Reliability design method of multi-directional die forging hydraulic press based on adaptive aggregation model

Abstract

The application discloses a kind of multi-direction die forging hydraulic press reliability design method based on adaptive aggregation model belongs to mechanical engineering reliability design technical field.For the problem that global and local are difficult to optimize in non-uniform response surface modeling of heterogeneous agent model and the key area prediction accuracy is insufficient due to static weight distribution, a dynamic weighting strategy is proposed. An optimization model is established with the minimum weight of the structure as the target and the stress deformation and modal frequency reliability as the constraint. Latin hypercube sampling is used. A polynomial chaos expansion and Kriging heterogeneous agent model is constructed. The precision radius is dynamically defined according to the weighted error ratio to divide the local high confidence area and the global smooth area. The global and local weights are calculated and the contribution rate of each base model is dynamically adjusted using the mixed weight. Reliability analysis is performed based on the aggregation model and iterative optimization is performed. The prediction accuracy of the key failure boundary area is significantly improved, the calculation cost is reduced, and the lightweight and reliability of the multi-direction die forging hydraulic press are optimized.

Description

Technical Field

[0001] This invention relates to the field of engineering structure reliability design optimization technology in mechanical engineering, and more specifically, to a reliability and lightweight design method for a multi-directional forging hydraulic press based on an adaptive heterogeneous polymerization model. Background Technology

[0002] Multi-directional die forging hydraulic presses are core forming equipment for large metal components in high-end equipment manufacturing fields such as aerospace and energy power. They are mainly used for precision forging of large and complex metal components such as aircraft landing gear and gas turbine discs.

[0003] Compared to traditional unidirectional forging hydraulic presses, multidirectional forging hydraulic presses can apply pressure to metal billets simultaneously in multiple directions, ensuring the strong and tough forming and uniform performance processing of large and complex components. During the forging process, multidirectional forging hydraulic presses not only apply loads in the longitudinal (main direction) direction, but also set auxiliary pressure heads in the transverse, radial, or oblique directions to achieve plastic deformation under multidimensional stress, thereby effectively improving the metal's microstructure, fluidity, and mechanical properties.

[0004] Multi-directional forging hydraulic presses are typically composed of large structural components such as upper crossbeams, columns, lower crossbeams, main hydraulic cylinders, side cylinders, and worktables. Their working performance directly determines the manufacturing quality and efficiency of these crucial national equipment.

[0005] In the traditional design of multi-directional forging hydraulic presses, in order to ensure the safety of the equipment under extreme working conditions, engineers usually adopt the method of "experience design plus safety factor". That is, the stress and deformation of the structure under rated load are calculated by finite element simulation, and a large safety margin is introduced to offset the risks caused by material performance fluctuations, manufacturing tolerances and load uncertainties.

[0006] This design pattern was of great historical significance in the early stages of industry development for ensuring basic equipment safety and preventing catastrophic failures. It was an inevitable choice given the limited computing power and lack of systematic uncertainty quantification methods at the time.

[0007] However, with the increasing demands for lightweight, high precision, and high reliability in high-end equipment, the limitations of traditional design models are becoming increasingly apparent, making it difficult to meet the actual needs of current multi-directional forging hydraulic press designs. Existing technologies mainly suffer from the following three shortcomings: First, the high cost of high-fidelity simulation calculations severely restricts the iterative efficiency of reliability analysis and optimization design. Multi-directional forging hydraulic presses have complex structures involving multiple physical effects such as contact nonlinearity, material nonlinearity, and geometric nonlinearity. A single high-fidelity finite element analysis often takes hours or even days. Reliability design optimization typically requires tens of thousands of sample evaluations. If the finite element model is directly called, the total computational load will increase exponentially, making it impossible to complete design iterations within a reasonable timeframe in engineering practice.

[0008] Early limitations in computing power forced the engineering community to adopt a design paradigm of "increasing the safety factor through deterministic analysis of a small number of samples," a paradigm that persists to this day. When introducing reliability design concepts, the technical approach often involves directly applying traditional Monte Carlo simulations to complex equipment, failing to fundamentally address the bottleneck of expensive high-fidelity model computation. Existing technologies focus on relying on a single high-fidelity model for massive sampling, lacking efficient surrogate model alternatives that can consider both global trends and local nonlinear characteristics. Correspondingly, this patent application establishes a new route for surrogate model construction based on an adaptive aggregation model, and adapts the dynamic accuracy radius algorithm to the non-uniform distribution characteristics of the multi-directional forging hydraulic press response surface—characterized by "overall smoothness but severe local stress concentration"—achieving high prediction accuracy at extremely low computational cost.

[0009] Second, existing surrogate models struggle to balance global stability with high local accuracy, leading to distorted predictions of critical failure boundaries. To reduce computational costs, current techniques often employ surrogate models such as polynomial chaotic expansion (PCE) or Kriging to replace finite element simulations. While PCE models excel at capturing global trends, they often require extremely high-order expansions when dealing with severely nonlinear regions such as local stress concentrations, resulting in a surge in basis functions or even failure. Kriging models, while adept at local fitting, suffer from significantly increased computational costs and insufficient global prediction stability in high-dimensional design spaces. More critically, existing aggregation models often employ fixed weights or static weighting strategies based solely on global errors, failing to dynamically adjust the model contribution rate according to the response characteristics of different regions in the design space. This results in insufficient prediction accuracy near critical failure boundaries, such as those with stresses exceeding 315 MPa.

[0010] In its early stages, surrogate modeling technology primarily focused on the global fitting capability of a single model. While later ensemble modeling concepts were proposed, they were constrained by the inertia of static weighting theory, failing to break free from the "one-size-fits-all" mindset regarding weight allocation. In applying ensemble models, the common inverse error weighting method is frequently used, neglecting the non-uniform characteristics of the response surface of specific engineering objects. Existing technologies focus on static weight allocation based on global statistical indicators, lacking a dynamic mechanism for nonlinearly coupling geometric distribution characteristics with local model error statistical characteristics. Correspondingly, this patent application establishes a mechanism based on a dynamic accuracy radius r...k The global-local hybrid dual-weight strategy, through a positive feedback mechanism, adapts to the differentiated requirements of global regression and local interpolation in different regions of the multi-directional die forging hydraulic press, fundamentally solving the technical contradiction that "global stability" and "local high precision" cannot be achieved simultaneously.

[0011] Third, sequential sampling strategies are inefficient and have unreasonable constraint resource allocation, leading to slow optimization convergence. Existing adaptive sampling criteria (such as the U function and EFF function) mostly adopt weighted sum forms, implicitly containing a "logical OR" relationship. This can easily lead to the selection of redundant samples due to the prominence of a single indicator, and the sampling region radius is mostly a fixed value, which cannot be dynamically adjusted according to the model confidence level, resulting in a large amount of expensive simulation resources being wasted in non-critical areas. At the same time, in multi-constraint optimization iterations, existing technologies treat all preset constraints (such as stress, deformation, and modal frequencies) equally and perform precise calculations without dynamically removing "safety constraints" far from the failure boundary, resulting in the dispersion of computational resources and hindering the exploration of key active constraints. In the early development of sampling theory, the main problem was "whether there are samples," forming a tradition of uniform sampling or simple heuristic sampling. Although the concept of multi-objectives was introduced later, simple linear weighted combinations were mostly used, lacking strict logical constraints on the comprehensive information gain of samples. In dealing with multi-constraint problems, this field is limited by the inertia of traditional mathematical programming thinking, and is accustomed to participating in iteration with all constraints, lacking the awareness of resource management for dynamic pruning.

[0012] Existing technologies focus on the linear superposition of single-dimensional indicators and parallel computation with full constraints, lacking a rigorous screening mechanism based on "logical AND" relationships and a constraint management strategy based on dynamic perception of reliability indicators. Existing technologies also lack the ability to adaptively adapt to the non-uniform characteristics of the response surface of multi-directional forging hydraulic presses, resulting in insufficient prediction accuracy near critical failure boundaries. This patent application establishes a sequential point-addition strategy based on the product-type adaptive sampling criterion in Formula 20, and through a maximum probable failure point (MPP)-oriented adaptive sampling and dynamic adjustment mechanism, it adapts to the physical characteristics of multi-directional forging hydraulic press optimization, where critical areas require detailed exploration while non-critical areas can be roughly monitored, significantly improving sampling efficiency and optimization convergence speed.

