A finite element correction method and system for a skip adaptive Kriging proxy model

Abstract

This application discloses a finite element method and system for correcting an adaptive Kriging surrogate model for skips. The method establishes an initial finite element model based on a scaled-down laboratory model of a mining skip, obtains experimentally measured response data, constructs an adaptive Kriging surrogate model, and establishes an objective function. An iterative loop is executed: a candidate sample pool is generated using hybrid sampling; the response and variance are predicted based on the surrogate model; posterior samples are screened using approximate Bayesian calculations; an adaptive hybrid point-addition strategy is used to dynamically adjust the weights of exploration, development, and boundary refinement to select new sample points and update the surrogate model; the iteration continues until the Kullback-Leibler divergence of two consecutive posterior sample distributions is less than a threshold, at which point the statistical characteristics of the posterior samples are calculated to obtain parameter estimates. This invention combines an adaptive surrogate model with approximate Bayesian calculations, reducing the number of calculations, avoiding the likelihood function problem, balancing global search and local development, and achieving high-precision and high-efficiency model correction.

Description

Technical Field

[0001] This application relates to the fields of structural engineering and computational mechanics, and in particular to a finite element method, system, and electronic device for adaptive Kriging proxy model of a winnowing basket. Background Technology

[0002] As a key heavy-duty piece of equipment in mine hoisting systems, the structural safety and reliability of mine skips directly affect the safe production and efficient operation of the mine. During the design, manufacturing, and service of skips, factors such as material property dispersion, manufacturing process deviations, boundary condition uncertainties, and complex load conditions often lead to significant differences between the initially established finite element model and the actual physical structure. This results in simulation predictions (such as static displacement response and dynamic modal frequencies) that do not match laboratory scaled-down models or field measurement data. Therefore, correcting the parameters of the finite element model using measured data to improve its accuracy and predictive ability has significant engineering value for skip structural optimization design, safety assessment, and life prediction.

[0003] Currently, the Kriging surrogate model-based finite element method for model correction is widely used in structural engineering. Its core idea is to replace computationally expensive finite element analysis with a surrogate model, thereby reducing iterations and improving computational efficiency. However, traditional static Kriging surrogate models rely on one-off experimental designs (such as Latin hypercube sampling), and their accuracy may be insufficient in global or local critical regions. Simultaneously, high-order matrix inversion and hyperparameter optimization increase training time, leading to low computational efficiency and difficulty in guaranteeing accuracy. Furthermore, probabilistic statistical methods based on Bayesian inference are commonly used to solve structural parameter identification problems in model correction, and their application in stochastic model correction in engineering has become increasingly widespread in recent years. However, Bayesian inference requires a complete estimate of the posterior probability density function of the parameters, but cannot provide a specific analytical solution. It requires establishing an accurate probability distribution function using a large amount of finite element analysis results and generating a posterior sample distribution using sampling methods, which is challenging for engineering applications. In addition, constructing explicit and easily computable likelihood functions for complex finite element responses presents significant difficulties. Therefore, the application of Bayesian model correction methods in the correction of high-dimensional parametric structural models still faces challenges.

[0004] Especially in the finite element model correction of mining skips, due to the complex structure and numerous parameters to be optimized (such as the thickness of the shroud, the size of the columns, the elastic modulus and density of the materials), traditional methods often require a large number of finite element calculations, resulting in high computational costs. At the same time, due to the limited and noisy measured data, constructing an accurate likelihood function is extremely difficult, making it difficult to directly apply Bayesian inference. In addition, existing surrogate model correction methods mostly focus on algorithm-level optimization and lack customized modeling and parameter selection mechanisms for specific engineering objects (such as mining skips), making it difficult to effectively combine measured response data from scaled-down laboratory models for efficient and accurate model correction. Summary of the Invention

[0005] The main objective of this application is to provide a finite element method, system, and electronic device for correcting an adaptive Kriging surrogate model. This method gradually improves the prediction accuracy of the Kriging model by employing an adaptive hybrid point-addition strategy. It also avoids the difficulty of handling the likelihood function in Bayesian inference by combining an approximate Bayesian computation method, and introduces a preset threshold and Euclidean distance to construct a true posterior approximation. The synergy of these two approaches maximizes the accuracy gain of the surrogate model, resulting in a more accurate correction with higher computational efficiency.

[0006] To achieve the above objectives, this application provides a finite element method for correcting an adaptive Kriging surrogate model for a skip, comprising: establishing an initial finite element model based on a scaled-down laboratory model of a mining skip, and experimentally obtaining measured response data; constructing an initial adaptive Kriging surrogate model, and constructing an objective function based on the measured response data, wherein the adaptive Kriging surrogate model takes the parameters to be optimized in the finite element model as input, and outputs the predicted model response value and prediction variance; wherein the parameters to be optimized include the thickness of the upper shroud, the thickness of the middle shroud, the elastic modulus of the shroud, the mass density of the shroud, the width of the column, the thickness of the column, the elastic modulus of the column, and the mass density of the column; executing an iterative loop until the convergence stopping criterion is met, wherein the iterative loop includes: generating a candidate sample pool according to a hybrid sampling strategy; outputting the model response prediction and prediction variance of each candidate sample in the candidate sample pool based on the current adaptive Kriging surrogate model; and performing an iterative loop according to an approximate Bayesian calculation. The selection criteria are used to select posterior samples from the candidate sample pool. The selection criteria are to retain candidate samples whose objective function values ​​of the model response prediction data and the measured response data are less than an adaptive preset threshold. The distribution of posterior samples approximates a high posterior probability region. New sample points are selected from the candidate sample pool according to an adaptive hybrid addition strategy. The adaptive hybrid addition strategy dynamically adjusts the weights of the exploration term, development term, and boundary refinement term of the addition value function. The exploration term corresponds to the prediction variance of the sample points in the candidate sample pool, the development term corresponds to the objective function value of the sample points in the candidate sample pool, and the boundary refinement term corresponds to the Gaussian kernel function value of the sample points in the candidate sample pool whose objective function value is close to the boundary region of the preset threshold. The new sample points are added to the training set, and the adaptive Kriging surrogate model is retrained and updated. The statistical characteristics of the posterior sample set that satisfy the convergence stopping criterion are calculated to obtain the finite element parameter correction values ​​of the adaptive Kriging surrogate model.

