Closed loop analysis method and system for long-span steel structure

Abstract

The application provides a large-span steel structure closed loop analysis method and system, the analysis method comprises the following steps: constructing a finite element model and a design parameter space, identifying key design parameters and key regions affecting the first N modal strain energy of the structure through initial sensitivity and modal analysis, and establishing a mapping relationship between the two; according to the parameter sensitivity contribution, a non-uniform sampling strategy is formulated, the sampling is encrypted in the high sensitivity parameter subspace, an initial sample set is generated, based on the sample and the finite element response, a hierarchical mixed kernel Kriging surrogate model containing a global long-range kernel and a multi-region local short-range kernel is constructed, the local kernel weight increases as the input point approaches the high sensitivity region, the iteration termination and the performance limit state are set, the composite point adding criterion integrating the prediction variance, the limit state distance and the cross-validation error is used to iteratively update the sample and the model, and after the condition is met, the structure performance analysis is completed by using the surrogate model.

Description

Technical Field

[0001] This application belongs to the field of structural analysis, and in particular relates to a closed-loop analysis method and system for large-span steel structures. Background Technology

[0002] Accurate performance analysis of long-span steel structures, such as static and dynamic response analysis, stability analysis, and reliability analysis, is crucial for ensuring safety and economic efficiency. The finite element method (FEM) is currently the standard tool for structural analysis, providing high-precision simulation results. However, FEM models for long-span steel structures are typically large-scale and highly nonlinear, requiring significant computational resources for a single analysis. When scenarios involving parameter optimization, uncertainty representation, or reliability assessment require thousands of model calls, the computational cost of FEM becomes prohibitive, severely limiting the efficiency and depth of engineering planning. Surrogate models are computationally inexpensive mathematical models that fit the complex relationship between input parameters and output response using a small number of high-fidelity finite element sample points, replacing time-consuming finite element simulations. Commonly used surrogate models include polynomial response surfaces, radial basis functions, support vector regression, and Kriging models. Among these, Kriging models are favored because they can simultaneously provide predicted values ​​and prediction uncertainties. During the sampling phase, space-filling planning methods such as Latin hypercube are often used to uniformly sample the entire design parameter space. However, this is inefficient for high-dimensional problems where the influence of input parameters varies, and a large number of sample points may fall in non-critical regions with smooth responses. Traditional Kriging models typically use a single global kernel function, which cannot simultaneously and accurately detect the multi-scale characteristics of large-span steel structures that exhibit both overall response and complex local behaviors. In the iterative point addition process of active learning, existing point addition criteria often focus on a single objective, such as maximizing the prediction variance or minimizing the prediction value, without comprehensively and evenly considering the multiple needs of improving the global accuracy of the model, exploring the performance limit boundary, and correcting existing model biases. As a result, the convergence speed and accuracy of the model need to be improved. Summary of the Invention

[0003] This invention proposes a closed-loop analysis method for large-span steel structures to address the problem that existing technologies fail to balance the multiple requirements of improving the global accuracy of the model, exploring performance limit boundaries, and correcting existing model biases, resulting in insufficient convergence speed and accuracy. The method includes the following steps: A finite element model and design parameter space of a large-span steel structure are obtained. Initial sensitivity analysis and modal analysis are performed based on the finite element model. Key design parameters that affect the strain energy of the first N modalities of the structure and corresponding key structural regions are identified. A mapping relationship between the key design parameter subspace and the key structural regions is established. Based on the sensitivity contribution of each key design parameter, a non-uniform sampling strategy in the design parameter space is determined. Sampling points are densified in the key design parameter subspace with high sensitivity to generate an initial sample point set. Based on the initial sample point set and the corresponding finite element response values, a hierarchical hybrid kernel function Kriging surrogate model is constructed. The hierarchical hybrid kernel function is composed of a global long-range correlation kernel representing the overall structural response and multiple local short-range correlation kernels corresponding to each key region of the structure, and the weight of each local kernel function is a symmetric function about the position of two input points in the corresponding key design parameter subspace, so that the closer the two input points are to the high-sensitivity region, the greater the weight of the corresponding local kernel function. Set the iteration termination condition and the structural performance limit state. When the termination condition is not met, calculate the composite addition criterion function value of the candidate sample points, select the point with the largest function value as the new sample point, update the sample point set and reconstruct the Kriging surrogate model. When the termination condition is met, use the Kriging surrogate model to perform performance analysis of the large-span steel structure.

[0004] Furthermore, the initial sensitivity analysis and modal analysis based on the finite element model, identifying key design parameters and corresponding key structural regions that affect the strain energy of the first N modalities of the structure, include: Modal analysis is performed on the finite element model to calculate the first N modes. For each mode, the percentage of strain energy of each element in the structure to the total strain energy is calculated, and a weighted sum is performed to obtain the comprehensive strain energy contribution of each element. The set of elements with the top 20% comprehensive strain energy contribution is selected to define the key region of the structure. For each identified critical region, the partial derivatives of the modal strain energy of the critical region with respect to all design parameters are calculated to obtain sensitivity information, and the top M design parameters that have the highest sensitivity influence on the region are identified as the critical design parameters of the region.

