A high-dimensional simulation black box parameter interval identification method, system, medium and device

Abstract

The application provides a high-dimensional simulation black box parameter interval identification method, system, medium and equipment. The performance constraint of the initialization population is calculated through the high-dimensional simulation black box. Based on the performance constraint, one individual in the initialization population that meets the constraint condition is selected as a feasible seed point, and an initial hyperbox is generated based on the feasible seed point. The initial hyperbox is sampled and counted, and the initial hyperbox is iteratively updated based on the sampling and counting result to obtain a candidate hyperbox. The confidence of the candidate hyperbox is evaluated to obtain a reliable lower limit. If the reliable lower limit is greater than the target reliability, the parameter interval identification result of the high-dimensional simulation black box is generated based on the candidate hyperbox. A high success rate starting point is searched through the performance constraint, and the initial hyperbox is iteratively updated to improve the reliability of the feasible region. Meanwhile, the confidence of the candidate hyperbox is evaluated to improve the reliability of the result.

Description

Technical Field

[0001] This application relates to the field of simulation technology, specifically to a method, system, medium, and device for identifying parameter ranges in a high-dimensional simulation black box. Background Technology

[0002] In the design and development of modern complex engineering systems, high-fidelity numerical simulation has become a core means of verifying product performance and guiding design decisions. With the continuous improvement of system integration and the increasing prominence of physical field coupling effects, simulation models face severe challenges in terms of parameter dimensions, nonlinear intensity, and computational cost. Specifically, engineering designs often involve dozens or even hundreds of design parameters, whose physical responses exhibit strong nonlinearity, multimodal characteristics, and even discontinuities. A single high-fidelity simulation solution (such as large-scale finite element analysis or computational fluid dynamics simulation) typically requires hours or even days of computational resources, fundamentally limiting the feasibility and efficiency of relying on massive simulation calls for design optimization.

[0003] Against this backdrop, traditional deterministic optimization methods (including gradient-based numerical optimization algorithms and various evolutionary algorithms) constitute the mainstream paradigm for engineering design optimization. The core logic of these methods is to search for one or more "optimal points" in a high-dimensional parameter space that best optimize the objective function. However, this "point-optimal" strategy has fundamental limitations in practical engineering applications: due to factors such as manufacturing tolerances, material property fluctuations, assembly deviations, and changes in the operating environment, design parameters cannot accurately reproduce their nominal optimal values ​​in actual production. Even small parameter perturbations can lead to a sharp deterioration in performance, or even cause the design point to fall into an infeasible region. In other words, traditional methods fail to consider the impact of inherent parameter fluctuations on performance robustness from the design source, and the obtained "optimal solutions" often lack manufacturability and reliability guarantees in practical engineering contexts.

[0004] For the specific need of "parameter feasible interval identification" in practical engineering, existing methods exhibit more profound shortcomings: The first category consists of methods based on interval arithmetic or affine arithmetic. These methods treat parameters as interval variables and propagate uncertainty through interval operations, thereby outputting a set of parameter intervals that satisfy the constraints. However, these methods require explicit analytical mathematical expressions for the objective function and constraints to perform interval expansion operations. This prerequisite is completely ineffective in the "simulation black box" scenarios prevalent in industry (i.e., the input-output relationship can only be obtained through numerical solutions, without closed-form expressions), rendering them unsuitable for engineering applications.

[0005] The second category comprises methods that fit feasible / infeasible decision boundaries based on one-time global sampling (such as Latin hypercube sampling or Monte Carlo methods) combined with subsequent classifiers (such as support vector machines (SVM), decision trees, or neural networks). This type of method attempts to transform the feasible region identification problem into a classification problem, but its inherent bottlenecks are: in high-dimensional parameter spaces, the sampling density required to cover the entire feasible region boundary increases exponentially with the dimension; under a limited sample budget, the resulting decision boundaries are often fuzzy, non-smooth, and contain a large number of holes or isolated points, lacking statistical guarantees of the feasibility of any point within the interval; furthermore, the hyperparameter selection and training process of the classifier (especially those based on kernel methods or deep learning models) itself introduces additional computational burden and uncertainty.

[0006] The third category consists of methods based on dimensional slicing or grid search. These methods either fix other dimensional parameters and scan the feasible boundary successively in a single dimension, or discretize the parameter space into a grid to evaluate feasibility point by point. Their computational cost explodes exponentially with the parameter dimension (i.e., the number of grid points increases exponentially with the dimension), making them completely infeasible for practical engineering problems (typically involving more than 10 dimensions).

[0007] In summary, the current field of engineering optimization and uncertainty quantification urgently needs an automated method that can directly connect with the high-fidelity simulation black box of industry, intelligently and efficiently explore high-dimensional complex design spaces, and output reliable and compact sets of parameter intervals with quantitative statistical confidence levels. Summary of the Invention

[0008] To address the aforementioned technical problems, this application is proposed. Embodiments of this application provide a method, system, medium, and device for identifying parameter ranges in a high-dimensional simulation black box.

[0009] According to one aspect of this application, a method for identifying parameter intervals in a high-dimensional simulation black box is provided, comprising: calculating performance constraints of an initial population using a high-dimensional simulation black box; wherein each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box, and the performance constraints include at least one constraint function, each constraint function being used to determine whether the output response of the high-dimensional simulation black box satisfies a preset feasible condition; based on the performance constraints, selecting an individual in the initial population that satisfies the constraint condition as a feasible seed point, and generating an initial superbox based on the feasible seed point; wherein the initial superbox is a neighborhood of the feasible seed point; sampling and statistically analyzing the initial superbox, and iteratively updating the initial superbox based on the sampling and statistical results to obtain candidate superboxes; evaluating the confidence of the candidate superboxes to obtain a confidence lower bound; if the confidence lower bound is greater than the target confidence, generating a parameter interval identification result for the high-dimensional simulation black box based on the candidate superboxes.

[0010] In one embodiment, selecting an individual in the initial population that satisfies the constraint conditions as a feasible seed point based on the performance constraints includes: calculating the degree of violation of the aggregate constraint of a single individual based on the performance constraints of that single individual; if there exists a single individual whose degree of violation of the aggregate constraint is equal to zero, then that single individual is selected as the feasible seed point.