[0007] Optionally, the measured response data includes the structural displacement response obtained through static load tests and the structural modal frequencies obtained through dynamic load tests, and the objective function is expressed as the square of the weighted normalized Euclidean distance between the measured response data and the model response prediction data.

[0008] Optionally, the hybrid sampling strategy includes: when the number of iterations is 1, using Latin hypercube sampling to generate a candidate sample pool in the parameter space; when the number of iterations is greater than or equal to 2 and less than or equal to 5, the space-filling sampling ratio is 50%~70%, the importance sampling ratio is 15%~25%, and the boundary sampling ratio is 15%~25%; when the number of iterations is greater than or equal to 6 and less than or equal to 10, the space-filling sampling ratio is 40%~45%, the importance sampling ratio is 40%~45%, and the boundary sampling ratio is 10%~20%; when the number of iterations is 11 or more, the space-filling sampling ratio is 15%~25%, the importance sampling ratio is 50%~70%, and the boundary sampling ratio is 15%~25%; wherein, the space-filling sampling uses the Latin hypercube method to globally explore the prior space of the parameters to be optimized; the importance sampling uses the Gaussian mixture model method to target and develop the high posterior probability regions that have been discovered; and the boundary sampling uses a boundary sampling method based on prediction variance to sample risk regions close to a preset threshold.

[0009] Optionally, the adaptive preset threshold shrinks adaptively with the number of iterations, the first... The preset threshold for the nth iteration is the nth The preset threshold of the next iteration is multiplied by a shrinkage coefficient, wherein the shrinkage coefficient is a positive number less than 1.

[0010] Optionally, the point-addition value function of the adaptive hybrid point-addition strategy is: ; In the formula, α is the weight of the exploration term, β is the weight of the development term, γ is the weight of the boundary refinement term, σ²(x) represents the variance of the adaptive Kriging surrogate model prediction for the sample points in the candidate sample pool, and 1 / J(x) represents the reciprocal of the objective function value for the sample points in the candidate sample pool, exp(-(J(x)- )² / (2σ²(x))) represents the Gaussian kernel function value of the sample points in the candidate sample pool whose objective function value is close to the preset threshold boundary region. This is represented as a preset threshold for approximate Bayesian computation; The adaptive hybrid point-addition strategy dynamically adjusts the weights of the exploration term, development term, and boundary refinement term in the point-addition value function, including: setting the exploration term weight greater than the development term weight and boundary refinement term weight in the early stage of iteration; setting the exploration term weight equal to or close to the development term weight in the middle stage of iteration; and setting the development term weight greater than the exploration term weight and boundary refinement term weight in the later stage of iteration.

[0011] Optionally, the convergence stopping criterion is as follows: calculate the Kullback-Leibler divergence between the posterior sample distributions of two consecutive iterations; when the Kullback-Leibler divergence is less than a preset divergence threshold, it is determined that the convergence stopping criterion is met and the iteration is terminated; when the Kullback-Leibler divergence is greater than or equal to the preset divergence threshold, the iteration loop continues.

[0012] Optionally, the parameter to be optimized is determined by the finite difference method average sensitivity analysis, including: generating a uniformly distributed sample set in the prior space of candidate parameters; calculating the normalized local sensitivity of each candidate parameter sample relative to the displacement response and modal frequency response; calculating the absolute value of the average sensitivity of each candidate parameter relative to the displacement response and modal frequency response; and selecting a preset number of parameters with the largest absolute value of average sensitivity as the parameter to be optimized.

[0013] Optionally, the initial adaptive Kriging surrogate model is constructed as follows: within the prior space of the parameters to be optimized, an initial training sample set is obtained using the Maximin Latin hypercube experimental design method, wherein the prior space is the ±10% deviation range of the initial parameter values; the initial training sample set is input into the initial finite element model to calculate the model response output; the initial adaptive Kriging surrogate model is trained using the initial training sample set as input and the model response as output.