[0005] Furthermore, the step of determining a non-uniform sampling strategy in the design parameter space based on the sensitivity contribution of each key design parameter, and densifying sampling points in the key design parameter subspace with high sensitivity to generate an initial sample point set, includes: Latin hypercube sampling is used to generate a set of basic sample points in the entire design parameter space. For each identified key design parameter subspace, several sample points are added proportionally in each subspace according to the magnitude of the sensitivity contribution. All sample points are then merged to form the initial sample point set.

[0006] Furthermore, the hierarchical hybrid kernel function is linearly superimposed from a global long-range correlation kernel representing the overall structural response and multiple local short-range correlation kernels corresponding to each key region of the structure, including: The hierarchical hybrid kernel function consists of a global long-range correlation kernel using a Gaussian kernel function and multiple local short-range correlation kernels using a Matern5 / 2 kernel function, and the hyperparameters in the kernel function are optimized and determined by the maximum likelihood estimation method.

[0007] Furthermore, the weights of each local kernel function are symmetric functions about the positions of the two input points in the corresponding key design parameter subspace, including: For each local kernel function, a radial basis function is defined with the center of the corresponding key design parameter subspace as the peak value and decaying with distance. For any two input points, the function values ​​of the two input points under the radial basis function are calculated and multiplied. The multiplication results of all local kernel functions are normalized and the normalized values ​​are used as the weighting factors of each local kernel function.

[0008] Furthermore, the composite addition criterion function value is obtained by summing the normalized surrogate model prediction variance, the reciprocal of the distance between the predicted response value and the limit state, and the leave-one-out cross-validation error by multiplying them by weighting coefficients of 0.4, 0.4, and 0.2, respectively.

[0009] Furthermore, the setting of the iteration termination condition includes: The iteration terminates when the total number of new sample points reaches the preset upper limit, or when the maximum prediction variance of the Kriging surrogate model in the entire design parameter space is lower than the preset threshold.

[0010] Furthermore, the performance analysis of large-span steel structures using the Kriging surrogate model includes: Monte Carlo simulations are performed based on the constructed Kriging surrogate model to conduct structural reliability analysis. In each simulation, a parameter combination is randomly generated according to the probability distribution of the design parameters, and the structural response value is calculated using the Kriging model. The number of times the response value exceeds the structural performance limit state is counted, and the failure probability of the structure is obtained by dividing the number of times by the total number of simulations.

[0011] Furthermore, this invention also provides a closed-loop analysis system for large-span steel structures, comprising the following modules: The generation module is used to obtain the finite element model and design parameter space of the large-span steel structure, perform initial sensitivity analysis and modal analysis based on the finite element model, identify the key design parameters that affect the strain energy of the first N modalities of the structure and the corresponding key structural regions, establish the mapping relationship between the key design parameter subspace and the key structural regions, and determine the non-uniform sampling strategy in the design parameter space according to the sensitivity contribution of each key design parameter. The sampling points are densified in the key design parameter subspace with high sensitivity to generate an initial sample point set. The construction module is used to construct a hierarchical hybrid kernel function Kriging surrogate model based on the initial sample point set and the corresponding finite element response values. The hierarchical hybrid kernel function is composed of a global long-range correlation kernel representing the overall response of the structure and multiple local short-range correlation kernels corresponding to each key region of the structure. The weight of each local kernel function is a symmetric function about the position of two input points in the corresponding key design parameter subspace, so that the closer the two input points are to the high-sensitivity region, the greater the weight of the corresponding local kernel function. The calculation module is used to set the iteration termination condition and the structural performance limit state. When the termination condition is not met, the composite addition criterion function value of the candidate sample points is calculated, the point with the largest function value is selected as the new sample point, the sample point set is updated and the Kriging surrogate model is reconstructed. When the termination condition is met, the performance analysis of the large-span steel structure is performed using the Kriging surrogate model.

[0012] Preferably, the initial sensitivity analysis and modal analysis based on the finite element model to identify key design parameters and corresponding key structural regions that affect the strain energy of the first N modalities of the structure includes: Modal analysis is performed on the finite element model to calculate the first N modes. For each mode, the percentage of strain energy of each element in the structure to the total strain energy is calculated, and a weighted sum is performed to obtain the comprehensive strain energy contribution of each element. The set of elements with the top 20% comprehensive strain energy contribution is selected to define the key region of the structure. For each identified critical region, the partial derivatives of the modal strain energy of the critical region with respect to all design parameters are calculated to obtain sensitivity information, and the top M design parameters that have the highest sensitivity influence on the region are identified as the critical design parameters of the region.

[0013] Preferably, the step of determining a non-uniform sampling strategy in the design parameter space based on the sensitivity contribution of each key design parameter, and densifying sampling points in the key design parameter subspace with high sensitivity to generate an initial sample point set, includes: Latin hypercube sampling is used to generate a set of basic sample points in the entire design parameter space. For each identified key design parameter subspace, several sample points are added proportionally in each subspace according to the magnitude of the sensitivity contribution. All sample points are then merged to form the initial sample point set.

