Move): At this point, k′ = k-1. In the geoelectric model, one layer is randomly selected for removal.

3. Layer Perturbation Move: In this case, k′=k. Under the condition that the number of layer interfaces remains unchanged, a layer interface is randomly selected to change position, and the change step size follows N(0,σ). move 2 )normal distribution; 4. Resistivity Change: At this point, k′=k, z′=z, the number of layers and the interface position remain unchanged, only the resistivity is changed, and the change step size follows N(ρ,σ) change 2 The resistivity of the interface is to be changed according to the normal distribution. Set the sampling probability of the first three perturbation types (Birth, Death, Perturbation) to 1 / 6, and increase the probability of updating Resistivity Change to 1 / 2.

6. The method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods according to claim 1, characterized in that: Whenever a model is generated, a accept / reject parameter is set to determine whether the model is accepted. Based on the Metropolis-Hastings sampling principle, the acceptance probability α(m'|m) is obtained using the following formula: In the formula, matrix J is the Jacobian matrix for transforming model m to model m′. When the transformation involves a jump between dimensions, the Jacobian matrix can normalize the volume difference between two spaces of different dimensions. The determinant of the Jacobian matrix takes the value |J| = 1. In the formula, p(d|m') / p(d|m), p(m') / p(m) and q(m|m') / q(m'|m) are the likelihood ratio, prior probability ratio and proposal probability ratio of the new and old models, respectively; During the RJMCMC sampling process, the above formula generates a number ξ randomly in the interval between 0 and 1, compares the size of ξ with α(m'|m), and if ξ < α(m'|m), the candidate model is accepted; otherwise, it is rejected, and sampling continues to generate a new proposed model until the model converges or reaches the maximum sampling threshold.

7. The method for identifying and assessing the structural parameters and reliability of substation grounding grids based on variable-dimensional Bayesian methods according to claim 1, characterized in that: In step S3, during Bayesian structural parameter identification, the likelihood function is the core of posterior probability calculation. The expression for the likelihood function is written as: Prior variance matrix C d The diagonal elements represent the reliability of the measurement data, i.e., the variance, and it is assumed by default that the data errors are mutually exclusive. C d The larger the determinant, the greater the measurement error. In this case, the influence of the prior factor should be increased during sampling. Therefore, a weighting factor ω2 is added to control the influence of prior information on sample generation. N d The likelihood function is a measure of the goodness of fit between the forward response data of a certain model structure parameters and the actual observed data, where is the number of observation data. The sampling convergence condition is defined as follows: the model's confidence interval and the standard deviation of its error are both sufficiently stable during the sampling iteration process. The stability condition for the model's confidence interval and the standard deviation of its error are set as follows: Where CR(x) is the boundary value of the confidence interval in the x-th sampling, S i This represents the current cumulative sampling count, excluding the sampling count during the Burn-in phase. S0 is the preset interval sampling count. When the Sth... i When the fluctuation of the confidence interval of the model in the second sampling is less than k1% compared with the confidence interval of the model in the previous S0 sampling, it is considered that the stability condition of the model confidence interval has been reached. The stability condition for the standard deviation of the error is that the system calculates the statistical characteristics of the model fitting error every certain number of iterations N_refresh, and maintains a sliding window N_end during the sampling process to record the root mean square error σ in each of the most recent N iterations. std When σ std When the value is less than the preset threshold σ, the sampling process is considered to have entered a stable phase, which is regarded as a signal of "sampling end". An upper limit is set for the number of consecutive rejected models. Once triggered, the sampling process will be automatically interrupted to avoid wasting computing resources.

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