[0011] In one embodiment, generating an initial hyperbox based on the feasible seed point includes: determining the initial half-width corresponding to each dimension based on the physical characteristics of each element in the parameter vector; using the initial half-width of each dimension as the extension distance in that dimension, and extending the distance by one initial half-width in each positive and negative direction along each dimension with the feasible seed point as the center, thereby constructing an axis-aligned initial hyperbox.

[0012] In one embodiment, the step of sampling and statistically analyzing the initial superbox and iteratively updating the initial superbox based on the sampling and statistical results to obtain candidate superboxes includes: sampling within the initial superbox to obtain multiple sample points; inputting the multiple sample points into the high-dimensional simulation black box to calculate the performance constraints of each sample point; determining the type of the corresponding sample point based on the performance constraints of each sample point; wherein the type of sample point includes feasible points and infeasible points; segmenting the initial superbox based on the types of the multiple sample points to obtain segmented regions; expanding the segmented regions based on dynamically adjusted growth factors to obtain expanded regions; and sampling, statistically analyzing, and iteratively updating the expanded regions again to obtain the candidate superboxes.

[0013] In one embodiment, segmenting the initial superbox based on the types of the plurality of sample points to obtain the segmented region includes: for sample points of type infeasible, calculating the cost of shrinking the parameter boundary of any dimension due to excluding the sample point; selecting the shrinkage method with the minimum cost to segment the initial superbox to obtain the segmented region.

[0014] In one embodiment, the confidence assessment of the candidate superbox to obtain the confidence lower bound includes: randomly sampling the candidate superbox to obtain a set of verification sample points; obtaining a prior distribution of the verification sample points using a standard uniform distribution; updating the distribution of the verification sample points based on the prior distribution and the type of the verification sample points to obtain a posterior distribution; and obtaining the confidence lower bound of the candidate superbox based on the posterior distribution.

[0015] In one embodiment, generating parameter range identification results for the high-dimensional simulation black box based on the candidate superbox includes: generating a structured data table and a multi-dimensional range visualization chart for the high-dimensional simulation black box based on the candidate superbox; wherein, the structured data table includes the parameter names and corresponding upper and lower limits of the high-dimensional simulation black box, and the multi-dimensional range visualization chart includes key parameter combinations.

[0016] According to another aspect of this application, a high-dimensional simulation black box parameter interval identification system is provided, comprising: a performance constraint calculation module, used to calculate the performance constraints of an initial population through a high-dimensional simulation black box; wherein each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box, and the performance constraint includes at least one constraint function, each constraint function being used to determine whether the output response of the high-dimensional simulation black box satisfies a preset feasible condition; a feasible seed selection module, used to select an individual in the initial population that satisfies the constraint condition as a feasible seed point based on the performance constraint, and generate an initial superbox based on the feasible seed point; wherein the initial superbox is the neighborhood of the feasible seed point; a candidate superbox iteration module, used to sample and statistically analyze the initial superbox, and iteratively update the initial superbox based on the sampling and statistical results to obtain candidate superboxes; a confidence evaluation module, used to evaluate the confidence of the candidate superboxes to obtain a confidence lower bound; and an identification result generation module, used to generate a parameter interval identification result of the high-dimensional simulation black box based on the candidate superbox if the confidence lower bound is greater than the target confidence.

[0017] According to another aspect of this application, a computer-readable storage medium is provided, the storage medium storing a computer program for performing any of the methods described above.

[0018] According to another aspect of this application, an electronic device is provided, comprising: a processor; a memory for storing processor-executable instructions; the processor being configured to perform any of the methods described above.

[0019] This application provides a method, system, medium, and device for identifying parameter intervals in a high-dimensional simulation black box. The method involves calculating performance constraints for an initial population using a high-dimensional simulation black box. Each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box. The performance constraints include at least one constraint function, each used to determine whether the output response of the high-dimensional simulation black box meets preset feasibility conditions. Based on the performance constraints, an individual in the initial population that meets the constraints is selected as a feasible seed point, and an initial superbox is generated based on the feasible seed point. The initial superbox is a neighborhood of the feasible seed point. The initial superbox is sampled and statistically analyzed, and iteratively updated based on the sampling and statistical results to obtain candidate superboxes. The confidence level of the candidate superboxes is evaluated to obtain a confidence lower bound. If the confidence lower bound is greater than the target confidence level, the parameter interval identification result of the high-dimensional simulation black box is generated based on the candidate superboxes. A high-success-rate starting point is searched through performance constraints, and the initial superbox is iteratively updated to improve the reliability of the feasible region. Simultaneously, the confidence level of the candidate superboxes is evaluated to improve the reliability of the result. Attached Figure Description

[0020] The above and other objects, features, and advantages of this application will become more apparent from the more detailed description of the embodiments of this application in conjunction with the accompanying drawings. The drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the embodiments of this application to explain this application and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.

[0021] Figure 1 This is a flowchart illustrating a high-dimensional simulation black box parameter range identification method provided in an exemplary embodiment of this application.

[0022] Figure 2 This is a schematic diagram of the structure of a high-dimensional simulation black box parameter range identification system provided in an exemplary embodiment of this application.

[0023] Figure 3 This is a structural diagram of an electronic device provided in an exemplary embodiment of this application. Detailed Implementation

[0024] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0025] Figure 1 This is a flowchart illustrating a high-dimensional simulation black box parameter range identification method provided in an exemplary embodiment of this application. Figure 1 As shown, the high-dimensional simulation black box parameter range identification method includes the following steps: Step 110: Initialize the performance constraints of the population through high-dimensional simulation black box calculation.

[0026] In this implementation, each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box. Performance constraints include at least one constraint function, each used to determine whether the output response of the high-dimensional simulation black box meets preset feasibility conditions. In one implementation, the constraint function can be represented as g. i The form (x)≤0, where g i The value of (x) represents the degree of deviation between the i-th performance index and its allowable limit, g i (x)≤0 indicates that the constraint is satisfied, g i (x)>0 indicates a violation of the constraint. This application initializes a population (containing multiple individuals, such as 50 individuals), with each individual corresponding to a parameter vector of a high-dimensional simulation black box (i.e., a vector composed of the design parameters of the high-dimensional simulation black box). For each individual, its performance constraints are calculated through the high-dimensional simulation black box to determine whether it meets the feasibility requirements.