[0014] Preferably, the hierarchical hybrid kernel function is linearly superimposed from a global long-range correlation kernel representing the overall structural response and multiple local short-range correlation kernels corresponding to each key region of the structure, including: The hierarchical hybrid kernel function consists of a global long-range correlation kernel using a Gaussian kernel function and multiple local short-range correlation kernels using a Matern5 / 2 kernel function, and the hyperparameters in the kernel function are optimized and determined by the maximum likelihood estimation method.

[0015] Preferably, the weights of each local kernel function are symmetric functions about the positions of the two input points in the corresponding key design parameter subspace, including: For each local kernel function, a radial basis function is defined with the center of the corresponding key design parameter subspace as the peak value and decaying with distance. For any two input points, the function values ​​of the two input points under the radial basis function are calculated and multiplied. The multiplication results of all local kernel functions are normalized and the normalized values ​​are used as the weighting factors of each local kernel function.

[0016] Preferably, the composite addition criterion function value is obtained by summing the normalized surrogate model prediction variance, the reciprocal of the distance between the predicted response value and the limit state, and the leave-one-out cross-validation error by multiplying them by weighting coefficients of 0.4, 0.4, and 0.2, respectively.

[0017] Preferably, the setting of the iteration termination condition includes: The iteration terminates when the total number of new sample points reaches the preset upper limit, or when the maximum prediction variance of the Kriging surrogate model in the entire design parameter space is lower than the preset threshold.

[0018] Preferably, the performance analysis of large-span steel structures using the Kriging surrogate model includes: Monte Carlo simulations are performed based on the constructed Kriging surrogate model to conduct structural reliability analysis. In each simulation, a parameter combination is randomly generated according to the probability distribution of the design parameters, and the structural response value is calculated using the Kriging model. The number of times the response value exceeds the structural performance limit state is counted, and the failure probability of the structure is obtained by dividing the number of times by the total number of simulations.

[0019] This invention identifies key design parameters and critical regions affecting structural performance in the early stages of analysis and establishes mapping relationships and a non-uniform sampling strategy accordingly. This makes the selection of initial sample points more targeted and reduces redundant calculations. The constructed hierarchical hybrid kernel function Kriging surrogate model combines a global long-range kernel with multiple local short-range kernels and applies sensitivity-related weights to the local kernel functions. This allows the surrogate model to simultaneously and accurately detect the overall response and fine-grained local features of the structure, improving the global fitting accuracy and local prediction capability of the surrogate model. During model iteration, the composite point addition criterion, combined with model uncertainty, limit state proximity, and model error, achieves a balance between global exploration and local development, enabling rapid convergence to an accurate solution with fewer sample points. This reduces the number of finite element analysis calls and computational costs while ensuring the accuracy and reliability of the performance analysis results for large-span steel structures. Attached Figure Description

[0020] Figure 1 A flowchart of a closed-loop analysis method for large-span steel structures provided by this invention; Figure 2 This is a schematic diagram of the high-dimensional variable state space hybrid driving core topology connection mode provided by the present invention; Figure 3 A schematic diagram of the full-space incremental search for advantage group verification, extraction, and screening mechanism provided by this invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] Example 1 In Embodiment 1 of the present invention, as Figure 1 As shown, a closed-loop analysis method for large-span steel structures includes the following steps: S1. Obtain the finite element model and design parameter space of the large-span steel structure. Based on the finite element model, perform initial sensitivity analysis and modal analysis to identify key design parameters and corresponding key structural regions that affect the strain energy of the first N modalities of the structure. Establish the mapping relationship between the key design parameter subspace and the key structural regions. Determine the non-uniform sampling strategy in the design parameter space according to the sensitivity contribution of each key design parameter. Densify the sampling points in the key design parameter subspace with high sensitivity to generate an initial sample point set. A parametric finite element model of a large-span steel structure, incorporating beam, shell, and solid elements, is established using finite element software such as ANSYS or ABAQUS. Member cross-sectional dimensions, material elastic modulus, and boundary support stiffness are defined as design parameters, forming a multi-dimensional design parameter space. Modal analysis is performed using the Block Lanczos method to calculate the first N natural frequencies and mode shapes of the structure. For sensitivity analysis, the partial derivatives of each design parameter with respect to the strain energy of each modality are calculated using direct differentiation or finite difference methods, serving as sensitivity indices. The sum of squares of the sensitivity indices of all parameters with respect to the strain energy of the first N modalities is summarized and sorted. Parameters whose cumulative contribution rate reaches a preset threshold, such as 90%, are selected as key design parameters. Simultaneously, based on the strain energy distribution contour maps of each mode shape, energy concentration areas are identified as key structural regions, thus establishing a mapping relationship where key parameters influence specific modes, and specific modes dominate the strain energy of specific regions. An improved Latin hypercube sampling method is used to generate an initial sample point set. A non-uniform probability density function is defined for the value range of each key design parameter. This function has a higher probability density in the region of high sensitivity, such as using a beta distribution or a Gaussian mixture model. Sample points under this non-uniform distribution are generated by the inverse transformation sampling method, while uniform sampling is maintained in the non-key parameter dimensions, and combined to form the initial sample point set.