[0014] To achieve the above objectives, this application also provides a finite element model correction system based on an adaptive Kriging surrogate model and approximate Bayesian calculation, the system comprising: The finite element modeling module is used to establish an initial finite element model based on the scaled-down laboratory model of a mining skip and to obtain experimental response data. The proxy model construction module is used to construct an initial adaptive Kriging proxy model. The adaptive Kriging proxy model takes the parameters to be optimized from the finite element model as input and the predicted values ​​and variances of the model response as output. The parameters to be optimized include the thickness of the upper plate, the thickness of the middle plate, the elastic modulus of the plate, the mass density of the plate, the width of the column, the thickness of the column, the elastic modulus of the column, and the mass density of the column. A loop module is used to execute an iterative loop until the convergence stopping criterion is met; the loop module includes: A sampling unit is used to generate a candidate sample pool based on a hybrid sampling strategy. The prediction unit is used to output the model response prediction and prediction variance of each candidate sample in the candidate sample pool based on the current adaptive Kriging surrogate model. The posterior screening unit is used to screen posterior samples from the candidate sample pool according to the screening criteria calculated by approximate Bayes. The screening criteria are to retain candidate samples whose objective function values ​​of the model response prediction data and the measured response data are less than an adaptive preset threshold. The distribution of the posterior samples is approximately in the high posterior probability region. An adaptive point addition unit is used to select new sample points from the candidate sample pool according to an adaptive hybrid point addition strategy. The adaptive hybrid point addition strategy is to dynamically adjust the weights of the exploration term, development term, and boundary refinement term of the point addition value function. The exploration term corresponds to the prediction variance of the sample points in the candidate sample pool, the development term corresponds to the objective function value of the sample points in the candidate sample pool, and the boundary refinement term corresponds to the Gaussian kernel function value of the sample points in the candidate sample pool whose objective function value is close to the preset threshold boundary region. The model update module is used to add new sample points to the training set and retrain and update the adaptive Kriging agent model. The parameter estimation module is used to calculate the statistical characteristics of the posterior sample set when the convergence stopping criterion is met, and to obtain the finite element parameter correction values ​​of the Kriging surrogate model.

[0015] To achieve the above objectives, this application also provides an electronic device, comprising: at least one processor, a memory, and an input / output unit; wherein the memory is used to store a computer program, and the processor is used to call the computer program stored in the memory to execute the finite element correction method for the adaptive Kriging proxy model provided in any of the foregoing embodiments.

[0016] This application proposes a finite element method, system, and electronic device for adapting a skip's adaptive Kriging surrogate model. The method involves establishing an initial finite element model based on a scaled-down laboratory model of a mining skip and obtaining experimentally measured response data. An initial adaptive Kriging surrogate model is constructed, and an objective function is built based on the measured response data. The adaptive Kriging surrogate model takes the parameters to be optimized from the finite element model as input and outputs the predicted model response and prediction variance. An iterative loop is executed until the convergence stopping criterion is met. The iterative loop includes: generating a candidate sample pool according to a hybrid sampling strategy; predicting the model response and prediction variance of each candidate sample in the candidate sample pool based on the current adaptive Kriging surrogate model; and selecting posterior samples from the candidate sample pool according to an approximate Bayesian computational screening criterion. The process involves retaining candidate samples whose objective function values ​​for both the predicted and measured response data are less than an adaptive preset threshold. New sample points are selected from the candidate sample pool using an adaptive hybrid addition strategy. This strategy dynamically adjusts the weights of the exploration, development, and boundary refinement terms in the addition value function. The exploration term corresponds to the prediction variance of the sample points in the candidate sample pool, the development term corresponds to the objective function value of the sample points in the candidate sample pool, and the boundary refinement term corresponds to the Gaussian kernel function value of the sample points in the candidate sample pool whose objective function value is close to the preset threshold boundary region. The new sample points are added to the training set, and the adaptive Kriging surrogate model is retrained and updated. The statistical characteristics of the posterior sample set that satisfy the convergence stopping criterion are calculated to obtain the finite element parameter correction values ​​of the adaptive Kriging surrogate model, which has the following beneficial effects: (1) The present invention uses an adaptive Kriging surrogate model as the mathematical surrogate model for the finite element model, which can solve the accuracy and computational cost problems caused by the static Kriging model relying on a single sampling. The adaptive Kriging surrogate model can maximize the accuracy gain in each iteration, and obtain higher surrogate model accuracy in the global and local key regions with the fewest number of finite element calculations.

[0017] (2) By adopting the approximate Bayesian calculation method, the likelihood function that is difficult to handle in Bayesian inference is avoided. A preset threshold and Euclidean distance are introduced to construct a true posterior approximation, resulting in better fitting results and higher computational efficiency.

[0018] (3) The adaptive Kriging proxy model and the approximate Bayesian calculation method work together to dynamically focus on key areas, which can achieve efficient allocation of computing resources, correct model deviations in real time, avoid error accumulation, and the correction results and efficiency of the finite element model are better than those of traditional methods. Attached Figure Description

[0019] Figure 1A flowchart illustrating an embodiment of the finite element correction method for the adaptive Kriging proxy model of the winnowing basket in this application; Figure 2 This is a schematic diagram of an embodiment of the finite element correction method for the adaptive Kriging proxy model of the winnowing basket in this application.

[0020] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0021] It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0022] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0023] This invention discloses a finite element method for correcting an adaptive Kriging surrogate model for skips, aiming to solve the problems of high computational cost, difficulty in obtaining the likelihood function, and low convergence efficiency in traditional finite element model correction. This method establishes an initial finite element model based on a scaled-down laboratory model of a mining skip, and experimentally obtains measured response data. An adaptive Kriging surrogate model is then constructed, using the parameters to be optimized as input and the predicted model response and variance as output, to replace the computationally expensive finite element model. An objective function is also constructed. During iterative iteration, a hybrid sampling strategy is used to generate a candidate sample pool. Based on the predicted sample response and variance of the current surrogate model, posterior samples are selected according to an approximate Bayesian calculation screening criterion. An adaptive hybrid addition strategy, dynamically adjusting the weights of the exploration, development, and boundary refinement terms of the addition value function, selects new sample points from the candidate sample pool to update the surrogate model. When the Kullback-Leibler divergence of two consecutive posterior sample distributions is less than a preset threshold, the statistical characteristics of the posterior sample set are calculated to obtain parameter estimates. This invention combines an adaptive Kriging surrogate model with approximate Bayesian computation, significantly reducing the number of calculations, avoiding the likelihood function problem, balancing global search and local development, and achieving high-precision and high-efficiency finite element model correction.