[0013] This patent application establishes a three-factor product-type adaptive sampling criterion and a probabilistic constraint dynamic intelligent screening mechanism. By adapting the maximum possible failure point guidance and error amplification coefficient to the physical characteristics of "critical areas need to be explored in detail and safe areas can be monitored roughly" in the optimization process of multi-directional die forging hydraulic press, it significantly improves sampling efficiency and optimization convergence speed.

[0014] In summary, traditional design methods for multi-directional forging hydraulic presses suffer from significant shortcomings in computational efficiency, model accuracy, and resource allocation, failing to meet the urgent needs of lightweight and high-reliability collaborative design for high-end equipment. Therefore, there is a pressing need to develop a reliability design method for multi-directional forging hydraulic presses based on an adaptive aggregation model. This method, through the construction of a dynamic weighted aggregation model, an efficient adaptive sampling strategy, and an intelligent constraint screening mechanism, aims to achieve an optimal balance between computational cost and prediction accuracy, providing scientific and efficient theoretical support and technical means for the optimized design of multi-directional forging hydraulic presses. Summary of the Invention

[0015] The purpose of this invention is to provide a technical solution to the problem that global trends and local features are difficult to optimize in a coordinated manner in the modeling of non-uniform response surfaces by heterogeneous proxy models. This overcomes the shortcomings of existing technologies that use static weight allocation strategies, which cannot dynamically adjust the contribution rate of multiple models according to the characteristics of the design space region, resulting in insufficient prediction accuracy in key regions of the response surface.

[0016] To achieve the above objectives, the reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model of the present invention includes the following steps: S1: Establish the following constraints: the failure probability of stress, deformation and modal frequency is not greater than the preset failure probability threshold or the equivalent reliability index is not less than the target reliability index. S2: The Latin hypercube sampling strategy is used to select initial sample points in the design space, and high-fidelity simulation is performed on the initial sample points to obtain structural response values, forming an initial training sample library; S3: Based on the initial training sample library, construct an aggregated model containing a first base model and a second base model. The first base model and the second base model are heterogeneous surrogate models with different mathematical mechanisms. The first basis model is used to characterize the global trend of the structural response, and the second basis model is used to describe the local deviation of the structural response. The steps to build an aggregation model include: Based on the coupling relationship between the geometric distribution characteristics of each sample point and the global and local error statistics of the first and second basis models at that sample point, the accuracy radius of the sample point is dynamically defined. Based on the relative position of the predicted point and the accuracy radius, the design space is divided into a local high confidence region and a global smooth region. Calculate the global and local weights of the first and second basis models, where the global weights are determined based on the generalized mean square cross-validation error, and the local weights are determined based on the coupling of leave-one cross-validation error and distance. Based on the region where the prediction point is located, the contribution rate of each base model is dynamically adjusted using a mixture of the global weight and the local weight to obtain the prediction response of the aggregate model. S4: Use this aggregation model to replace the high-fidelity simulation for reliability analysis, and obtain failure probability and gradient information; S5: Based on the failure probability and the gradient information, the design variables are iteratively updated using a sequential approximation programming algorithm until the convergence condition is met, and the optimal structural parameters that satisfy all reliability constraints are output.

[0017] The first basis model is the global trend basis model, i.e., the PCE model, which is a sparse polynomial chaotic expansion model constructed using the least angle regression algorithm. The second basis model is the local bias basis model, which is a Kriging model constructed using the Gaussian kernel function.

[0018] In S3, the method for dynamically defining the precision radius of sample points is: Based on the ratio P of the local weighted error to the global weighted error at the sample point k With nonlinear judgment threshold P th The relationship determines the precision radius r at the sample point based on the specific circumstances. k : When P k Greater than the nonlinearity threshold P th When the sample point is determined to be in a strongly nonlinear region, according to the formula r k =D k ×max(δ,1-λ×(P k -P th )) Calculate this precision radius to narrow down the local influence range and focus on local features; When P k Less than or equal to the nonlinear decision threshold P th When the sample point is determined to be in a smooth region, according to the formula r k =D k ×(1+λ×(P th -P k )) Calculate this precision radius to expand the local influence range and improve computational efficiency; Where D k It is half the Euclidean distance between the sample point and the other nearest sample point, reflecting the geometric sparsity around the sample point; P k = (wCV) k L ) / (wCV k G ), which is the ratio of the local weighted error to the global weighted error at that sample point; λ is a preset adjustment coefficient used to control the weight of the influence of this error ratio on the accuracy radius; δ is a lower limit coefficient used to ensure that the radius of this precision is not zero or negative.

[0019] The steps for calculating the global and local weights of the global trend basis model and the local deviation basis model in S3 include: Calculate the global weight w according to formula 11. i G Formula 11 is: ; Among them, w i G E represents the global weights of the i-th base model; i Let be the generalized mean squared cross-validation error (GMSE) of the i-th base model, calculated according to the formula in the second row of Equation 11; n is the number of samples; N m N represents the total number of base models. m =2; y k For sample point x k The actual response value; y^ k To construct the i-th base model using all sample points except (xk, yk) in x k Predicted response value at point; Calculate the local weight ω according to formula 12. i L Formula 12 is: ; Where, ω i L e represents the local weights of the i-th base model; ik W represents the leave-one-out cross-validation error of the i-th base model at sample point xk; ik I represents the weight value of the i-th base model at the k-th sample point; k (x) is the distance function related to the Euclidean distance between the predicted point and the sample point xk. N is the total number of training samples.

[0020] In S3, the steps for dynamically adjusting the mixed weights based on the region where the predicted point is located include: When the normalized distance between the predicted point and the nearest sample point is less than or equal to the preset threshold Rn for local region segmentation, the predicted point is determined to be within a local high-confidence region, and the mixed weight ω i H For the global weight w i G With the local weight ω i L The product; When the normalized distance is greater than the global region partitioning preset threshold Rf, the predicted point is determined to be within the global smooth region, and the mixed weight ω is... i H Equal to the global weight w iG ; Wherein, the normalized distance is the ratio of the Euclidean distance from the predicted point to the nearest sample point to the accuracy radius rk.

[0021] According to the mixed weight ω i H The predicted values ​​of each base model are linearly weighted and aggregated to obtain the predicted response.

[0022] The linear weighted aggregation formula is Equation 9: y^ EoS (x) = w1y^1(x) + w2y^2(x); where y^ EoS Let y^1(x) and y^2(x) be the response values ​​of the aggregate model at sample point x, and y^2(x) be the response values ​​of the PCE model and the Kriging model (first basis model and second basis model), respectively, at response x; w1 and w2 are the weights of the PCE model and the Kriging model, respectively, and the weights must satisfy Formula 10: w i ≥0 and w1+w2=1, i=1,2.

[0023] Step S4 also includes step S6: Based on this aggregation model, a local sampling region is constructed near the maximum probable failure point (MPP) corresponding to the current design point, and a three-factor product learning function LF is used. EoS-PK New sample points are selected within the local sampling area to update the initial training sample library and reconstruct the aggregated model until the relative error between the predicted value and the actual response value of the aggregated model is less than a preset threshold eps, where eps is a very small positive number added to avoid the denominator being zero.

[0024] In step S6, the sampling radius R of the local sampling area is calculated according to formula 17, which is: R = (1.5 + 0.5·c e )·β j t ; Where R is the local sampling radius, β j t Let c be the target reliability index for the j-th constraint; e The error amplification factor is determined based on the following statistical properties: around this MPP, with a factor of β... j t Candidate sample points are uniformly generated within a spherical region of radius , and the prediction standard deviation of the aggregation model at the candidate sample points is calculated. Once R is determined, the learning function LF EoS-PK Calculated according to Formula 20, Formula 20 is the formula including the predictive standard deviation σ. PK Normalized indicator value u PK Minimum sample distance d minand the multinomial coupling form of the standard normal distribution function, or using the predicted standard deviation σ PK The normalized indicator value u PK The minimum sample distance d min The product of the normalized values ​​of the three; Formula 20 is: ; Where, σ PK This represents the standard deviation of the predictions of the aggregation model (EoS-PK) at the candidate sample points, a statistic reflecting the prediction uncertainty at that point; PK This is the normalized indicator value of the predicted value relative to the failure boundary.