[0023] In one embodiment, for each selected key region, the partial derivatives of the modal strain energy of that region with respect to all design parameters in the structural system are calculated to obtain sensitivity information. The design parameters that have the most significant impact on the strain energy of that region, such as the top M partial derivative values, are extracted and combined into a specific multidimensional space to form a key design parameter subspace for that region. This achieves the mapping of a specific physical failure region dominated by a specific set of parameters.

[0024] In some embodiments, the initial sensitivity analysis and modal analysis based on the finite element model to identify key design parameters and corresponding key structural regions that affect the strain energy of the first N modalities of the structure includes: Modal analysis is performed on the finite element model to calculate the first N modes. For each mode, the percentage of strain energy of each element in the structure to the total strain energy is calculated, and a weighted sum is performed to obtain the comprehensive strain energy contribution of each element. The set of elements with the top 20% comprehensive strain energy contribution is selected to define the key region of the structure. For each identified critical region, the partial derivatives of the modal strain energy of the critical region with respect to all design parameters are calculated to obtain sensitivity information, and the top M design parameters that have the highest sensitivity influence on the region are identified as the critical design parameters of the region.

[0025] Modal analysis of large-span steel structures was performed using finite element analysis software such as ANSYS or ABAQUS. The first N natural modes were calculated, with N preferably set to 15 to cover the main low-frequency vibrations. For the i-th mode, i=1,2, 15. Extract the strain energy of all j elements. And calculate the total strain energy of this mode. The weights are based on the reciprocal of the square of the modal frequency. , and normalize it. =1, representing the percentage of strain energy for each element in each mode. Weighted summation is performed to obtain the comprehensive strain energy contribution of each unit. Arrange all units according to The values ​​are sorted from highest to lowest, and the top 20% of the units are selected to form the key regions of the structure. For example, for a model containing 50,000 units, the 10,000 units with the highest contribution are identified as key regions.

[0026] For each identified critical region, the partial derivatives of the total weighted strain energy with respect to all design parameters are calculated using the finite difference method to represent the sensitivity of each parameter to that region. For example, a certain design parameter... Perturb by ±1% near the midpoint, recalculate the strain energy in the critical region, and obtain the numerical derivative. For each critical region k, the parameters with the highest absolute values ​​of strain energy sensitivity to that region (ranked by M) are identified as the key design parameters for that region. The preferred value for M is 2 or 3. A mapping relationship between specific structural regions and the most relevant design parameters is established.

[0027] In some embodiments, determining a non-uniform sampling strategy in the design parameter space based on the sensitivity contribution of each key design parameter, and densifying sampling points in the key design parameter subspace with high sensitivity to generate an initial sample point set includes: Latin hypercube sampling is used to generate a set of basic sample points in the entire design parameter space. For each identified key design parameter subspace, several sample points are added proportionally in each subspace according to the magnitude of the sensitivity contribution. All sample points are then merged to form the initial sample point set.

[0028] Assuming the total design parameter dimension is D=10, the planned total number of initial sample points is... =120. Within the entire 10-dimensional design parameter space, a set of uniformly distributed basic sample points is generated using Latin hypercube sampling, with a quantity of... =50. Based on the K key design parameter subspaces identified in the preceding steps, for example, K=4, calculate the cumulative sensitivity contribution of each subspace. The remaining supplementary sample point quota , =70, based on the sensitivity contribution ratio of each subspace. The allocation is then performed. For example, if the sensitivity contribution ratios of the four subspaces are 40%, 30%, 20%, and 10%, respectively, then additional resources are added to each of the four subspaces. =28, =21, =14, =7 sample points.

[0029] In a specific subspace, for example, one defined by parameters and When 28 sample points are added to the constructed two-dimensional subspace, LHS sampling is performed only within this two-dimensional subspace, while the values ​​of the other 8 non-critical parameters are fixed at the median or mean of the planned range. The 50 basic sample points are merged with a total of 70 supplementary sample points, and any duplicate points are removed to obtain an initial set of sample points densified in the sensitive area. Finite element analysis is then performed on these 120 sample points to obtain the corresponding structural response values.