[0024] Reference Figure 1 and Figure 2 The finite element correction method for the adaptive Kriging proxy model of the winnowing basket provided in the first embodiment of this application may include the following: S101. Based on the scaled-down laboratory model of the mine skip, establish an initial finite element model and obtain measured response data through experiments. The boundary conditions of the initial finite element model should match the actual structure and have a certain degree of accuracy.

[0025] Specifically, based on the existing drawings of the scaled-down model of the mine skip laboratory, an initial finite element model is constructed, and its boundary conditions are consistent with the actual scaled-down model to ensure the accuracy of the initial model.

[0026] In one embodiment of this application, the measured response data includes the structural displacement response obtained through static load tests and the structural modal frequencies obtained through dynamic load tests. The objective function is expressed as the square of the weighted normalized Euclidean distance between the measured response data and the model response prediction data.

[0027] Specifically, the measured response data were obtained through static and dynamic load tests, including the displacement response at three measuring points on the model (static load test) and the first four modal frequencies (dynamic load test), providing fundamental data for the subsequent construction of the objective function. By accurately constructing the initial model and obtaining measured data, the reliability of the model correction baseline is ensured, providing a true reference for subsequent surrogate model construction and parameter optimization. The static and dynamic load tests include static and dynamic tests; the static tests obtain the structural displacement response, and the dynamic tests obtain the structural modal frequencies.

[0028] S102. Construct an initial adaptive Kriging surrogate model and build an objective function based on the measured response data. The adaptive Kriging surrogate model takes the parameters to be optimized from the finite element model as input and outputs the predicted values ​​and variances of the model response. The parameters to be optimized include the thickness of the upper enclosure, the thickness of the middle enclosure, the elastic modulus of the enclosure, the mass density of the enclosure, the width of the column, the thickness of the column, the elastic modulus of the column, and the mass density of the column.

[0029] In this embodiment, the initial adaptive Kriging proxy model is constructed in the following way: The prior space for the parameters to be optimized was selected as the ±10% deviation range of the initial parameter values. Forty initial training samples were selected using the Maximin Latin hypercube experimental design method. These samples were input into the initial finite element model to obtain the calculated response output (displacement at three measurement points and the first four modes). Using the initial training sample set as input and the model's calculated response as output, an initial adaptive Kriging surrogate model was trained.

[0030] In this embodiment, the objective function is expressed as the square of the weighted normalized Euclidean distance between the measured response data of the skip test and the response prediction data of the skip adaptive Kriging surrogate model, and the expression is: ; Where: subscript 'e' represents the experimental value, and subscript 'a' represents the model response prediction value. N r Nf These represent the number of static measurement points and the number of modal frequencies, respectively. ω r,l ω f,i These are the weighting coefficients for the static residual term and the modal frequency residual term, respectively, σ r,l σ f,i r represents the standard deviation of static displacement test and modal frequency test, respectively. e,l r a,l Let f represent the experimental displacement response and the model predicted displacement response at the l-th measuring point under static loading conditions, respectively. e,i f a,i Let J(x) and Y(x) represent the experimental modal frequency and the model predicted modal frequency of the i-th mode, respectively. The selection criterion is to retain candidate samples whose objective function value J(x) is less than an adaptive preset threshold; the preset threshold shrinks adaptively with iteration, with a shrinkage coefficient of 0.95, i.e., the i-th mode... The threshold for the iteration = the first iteration The threshold is multiplied by 0.95 to gradually narrow the screening range and focus on the optimal parameter area.

[0031] The smaller the value of the objective function J(x), the closer the model response prediction is to the measured data. The goal of the finite element model correction is to optimize the objective function value to approach 0.

[0032] In this embodiment, the parameters to be optimized are determined through finite difference method average sensitivity analysis, including: Generate a uniformly distributed sample set within the prior space of candidate parameters; Calculate the normalized local sensitivity of each candidate parameter sample relative to the displacement response and modal frequency response; Calculate the average absolute value of the sensitivity of each candidate parameter relative to the displacement response and modal frequency response; Select the preset quantity parameter with the largest absolute value of average sensitivity as the parameter to be optimized.

[0033] For example, the parameter selection method to be optimized employs finite difference method average sensitivity analysis. The normalized sensitivity equation for each sample disturbance relative to displacement and modal frequency calculated by the finite difference method is expressed as follows: ; ; ; in: This represents the number of static measurement points. The number of modal frequencies considered in the model, d s The number of candidate parameters. To generate a uniformly distributed number of samples in the parameter prior space. , These are the displacement local sensitivity and frequency local sensitivity of the j-th candidate parameter in the k-th sample, respectively. Δ represents the ratio of small perturbations to the finite element model parameters, typically set to 0.01. This indicates that the displacement response of the k-th sample at the l-th static measuring point is obtained by calculating using the finite element model. This means that the frequency of the k-th sample in the i-th order is obtained by calculating using the finite element model.

[0034] The absolute value of the average sensitivity of the j-th candidate parameter relative to the displacement response of the l-th static measuring point The equation is expressed as: ; The absolute value of the average sensitivity of the j-th candidate parameter with respect to the i-th modal frequency The equation is expressed as: ; Calculate the absolute value of the average sensitivity of each parameter, select the parameters with the largest absolute value (preset number of such parameters), and combine these parameters as the parameters to be optimized.

[0035] S103. Execute the iterative loop until the convergence stopping criterion is met.

[0036] S1031. Generate a candidate sample pool based on the hybrid sampling strategy.