[0025] Real-time monitoring of the current reliability index β for each probability constraint; When β is greater than twice the target reliability index β of the j-th constraint j t When the probability constraint is determined to be an inactive constraint, the exact calculation and gradient solution of the inactive constraint are eliminated in this iteration, and the computing resources are concentrated on the active constraint set.

[0026] The steps involved in constructing a heterogeneous proxy model that incorporates at least two different mathematical mechanisms include: A sparse multinomial chaotic expansion model is constructed using the least angle regression (LARS) algorithm combined with cross-validation to characterize the global trend of the structural response. A Kriging model is constructed using a Gaussian kernel function, and the hyperparameters are optimized by maximum likelihood estimation to describe the local bias of the structural response.

[0027] Step S4 includes: Using this aggregation model, the reliability index method (RIA) is employed to search for the point closest to the origin on the limit state surface in the standard normal space, which is then taken as the maximum probable failure point (MPP). Using the MPP as the sampling center, the failure probability and gradient information are calculated using the importance sampling method.

[0028] The present invention has the following advantages: By introducing a precision radius defined by the coupling of geometric distribution characteristics and error statistics, the design space is dynamically divided into a local high-confidence region and a global smooth region. Dynamic mixed weighting is then performed using weights based on global errors and weights based on local errors, respectively. This solves the technical problem that global trends and local features are difficult to optimize in a coordinated manner in the modeling of non-uniform response surfaces by heterogeneous surrogate models. It overcomes the shortcomings of existing technologies that have insufficient prediction accuracy in key regions of the response surface due to the use of static weight allocation strategies, and achieves a significant improvement in prediction accuracy in local stress concentration regions while maintaining global stability.

[0029] This invention establishes the error ratio P by dynamically defining the precision radius of sample points. k And the scope of influence r k Positive feedback mechanism; When a certain region has poor local fitting (P) k When r increases, k Automatically shrinking the interpolation neighborhood of the local model eliminates interference from distant smooth points, forcibly improving the focusing accuracy of models that excel at local interpolation in that region; conversely, r k This shrinkage strengthens the model's advantage in global regression; this mechanism enables an adaptive redistribution of model weights as the response surface becomes nonlinear.

[0030] The global weights are allocated based on the reciprocal of GMSE, ensuring that models with excellent global performance receive higher base weights. The local weights are calculated based on leave-one error and distance coupling, ensuring that models with high fitting accuracy in the vicinity of the prediction point receive higher local weights. The combination of the two achieves adaptive allocation of the advantages of heterogeneous models.

[0031] By employing a product-based mixed weighting method within this local high-confidence region, the model is forced to possess both excellent global and local fitting performance to obtain high weights in this region, ensuring prediction accuracy in key areas. Within this global smooth region, the model primarily relies on global weights, guaranteeing global stability. This partitioned dynamic weighting strategy achieves synergistic optimization of global trends and local features.

[0032] By adopting a three-factor product learning function, a strict "logical AND" relationship is established. The "weakest link effect" is used to force candidate points to simultaneously meet three conditions: high uncertainty, proximity to the failure boundary, and spatial sparsity. This avoids sample redundancy caused by the traditional summation form and significantly improves sampling efficiency and model convergence speed near the failure boundary.

[0033] The dynamic sampling radius R can automatically expand or contract according to the confidence level of the current model near the MPP, expanding the exploration range when the model uncertainty is high and focusing on fine-grained search when the model tends to converge; the three-factor product form ensures that the comprehensive information gain of the new samples is maximized, effectively balancing exploration and utilization.

[0034] By dynamically eliminating inactive constraints during the iteration process, a "safety buffer" is constructed to avoid wasting expensive computing resources in safe areas far from the failure boundary. This significantly reduces the computational dimension of the optimization problem and accelerates the convergence of the overall optimization trajectory to the global optimum.

[0035] By employing the LARS algorithm to construct a sparse PCE, the problem of term explosion caused by high-dimensional variables is solved, ensuring the efficiency of global trend characterization. By using Gaussian kernel Kriging, the fitting ability for local nonlinear deviations is enhanced, and the Kriging part can also provide prediction variance to directly serve uncertainty-based analysis and reliability analysis. The targeted training strategies of both provide a high-quality base model foundation for the high-precision prediction of this aggregate model, and the model accuracy index provides a comprehensive performance evaluation, ensuring the reliability of the model.

[0036] By employing RIA to quickly locate the MPP and using it as a benchmark for important sampling, the number of samples required for failure probability calculation is significantly reduced, improving the efficiency of reliability analysis. Furthermore, the PCE and Kriging models serve as mature base models with rich algorithm libraries, and the aggregation and weighting logic of EoS-PK is clear, making it easy to integrate and deploy in existing simulation and optimization platforms. It is particularly suitable for complex structures operating in uncertain environments, such as multi-directional forging hydraulic presses. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of a multi-directional forging hydraulic press, showing the relative positions of the upper crossbeam, column, lower crossbeam, main hydraulic cylinder, side cylinder, and worktable.

[0038] Figure 2 The design optimization variable marking diagram for the multi-directional die forging hydraulic press shows the specific marking positions of the design variables of the key structures of the upper crossbeam, column, and lower crossbeam on the equipment.

[0039] Figure 3 This document presents a flowchart for the reliability design optimization of a multi-directional forging hydraulic press, illustrating the overall process from initial sampling, high-fidelity simulation, heterogeneous surrogate model aggregation model construction, maximum probable failure point location, adaptive sampling, probabilistic constraint screening, failure probability calculation, to optimization iteration. This flowchart is used to solve the reliability design optimization mathematical model shown in Equation 1. By replacing high-fidelity simulation with an adaptive aggregation model and combining MPP-guided sampling and dynamic constraint management, the optimal design variables that satisfy probabilistic constraints are efficiently obtained.

[0040] Figure 4 The flowchart of the EoS-PK aggregation strategy illustrates the specific logical flow of dynamic precision radius calculation based on the coupling of geometric distribution characteristics and error statistics characteristics, design space division into local high confidence regions and global smooth regions, global weight and local weight calculation, hybrid weight determination, and heterogeneous proxy model aggregation. Detailed Implementation

[0041] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0042] like Figures 1 to 4 As shown, this implementation adopts a full-process closed-loop optimization strategy. It replaces high-fidelity simulation with an adaptive heterogeneous aggregation model, and combines dynamic accuracy radius partitioning weighting, local adaptive point addition, and intelligent constraint screening mechanisms to achieve efficient and reliable design optimization of the multi-directional forging hydraulic press. Specifically, it includes the following five stages: Phase 1: Establishment of a reliability design optimization model.

[0043] First, we establish a function with the objective of minimizing the structural weight of the multi-directional forging hydraulic press, and ensure that the failure probability of stress, deformation, and modal frequency is not greater than a preset failure probability threshold (or the equivalent reliability index is not less than the target reliability index β). j t The reliability design optimization model is constrained by the following: the design variables include key dimensions such as the column cross-section width and height, the web thickness of the upper beam and the structural parameters of the lower beam, and the random variables include the material elastic modulus, yield strength and working load.

[0044] Phase Two: Initial Sampling.

[0045] The Latin hypercube sampling strategy is used to select initial sample points in the design space, and high-fidelity simulation is performed on these initial sample points to obtain structural response values, thus forming an initial training sample library.

[0046] Phase 3: Construction of Heterogeneous Proxy Model and Adaptive Aggregation.

[0047] Based on the initial training sample library, an aggregate model is constructed, comprising a first basis model and a second basis model. These two basis models are heterogeneous surrogate models with different mathematical principles. The first basis model characterizes the global trend of the structural response, employing the Least Angle Regression (LARS) algorithm combined with cross-validation to construct a sparse multinomial chaotic expansion model. The second basis model describes the local biases of the structural response, using a Gaussian kernel function to construct a Kriging model and optimizing hyperparameters through maximum likelihood estimation. The ratio P of the local weighted error to the global weighted error at each sample point is used as the basis for the model's design. k The relationship with the preset threshold determines the precision radius r of the sample point in different cases. kThe accuracy radius is reduced in the strongly nonlinear region and expanded in the smooth region. Global and local weights of the first and second basis models are calculated, where the global weight is determined based on the generalized mean square cross-validation error, and the local weight is determined based on the coupling of leave-one-out cross-validation error and distance. The design space is divided into a local high-confidence region and a global smooth region according to the relative position of the prediction point and the accuracy radius. When the prediction point is within the local high-confidence region, the hybrid weight ω... i H For the global weight w i G With the local weight ω i L The product of the product and the mixed weight ω when the predicted point is within the global smooth region. i H Equal to the global weight w i G The predicted values ​​of each base model are linearly weighted and aggregated according to the mixed weights to obtain the predicted response, thereby establishing an adaptive aggregation model (EoS-PK) that combines global stability and local high accuracy.