[0027] Step 120: Based on performance constraints, select an individual in the initial population that meets the constraints as a feasible seed point, and generate an initial hyperbox based on the feasible seed point.

[0028] The initial superbox is the neighborhood of the feasible seed point. Based on the calculated performance constraints of the individuals, this application selects an individual that satisfies the constraints as a feasible seed point, and generates an initial superbox based on the feasible seed point.

[0029] Step 130: Perform sampling statistics on the initial superboxes, and iteratively update the initial superboxes based on the sampling statistics results to obtain candidate superboxes.

[0030] This application obtains candidate superboxes by sampling, classifying and statistically updating the iterative region in the initial superbox through an autonomous loop iteration method. In other words, it obtains a reliable region by iteratively updating the initial matrix region.

[0031] Step 140: Evaluate the confidence level of the candidate superboxes to obtain the lower confidence limit.

[0032] This application conducts a confidence assessment on the candidate superbox to obtain its credibility.

[0033] Step 150: If the lower confidence limit is greater than the target confidence level, then generate the parameter interval identification result of the high-dimensional simulation black box based on the candidate superbox.

[0034] If the lower confidence limit is greater than the target confidence level, it means that the reliability of the candidate superbox obtained so far meets the requirements. At this time, the parameter interval identification result of the high-dimensional simulation black box is generated based on the candidate superbox.

[0035] This application provides a method for identifying parameter intervals in a high-dimensional simulation black box. The method calculates performance constraints for an initial population using a high-dimensional simulation black box. Each individual in the initial population corresponds to a parameter vector in the high-dimensional simulation black box, and the performance constraint characterizes the difference between each element in the parameter vector and its corresponding limit. Based on the performance constraint, an individual in the initial population that satisfies the constraint is selected as a feasible seed point, and an initial superbox is generated based on the feasible seed point. The initial superbox is a neighborhood of the feasible seed point. The initial superbox is sampled and statistically analyzed, and iteratively updated based on the sampling and statistical results to obtain candidate superboxes. The confidence level of the candidate superboxes is evaluated to obtain a confidence lower bound. If the confidence lower bound is greater than the target confidence level, the parameter interval identification result of the high-dimensional simulation black box is generated based on the candidate superbox. A high-success-rate starting point is searched through performance constraints, and the initial superbox is iteratively updated to improve the reliability of the feasible region. Simultaneously, the confidence level of the candidate superboxes is evaluated to improve the reliability of the result.

[0036] In one embodiment, step 120 can be implemented as follows: based on the performance constraints of a single individual, calculate the degree of violation of the aggregate constraints of that individual; if there exists a single individual whose degree of violation of the aggregate constraints is equal to zero, then that single individual is used as a feasible seed point.

[0037] This application calculates the degree of violation of aggregation constraints based on the performance constraints of each individual entity. The specific calculation formula is as follows: ,in, For individuals The degree of violation of aggregation constraints, where m is the total number of performance constraints. Let be the value of the i-th constraint function, that is, the deviation between the i-th output response of the high-dimensional simulation black box and its corresponding allowable limit. ≤0 indicates that the constraint is satisfied. >0 indicates a violation of the constraint. =0 if and only if all constraints are satisfied, i.e., the individual is a feasible solution.

[0038] If a single individual has an aggregation constraint violation level of zero, then that single individual is considered a feasible seed point. Preferably, this application can evaluate the individuals sequentially according to their order in the population. When an individual is selected that satisfies the constraint... When an individual is found, the screening process stops, and that individual is designated as a feasible seed point to improve screening efficiency. If no feasible solution is found within the preset simulation budget, an alternative strategy (such as particle swarm optimization or Bayesian optimization) is automatically switched to continue the search, ensuring that a reliable seed point is obtained with a very high success rate and low computational cost, provided that the feasible region is not empty.

[0039] In one embodiment, the specific implementation of step 120 above may be as follows: based on the physical characteristics of each element in the parameter vector, determine the initial half-width corresponding to each dimension; take the initial half-width of each dimension as the expansion distance in that dimension, and expand by a distance of one initial half-width in each positive and negative direction along each dimension with the feasible seed point as the center, to construct an axis-aligned initial superbox.

[0040] After selecting feasible seed points, this application determines the corresponding initial half-width based on the physical characteristics (engineering physical meaning, nominal value, or local sensitivity) of each parameter. Under the premise that the performance response is continuous and smooth within the neighborhood of the feasible seed points, it ensures that the constructed axis-aligned initial superbox has a high probability of feasibility. The expression for the initial superbox is: ,in, For dimension vector space, for The Element values ​​in each dimension A feasible seed point The Values ​​of each dimension For the first The initial half-width of each dimension.

[0041] In one embodiment, step 130 can be implemented as follows: sampling is performed within the initial superbox to obtain multiple sample points; the multiple sample points are input into a high-dimensional simulation black box to calculate the performance constraints of each sample point; based on the performance constraints of each sample point, the type of the corresponding sample point is determined; wherein, the type of the sample point includes feasible points and infeasible points; the initial superbox is segmented based on the types of the multiple sample points to obtain segmented regions; the segmented regions are expanded based on dynamically adjusted growth factors to obtain expanded regions; the expanded regions are sampled, statistically analyzed, and iteratively updated again to obtain candidate superboxes.

[0042] Specifically, this application is located in the current matrix region. (No. The current matrix region in the next iteration, with the initial hyperbox as... Inside, a space-filling experimental design method (preferably Latin hypercube sampling) is used to generate a set of samples with a quantity of [number missing]. m sample points Sampling is strictly limited to Within the boundaries, the focus of the exploration was ensured, and the sample size was [not specified]. m Setting and Problem Dimensions d This approach allows for the acquisition of effective statistical insights into the feasibility distribution within the current matrix region at a controllable computational cost. The sample set... Submit the computation to a high-dimensional simulation black box for concurrent computation, obtain its performance constraints, and then apply the preset performance constraints. If the value is ≤0, each sample point will be automatically classified as a "feasible point" (and included in the set). ) or "infeasible points" (included in the set) ), and calculate the observation feasibility ratio for the current matrix region. This ratio serves as a reflection The core real-time feedback signal of the inner region's "health" or "purity" is then used to segment the initial superbox according to the type of multiple sample points, resulting in segmented regions. These segmented regions are then expanded using dynamically adjusted growth factors, resulting in expanded regions. The expanded regions are then sampled, statistically analyzed, and iteratively updated again to obtain candidate superboxes.