[0037] In this embodiment, the hybrid sampling strategy includes: When the number of iterations is 1, Latin hypercube sampling is used to generate a candidate sample pool in the parameter space; When the number of iterations is greater than or equal to 2 and less than or equal to 5, the space filling sampling ratio is 50%~70%, the importance sampling ratio is 15%~25%, and the boundary sampling ratio is 15%~25%. When the number of iterations is greater than or equal to 6 and less than or equal to 10, the space filling sampling ratio is 40%~45%, the importance sampling ratio is 40%~45%, and the boundary sampling ratio is 10%~20%. When the number of iterations is 11 or more, the space filling sampling ratio is 15%~25%, the importance sampling ratio is 50%~70%, and the boundary sampling ratio is 15%~25%. Among them, the space filling sampling adopts the Latin hypercube method to explore the prior space of the parameters to be optimized globally; the importance sampling adopts the Gaussian mixture model method to develop the high posterior probability regions that have been discovered; and the boundary sampling adopts the boundary sampling method based on prediction variance to sample risk regions close to the preset threshold.

[0038] For example, the number of iterations At that time, Latin hypercube sampling was used to generate 1000 candidate sample points; At that time, space filling sampling (using the Latin hypercube method) accounted for 60%, importance sampling (using the Gaussian mixture model method) accounted for 20%, and boundary sampling (using the prediction variance-based sampling method) accounted for 20%. At that time, the sampling proportions of the three types were 40%, 40%, and 20%, respectively; When the sampling ratio is 20%, 60%, and 20% respectively, the percentages are 20%, 60%, and 20%. The sampling ratio is dynamically adjusted according to the iteration process to balance spatial exploration and sampling in key areas, thereby improving the representativeness and effectiveness of the sample pool.

[0039] S1032. Predict the model response and prediction variance of candidate samples based on the current adaptive Kriging surrogate model.

[0040] Specifically, each sample in the candidate sample pool is input into the current iteration of the adaptive Kriging surrogate model to quickly calculate the model response prediction value (corresponding to the displacement and modal frequency of the measurement point) and the prediction variance of each sample. This eliminates the need for repeated complex finite element simulations, improving iteration efficiency.

[0041] By using a surrogate model to replace traditional finite element simulation, computational costs are significantly reduced. At the same time, the prediction variance reflects the uncertainty of the model prediction, providing a basis for subsequent sampling and point addition.

[0042] S1033. Based on the screening criteria of approximate Bayesian calculation, posterior samples are screened from the candidate sample pool. The screening criteria are to retain candidate samples whose objective function values ​​of the model response prediction data and the measured response data are less than an adaptive preset threshold. Specifically, the adaptive preset threshold shrinks adaptively with the number of iterations, the th... The preset threshold for the nth iteration is the nth The preset threshold for each iteration is multiplied by a shrinkage coefficient, where the shrinkage coefficient is a positive number less than 1.

[0043] S1034. Select new sample points from the candidate sample pool according to the adaptive hybrid addition strategy. The adaptive hybrid addition strategy dynamically adjusts the weights of the exploration term, development term, and boundary refinement term of the addition value function. The exploration term corresponds to the prediction variance of the sample points in the candidate sample pool, the development term corresponds to the objective function value of the sample points in the candidate sample pool, and the boundary refinement term corresponds to the Gaussian kernel function value of the sample points in the candidate sample pool whose objective function value is close to the preset threshold boundary region. Specifically, the point-addition value function of the adaptive hybrid point-addition strategy is: ; Pick The sample point with the highest preset value is the most valuable new sample point.

[0044] In the formula: α is the weight of the exploration term, β is the weight of the development term, and γ is the weight of the boundary refinement term. σ²(x) represents the variance of the adaptive Kriging surrogate model prediction of the sample points in the candidate sample pool, 1 / J(x) represents the reciprocal of the objective function value of the sample points in the candidate sample pool, exp(-(J(x)-ε)² / (2σ²(x))) represents the Gaussian kernel function value of the sample points in the candidate sample pool whose objective function value is close to the preset threshold boundary region, and ε represents the preset threshold calculated by approximate Bayes.

[0045] By dynamically adjusting the three types of weights, a balance is achieved between global exploration and local development and boundary refinement, ensuring that newly added sample points have the highest value and improving the efficiency of surrogate model updates.

[0046] For example, in this embodiment, the three types of weights are dynamically adjusted to emphasize exploration items in the early stage of iteration, balance exploration items and development items in the middle stage of iteration, and emphasize development items in the later stage of iteration.

[0047] =1~5, =0.6, =0.2, =0.2; =6~10, =0.4, =0.4, =0.2; =11~End, =0.2, =0.6, =0.2.

[0048] S104. Add the newly added sample points to the training set and retrain and update the adaptive Kriging surrogate model; calculate the statistical characteristics of the posterior sample set when the convergence stopping criterion is satisfied, and obtain the finite element parameter correction values ​​of the adaptive Kriging surrogate model.

[0049] Specifically, the three newly selected sample points are added to the initial training set each time to supplement the training data, retrain the adaptive Kriging surrogate model, update the model parameters, and improve the model's prediction accuracy in the parameter space.

[0050] By continuously supplementing high-value samples, the accuracy of the surrogate model is gradually optimized, ensuring the accuracy of subsequent predictions and screenings, and driving the iteration to converge toward the optimal parameter region.

[0051] In this step, the convergence stopping criterion is: Calculate the Kullback-Leibler divergence between the posterior sample distributions of two consecutive iterations; When the Kullback-Leibler divergence is less than a preset divergence threshold, the convergence stopping criterion is satisfied, and the iteration is terminated. The iteration continues when the Kullback-Leibler divergence is greater than or equal to the preset divergence threshold.