[0048] Phase 4: Reliability analysis, adaptive sampling, and constraint management.

[0049] This aggregation model is used to replace the high-fidelity simulation for reliability analysis: the reliability index method (RIA) is used to search for the point closest to the origin on the limit state surface in the standard normal space as the maximum probable failure point (MPP), and the failure probability and gradient information are calculated using importance sampling with the MPP as the sampling center; the current reliability index β of each probability constraint is monitored in real time, and when β is greater than twice the target reliability index β... j t The probability constraint is determined to be an inactive constraint and removed, and computational resources are concentrated on the active constraint set; a local sampling region is constructed near the maximum probable failure point (MPP), and the dynamic sampling radius R is calculated according to formula 17, using the three-factor product learning function LF. EoS-PK New sample points are selected within this local sampling region to update the initial training sample library and reconstruct the aggregated model until the relative error between the predicted value and the true response value of the aggregated model is less than a preset threshold eps, where eps is a very small positive number added to avoid zero denominators, typically 1×10. -6 Up to 1×10 -3 .

[0050] Phase 5: Sequence approximate programming and optimization convergence.

[0051] Based on the failure probability and gradient information, the design variables are iteratively updated using a sequential approximate programming algorithm. The above reliability analysis and model update process is repeated until the convergence condition is met (including the failure probability of three consecutive iterations meeting the constraint condition and the relative change rate of the design variables being less than the threshold). The optimal structural parameters that satisfy all reliability constraints are output, thus completing the reliability and lightweight design of the multi-directional die forging hydraulic press.

[0052] The present invention will now be described in detail.

[0053] The reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model disclosed in this invention (corresponding to stages one to five above) includes the following steps: S1: Establish a reliability index where the failure probability due to stress, deformation, and modal frequency is no greater than a preset failure probability threshold, or an equivalent reliability index is no less than the target reliability index (β). j t ) are constraints; S2: The Latin hypercube sampling strategy is used to select initial sample points in the design space, and high-fidelity simulation is performed on the initial sample points to obtain structural response values, forming an initial training sample library; S3: Based on the initial training sample library, construct an aggregated model containing a first base model and a second base model. The first base model and the second base model are heterogeneous surrogate models with different mathematical mechanisms. The first basis model is used to characterize the global trend of the structural response, and the second basis model is used to describe the local deviation of the structural response. The steps to build an aggregation model include: Based on the coupling relationship between the geometric distribution characteristics of each sample point and the global and local error statistics of the first and second basis models at that sample point, the accuracy radius of the sample point is dynamically defined. Based on the relative position of the predicted point and the accuracy radius, the design space is divided into a local high confidence region and a global smooth region. Calculate the global and local weights of the first and second basis models, where the global weights are determined based on the generalized mean square cross-validation error, and the local weights are determined based on the coupling of leave-one cross-validation error and distance. Based on the region where the prediction point is located, the contribution rate of each base model is dynamically adjusted using a mixture of the global weight and the local weight to obtain the prediction response of the aggregate model. S4: Use this aggregation model to replace the high-fidelity simulation for reliability analysis, and obtain failure probability and gradient information; S5: Based on the failure probability and the gradient information, the design variables are iteratively updated using a sequential approximation programming algorithm until the convergence condition is met, and the optimal structural parameters that satisfy all reliability constraints are output.

[0054] The objective function in step S1 is the structural weight of the multi-directional forging hydraulic press, which consists of the weight of the upper crossbeam, the column, the lower crossbeam, and other components. The constraints are reliability indices related to stress, deformation, and modal frequency. These reliability indices are characterized by a failure probability not exceeding a preset reliability index threshold or, equivalently, a reliability index not less than a target value. The preset failure probability threshold corresponds to the target reliability index β. j t Satisfying relation P target =Φ(-β j t When the target reliability index β j t When the value is 3.0, the corresponding preset failure probability threshold is Φ(-3.0)≈0.00135.

[0055] To ensure the service performance of the multi-directional forging hydraulic press, reduce its manufacturing cost, and consider the uncertainties in the structural parameters of each component, this patent utilizes a reliability design optimization method to perform lightweight design on the multi-directional forging hydraulic press. With minimizing the weight M(μ) of the multi-directional forging hydraulic press as the objective function, and satisfying the reliability of stress, deformation, and modal frequency under comprehensive loading conditions as the constraint, a reliability design optimization model is established in step S1. Its general mathematical expression is: finding the design variable vector μ such that the objective function M(μ) is minimized, and the probabilistic constraint P is satisfied. f (g j (X)>C j )≤P target Or equivalent reliability index constraint β j ≥β j t Where X is a vector of random variables following a preset probability distribution, and C... j P is the threshold for the j-th constraint. target β is the maximum allowable failure probability. j β is the current reliability metric. j t The target reliability index.

[0056] The reliability design optimization model established in step S1 can be specifically adopted using Formula 1:

[0057] In Formula 1, μ is the design variable, M(μ) is the weight of the multi-directional forging hydraulic press; P f (·) is a probability operation, g s (X)>315 means the maximum stress is greater than the allowable stress of 315 MPa, g d (X)>2.7 means the maximum deformation is greater than the allowable deformation of 2.7 mm, g m(X)≤30 means the first-order modal frequency is less than or equal to the allowable modal frequency of 30Hz; μ (0) These are the initial design parameters, β i t It is a reliability index, and Φ(*) is the cumulative distribution function of the standard normal distribution. The maximum stress, maximum deformation, and first-order modal frequency at structural parameter X can be obtained through finite element simulation.

[0058] For the complex nonlinear, multi-constraint reliability optimization problem described in Equation 1, this invention adopts the following... Figure 3 The solution is obtained using the full-process closed-loop optimization method shown. This method replaces the implicit response function in Equation 1 by constructing a high-precision EoS-PK aggregation model. It utilizes dynamic precision radius weight allocation and a three-factor product sampling strategy to efficiently find the optimal design variable μ that satisfies all probability constraints in Equation 1 and minimizes the weight M(μ) while ensuring the prediction accuracy of key areas. The specific steps are as follows: (1) Initial sampling: 30 initial sample points were selected in the design space using the Latin hypercube sampling (LHS) strategy.

[0059] (2) Finite element simulation: Finite element simulation is performed on the initial sample points to obtain the maximum stress, maximum deformation and first-order modal frequency of the multi-directional forging hydraulic press under different load conditions, forming an initial training sample library.

[0060] (3) Construction of PCE and Kriging models: Based on the initial sample set, the sparse polynomial chaotic expansion (PCE) model is constructed by combining the least angle regression (LARS) algorithm with cross-validation to characterize the global trend; at the same time, the Kriging model based on the Gaussian kernel function is constructed, and the hyperparameters are optimized by maximum likelihood estimation to describe the local bias.

[0061] (4) Construction of the aggregated model EoS-PK: Define the accuracy radius to divide the design space into local and global regions, dynamically calculate the global weight and local adaptive weight according to the prediction point position, and construct an EoS-PK model that has both global stability and local high accuracy.

[0062] (5) Calculation of the maximum possible failure point: The EoS-PK model is called, and the reliability index method (RIA) is used to search for the limit state point closest to the origin on the limit state surface in the standard normal space (U space), which is the maximum possible failure point (MPP).

[0063] (6) Local adaptive sampling: A local sampling region is constructed near the MPP, and a three-factor product-based adaptive sampling criterion (LF) is introduced. EoS-PK This effectively identifies points with "high prediction variance", "extremely close to the failure boundary", and far away from existing sample points as incremental samples.

[0064] (7) EoS-PK model update: Finite element simulation is performed on the new samples, and the obtained real response data is fed back to the sample library to reconstruct the EoS-PK model and realize the adaptive update of the model.

[0065] (8) Probabilistic constraint feasibility judgment: The probabilistic constraint status is judged based on the distance (reliability index β) from the current design point to the limit state constraint boundary; if β is greater than the given value c, the probabilistic constraint is considered invalid and is removed in this important sampling and optimization iteration to reduce the computational dimension.