[0030] S2. Based on the initial sample point set and the corresponding finite element response values, a hierarchical hybrid kernel function Kriging surrogate model is constructed. The hierarchical hybrid kernel function is formed by the linear superposition of a global long-range correlation kernel representing the overall structural response and multiple local short-range correlation kernels corresponding to each key region of the structure. The weight of each local kernel function is a symmetric function about the position of two input points in the corresponding key design parameter subspace, so that the closer the two input points are to the high-sensitivity region, the greater the weight of the corresponding local kernel function. Run the finite element model to calculate the response values ​​corresponding to the initial sample point set, such as the maximum displacement or maximum stress of the structure. Use the SMT or GPy toolbox in Python to build a Kriging surrogate model. The hierarchical hybrid kernel function is mathematically represented as a weighted sum of the global kernel function and each local kernel function. The global long-range correlation kernel is chosen as the Gaussian radial basis function, which is a negative exponential function of the squared Euclidean distance between input points, used to detect the overall smoothness trend of the structural response. The local short-range correlation kernel is chosen as Matern5 / 2 (also known as...). The kernel function, whose correlation decays faster with distance, is used to simulate drastic local changes in response within critical regions of the structure. For the i-th local kernel function, the weight function is defined as a Gaussian function of the distance between the mean point of the coordinates of the two input points in the i-th critical design parameter subspace and the high-sensitivity center point of that subspace. This ensures that the weights are close to one when both input points are close to the high-sensitivity center and close to zero when they are far away. All hyperparameters of the model, including the length scale of the kernel function, variance, and decay coefficient of the weight function, are optimized by maximizing the logarithmic marginal likelihood function using the L-BFGS-B algorithm. The two input points are any two sets of design parameter samples existing in the multidimensional design parameter space when calculating the correlation of the Kriging surrogate model space. During model training, they represent any two known structural design points in the sample set; during model prediction, they represent a known sample point and an unknown prediction point whose response needs to be calculated. The model calculates the relative distance and position of the two input points in the parameter space, substitutes them into the kernel function, evaluates the similarity between the two design schemes, and then determines how much reference value the structural response result of one point has for the other point.

[0031] In some embodiments, the hierarchical hybrid kernel function is formed by the linear superposition of a global long-range correlation kernel representing the overall structural response and multiple local short-range correlation kernels corresponding to each key region of the structure, including: The hierarchical hybrid kernel function consists of a global long-range correlation kernel using a Gaussian kernel function and multiple local short-range correlation kernels using a Matern5 / 2 kernel function, and the hyperparameters in the kernel function are optimized and determined by the maximum likelihood estimation method.

[0032] The method employs a hierarchical hybrid kernel function Kriging surrogate model, which is a network model. The input to this network model is a D-dimensional design parameter vector. , representing a set of design parameters for a large-span steel structure, such as the section height of the main truss members, coordinates of key nodes, etc.; the output of this network model is a probabilistic prediction of the structural response to a given input x, including the predicted mean. and prediction variance ,in The predicted value of the structural response. This indicates the uncertainty of the predicted value. The core structure of this network model is the hierarchical hybrid kernel function, expressed as follows: .like Figure 2 As shown, global kernel Using Gaussian kernel function It is used to detect the overall smoothing trend of structural response, and hyperparameters include variance. and length scale in D dimensions Local nucleus For the k-th critical region, the Matern5 / 2 kernel function is used. ,in The input point x and The weighted distance within the k-th subspace. The Matern5 / 2 kernel can simulate non-smooth response behavior within local regions. Weighting function. This controls the activation range of the local nucleus.

[0033] All hyperparameters of the model All values ​​are determined by maximizing the logarithmic marginal likelihood function. This optimization process utilizes the L-BFGS-B gradient descent algorithm, given initial sample data. In this case, we seek the combination of hyperparameters that best explains the observed data. For example, initially, we can set all variance hyperparameters to 1.0 and all length scales to 1 / 4 of the design range, and start the optimizer to iterate until the log-likelihood function value converges.

[0034] In some embodiments, the weights of each local kernel function are symmetric functions about the positions of the two input points in the corresponding critical design parameter subspace, including: For each local kernel function, a radial basis function is defined with the center of the corresponding key design parameter subspace as the peak value and decaying with distance. For any two input points, the function values ​​of the two input points under the radial basis function are calculated and multiplied. The multiplication results of all local kernel functions are normalized and the normalized values ​​are used as the weighting factors of each local kernel function.

[0035] For the k-th local kernel function, determine the center point of the corresponding key design parameter subspace. For example, if the subspace is composed of parameters [200,300]mm and If the value is [0.8, 1.2], then the center point is... Given (250, 1.0), define a Gaussian radial basis function RBF. The summation is performed within the dimension d of the subspace. Scale parameter. To control the scope of influence, it is preferable to set it to one-quarter of the design range for that dimension. =25, =0.1.

[0036] For any two input points x and y Calculate their function values ​​under RBF. and The unnormalized weighted components are the product of the two. This ensures that the weights of the local kernel are prominent only when both input points are simultaneously close to the center of the subspace. The weight components of all K local kernels are normalized to obtain the weight factors. The weights are always summed to 1, ensuring a smooth transition of the model between different regions. Optionally, radial basis functions are constructed centered on the design point or nominal design point with the highest sensitivity within the key parameter subspace.

[0037] S3. Set the iteration termination condition and structural performance limit state. When the termination condition is not met, calculate the composite addition criterion function value of the candidate sample points, select the point with the largest function value as the new sample point, update the sample point set and reconstruct the Kriging surrogate model. When the termination condition is met, use the Kriging surrogate model to perform performance analysis of the large-span steel structure.