[0052] Specifically, the convergence stopping criterion is to calculate the Kullback-Leibler divergence of the posterior sample distribution after two consecutive iterations, and terminate the iteration when the divergence is less than a preset divergence threshold; in this embodiment, a total of 17 iterations were performed, satisfying the convergence criterion. Subsequently, the average value of the posterior sample set obtained from the last screening is calculated as the parameter estimate for the finite element model correction. Obviously, using the Kullback-Leibler divergence to determine convergence ensures that the parameter distribution tends to stabilize when the iteration terminates; using the average value of the posterior samples as the parameter estimate improves the reliability and accuracy of the parameter correction.

[0053] If the convergence stopping criterion is met, the iteration ends, and the posterior sample set obtained from the last approximate Bayesian calculation is used as the final result for estimating the uncertainty of the model parameters. The average of all posterior sample points is calculated as the optimal estimate of the corrected finite element model. Otherwise, the iteration cycle continues.

[0054] In one specific embodiment, using finite element calculation data from a scaled-down laboratory model of a mining skip, this method is employed to correct the finite element model, specifically including the following steps: Step 1) Construct a finite element model based on the existing drawings of the scaled-down laboratory model of the mining skip.

[0055] Step 2) Obtain measured response data. In this example, the displacement and the first four frequencies at three measuring points on the model are obtained as measured data.

[0056] Step 3) Selection of parameters to be optimized In this example, 11 parameters of the scaled-down laboratory model of the mine skip are selected as candidate parameters: upper plate thickness, middle plate thickness, lower plate thickness, plate elastic modulus, plate mass density, column width, column thickness, column elastic modulus, column mass density, support plate thickness, and lifting hole diameter.

[0057] The average sensitivity analysis using the finite difference method was employed to calculate the absolute values ​​of the average sensitivity of each parameter relative to the displacement and fourth-order modal frequency values ​​of the three static measuring points, as shown in Table 1 below.

[0058] Table 1 Calculation results of the absolute value of average sensitivity

[0059] For example, in the data in the table above, the average absolute value of the sensitivity of the upper plate thickness parameter relative to the displacement response of static measuring point 1 is 0.0732.

[0060] The calculation formula is as follows: ; In this example: l represents the location of static measuring point 1, and j represents the thickness parameter of the upper plate. The value represents the displacement response at static measuring point 1, and k is the number of samples. The average absolute value of the sensitivity of the upper plate thickness parameter to the displacement response at static measuring point 1 with k samples is 0.0732.

[0061] After comparative analysis, the average absolute values ​​of the sensitivity of the three parameters—lower plate thickness, support plate thickness, and lifting hole diameter—to displacement and modal frequency response are all approximately 0. The final selected parameters to be optimized are: upper plate thickness, middle plate thickness, plate elastic modulus, plate mass density, column width, column thickness, column elastic modulus, and column mass density, totaling eight parameters.

[0062] Step 4) Construct an initial adaptive Kriging proxy model and construct an objective function based on the load test response data.

[0063] Step 41) Collect the initial training set of parameters to be optimized, construct the initial adaptive Kriging proxy model and participate in the iteration.

[0064] The parameters to be optimized are taken as prior values ​​with a deviation of ±10% from the initial values. Forty initial samples are selected within the spatial range as inputs, and the characteristic quantities of the finite element model (displacement magnitudes at three measurement points and the first four modes) are calculated as outputs. These 40 sets of inputs and outputs are saved as training data to construct the initial Kriging model.

[0065] Step 42) Construct the objective function as the square of the weighted normalized Euclidean distance between the measured response data of the skip test and the response prediction data of the skip adaptive Kriging surrogate model.

[0066] This embodiment constructs the objective function expression based on the measured response data from the skip load test and the response prediction data from the adaptive Kriging surrogate model: ; Where: subscript 'e' represents the experimental value, and subscript 'a' represents the model response prediction value. N r N f These represent the number of static measurement points and the number of modal frequencies, respectively. ω r,l ω f,iThese are the weighting coefficients for the static residual term and the modal frequency residual term, respectively. Considering that dynamic characteristics are inherent properties of the structure and do not change with external loads, while static displacements change with the skip load conditions, using the modal frequencies of dynamic characteristics is more accurate than using static loads. Therefore, the weight ω is chosen as the weighting coefficient. r,l =0.4、ω f,i =0.6.

[0067] σ r,l σ f,i These represent the standard deviations of static displacement testing and modal frequency testing, respectively, obtained through multiple experiments. , f represents the experimental displacement response and the model predicted displacement response at the l-th measuring point under static loading conditions, respectively. e,i f a,i Let represent the experimental modal frequency and the model predicted modal frequency of the i-th mode, respectively.

[0068] Step 5) Construct a sample pool using approximate Bayesian sampling. Quickly obtain the model response predictions and their variances for each sample point in this pool using the current Kriging surrogate model. Apply the screening criteria of approximate Bayesian computation to select posterior samples from the candidate sample pool. Use an adaptive hybrid addition strategy to select the three most valuable new sample points from the candidate sample pool to expand the training set, and retrain and update the adaptive Kriging surrogate model. Determine if the convergence stopping criterion is met; otherwise, repeat Step 5.

[0069] Step 6) After the iteration, a total of 17 iterations were performed in this embodiment. The posterior sample set obtained from the final approximate Bayesian calculation was used as the final result for estimating the uncertainty of the model parameters. The average value of all posterior sample points was calculated as the optimal estimate of the corrected finite element model. The initial and corrected values ​​of the parameters to be corrected are shown in Table 2 below: Table 2 Initial and corrected values ​​of the parameters to be corrected

[0070] The comparison between the calculated response data and the measured response data of the finite element model before and after the correction is shown in Table 3 below: Table 3 Comparison of calculated and measured response data from the finite element model before and after correction.