[0066] (9) Failure probability and gradient calculation: For the effective probability constraint, the failure probability and gradient are calculated by using the importance sampling (IS) strategy with MPP as the sampling center.

[0067] (10) Iterative design point calculation: Using the failure probability and gradient information obtained in step (9), the Sequential Approximate Programming (SAP) algorithm is used to quickly find the next design point X. (k+1) .

[0068] (11) Convergence condition: If the failure probability of three consecutive iterations satisfies the constraint condition, and If the condition is met, then jump to the end; if not, let k = k + 1 and return to step (5).

[0069] (12) End: Output the optimal structural parameters and lightweight design results that satisfy all reliability constraints, and complete the design. Figure 3 The full-process closed-loop optimization design is shown.

[0070] The "dynamic precision" radius algorithm in this invention refers to a mechanism that automatically calculates the precision radius based on the distribution of sample points and dynamically adjusts the region weights.

[0071] The objective function M(μ) in step S1 is specifically represented by the total weight of the multi-directional forging hydraulic press, which is constructed as Formula 2 based on various dimensional parameters: M(μ) = W1 + 2W2 + W3 + R. In Formula 2, W1 is the weight of the upper crossbeam, W2 is the weight of a single column (with a coefficient of 2 due to the symmetrical structure of the double column), W3 is the weight of the lower crossbeam, and R is the weight of other components. The constraints (reliability preset indicators) include: stress reliability constraint: the probability that the maximum stress exceeds 315MPa is not greater than Φ(﹣3.0); deformation reliability constraint: the probability that the maximum deformation exceeds 2.7mm is not greater than Φ(﹣3.0); modal reliability constraint: the probability that the first modal frequency is lower than 30Hz is not greater than Φ(﹣3.0).

[0072] Step S1, the objective function, constraints, design variables, and the limitations of random variables all correspond to the first stage mentioned above, namely the establishment of the reliability design optimization model.

[0073] The calculation methods for each part of Formula 2 are shown in Formula 3: .

[0074] Where R1, R2 and R3 represent the weights of the upper beam, column and lower beam outside the design domain, respectively.

[0075] The high-fidelity simulation in step S2 includes, but is not limited to, finite element analysis.

[0076] The heterogeneous surrogate models in step S3 include, but are not limited to, global trend characterization models based on orthogonal polynomial basis function expansion and local bias description models based on Gaussian process regression.

[0077] The precision radius in step S3 is determined based on half of the Euclidean distance between the sample point and its nearest neighbor sample point, and the ratio of the global weighted error to the local weighted error at the sample point.

[0078] By introducing a precision radius defined by the coupling of geometric distribution characteristics and error statistics, the design space is dynamically divided into a local high-confidence region and a global smooth region. Dynamic mixed weighting is then performed using weights based on global errors and weights based on local errors, respectively. This solves the technical problem that global trends and local features are difficult to optimize in a coordinated manner in the modeling of non-uniform response surfaces by heterogeneous surrogate models. It overcomes the shortcomings of existing technologies that have insufficient prediction accuracy in key regions of the response surface due to the use of static weight allocation strategies, and achieves a significant improvement in prediction accuracy in local stress concentration regions while maintaining global stability.

[0079] The reliability analysis in step S4 includes searching for the most likely failure point (MPP) in the standard normal space, and using the MPP as the sampling center, calculating the failure probability and the gradient information using the importance sampling method.

[0080] Taking a certain type of multi-directional forging hydraulic press as an example, it mainly includes an upper crossbeam, a column, a lower crossbeam, a main hydraulic cylinder, and a side cylinder. In step S1, a parametric finite element model is established: the key dimensions of the column cross-section width and height, and the web thickness of the upper crossbeam are selected as design variables μ; the material elastic modulus, yield strength, and working load are set as random variables X, which follow a normal distribution or a log-normal distribution; the mesh is generated using hexahedral elements, and local refinement is performed in the stress concentration area to ensure the convergence and accuracy of the finite element calculation results.

[0081] The first basis model is the global trend basis model, i.e., the PCE model, which is a sparse polynomial chaotic expansion model constructed using the least angle regression algorithm. The second basis model is the local bias basis model, which is a Kriging model constructed using the Gaussian kernel function.

[0082] In S3, the method for dynamically defining the precision radius of sample points is: Based on the ratio P of the local weighted error to the global weighted error at the sample point k With nonlinear judgment threshold P th The relationship determines the precision radius r at the sample point based on the specific circumstances. k : When P k Greater than the nonlinearity threshold P th When the sample point is determined to be in a strongly nonlinear region, according to the formula r k =D k ×max(δ,1-λ×(P k -P th )) Calculate this precision radius to narrow down the local influence range and focus on local features; When P k Less than or equal to the nonlinear decision threshold P th When the sample point is determined to be in a smooth region, according to the formula r k =D k ×(1+λ×(P th -P k )) Calculate this precision radius to appropriately expand the local influence range and improve computational efficiency; Where D k It is half the Euclidean distance between the sample point and the other nearest sample point, reflecting the geometric sparsity around the sample point; P k = (wCV) k L ) / (wCV k G ), which is the local weighted error (wCV) at that sample point. k L ) and global weighted error (wCV) k G The ratio of ) λ is a preset adjustment coefficient used to control the weight of the influence of this error ratio on the accuracy radius; δ is a lower limit coefficient used to ensure that the radius of this precision is not zero or negative.

[0083] Formula r k =D k ×max(δ,1-λ×(P k -P th(Strongly nonlinear region) and formula r k =D k ×(1+λ×(P th -P k The smooth region is combined into Formula 15, which is used to dynamically determine the accuracy radius of the sample point based on the degree of nonlinearity of the sample point. Nonlinearity threshold P th It is usually set to 1.0.

[0084] δ is the lower limit coefficient, typically taken as 0.3 to 0.5, used to ensure that when P k Significantly greater than the threshold leads to (1-λ×(P) k -P th When the value is negative, the precision radius r k Keep as δ×D k This ensures numerical stability without losing its physical meaning. The adjustment coefficient λ typically ranges from 0.5 to 5.0. In practical applications, the optimal parameter can be selected by cross-validation, which minimizes the generalized root mean square error of the aggregation model on the validation set. For highly nonlinear structures such as multi-directional forging hydraulic presses, a value of 1.0 to 2.0 is recommended for λ to balance the transition between global and local weights.

[0085] Global weighted error wCV k G It is a weighted value obtained by dividing the original prediction error of the k-th sample point obtained by leave-one-out cross-validation of the global PCE model by the global root mean square error (RMSE) of the entire design space for normalization, and then multiplying it by the global distance weight coefficient between the point and all sample points; wherein, the global distance weight coefficient decreases as the distance increases, and its decay range covers the entire design space.

[0086] Local weighted error wCV k L It is a weighted value obtained by multiplying the original prediction error of the k-th sample point obtained by leave-one-out cross-validation of the local Kriging model by the local distance weight coefficient between the point and its neighboring sample points; wherein, the local distance weight coefficient adopts the form of Gaussian kernel function, and its influence range is dynamically determined by the nearest neighbor distance of the sample point, and only the sample error within the preset neighborhood is given significant weight.

[0087] This invention establishes the error ratio P by dynamically defining the precision radius of sample points. k And the scope of influence r k Positive feedback mechanism; When a certain region has poor local fitting (P) k When r increases, kAutomatically shrinking the interpolation neighborhood of the local model eliminates interference from distant smooth points, forcibly improving the focusing accuracy of models that excel at local interpolation in that region; conversely, r k This shrinkage strengthens the model's advantage in global regression; this mechanism enables an adaptive redistribution of model weights as the response surface becomes nonlinear.

[0088] The steps for calculating the global and local weights of the global trend basis model (PCE model) and the local deviation basis model (Kriging model) in S3 include: Calculate the global weight w according to formula 11. i G Formula 11 is: ; Among them, w i G E represents the global weights of the i-th base model; i Let be the generalized mean squared cross-validation error (GMSE) of the i-th base model, calculated according to the formula in the second row of Equation 11; n is the number of samples; N m N represents the total number of base models. m =2; y k For sample point x k The actual response value; y^ k To construct the i-th base model using all sample points except (xk, yk) in x k Predicted response value at point; Calculate the local weight ω according to formula 12. i L Formula 12 is: ; Where, ω i L e represents the local weights of the i-th base model; ik W represents the leave-one-out cross-validation error of the i-th base model at sample point xk; ik I represents the weight value of the i-th base model at the k-th sample point; k (x) is the distance function related to the Euclidean distance between the predicted point and the sample point xk. N is the total number of training samples.