[0038] The iteration termination condition is set to reach a preset maximum number of additions or the model's prediction accuracy metric, such as root mean square error, falling below a certain threshold. The structural performance limit state is defined as a function, for example... ,in For the allowable stress of the material, This represents the predicted maximum stress of the structure. For a large number of candidate sample points within the design parameter space, the composite point-addition criterion function value is calculated. The first term, the surrogate model prediction variance, is obtained from the covariance matrix of the Kriging model. The second term, the reciprocal of the distance between the predicted response value and the limit state, is calculated by substituting the mean prediction result of the Kriging model into the limit state function; to prevent the denominator from being zero, a minimal positive constant is added to the denominator. The third term, the leave-one-out cross-validation error, is calculated for all current sample points. A radial basis function interpolation model is constructed using the error values ​​of discrete points, and this interpolation model is used to estimate the cross-validation error at any candidate sample point location. The values ​​of the above three indicators in all candidate points are respectively normalized to their minimum and maximum values, unifying the range to 0 to 1, such as... Figure 3 As shown, the three normalized indicators are assigned preset weights and linearly weighted to obtain the composite point criterion function value. A genetic algorithm or particle swarm optimization algorithm is used to search the entire design parameter space for candidate points that maximize the composite function value, which are then used as new sample points. The finite element method is called to calculate the true response value of the newly added sample point, and this response value is added to the sample point set. The hyperparameters of the Kriging surrogate model are retrained using the updated sample point set. This process is repeated until the iteration termination condition is met. The trained Kriging surrogate model is used to replace the finite element model for large-scale Monte Carlo simulations. The failure probability of the structure is obtained by calculating the proportion of failed samples to the total samples, or the model can be used as the fitness function of an optimization algorithm for structural optimization.

[0039] In some embodiments, the composite addition criterion function value is obtained by summing the normalized surrogate model prediction variance, the reciprocal of the distance between the predicted response value and the limit state, and the leave-one-out cross-validation error by weighting coefficients of 0.4, 0.4, and 0.2, respectively.

[0040] In each iteration step, a large set containing, for example, 20,000 candidate points is generated across the entire design space. For each candidate point... Calculate the three criterion components: surrogate model prediction variance This value, obtained from the Kriging model, represents the model's uncertainty at that point. It is the reciprocal of the distance between the predicted response and the limiting state. ,in It is the predicted mean. It is the structural performance failure threshold. It's a decimal to prevent the denominator from being zero. The leave-one-out method for cross-validation error... By searching The k nearest neighbors of the existing sample points, such as k=5, are obtained by calculating the weighted average of the LOO-CV error of the neighboring points. The weights are inversely proportional to the distance.

[0041] After calculating the U, P, and E components of all candidate points, min-max normalization is performed on each component sequence to scale the values ​​of the component sequence to the [0,1] interval, resulting in... , , Composite addition criterion function value The result is obtained through weighted summation: Choice makes The candidate point with the largest value is used as the next new sample point for high-precision finite element calculation. This strategy takes into account global exploration, local optimization and model correction.

[0042] In some embodiments, setting the iteration termination condition includes: The iteration terminates when the total number of new sample points reaches the preset upper limit, or when the maximum prediction variance of the Kriging surrogate model in the entire design parameter space is lower than the preset threshold.

[0043] The termination of the iteration process is controlled by two conditions; either condition must be met to stop. The first condition is a computational resource budget constraint: setting an upper limit on the total number of sample points. ,For example =250. If the initial number of sample points is 120, then a maximum of 130 points can be added during the active learning process. Check the total number of sample points after each iteration. ,like If the iteration terminates, then the iteration ends.

[0044] The second condition is the model convergence assessment: setting a maximum prediction variance threshold. After each iteration of the model update, the prediction variance of the Kriging model is calculated on a large number of candidate points used to evaluate the addition criterion. And find the maximum value among them. The maximum value is compared with a preset threshold. Threshold The selection of [a specific value] is related to the magnitude of the response value; for example, if the variance of the response value is approximately 1000 MPa... 2 Then you can set =1.0MPa 2 If detected This indicates that the uncertainty of the surrogate model within the entire design space is sufficiently low, the model has converged, and the iteration terminates. The dual conditions ensure that the analysis neither exceeds the budget nor stops in time when the model reaches sufficient accuracy. Termination conditions can also be set when the maximum value of the composite addition criterion function is less than a preset threshold, or when the rate of change of the predicted failure probability over K consecutive iterations is less than the tolerance.

[0045] In some embodiments, the performance analysis of large-span steel structures using the Kriging proxy model includes: Monte Carlo simulations are performed based on the constructed Kriging surrogate model to conduct structural reliability analysis. In each simulation, a parameter combination is randomly generated according to the probability distribution of the design parameters, and the structural response value is calculated using the Kriging model. The number of times the response value exceeds the structural performance limit state is counted, and the failure probability of the structure is obtained by dividing the number of times by the total number of simulations.

[0046] All design parameters are assigned probability distribution models. For example, the elastic modulus E of steel follows a normal distribution with a mean of 2.06e5 MPa and a standard deviation of 6000 MPa; the dead load G follows a normal distribution with a mean of the design value and a coefficient of variation of 0.07; and the wind load W follows an extreme value type I distribution. A large-scale Monte Carlo simulation is performed, with the number of simulations... Set as to To ensure the accuracy of estimations for low-probability events.