[0043] In one embodiment, the specific implementation of step 130 above may be as follows: for sample points of type infeasible points, calculate the cost of shrinking the parameter boundary of any dimension due to excluding the sample point; select the shrinkage method with the minimum cost to segment the initial hyperbox and obtain the segmented region.

[0044] Based on classification and This application is from The method involves quickly "pruning" a new, maximum axis-aligned superbox that completely eliminates all known bad points. Specifically, this is achieved by implementing the "minimum cost elimination" principle: for... Every bad point in b The algorithm evaluation needs to shrink in order to exclude it. When considering any dimensional boundary, the number of known good points that will be excluded (i.e., the "cost") is considered. This application selects the dimension that minimizes this cost and shrinks accordingly. Boundaries in this dimension to exclude bad pixels b By performing this process sequentially on all bad points, the resulting superbox is mathematically guaranteed to contain no known bad points while preserving the known good points to the maximum extent. This method relies solely on the coordinates and feasibility labels of the sample points, requiring no additional simulation calls, and is particularly suitable for handling high-dimensional ( d The problem of large values ​​is crucial, and efficient boundary calculation is decoupled from simulation costs.

[0045] This application utilizes feedback signals The strategy involves intelligently expanding the segmented region, first by pre-setting a target health level to be maintained. (e.g., 0.75), representing an acceptable level of exploratory risk, is then adjusted in real time by a dynamic feedback controller. ,in, For the first Growth factors during the next iteration. If Higher than ,but Increase to encourage more aggressive expansion; conversely... Reduce to adopt a conservative approach. Then, use the geometric center of the segmented region. Using a fixed base point, multiply the width of the segmented region in each dimension by the updated growth factor. Symmetric expansion is then performed. However, it is necessary to ensure the new candidate superboxes after expansion are symmetrically expanded. The algorithm's feasible region is monotonically reduced (non-increasing) because it is completely contained within the "pure sub-superbox" obtained after the previous segmentation, which excludes all known bad pixels. This ensures that historical bad pixel information is always respected. If the expansion operation exceeds the boundary of this pure sub-superbox, then that boundary is used as the boundary. The final boundary. Based on this, the next generation of candidate superboxes is generated. .

[0046] This loop continues until a preset convergence criterion is met, such as the relative growth of the superbox volume repeatedly falling below a threshold, or the center position of the superbox stabilizing. At this point, the exploration phase terminates, and a candidate superbox that has been sufficiently expanded and covers the main continuous feasible region is output. As input for the consolidation phase.

[0047] In one embodiment, step 140 can be implemented as follows: randomly sampling candidate superboxes to obtain a set of verification sample points; obtaining a prior distribution of verification sample points using a standard uniform distribution; updating the distribution of verification sample points based on the prior distribution and the type of verification sample points to obtain a posterior distribution; and obtaining a confidence lower bound for candidate superboxes based on the posterior distribution.

[0048] This application uses candidate superboxes As the current operational target, confirmatory sampling is performed first. Unlike the active sampling in the exploratory phase, this phase focuses on satisfying the basic assumptions of statistical inference. Therefore, in The internal method uses simple random sampling to generate a set of numbers. Validation sample point set The generated validation samples satisfy the (approximate) independent and identically distributed condition, providing a valid data foundation for subsequent Bayesian inference. The validation sample size... It can be set or dynamically adjusted according to the desired statistical accuracy and calculation budget.

[0049] Subsequently, a core Bayesian confidence assessment is performed, specifically, the candidate superboxes are... The true probability that any point within the inner circle is feasible The model is performed as a random variable to represent the uncertainty of this parameter. When validation data is not yet available, an uninformative prior distribution is used. Beta (1,1) (i.e., a uniform distribution on [0,1]) is used to represent the... The initial understanding; after obtaining the verification data in this round, it was observed that One feasible point and For each infeasible point, an update is performed using Bayes' theorem. Since the likelihood function of the Bernoulli trial is conjugate to the Beta prior distribution... The posterior distribution can be analytically derived as Beta ( +1, +1). Based on this post-abortive distribution, the system calculates a key statistical decision quantity: at the significance level... (e.g., δ=0.05) Lower one-sided confidence limit This value satisfies (For example, 95%), of which, This represents the candidate superbox based on the current limited sample. Overall feasibility The most conservative statistical estimate, which combines the observed feasible proportions with the uncertainty brought about by the sample size, means that: The certainty that the actual feasibility rate is not lower than this value.

[0050] Finally, conditional decisions are made based on statistical evidence, driving iteration; the decision-making logic is entirely based on quantified statistical evidence. Dominant. If ≥ (A feasibility rate of the project target, such as 95%) indicates that the current data provides sufficiently strong evidence that the project can be feasible. Support at confidence level Once the assertion satisfies the engineering requirements, the algorithm terminates and outputs the result. .like < This indicates that the statistical evidence is insufficient. In this case, a key active purification strategy is adopted: calling a fast segmentation algorithm, based on the good and bad points already identified in the current round of validation samples, and then segmenting from the current superbox. A new sub-superbox, smaller in size but with expected higher "purity," is cut out from the sample and eliminated from all observed defects, then enters the next round of verification. This iterative "evaluation-purification" mechanism, while ensuring statistical rigor, avoids the cost trap of simply relying on exponentially increasing the verification sample size to gain confidence. Each unsuccessful verification attempt is transformed into an effective correction and focus on the solution space boundary, thus efficiently approximating and ultimately verifying a highly reliable and robust parameter range with far fewer simulations than traditional statistical verification methods.

[0051] In one embodiment, step 150 can be implemented as follows: generating a structured data table and a multi-dimensional interval visualization chart of a high-dimensional simulation black box based on candidate superboxes; wherein, the structured data table includes the parameter names and corresponding upper and lower limits of the high-dimensional simulation black box, and the multi-dimensional interval visualization chart includes key parameter combinations.