[0071] Based on the comparison of parameters before and after finite element model correction and the comparison of model calculated response values ​​with measured response data, the finite element correction method of the skip adaptive Kriging proxy model proposed in this invention can reduce the error between the model calculated response and the measured response by changing the model parameters, thereby achieving the purpose of finite element correction.

[0072] The beneficial effects of this embodiment: This embodiment significantly reduces the number of calculations in the finite element model by constructing an adaptive Kriging surrogate model, and maximizes the accuracy gain in each iteration. It adopts the approximate Bayesian computation (ABC) method to avoid the problem of difficulty in obtaining the likelihood function in traditional Bayesian inference. By combining the hybrid sampling strategy and the adaptive hybrid point addition strategy, it improves the local convergence speed while ensuring the global search capability, and realizes high-precision and high-efficiency finite element model correction.

[0073] Based on the above embodiments, this application also provides a finite element model correction system based on an adaptive Kriging surrogate model and approximate Bayesian calculation, used to solve the same technical problem as the method embodiments. The system includes: The finite element modeling module is used to establish an initial finite element model based on the scaled-down laboratory model of a mining skip and to obtain experimental response data. The surrogate model building module is used to build an initial adaptive Kriging surrogate model. The adaptive Kriging surrogate model takes the parameters to be optimized from the finite element model as input and outputs the predicted values ​​of the model response and the prediction variance. A loop module is used to execute an iterative loop until the convergence stopping criterion is met; the loop module includes: A sampling unit is used to generate a candidate sample pool based on a hybrid sampling strategy. The prediction unit is used to output the model response prediction and prediction variance of each candidate sample in the candidate sample pool based on the current adaptive Kriging surrogate model. The posterior screening unit is used to screen posterior samples from the candidate sample pool according to the screening criteria calculated by approximate Bayes. The screening criteria are to retain candidate samples whose objective function values ​​of the model response prediction data and the measured response data are less than an adaptive preset threshold. The distribution of the posterior samples is approximately in the high posterior probability region. An adaptive point addition unit is used to select new sample points from the candidate sample pool according to an adaptive hybrid point addition strategy. The adaptive hybrid point addition strategy is to dynamically adjust the weights of the exploration term, development term, and boundary refinement term of the point addition value function. The exploration term corresponds to the prediction variance of the sample points in the candidate sample pool, the development term corresponds to the objective function value of the sample points in the candidate sample pool, and the boundary refinement term corresponds to the Gaussian kernel function value of the sample points in the candidate sample pool whose objective function value is close to the preset threshold boundary region. The model update module is used to add new sample points to the training set and retrain and update the adaptive Kriging agent model.

[0074] The parameter estimation module is used to calculate the statistical characteristics of the posterior sample set when the convergence stopping criterion is met, and to obtain the finite element parameter correction values ​​of the Kriging surrogate model.

[0075] To achieve the above objectives, this application also provides an electronic device, comprising: at least one processor, a memory, and an input / output unit; wherein the memory is used to store a computer program, and the processor is used to call the computer program stored in the memory to execute the finite element correction method for the adaptive Kriging proxy model provided in any of the foregoing embodiments.

[0076] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A finite element method for correcting an adaptive Kriging surrogate model of a winnowing basket, characterized in that, include: Based on the scaled-down laboratory model of a mining skip, an initial finite element model was established and measured response data were obtained. Based on the measured response data, an objective function is constructed, and an initial adaptive Kriging proxy model is built. The adaptive Kriging proxy model takes the parameters to be optimized from the finite element model as input and the predicted values ​​and variances of the model response as output. The parameters to be optimized include the thickness of the upper plate, the thickness of the middle plate, the elastic modulus of the plate, the mass density of the plate, the width of the column, the thickness of the column, the elastic modulus of the column, and the mass density of the column. Execute an iterative loop until the convergence stopping criterion is met, wherein the iterative loop includes: A candidate sample pool is generated based on a hybrid sampling strategy; Based on the current adaptive Kriging surrogate model, predict the model response and prediction variance of each candidate sample in the candidate sample pool; Based on the approximate Bayesian calculation screening criterion, posterior samples are screened from the candidate sample pool. The screening criterion is to retain candidate samples whose objective function values ​​of the model response and the measured response data are less than an adaptive preset threshold. New sample points are selected from the candidate sample pool according to the adaptive hybrid addition strategy. The adaptive hybrid addition strategy dynamically adjusts the exploration weight, development weight and boundary refinement weight, wherein the exploration weight corresponds to the region with high prediction variance, the development weight corresponds to the region with high posterior probability, and the boundary refinement weight corresponds to the boundary region close to the preset threshold. The newly added sample points are added to the training set, and the adaptive Kriging surrogate model is retrained and updated. The statistical characteristics of the posterior sample set when the convergence stopping criterion is satisfied are calculated to obtain the parameter estimates of the finite element model correction.

2. The finite element correction method for the adaptive Kriging surrogate model of the winnowing basket according to claim 1, characterized in that, The measured response data includes the structural displacement response obtained through static load tests and the structural modal frequencies obtained through dynamic load tests. The objective function is expressed as the square of the weighted normalized Euclidean distance between the measured response data and the model simulation response data.