[0047] In the i-th simulation, a sample value is randomly drawn from the corresponding probability distribution for each design parameter to form a parameter vector. .Will The input is fed into a pre-trained Kriging surrogate model, and the predicted mean of the structural response is obtained rapidly within microseconds. Define the limit state function of the structure, for example, for deflection control. The allowable deflection =Span L / 250. If the calculated... If the simulation fails, the simulation is considered a failure event, and the failure counter is activated. Increment by one. Loop. After that, the failure probability of the structure Estimated as For example, if in In this simulation, 25 failures were observed, therefore the failure probability is... The corresponding reliability index for ≈4.05.

[0048] To verify the effectiveness of the hierarchical mixed kernel function and the composite addition criterion, further experimental verification was conducted. Specifically: The experimental conditions consisted of a large-span steel truss structure with 10 design parameters. The goal was to construct a high-precision surrogate model with a total of 120 sample points. Comparative scheme A used a standard Kriging model with a single global Gaussian kernel function. Invention B employed a hierarchical hybrid kernel function, consisting of a global Gaussian kernel and multiple local Matern5 / 2 kernel functions weighted by radial basis functions. On the same 1000-point validation set, the root mean square error (RMSE) of scheme A was 9.5 MPa, with a coefficient of determination of 0.95. Invention B further reduced the RMSE to 5.1 MPa, achieving a coefficient of determination of 0.99.

[0049] The hybrid kernel function model of this invention B has higher fitting accuracy because the global Gaussian kernel is responsible for detecting the overall smooth trend of the structural response, while the local Matern kernel set for key regions can more flexibly simulate the complex or non-smooth behavior that may exist in the local region. The hierarchical modeling is more in line with the characteristics of complex structural responses, thereby achieving a more accurate approximation of the real response surface.

[0050] Example 2 Embodiment 2 of the present invention provides a closed-loop analysis system for large-span steel structures, comprising the following modules: The generation module is used to obtain the finite element model and design parameter space of the large-span steel structure, perform initial sensitivity analysis and modal analysis based on the finite element model, identify the key design parameters that affect the strain energy of the first N modalities of the structure and the corresponding key structural regions, establish the mapping relationship between the key design parameter subspace and the key structural regions, and determine the non-uniform sampling strategy in the design parameter space according to the sensitivity contribution of each key design parameter. The sampling points are densified in the key design parameter subspace with high sensitivity to generate an initial sample point set. The construction module is used to construct a hierarchical hybrid kernel function Kriging surrogate model based on the initial sample point set and the corresponding finite element response values. The hierarchical hybrid kernel function is composed of a global long-range correlation kernel representing the overall response of the structure and multiple local short-range correlation kernels corresponding to each key region of the structure. The weight of each local kernel function is a symmetric function about the position of two input points in the corresponding key design parameter subspace, so that the closer the two input points are to the high-sensitivity region, the greater the weight of the corresponding local kernel function. The calculation module is used to set the iteration termination condition and the structural performance limit state. When the termination condition is not met, the composite addition criterion function value of the candidate sample points is calculated, the point with the largest function value is selected as the new sample point, the sample point set is updated and the Kriging surrogate model is reconstructed. When the termination condition is met, the performance analysis of the large-span steel structure is performed using the Kriging surrogate model.

[0051] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0052] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A closed-loop analysis method for large-span steel structures, characterized in that, Includes the following steps: A finite element model and design parameter space of a large-span steel structure are obtained. Initial sensitivity analysis and modal analysis are performed based on the finite element model. Key design parameters that affect the strain energy of the first N modalities of the structure and corresponding key structural regions are identified. A mapping relationship between the key design parameter subspace and the key structural regions is established. Based on the sensitivity contribution of each key design parameter, a non-uniform sampling strategy in the design parameter space is determined. Sampling points are densified in the key design parameter subspace with high sensitivity to generate an initial sample point set. Based on the initial sample point set and the corresponding finite element response values, a hierarchical hybrid kernel function Kriging surrogate model is constructed. The hierarchical hybrid kernel function is composed of a global long-range correlation kernel representing the overall structural response and multiple local short-range correlation kernels corresponding to each key region of the structure, and the weight of each local kernel function is a symmetric function about the position of two input points in the corresponding key design parameter subspace, so that the closer the two input points are to the high-sensitivity region, the greater the weight of the corresponding local kernel function. Set the iteration termination condition and the structural performance limit state. When the termination condition is not met, calculate the composite addition criterion function value of the candidate sample points, select the point with the largest function value as the new sample point, update the sample point set and reconstruct the Kriging surrogate model. When the termination condition is met, use the Kriging surrogate model to perform performance analysis of the large-span steel structure.