[0052] This application will use statistically verified superboxes. Converted into two directly usable project formats: one is a structured data table, which clearly lists all... d The design parameters include the name of the parameter, the verified lower and upper limits of the allowable variation, and optional nominal values ​​(such as the midpoint of the interval); secondly, multi-dimensional interval visualization charts are automatically generated for key parameter groups or subsystems, such as intuitive display forms like the "force-deformation feasible channel" diagram. This channel diagram connects the allowable intervals of multiple related parameters (such as characteristic force values ​​at different deformation stages) of the same physical component (such as an energy-absorbing box) in physical order to form a "channel" that characterizes the allowable range of the component's performance, providing intuitive and quantitative graphical standards for subsystem design and supplier specifications.

[0053] Preferably, for revealing Which boundary controls are most critical for maintaining overall robustness? This application addresses all 2 d The system undergoes perturbation testing at each parameter boundary (upper and lower bounds for each parameter). Specifically, for each specific boundary (e.g., parameter...) i The upper realm u i This involves fine-tuning the current interval width outward by a small relative amount (e.g., 1% of the current interval width) to create a slightly enlarged test superbox, while keeping all other boundaries unchanged. A small-scale, rapid validation sampling is then performed within this test superbox, and the same Bayesian inference method is used to calculate the lower confidence limit of the perturbed superbox's feasibility. The importance of this boundary is determined by the decrease in the lower confidence limit Δ. = - 'Quantification. Δ' The larger the value, the more "sensitive" or "fragile" the boundary is; even a slight loosening of this boundary will lead to a significant deterioration in statistical performance. This applies to all boundaries corresponding to Δ... The values ​​are mapped into a matrix with parameters as rows and boundary types (low / high) as columns, generating a parameter boundary sensitivity heatmap. The heatmap uses color gradients (such as red-yellow-green) to intuitively encode the sensitivity levels, thus clearly identifying the "critical boundaries" that require the most stringent process control and quality monitoring, providing data-driven priority guidance for tolerance allocation and production resource focus.

[0054] Preferably, this application can also quickly diagnose the root causes of failures in existing designs that are commonly found to have substandard performance in engineering, and pinpoint the few key parameters leading to infeasibility. Specifically, for this purpose, a special constrained optimization problem is constructed and solved: the decision variables are still all d There are 1 parameter; the imposed constraint is that there must be at least 1 parameter. dM One parameter (e.g., 90% of the parameters, i.e.) M =0.1 d The value of ) must strictly fall within the verified robust range. The optimization objective is set to maximize the degree of violation of the original performance constraints (e.g., minimize the safety margin). By employing a global optimizer such as differential evolution to solve this problem, the algorithm will automatically explore and adjust the allowed parameters under the strong constraint that "most parameters must adhere to robust intervals". M The algorithm uses several "free" parameters to find the combination that results in the worst design performance (i.e., the most likely failure). After optimization, it analyzes which parameter values ​​fall within the optimal solution. Outside the range, these parameters (the number of which does not exceed) M These parameters are identified as key factors leading to failure. This analysis transforms the vague "poor design" problem into a clear list of parameter-level improvements, allowing design modifications to focus on the few most critical and effective changes, greatly improving the efficiency of design iterations.

[0055] To make the objectives, technical solutions, and advantages of this application clearer, a representative industrial-grade high-dimensional application example—"robust design space recognition for frontal collision crashworthiness"—is used below to provide a complete and detailed explanation of this application. Those skilled in the art should understand that this embodiment is merely an example used to illustrate the technical process and significant effects of this application, and not as a limitation on its sole application.

[0056] This embodiment aims to solve the robustness quantification problem in the frontal collision safety performance design of a newly developed vehicle model. The specific design objective is to ensure that, during a 100% frontal rigid barrier collision at a standard speed of 56 km / h, the maximum value of the critical physical quantity used to evaluate the structural integrity of the passenger compartment—the acceleration pulse at the base of the B-pillar—is achieved. a max It shall not exceed 40% of the regulations. g Limits, i.e., satisfying constraints a max ≤40 g The black-box simulation system used is a high-fidelity finite element model of the whole vehicle's nonlinear transient dynamics containing approximately 1.5 million elements, and explicit integration calculations are performed using the industry-standard LS-DYNA solver.

[0057] To achieve a parametric description of the design space, this application employs a dimensionality reduction method based on engineering features. It selects 12 key front-end structures (including front longitudinal beam segments, energy-absorbing boxes, subframe connections, etc.) that play a dominant role in frontal collision energy absorption. The dynamic force-deformation (crushing) curve of each structure is parametrically characterized using five characteristic force values ​​with clear physical meaning: initial peak force, plateau force, compaction initiation force, compaction slope coefficient, and final force value. Thus, a total of [number missing] forces are defined. d =12×5=60 design parameters, constituting the design vector. x ∈R 60 The value range of each parameter (global design space) is predefined by physical constraints such as material properties, process feasibility, and structural layout. In this high-dimensional (60-dimensional), highly nonlinear, and computationally expensive simulation black box environment, how can we automatically identify a set of allowable parameter interval combinations within a limited and extremely valuable computational budget (e.g., a total of no more than 2000 simulations, corresponding to approximately 3000 CPU hours or compressed to several weeks of actual time using a high-performance cluster) so that the whole-vehicle collision simulation results driven by any sampled parameter combination (corresponding to 12 force-deformation curves) within this interval box can satisfy the acceleration constraints with a very high statistical probability (e.g., no less than 97%).