3. The finite element correction method for the adaptive Kriging surrogate model of the winnowing basket according to claim 1 or 2, characterized in that, The hybrid sampling strategy includes: When the number of iterations is 1, Latin hypercube sampling is used to generate a candidate sample pool in the parameter space; When the number of iterations is greater than or equal to 2 and less than or equal to 5, the space filling sampling ratio is 50%~70%, the importance sampling ratio is 15%~25%, and the boundary sampling ratio is 15%~25%. When the number of iterations is greater than or equal to 6 and less than or equal to 10, the space filling sampling ratio is 40%~45%, the importance sampling ratio is 40%~45%, and the boundary sampling ratio is 10%~20%. When the number of iterations is 11 or more, the space filling sampling ratio is 15%~25%, the importance sampling ratio is 50%~70%, and the boundary sampling ratio is 15%~25%. Among them, the space filling sampling adopts the Latin hypercube method to explore the prior space of the parameters to be optimized globally; the importance sampling adopts the Gaussian mixture model method to develop the high posterior probability regions that have been discovered; and the boundary sampling adopts the boundary sampling method based on prediction variance to sample risk regions that are close to the preset threshold.

4. The finite element correction method for the adaptive Kriging surrogate model of the winnowing basket according to claim 1, characterized in that, The adaptive preset threshold shrinks adaptively with the number of iterations, the first... The preset threshold for the nth iteration is the nth The preset threshold of the next iteration is multiplied by a shrinkage coefficient, wherein the shrinkage coefficient is a positive number less than 1.

5. The finite element correction method for the adaptive Kriging surrogate model of the winnowing basket according to claim 1, characterized in that, The point-addition value function of the adaptive hybrid point-addition strategy is: ； In the formula, α is the exploration weight, β is the development weight, γ is the boundary refinement weight, σ²(x) represents the region of high uncertainty, 1 / J(x) represents the region of high posterior probability, and exp(-(J(x)- )² / (2σ²(x))) represents the boundary region, This is represented as a preset threshold for approximate Bayesian computation; The adaptive hybrid point-addition strategy dynamically adjusts the exploration weight, development weight, and boundary refinement weight, including: setting the exploration weight to be greater than the development weight and boundary refinement weight in the early stage of iteration; setting the exploration weight to be equal to or close to the development weight in the middle stage of iteration; and setting the development weight to be greater than the exploration weight and boundary refinement weight in the later stage of iteration.

6. The finite element correction method for the adaptive Kriging surrogate model of the winnowing basket according to claim 1, characterized in that, The convergence stopping criterion is as follows: Calculate the Kullback-Leibler divergence between the posterior sample distributions of two consecutive iterations; When the Kullback-Leibler divergence is less than a preset divergence threshold, the convergence stopping criterion is satisfied, and the iteration is terminated. The iteration continues when the Kullback-Leibler divergence is greater than or equal to a preset divergence threshold.

7. The finite element correction method for the adaptive Kriging surrogate model of the winnowing basket according to claim 1, characterized in that, The parameters to be optimized were determined through finite difference average sensitivity analysis, which included: Generate a uniformly distributed set of candidate parameter samples within the parameter space; Calculate the normalized local sensitivity of each candidate parameter sample relative to the displacement response and modal frequency response; Calculate the average absolute value of the sensitivity for each candidate parameter; Select the preset quantity parameter with the largest absolute value of average sensitivity as the parameter to be optimized.

8. The finite element correction method for the adaptive Kriging surrogate model of the winnowing basket according to claim 1, characterized in that, The initial adaptive Kriging proxy model is constructed in the following way: Within the value space of the parameter to be optimized, the Maximin Latin hypercube experimental design method is used to obtain the initial training sample set, where the value space is the ±10% deviation range of the initial parameter value. The initial training sample set is input into the initial finite element model to calculate the model response output; the initial adaptive Kriging surrogate model is trained using the initial training sample set as input and the model response output as output.

9. A finite element correction system for an adaptive Kriging surrogate model of a winnowing basket, characterized in that, include: The finite element modeling module is used to establish an initial finite element model and obtain measured response data based on the scaled-down laboratory model of the mine skip. The objective function construction module is used to construct an objective function based on the measured response data; The proxy model construction module is used to construct an initial adaptive Kriging proxy model. The adaptive Kriging proxy model takes the parameters to be optimized from the finite element model as input and the predicted values ​​and variances of the model response as output. The parameters to be optimized include the thickness of the upper plate, the thickness of the middle plate, the elastic modulus of the plate, the mass density of the plate, the width of the column, the thickness of the column, the elastic modulus of the column, and the mass density of the column. The sampling module is used to generate a candidate sample pool based on a hybrid sampling strategy; The prediction module is used to predict the model response and prediction variance of each candidate sample in the candidate sample pool based on the current adaptive Kriging surrogate model. The posterior screening module is used to screen posterior samples from the candidate sample pool according to the screening criteria calculated by approximate Bayesian calculation. The screening criteria are to retain candidate samples whose objective function values ​​of the model response and the measured response data are less than an adaptive preset threshold. An adaptive point addition module is used to select new sample points from the candidate sample pool according to an adaptive hybrid point addition strategy, wherein the adaptive hybrid point addition strategy dynamically adjusts the exploration weight, development weight and boundary refinement weight. The model update module is used to add the newly added sample points to the training set and retrain and update the adaptive Kriging proxy model; the convergence judgment module is used to determine whether the convergence stopping criterion is met. The parameter estimation module is used to calculate the statistical characteristics of the posterior sample set when the convergence stopping criterion is met, and to obtain the parameter estimates of the finite element model.

10. An electronic device comprising a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the finite element correction method for the adaptive Kriging proxy model as described in any one of claims 1 to 8.

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