2. The method according to claim 1, characterized in that, The initial sensitivity analysis and modal analysis based on the finite element model are performed to identify key design parameters and corresponding key structural regions that affect the strain energy of the first N modalities of the structure, including: Modal analysis is performed on the finite element model to calculate the first N modes. For each mode, the percentage of strain energy of each element in the structure to the total strain energy is calculated, and a weighted sum is performed to obtain the comprehensive strain energy contribution of each element. The set of elements with the top 20% comprehensive strain energy contribution is selected to define the key region of the structure. For each identified critical region, the partial derivatives of the modal strain energy of the critical region with respect to all design parameters are calculated to obtain sensitivity information, and the top M design parameters that have the highest sensitivity influence on the region are identified as the critical design parameters of the region.

3. The method according to claim 1, characterized in that, The step of determining a non-uniform sampling strategy in the design parameter space based on the sensitivity contribution of each key design parameter, and densifying sampling points in the key design parameter subspace with high sensitivity to generate an initial sample point set includes: Latin hypercube sampling is used to generate a set of basic sample points in the entire design parameter space. For each identified key design parameter subspace, several sample points are added proportionally in each subspace according to the magnitude of the sensitivity contribution. All sample points are then merged to form the initial sample point set.

4. The method according to claim 1, characterized in that, The hierarchical hybrid kernel function is composed of a global long-range correlation kernel representing the overall structural response and multiple local short-range correlation kernels corresponding to key regions of the structure, linearly superimposed, including: The hierarchical hybrid kernel function consists of a global long-range correlation kernel using a Gaussian kernel function and multiple local short-range correlation kernels using a Matern5 / 2 kernel function, and the hyperparameters in the kernel function are optimized and determined by the maximum likelihood estimation method.

5. The method according to claim 1, characterized in that, The weights of each local kernel function are symmetric functions about the positions of the two input points in the corresponding key design parameter subspace, including: For each local kernel function, a radial basis function is defined with the center of the corresponding key design parameter subspace as the peak value and decaying with distance. For any two input points, the function values ​​of the two input points under the radial basis function are calculated and multiplied. The multiplication results of all local kernel functions are normalized and the normalized values ​​are used as the weighting factors of each local kernel function.

6. The method according to claim 1, characterized in that, The composite addition criterion function value is obtained by summing the normalized surrogate model prediction variance, the reciprocal of the distance between the predicted response value and the limit state, and the leave-one-out cross-validation error by multiplying them by weighting coefficients of 0.4, 0.4, and 0.2, respectively.

7. The method according to claim 1, characterized in that, The defined iteration termination condition includes: The iteration terminates when the total number of new sample points reaches the preset upper limit, or when the maximum prediction variance of the Kriging surrogate model in the entire design parameter space is lower than the preset threshold.

8. The method according to claim 1, characterized in that, The performance analysis of large-span steel structures using the Kriging surrogate model includes: Monte Carlo simulations are performed based on the constructed Kriging surrogate model to conduct structural reliability analysis. In each simulation, a parameter combination is randomly generated according to the probability distribution of the design parameters, and the structural response value is calculated using the Kriging model. The number of times the response value exceeds the structural performance limit state is counted, and the failure probability of the structure is obtained by dividing the number of times by the total number of simulations.

9. A closed-loop analysis system for large-span steel structures, characterized in that, Includes the following modules: The generation module is used to obtain the finite element model and design parameter space of the large-span steel structure, perform initial sensitivity analysis and modal analysis based on the finite element model, identify the key design parameters that affect the strain energy of the first N modalities of the structure and the corresponding key structural regions, establish the mapping relationship between the key design parameter subspace and the key structural regions, and determine the non-uniform sampling strategy in the design parameter space according to the sensitivity contribution of each key design parameter. The sampling points are densified in the key design parameter subspace with high sensitivity to generate an initial sample point set. The construction module is used to construct a hierarchical hybrid kernel function Kriging surrogate model based on the initial sample point set and the corresponding finite element response values. The hierarchical hybrid kernel function is composed of a global long-range correlation kernel representing the overall response of the structure and multiple local short-range correlation kernels corresponding to each key region of the structure. The weight of each local kernel function is a symmetric function about the position of two input points in the corresponding key design parameter subspace, so that the closer the two input points are to the high-sensitivity region, the greater the weight of the corresponding local kernel function. The calculation module is used to set the iteration termination condition and the structural performance limit state. When the termination condition is not met, the composite addition criterion function value of the candidate sample points is calculated, the point with the largest function value is selected as the new sample point, the sample point set is updated and the Kriging surrogate model is reconstructed. When the termination condition is met, the performance analysis of the large-span steel structure is performed using the Kriging surrogate model.

10. The system according to claim 9, characterized in that, The initial sensitivity analysis and modal analysis based on the finite element model are performed to identify key design parameters and corresponding key structural regions that affect the strain energy of the first N modalities of the structure, including: Modal analysis is performed on the finite element model to calculate the first N modes. For each mode, the percentage of strain energy of each element in the structure to the total strain energy is calculated, and a weighted sum is performed to obtain the comprehensive strain energy contribution of each element. The set of elements with the top 20% comprehensive strain energy contribution is selected to define the key region of the structure. For each identified critical region, the partial derivatives of the modal strain energy of the critical region with respect to all design parameters are calculated to obtain sensitivity information, and the top M design parameters that have the highest sensitivity influence on the region are identified as the critical design parameters of the region.

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