[0058] The method provided in this application is applied to the above-mentioned problems, and its fully automated execution process is as follows: First, an improved differential evolution algorithm is configured and started, prioritizing the search for feasible points. This improved algorithm, based on the standard differential evolution algorithm, employs a constraint-first sorting mechanism (i.e., sorting by the degree of violation of aggregate constraints). Sort the individuals. Smaller individuals have higher priority in selection, and an adaptive parameter adjustment strategy is used (dynamically adjusting the mutation scaling factor and crossover probability according to the proportion of feasible solutions in the current population) to ensure that the search process can still converge effectively in a high-dimensional space with a sparse feasible region. The algorithm population size is set to 50, which is a reasonable value determined based on the dimension of the 60-dimensional optimization problem in this embodiment, taking into account both population diversity and computational efficiency. In differential evolution algorithms, the population size is usually related to the problem dimension, and the commonly used empirical range is 5 to 10 times the problem dimension; however, for the high computational cost simulation scenario faced by this application, it is necessary to strictly control the computational cost of a single iteration while maintaining sufficient diversity. Therefore, taking 50 (slightly lower than 5 times the empirical lower limit) is a reasonable engineering value adopted after fully balancing exploration capability and simulation budget. The algorithm aims to minimize the degree of constraint violation and performs parallel simulation search in a 60-dimensional global design space. After about 8 generations of evolution (a total of 8 × 50 = 400 parallel simulations), the algorithm successfully locates a feasible seed design point. The corresponding simulation results are a max =38.5 g This satisfies all constraints. Then, with... Using this as a baseline, and based on engineering experience and estimates of local performance continuity, a conservative offset of ±10% is set for each parameter as the initial half-width, building upon its current value. This allows for the construction of a 60-dimensional axis-aligned initial hyperbox. This establishes a definite, small-scale, and highly feasible starting point for subsequent explorations.

[0059] Then, we enter the exploration phase, with the parameter set to: the number of sampling points per iteration. m =80, target area health level =0.75, initial growth factor =1.05. The system starts its autonomous iterative loop: at the... k In the round of iteration, in the current candidate superbox Internally, 80 design schemes were generated using Latin hypercube sampling. These 80 simulation tasks are submitted in parallel using a high-performance computing cluster (e.g., 100 computing nodes); after the simulation is completed, according to... a max ≤40 g The constraints classify the samples. Assuming a round yields 68 feasible points (good points) and 12 infeasible points (bad points), then observe the proportion of feasible points. =68 / 80=0.85; Based on the coordinate information of these 68 good points and 12 bad points, the fast cutting algorithm is invoked. Adhering to the principle of minimum cost elimination, it intelligently selects the shrinkage dimension to generate a pure sub-superbox that completely excludes the 12 bad points while retaining the best points (e.g., retaining 62). Because... =0.85> The adaptive controller adjusts the growth factor according to preset rules, assuming it is updated to... =1.13, then using the geometric center of the superbox as the base point, multiply the width of all 60 dimensions of the interval by 1.13 to perform symmetrical expansion, but ensure that the expanded new candidate superbox is completely contained within the pure sub-superboxes obtained in the previous round of segmentation, forming new and larger candidate superboxes, thus completing one round of iteration. This loop is automatically repeated, continuously monitoring the growth rate of the superbox volume and the center movement. After a total of 22 rounds of iteration, the growth of the superbox volume slows down significantly (the relative growth rate is below 2% for several consecutive times), and the exploration is determined to have converged. At this time, the output candidate superboxes are... The volume is approximately the initial superbox The 8.3 times that of the previous one indicates that the largest and most continuous potential feasible area in the design has been initially identified, and the cumulative number of simulations consumed in the exploration phase was 22×80=1760.

[0060] After the exploration is completed, it will automatically switch to the consolidation and verification mode, and the input will be... The preset validation objective is to ensure the true feasibility rate within the final interval at a 95% confidence level (δ=0.05). ≥97% (ρtarget=0.97), where, in the first round of verification: The internal structure is generated using simple random sampling. =100 validation samples were used, and parallel simulations were performed. The results were very satisfactory; all 100 samples were feasible. =100; Bayesian evaluation: Using the uninformative prior Beta(1,1), the feasibility rate is calculated based on the observed data (100 for success, 0 for failure). The posterior distribution is Beta(101,1). Further calculations are performed to determine the lower one-sided confidence limit of this distribution at a 95% confidence level. This can be obtained through calculation or table lookup. ≈0.983; due to the calculated statistically guaranteed value Greater than the project target value =0.97, indicating that the current statistical evidence is sufficiently strong, the algorithm terminates immediately without further sampling or purification, and confirms... That is, the final solution space that satisfies the requirements. The consolidation phase only requires 100 simulations. In this process, initialization (400 simulations) + exploration (1760 simulations) + consolidation (100 simulations) = 2260 simulations. With the support of a high-performance cluster, the total computation time is compressed to within an acceptable engineering cycle.

[0061] This application not only outputs the range, but also generates a series of knowledge products that can directly guide engineering practice: Feasible channel design specifications: The system will The allowable ranges of five characteristic force parameters belonging to the same energy-absorbing structure are connected in the order of their physical deformation, automatically generating 12 "force-deformation feasible channels". This chart provides a clear and quantified performance design "channel" for each key component, which can be directly used as an objective specification for suppliers to design components and conduct bench tests and acceptance, realizing the accurate and robust decomposition of the whole vehicle target to the subsystem requirements.

[0062] Critical Boundary Sensitivity Heatmap: The automatically executed boundary sensitivity analysis revealed that among all 120 parameter boundaries, the upper bound of parameter F22 (the platform force of the second segment of the left front longitudinal beam) and the lower bound of parameter F41 (the initial peak force of the right energy-absorbing box) are the most sensitive. Even a slight expansion of these boundaries can lead to a significant decrease in the statistical feasibility guarantee value. This information is highlighted in red on the sensitivity heatmap: the most stringent process control must be implemented for these “critical boundaries” to optimize the allocation of quality control resources.

[0063] Precise diagnosis of design flaws: targeting a historically existing design that fails to meet collision performance standards. a max =42 g The old design was modified to enable the reverse identification function for key parameters. The system setting constraint requires that "at least 54 (90%) parameters must be located in..." The system was then optimized to maximize the violation of constraints. The optimization results precisely indicated that only the values ​​of parameters F8 and F35 significantly exceeded their robust allowable range. The diagnosis was that the collision safety issues of this vehicle model were likely mainly due to insufficient initial peak force of a specific energy-absorbing box and excessive plateau force of a certain longitudinal beam. Design improvements could immediately focus on the structural optimization of these two components, avoiding blind adjustments and expected to save significant development time and costs.

[0064] To verify the results of this application, under the premise of being completely independent of the algorithm execution process, in the final solution space... Internally, 200 completely random design schemes were generated, and each was subjected to high-fidelity simulation testing. Of these 200 independent random samples, 199 designs successfully satisfied the collision acceleration constraints. a max ≤40 g The observed feasibility rate is as high as 99.5%. This exceptionally high feasibility rate of 99.5% exceeds the statistical guarantee (98.3% confidence lower limit) given by the algorithm itself based on 100 validation samples. This confirms the solution space identified in this application. It possesses high engineering robustness, and the application itself exhibits good conservatism, providing ample safety margins for engineering design.