[0089] The local weight calculation adopts a spatial model-based calculation method, the core idea of ​​which depends on the cross-validation error of a single surrogate model at the sample point and the Euclidean distance between the prediction point and the sample point.

[0090] global weight w i G This reflects the overall approximate performance of the base model across the entire design space.

[0091] Local weight ω i L This reflects the local fitting performance of the base model in the region near the prediction point.

[0092] The distance function I k (x) is usually expressed as the reciprocal of the square of the Euclidean distance or the Gaussian kernel function, representing the degree to which the predicted point is affected by the sample point.

[0093] The global weights are allocated based on the reciprocal of GMSE, ensuring that models with excellent global performance receive higher base weights. The local weights are calculated based on leave-one error and distance coupling, ensuring that models with high fitting accuracy in the vicinity of the prediction point receive higher local weights. The combination of the two achieves adaptive allocation of the advantages of heterogeneous models.

[0094] Formulas 11 and 12 are calculated in parallel to obtain w. i G and ω i L This is used for subsequent mixed weight calculations.

[0095] In S3, the steps for dynamically adjusting the mixed weights based on the region where the predicted point is located include: When the normalized distance between the predicted point and the nearest sample point is less than or equal to the preset threshold Rn for local region segmentation, the predicted point is determined to be within a local high-confidence region, and the mixed weight ω i H For the global weight w i G With the local weight ω i L The product; When the normalized distance is greater than the global region partitioning preset threshold Rf, the predicted point is determined to be within the global smooth region, and the mixed weight ω is... i H Equal to the global weight w i G ; Wherein, the normalized distance is the Euclidean distance from the predicted point to the nearest sample point and the accuracy radius r. k The ratio of .

[0096] According to the mixed weight ω i H The predicted values ​​of each base model are linearly weighted and aggregated to obtain the predicted response.

[0097] The local high confidence region is defined as the region where the normalized distance between the predicted point and the nearest sample point is less than or equal to a preset threshold Rn for local region segmentation, where the normalized distance is the Euclidean distance from the predicted point to the nearest sample point and the accuracy radius r. k The ratio of .

[0098] The global smooth region is defined as the region where the normalized distance is greater than the global region division preset threshold Rf.

[0099] The calculation of normalized distance (the ratio of Euclidean distance to the precision radius) is a standard technique in spatial distance measurement, and is performed using Equation 13. Equation 13 is: ; In Formula 13, the normalized distance is defined as follows: Among them, ‖xx k ‖ represents the relationship between the predicted point x and its nearest sample point x. k The Euclidean distance between them, r k This is the precision radius at that sample point. This is the normalized distance. The range of values ​​for is 0≤ ≤1 (when the Euclidean distance does not exceed the accuracy radius) has the physical meaning of converting the absolute distance between the predicted point and the sample point into a dimensionless relative position index relative to the accuracy radius, thereby eliminating the influence of the difference in accuracy radius at different sample points on the distance measurement and realizing a standardized judgment benchmark for spatial region division.

[0100] The threshold comparison logic for region division based on this normalized distance is a conventional technique for partitioning, and can be found in Formula 14. Formula 14 is: ; In Formula 14, the threshold comparison logic for region partitioning is defined as follows: directly using the predicted point x and its nearest sample point x k Euclidean distance between them ||xx k || The precision radius r corresponding to this sample point k Comparison: When ||x−x k ||≤r k Time (equivalent to normalized distance) ≤1), indicating that the predicted point is located in the local region R. n (i.e., the local high confidence region); when ||x−x k ‖>r k Time (equivalent to normalized distance) >1), indicating that the prediction point is located in the global region R. f (i.e., the global smooth region). Where R... n and R f These represent the regions closest to and furthest from the sample point, respectively.

[0101] The linear weighted aggregation formula is Equation 9: y^ EoS(x) = w1y^1(x) + w2y^2(x); where y^ EoS Let y^1(x) and y^2(x) be the response values ​​of the aggregate model at sample point x, and y^2(x) be the response values ​​of the PCE model and the Kriging model (first basis model and second basis model), respectively, at response x; w1 and w2 are the weights of the PCE model and the Kriging model, respectively, and the weights must satisfy Formula 10: w i ≥0 and w1+w2=1, i=1,2.

[0102] By employing a product-based mixed weighting method within this local high-confidence region, the model is forced to possess both excellent global and local fitting performance to obtain high weights in this region, ensuring prediction accuracy in key areas. Within this global smooth region, the model primarily relies on global weights, guaranteeing global stability. This partitioned dynamic weighting strategy achieves synergistic optimization of global trends and local features.

[0103] Step S4 also includes step S6: Based on this aggregation model, a local sampling region is constructed near the maximum probable failure point (MPP) corresponding to the current design point, and Using the three-factor product learning function LF EoS-PK New sample points are selected within the local sampling area to update the initial training sample library and reconstruct the aggregated model until the relative error between the predicted value and the actual response value of the aggregated model is less than a preset threshold eps, where eps is a very small positive number added to avoid the denominator being zero.

[0104] Specifically, S6 should be executed after S4 determines the MPP. The preset threshold eps is typically 1×10. -6 Up to 1×10 -3 Alternatively, it can be determined based on the dimensions and numerical range of the response value.

[0105] The local sampling area is centered on the MPP, and its sampling radius is dynamically determined based on the error amplification factor and the target reliability index.

[0106] The learning function LF EoS-PK The aggregation model is used to calculate the predicted standard deviation σPK at the candidate sample point, the normalized distance from the predicted value of the candidate sample point to the failure boundary, and the minimum distance d from the candidate sample point to the existing sample set. min The product of the three.

[0107] By adopting a three-factor product learning function, a strict "logical AND" relationship is established. The "weakest link effect" is used to force candidate points to simultaneously meet three conditions: high uncertainty, proximity to the failure boundary, and spatial sparsity. This avoids sample redundancy caused by the traditional summation form and significantly improves sampling efficiency and model convergence speed near the failure boundary.

[0108] The termination criterion for step S6 is that the relative error between the predicted value and the actual response value of the aggregation model is less than a preset threshold eps, where eps is a very small positive number added to avoid the denominator being zero.

[0109] In step S6 (S6 belongs to S4), the sampling radius R of the local sampling area is calculated according to formula 17, which is: R=(1.5+0.5·c e )·β j t ; Where R is the local sampling radius, β j t Let c be the target reliability index for the j-th constraint; e The error amplification factor is determined based on the following statistical properties: around this MPP, with a factor of β... j t Candidate sample points are uniformly generated within a spherical region of radius , and the prediction standard deviation of the aggregation model at the candidate sample points is calculated. That is, based on the MPP as the center, β j t The statistical properties of the prediction standard deviation of the aggregation model at candidate sample points uniformly generated in a sphere of radius c are determined; e The specific calculation formula is Formula 18: ; Where M is the value centered at MPP point, β j t σ is the number of candidate sample points uniformly generated in a sphere of radius . In the lightweight design of multiple die forging hydraulic presses, this value is taken as 10000; PKj k The standard deviation of the aggregate model prediction at the k-th candidate sample point is calculated using Equation 19: σ PKj k =w1 G ×σ P k +w2 G ×σ K k ;σ P k Predict the standard deviation for the Kriging model; Once R is determined, the learning function LFEoS-PK Calculated according to Formula 20, Formula 20 is the formula including the predictive standard deviation σ. PK Normalized indicator value u PK Minimum sample distance d min and the multinomial coupling form of the standard normal distribution function, or using the predicted standard deviation σ PK The normalized indicator value u PK The minimum sample distance d min The product of the normalized values ​​of the three; Formula 20: ; Where, σ PK This represents the standard deviation of the predictions of the aggregation model (EoS-PK) at the candidate sample points, a statistic reflecting the prediction uncertainty at that point; PK This is the normalized indicator value of the predicted value relative to the failure boundary.

[0110] In calculating the learning function LF EoS-PK Previously, the three factors needed to be normalized to eliminate the influence of dimensions; specifically, the predicted standard deviation σ was normalized. PK (or σ) PKj Divide by the maximum standard deviation of the current candidate sample set; keep the normalized distance term from the failure boundary between 0 and 1; set the minimum sample distance d min Divide by the characteristic length or maximum distance of the current design space; the normalized three-factor product is the final learning function value.