[0065] Figure 2 This is a schematic diagram of the structure of a high-dimensional simulation black box parameter range identification system provided in an exemplary embodiment of this application. For example... Figure 2As shown, the high-dimensional simulation black box parameter interval identification system 40 includes: a performance constraint calculation module 41, used to calculate the performance constraints of the initial population through the high-dimensional simulation black box; wherein, each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box, and the performance constraint includes at least one constraint function, each constraint function being used to determine whether the output response of the high-dimensional simulation black box meets the preset feasible conditions; a feasible seed selection module 42, used to select an individual in the initial population that meets the constraint conditions as a feasible seed point based on the performance constraints, and generate an initial superbox based on the feasible seed point; wherein, the initial superbox is the neighborhood of the feasible seed point; a candidate superbox iteration module 43, used to sample and statistically analyze the initial superbox, and iteratively update the initial superbox based on the sampling and statistical results to obtain candidate superboxes; a confidence evaluation module 44, used to evaluate the confidence of the candidate superboxes to obtain a confidence lower limit; and an identification result generation module 45, used to generate the parameter interval identification result of the high-dimensional simulation black box based on the candidate superbox if the confidence lower limit is greater than the target confidence.

[0066] This application provides a high-dimensional simulation black box parameter interval identification system. The performance constraint calculation module 41 calculates the performance constraints of the initial population using the high-dimensional simulation black box. Each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box. The performance constraints include at least one constraint function, each used to determine whether the output response of the high-dimensional simulation black box meets preset feasibility conditions. The feasible seed selection module 42, based on the performance constraints, selects an individual in the initial population that meets the constraints as a feasible seed point, and generates an initial hyperbox based on the feasible seed point. The initial hyperbox is a feasible seed point. The neighborhood of the seed point is defined; the candidate superbox iteration module 43 samples and statistically analyzes the initial superbox, and iteratively updates the initial superbox based on the sampling and statistical results to obtain candidate superboxes; the confidence evaluation module 44 evaluates the confidence of the candidate superboxes to obtain a confidence lower limit; if the confidence lower limit is greater than the target confidence, the recognition result generation module 45 generates the parameter interval recognition result of the high-dimensional simulation black box based on the candidate superboxes; a high success rate starting point is searched through performance constraints, and the initial superbox is iteratively updated to improve the reliability of the feasible region, while the confidence of the candidate superboxes is evaluated to improve the confidence of the result.

[0067] In one embodiment, the feasible seed selection module 42 can be further configured to: calculate the degree of violation of the aggregate constraint of a single individual based on the performance constraints of the single individual; if there exists a single individual whose degree of violation of the aggregate constraint is equal to zero, then the single individual is selected as a feasible seed point.

[0068] In one embodiment, the feasible seed selection module 42 can be further configured to: determine the initial half-width corresponding to each dimension based on the physical characteristics of each element in the parameter vector; take the initial half-width of each dimension as the expansion distance in that dimension, and expand by a distance of one initial half-width in each positive and negative direction along each dimension with the feasible seed point as the center, to construct an axis-aligned initial superbox.

[0069] In one embodiment, the candidate superbox iteration module 43 can be further configured to: sample within the initial superbox to obtain multiple sample points; input the multiple sample points into a high-dimensional simulation black box to calculate the performance constraints of each sample point; determine the type of the corresponding sample point based on the performance constraints of each sample point; wherein the type of the sample point includes feasible points and infeasible points; segment the initial superbox based on the types of the multiple sample points to obtain segmented regions; expand the segmented regions based on dynamically adjusted growth factors to obtain expanded regions; and perform sampling statistics and iterative updates on the expanded regions again to obtain candidate superboxes.

[0070] In one embodiment, the candidate superbox iteration module 43 can be further configured to: calculate the cost of shrinking the parameter boundary of any dimension due to excluding the sample point for a sample point of type infeasible; select the shrinkage method with the minimum cost to segment the initial superbox and obtain the segmented region.

[0071] In one embodiment, the confidence assessment module 44 can be further configured to: randomly sample candidate superboxes to obtain a set of verification sample points; obtain a prior distribution of the verification sample points using a standard uniform distribution; update the distribution of the verification sample points based on the prior distribution and the type of the verification sample points to obtain a posterior distribution; and obtain the confidence lower limit of the candidate superbox based on the posterior distribution.

[0072] In one embodiment, the identification result generation module 45 can be further configured to: generate a structured data table and a multi-dimensional interval visualization chart of a high-dimensional simulation black box based on candidate superboxes; wherein, the structured data table includes the parameter names and corresponding upper and lower limits of the high-dimensional simulation black box, and the multi-dimensional interval visualization chart includes key parameter combinations.

[0073] Below, for reference Figure 3 This application describes an electronic device according to embodiments thereof. The electronic device may be either or both of a first device and a second device, or a standalone device independent of them, which may communicate with the first device and the second device to receive acquired input signals from them.

[0074] Figure 3 A block diagram of an electronic device according to an embodiment of this application is illustrated.

[0075] like Figure 3As shown, the electronic device 10 includes one or more processors 11 and memory 12.

[0076] The processor 11 may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device 10 to perform desired functions.

[0077] The memory 12 may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory. The non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage medium, and the processor 11 may execute the program instructions to implement the methods of the various embodiments of this application described above and / or other desired functions. Various contents such as input signals, signal components, and noise components may also be stored in the computer-readable storage medium.

[0078] In one example, the electronic device 10 may also include an input device 13 and an output device 14, which are interconnected via a bus system and / or other forms of connection mechanism (not shown).

[0079] When the electronic device is a standalone device, the input device 13 can be a communication network connector for receiving the collected input signals from the first device and the second device.

[0080] In addition, the input device 13 may also include, for example, a keyboard, a mouse, etc.

[0081] The output device 14 can output various information to the outside, including determined distance information, direction information, etc. The output device 14 may include, for example, a display, a speaker, a printer, and a communication network and its connected remote output devices, etc.

[0082] Of course, for the sake of simplicity, Figure 3 Only some of the components of the electronic device 10 relevant to this application are shown in this illustration; components such as buses, input / output interfaces, etc., are omitted. In addition, the electronic device 10 may include any other suitable components depending on the specific application.

[0083] In addition to the methods and apparatus described above, embodiments of this application may also be computer program products, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the methods according to various embodiments of this application described in the "Exemplary Methods" section above.

[0084] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of this application. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0085] Furthermore, embodiments of this application may also be computer-readable storage media storing computer program instructions thereon, which, when executed by a processor, cause the processor to perform the steps in the methods according to various embodiments of this application described in the "Exemplary Methods" section above.

[0086] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0087] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the application to the necessity of employing the aforementioned specific details for implementation.

[0088] The block diagrams of devices, apparatuses, devices, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0089] It should also be noted that in the apparatus, equipment, and methods of this application, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of this application.

[0090] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of this application. Therefore, this application is not intended to be limited to the aspects shown herein, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0091] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this application to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A method for identifying parameter ranges in a high-dimensional simulation black box, characterized in that, include: The performance constraints of the initial population are calculated using a high-dimensional simulation black box; wherein each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box, and the performance constraints include at least one constraint function, each constraint function being used to determine whether the output response of the high-dimensional simulation black box meets preset feasibility conditions; Based on the performance constraints, an individual in the initial population that satisfies the constraints is selected as a feasible seed point, and an initial superbox is generated based on the feasible seed point; wherein, the initial superbox is the neighborhood of the feasible seed point; The initial superbox is sampled and statistically analyzed, and the initial superbox is iteratively updated based on the sampling and statistical results to obtain candidate superboxes; The confidence level of the candidate superboxes is evaluated to obtain the lower confidence limit; If the lower confidence limit is greater than the target confidence level, then the parameter interval identification result of the high-dimensional simulation black box is generated based on the candidate superbox.

2. The method for identifying parameter ranges in a high-dimensional simulation black box according to claim 1, characterized in that, The step of selecting an individual in the initial population that satisfies the constraint as a feasible seed point based on the performance constraint includes: Calculate the degree of violation of aggregation constraints for a single individual based on the performance constraints of that individual. If there exists a single individual whose aggregation constraint violation level is equal to zero, then that single individual is used as the feasible seed point.

3. The method for identifying parameter ranges in a high-dimensional simulation black box according to claim 1, characterized in that, The process of generating an initial hyperbox based on the feasible seed points includes: Based on the physical characteristics of each element in the parameter vector, determine the initial half-width corresponding to each dimension; Using the initial half-width of each dimension as the extension distance in that dimension, and taking the feasible seed point as the center, extend the distance by one half-width in each positive and negative direction of each dimension to construct an axis-aligned initial superbox.

4. The method for identifying parameter ranges in a high-dimensional simulation black box according to claim 1, characterized in that, The process of sampling and statistically analyzing the initial superbox, and iteratively updating the initial superbox based on the sampling and statistical results, yields candidate superboxes including: Sampling is performed within the initial superbox to obtain multiple sample points; Input the multiple sample points into the high-dimensional simulation black box and calculate the performance constraints for each sample point; Based on the performance constraints of each sample point, the type of the corresponding sample point is determined; the sample point type includes feasible points and infeasible points. The initial superbox is segmented based on the types of the multiple sample points to obtain segmented regions; Based on dynamically adjusted growth factors, the segmented region is expanded to obtain an expanded region; The expanded region is sampled, statistically analyzed, and iteratively updated again to obtain the candidate superbox.

5. The method for identifying parameter ranges in a high-dimensional simulation black box according to claim 4, characterized in that, The segmentation of the initial superbox based on the types of the multiple sample points to obtain segmented regions includes: For a sample point of type infeasible, calculate the cost of shrinking the parameter boundary of any dimension due to excluding the sample point. The initial superbox is segmented using the shrinkage method with the lowest replacement value to obtain the segmented region.

6. The method for identifying parameter ranges in a high-dimensional simulation black box according to claim 1, characterized in that, The confidence assessment of the candidate superboxes to obtain the lower confidence limit includes: Randomly sample the candidate superboxes to obtain a set of verification sample points; The prior distribution of the validation sample points was obtained using a standard uniform distribution. Based on the prior distribution and the type of the validation sample points, the distribution of the validation sample points is updated to obtain the posterior distribution; Based on the posterior distribution, the confidence lower bound of the candidate superbox is obtained.

7. The method for identifying parameter ranges in a high-dimensional simulation black box according to claim 1, characterized in that, The parameter range identification results generated based on the candidate superboxes for the high-dimensional simulation black box include: Based on the candidate superboxes, a structured data table and a multi-dimensional interval visualization chart are generated for the high-dimensional simulation black box; wherein, the structured data table includes the parameter names and corresponding upper and lower limits of the high-dimensional simulation black box, and the multi-dimensional interval visualization chart includes key parameter combinations.

8. A high-dimensional simulation black box parameter range identification system, characterized in that, include: The performance constraint calculation module is used to calculate the performance constraints of the initial population through a high-dimensional simulation black box; wherein, each individual in the initial population corresponds to a parameter vector of the high-dimensional simulation black box, and the performance constraint includes at least one constraint function, each constraint function being used to determine whether the output response of the high-dimensional simulation black box meets the preset feasibility conditions; A feasible seed selection module is used to select an individual in the initial population that satisfies the constraint conditions as a feasible seed point based on the performance constraints, and generate an initial superbox based on the feasible seed point; wherein, the initial superbox is the neighborhood of the feasible seed point; The candidate superbox iteration module is used to sample and statistically analyze the initial superbox, and iteratively update the initial superbox based on the sampling and statistical results to obtain candidate superboxes. The confidence assessment module is used to assess the confidence of the candidate superbox and obtain the confidence lower limit; The recognition result generation module is used to generate the parameter interval recognition result of the high-dimensional simulation black box based on the candidate superbox if the lower confidence limit is greater than the target confidence level.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program for performing the method described in any one of claims 1-7.

10. An electronic device, characterized in that, include: processor; Memory used to store the processor's executable instructions; The processor is used to execute the method described in any one of claims 1-7.

Images