[0111] The dynamic sampling radius R can automatically expand or contract according to the confidence level of the current model near the MPP, expanding the exploration range when the model uncertainty is high and focusing on fine-grained search when the model tends to converge; the three-factor product form ensures that the comprehensive information gain of the new samples is maximized, effectively balancing exploration and utilization.

[0112] Step S5 also includes: real-time monitoring of the current reliability index β of each probabilistic constraint (corresponding to the intelligent constraint screening step in stage four); When β is greater than twice the target reliability index β of the j-th constraint j t When the probability constraint is determined to be an inactive constraint, the exact calculation and gradient solution of the inactive constraint are eliminated in this iteration, and the computing resources are concentrated on the active constraint set.

[0113] The reliability index β is the minimum distance from the current design point to the limit state constraint boundary in the standard normal space. This inactive constraint is only monitored coarsely and is no longer updated through high-fidelity simulation.

[0114] By dynamically eliminating inactive constraints during the iteration process, a "safety buffer" is constructed to avoid wasting expensive computing resources in safe areas far from the failure boundary. This significantly reduces the computational dimension of the optimization problem and accelerates the convergence of the overall optimization trajectory to the global optimum.

[0115] The threshold for this 2x target reliability index is set based on the tail decay characteristic in probability theory; when the reliability index β > 2β j t When this happens, the corresponding failure probability Pf = Φ(﹣β) will be less than Φ(﹣2β). j t For example, when the target reliability index β j t When 2β = 3.0, j t =6.0, at which point the failure probability has dropped to 10%. -9 The magnitude is far below the allowable range in engineering; under these circumstances, the contribution of this constraint to the gradient of the design variables approaches zero, and continuing to calculate precisely would be an ineffective input with diminishing marginal benefits; therefore, this threshold is not arbitrarily set by experience, but is a theoretical derivation based on the exponential decay characteristic of the failure probability.

[0116] The steps for constructing a heterogeneous proxy model containing at least two different mathematical mechanisms include (corresponding to stage three: heterogeneous proxy model construction and adaptive aggregation): A sparse multinomial chaotic expansion model is constructed using the least angle regression (LARS) algorithm combined with cross-validation to characterize the global trend of the structural response. A Kriging model is constructed using a Gaussian kernel function, and the hyperparameters are optimized by maximum likelihood estimation to describe the local bias of the structural response.

[0117] The sparse polynomial chaotic expansion model uses sparse regression to automatically remove redundant polynomial basis functions.

[0118] The covariance structure of the Gaussian kernel function is determined based on the Euclidean distance between the sample points and the hyperparameter.

[0119] The Kriging model is based on Gaussian process regression, and its prediction form is y(x)=f(x). T ·β+z(x), where f(x) is the regression basis function, β is the regression coefficient, and z(x) is a coefficient with zero mean and covariance structure given by Cov[z(x),z(x')]=σ 2 A Gaussian random process defined by R(x,x',θ), where R(x,x',θ) is a function using a Gaussian kernel function (e.g., R(x,x',θ)=exp(-Σ). i=1 d θi(x i -x' i) 2 The related function of Gaussian process regression is θ, which is a hyperparameter. The mathematical principle and hyperparameter optimization method of the Gaussian process regression are well-known technologies in this field.

[0120] By employing the LARS algorithm to construct a sparse PCE, the problem of term explosion caused by high-dimensional variables is solved, ensuring the efficiency of global trend characterization. By using Gaussian kernel Kriging, the fitting ability for local nonlinear deviations is enhanced. The targeted training strategies of both provide a high-quality base model foundation for the high-precision prediction of this aggregated model.

[0121] The specific steps for constructing a sparse polynomial chaotic expansion model using the Least Angle Regression (LARS) algorithm include: starting from an empty model, gradually adding the basis functions with the highest correlation to the residuals to the active set; in each iteration, using leave-one-out cross-validation to calculate the prediction error of the current model; when the cross-validation error reaches its minimum or no longer decreases significantly, stopping the addition of basis functions, thereby automatically determining the optimal polynomial order and number of terms, and eliminating redundant basis functions.

[0122] This sparse polynomial chaotic expansion model is based on orthogonal polynomial basis function expansion, and its mathematical form is y(X)=Σ α∈A c α ·Ψ α (X), where Ψ α (X) are orthogonal polynomial basis functions with respect to the input variable X, c α Let A be the expansion coefficients and A be the sparse index set. The selection of the orthogonal polynomial basis functions and the calculation of the expansion coefficients are well-known techniques in the field. For details, please refer to relevant literature on polynomial chaotic expansion. This invention automatically determines the optimal sparse index set A using the LARS algorithm.

[0123] Step S4 includes: using the aggregation model, employing the Reliability Index Method (RIA) (corresponding to the reliability analysis and maximum probable failure point calculation step in stage four) to search for the point closest to the origin on the limit state surface in the standard normal space as the maximum probable failure point (MPP); using the MPP as the sampling center, employing the importance sampling method to calculate the failure probability and the gradient information.

[0124] The Reliability Index Method (RIA) obtains the Maximum Probability of Failure (MPP) by solving a constrained optimization problem, where the constraint condition is that the limit state function equals zero. The importance sampling method increases the probability of sample points falling into the failure domain by changing the random sampling center to this MPP. By using RIA to quickly locate the MPP and using it as a benchmark for importance sampling, the number of samples required to calculate the failure probability is significantly reduced, improving the efficiency of reliability analysis.

[0125] The dynamic adjustment of the precision radius, the calculation of the normalized distance, and the method for determining iterative convergence in this invention are all well-known technologies in the field of adaptive surrogate model optimization and reliability design. Those skilled in the art can directly implement these technologies based on the functions and input-output relationships, combined with standard mathematical tools, without needing to elaborate on the specific intermediate algebraic formulas.

[0126] Parameter and formula support: Parameters W1, W2, and W3: Units are kg or t, representing the weight of the component.

[0127] Parameter μ: is a vector of design variables, including key dimensions such as the column cross-section width and height of the multi-directional forging hydraulic press, the web thickness of the upper crossbeam, and the structural parameters of the lower crossbeam; Parameter X: is a vector of random variables, including the material's elastic modulus, yield strength, and working load.

[0128] In Formula 2, parameter R represents the weight of other components: the unit is kg or t, and it is the weight of other structural components of the multi-directional forging hydraulic press other than the upper crossbeam, column, and lower crossbeam.

[0129] Parameter r k The unit is a length unit (e.g., mm), and the precision radius is a design parameter of this invention.

[0130] Parameter D k The unit is length, and it represents the semi-nearest neighbor distance, derived from the geometric coordinates of the sample points.

[0131] Parameter P k : Dimensionless, representing the weighted error ratio, derived from the calculation of the ratio of global weighted error to local weighted error.

[0132] Parameter λ: dimensionless, is an adjustment coefficient, and belongs to the preset design parameters of this invention.

[0133] Formula input: D k P k λ; Formula output: r k This output is used for subsequent region division.

[0134] Parameter w i G : Dimensionless, representing the global weight coefficient, derived from the reciprocal normalization of the generalized mean square cross-validation error.

[0135] Parameter E i (GMSE): Dimensionless or the square of the response value, which is the generalized mean square cross-validation error, derived from cross-validation calculation.

[0136] Parameter ω i L : Dimensionless, representing local weighting coefficients derived from the coupled calculation of leave-one-out cross-validation error and distance.

[0137] Parameter e ik : Has the same dimensions as the response value, representing leave-one cross-validation error, which originates from point-by-point cross-validation.

[0138] Parameter I k (x): Dimensionless, is the distance influence function, derived from Euclidean distance calculation.

[0139] Parameter N m : Dimensionless, representing the total number of basic models. In this invention, N m =2 (PCE model and Kriging model).

[0140] Parameter ω i H It is a mixed weight.

[0141] Parameter σPK: has the same dimensions as the response value, and is the standard deviation of the aggregate model's predictions, derived from the quantification of the prediction uncertainty of the aggregate model.

[0142] Parameter d min The unit is length, representing the minimum sample distance, derived from Euclidean distance calculation.

[0143] In Formula 17, parameter R is the local sampling radius: the unit is length unit or standardized distance, which is the radius of the local sampling area constructed near the maximum probable failure point MPP, derived from the coupled calculation of error amplification factor and target reliability.

[0144] Parameter c e : Dimensionless, representing the error amplification factor, derived from the prediction error statistics of candidate sample points.

[0145] Parameter β j t : Dimensionless, is the target reliability index of the j-th constraint, is a parameter known in the field, and is set according to the design safety level.

Claims

1. A reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model, characterized in that, Includes the following steps: S1: Establish the following constraints: the failure probability of stress, deformation and modal frequency is not greater than the preset failure probability threshold or the equivalent reliability index is not less than the target reliability index. S2: The Latin hypercube sampling strategy is used to select initial sample points in the design space, and high-fidelity simulation is performed on the initial sample points to obtain structural response values, forming an initial training sample library; S3: Based on the initial training sample library, construct an aggregated model containing a first base model and a second base model. The first base model and the second base model are heterogeneous surrogate models with different mathematical mechanisms. The first basis model is used to characterize the global trend of the structural response, and the second basis model is used to describe the local deviation of the structural response. The steps to build an aggregation model include: Based on the coupling relationship between the geometric distribution characteristics of each sample point and the global and local error statistics of the first and second basis models at that sample point, the accuracy radius of the sample point is dynamically defined. Based on the relative position of the predicted point and the accuracy radius, the design space is divided into a local high confidence region and a global smooth region. Calculate the global and local weights of the first and second basis models, where the global weights are determined based on the generalized mean square cross-validation error, and the local weights are determined based on the coupling of leave-one cross-validation error and distance. Based on the region where the prediction point is located, the contribution rate of each base model is dynamically adjusted using a mixture of the global weight and the local weight to obtain the prediction response of the aggregate model. S4: Use this aggregation model to replace the high-fidelity simulation for reliability analysis, and obtain failure probability and gradient information; S5: Based on the failure probability and the gradient information, the design variables are iteratively updated using a sequential approximation programming algorithm until the convergence condition is met, and the optimal structural parameters that satisfy all reliability constraints are output.

2. The reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model according to claim 1, characterized in that: The first basis model is the global trend basis model, i.e., the PCE model, which is a sparse multinomial chaotic expansion model constructed using the least angle regression algorithm. The second basis model is the local bias basis model, which is a Kriging model constructed using the Gaussian kernel function. In S3, the method for dynamically defining the precision radius of sample points is: Based on the ratio P of the local weighted error to the global weighted error at the sample point k With nonlinear judgment threshold P th The relationship determines the precision radius r at the sample point based on the specific circumstances. k : When P k Greater than the nonlinearity threshold P th When the sample point is determined to be in a strongly nonlinear region, according to the formula r k =D k ×max(δ,1-λ×(P k -P th )) Calculate this precision radius to narrow down the local influence range and focus on local features; When P k Less than or equal to the nonlinear decision threshold P th When the sample point is determined to be in a smooth region, according to the formula r k =D k ×(1+λ×(P th -P k )) Calculate this precision radius to expand the local influence range and improve computational efficiency; Where D k It is half the Euclidean distance between the sample point and the other nearest sample point, reflecting the geometric sparsity around the sample point; P k = (wCV) k L ) / (wCV k G ), which is the ratio of the local weighted error to the global weighted error at that sample point; λ is a preset adjustment coefficient used to control the weight of the influence of this error ratio on the accuracy radius; δ is a lower limit coefficient used to ensure that the radius of this precision is not zero or negative.

3. The reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model according to claim 2, characterized in that, The steps for calculating the global and local weights of the global trend basis model and the local deviation basis model in S3 include: Calculate the global weight w according to formula 11. i G Formula 11 is: ; Among them, w i G E represents the global weights of the i-th base model; i Let be the generalized mean squared cross-validation error (GMSE) of the i-th base model, calculated according to the formula in the second row of Equation 11; n is the number of samples; N m N represents the total number of base models. m =2; y k For sample point x k The actual response value; y^ k To construct the i-th base model using all sample points except (xk, yk) in x k Predicted response value at point; Calculate the local weight ω according to formula 12. i L Formula 12 is: ; Where, ω i L e represents the local weights of the i-th base model; ik W represents the leave-one-out cross-validation error of the i-th base model at sample point xk; ik I represents the weight value of the i-th base model at the k-th sample point; k (x) is the distance function related to the Euclidean distance between the predicted point and the sample point xk. N is the total number of training samples.

4. The reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model according to any one of claims 1 to 3, characterized in that: In S3, the steps for dynamically adjusting the mixed weights based on the region where the predicted point is located include: When the normalized distance between the predicted point and the nearest sample point is less than or equal to the preset threshold Rn for local region segmentation, the predicted point is determined to be within a local high-confidence region, and the mixed weight ω i H For the global weight w i G With the local weight ω i L The product; When the normalized distance is greater than the global region partitioning preset threshold Rf, the predicted point is determined to be within the global smooth region, and the mixed weight ω is... i H Equal to the global weight w i G ; Wherein, the normalized distance is the ratio of the Euclidean distance from the predicted point to the nearest sample point to the accuracy radius rk; According to the mixed weight ω i H The predicted values ​​of each base model are linearly weighted and aggregated to obtain the predicted response; The linear weighted aggregation formula is Equation 9: y^ EoS (x) = w1y^1(x) + w2y^2(x); where y^ EoS Let y^1(x) be the response value of the aggregation model at sample point x, and y^2(x) be the response values ​​of the PCE model and the Kriging model at response x, respectively; w1 and w2 are the weights of the PCE model and the Kriging model, respectively, and the weights must satisfy Formula 10: w i ≥0 and w1+w2=1, i=1,2.

5. The reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model according to any one of claims 1 to 4, characterized in that, Step S4 also includes step S6: Based on this aggregation model, a local sampling region is constructed near the maximum probable failure point (MPP) corresponding to the current design point, and a three-factor product learning function LF is used. EoS-PK New sample points are selected within the local sampling area to update the initial training sample library and reconstruct the aggregated model until the relative error between the predicted value and the actual response value of the aggregated model is less than a preset threshold eps, where eps is a very small positive number added to avoid the denominator being zero.

6. The reliability design method for a multi-directional forging hydraulic press based on an adaptive aggregation model according to claim 5, characterized in that: In step S6, the sampling radius R of the local sampling area is calculated according to formula 17, which is: R = (1.5 + 0.5·c e )·β j t ; Where R is the local sampling radius, β j t Let c be the target reliability index for the j-th constraint; e The error amplification factor is determined based on the following statistical properties: around this MPP, with a factor of β... j t Candidate sample points are uniformly generated within a spherical region of radius , and the prediction standard deviation of the aggregation model at the candidate sample points is calculated. Once R is determined, the learning function LF EoS-PK Calculated according to Formula 20, Formula 20 is the formula including the predictive standard deviation σ. PK Normalized indicator value u PK Minimum sample distance d min and the multinomial coupling form of the standard normal distribution function, or using the predicted standard deviation σ PK The normalized indicator value u PK The minimum sample distance d min The product of the normalized values ​​of the three; Formula 20 is: ； Where, σ PK This represents the standard deviation of the predictions of the aggregation model (EoS-PK) at the candidate sample points, a statistic reflecting the prediction uncertainty at that point; PK This is the normalized indicator value of the predicted value relative to the failure boundary.

7. The method according to any one of claims 1 to 6, characterized in that, Step S5 also includes: Real-time monitoring of the current reliability index β for each probability constraint; When β is greater than twice the target reliability index β of the j-th constraint j t When the probability constraint is determined to be an inactive constraint, the exact calculation and gradient solution of the inactive constraint are eliminated in this iteration, and the computing resources are concentrated on the active constraint set.

8. The method according to any one of claims 1 to 7, characterized in that, The steps involved in constructing a heterogeneous proxy model that incorporates at least two different mathematical mechanisms include: A sparse multinomial chaotic expansion model is constructed using the least angle regression (LARS) algorithm combined with cross-validation to characterize the global trend of the structural response. A Kriging model is constructed using a Gaussian kernel function, and the hyperparameters are optimized by maximum likelihood estimation to describe the local bias of the structural response.

9. The method according to any one of claims 1 to 8, characterized in that, Step S4 includes: Using this aggregation model, the reliability index method (RIA) is employed to search for the point closest to the origin on the limit state surface in the standard normal space, which is then taken as the maximum probable failure point (MPP). Using the MPP as the sampling center, the failure probability and gradient information are calculated using the importance sampling method.

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