A method for determining key influencing factors based on a complex simulation system

Abstract

This disclosure relates to the field of simulation, and embodiments of this disclosure provide a method for determining key influencing factors based on a complex simulation system. In one specific embodiment, the method includes: responding to a factor analysis request instruction from the simulation system; acquiring multiple experimental factors and conditional constraint rules and constructing a correlation coefficient matrix; generating an initial uniform sample set; performing correlation feature mapping processing on the initial uniform sample set based on the correlation coefficient matrix to obtain a first uniform sample set; splitting the first uniform sample set and performing nonlinear constraint optimization and reorganization through the interior point method to obtain a combined sample matrix for sensitivity analysis; mapping the combined sample matrix to the actual value range of each experimental factor and performing conditional constraint processing on the mapped combined sample matrix to obtain a second uniform sample set; inputting the second uniform sample set into the simulation system to obtain simulation results; and calculating the influence coefficient of each experimental factor based on the second uniform sample set and the simulation results using the sensitivity analysis method.

Description

Technical Field

[0001] This disclosure relates to the field of simulation. More specifically, it relates to a method for determining key influencing factors based on complex simulation systems. Background Technology

[0002] In sensitivity analysis of complex simulation systems, variance-based analysis methods are commonly used to quantify the influence of each experimental factor on the simulation results. Mathematically, these methods typically require cross-combining and mechanically concatenating sample columns between different basic sample matrices to construct a dedicated combined matrix for variance decomposition calculation.

[0003] However, when faced with the common numerical correlations among experimental factors in real-world engineering systems, this traditional matrix reconstruction method faces a fundamental logical conflict: directly executing the mechanical splicing of sample columns will directly destroy the originally established factor correlation structure; while forcibly correcting the correlation through conventional methods such as overall numerical translation will disrupt the uniform distribution characteristics of the samples in the multidimensional parameter space. This deficiency, which cannot simultaneously consider and maintain the factor correlation structure and the uniformity of sample distribution during matrix reconstruction, results in the final constructed input samples failing to accurately reproduce the physical coupling environment of the system, leading to serious deviations in the calculated influence coefficients and making it impossible to accurately identify the true key influencing factors. Summary of the Invention

[0004] The purpose of this disclosure is to provide a method for determining key influencing factors based on complex simulation systems, in order to solve the problem that existing technologies cannot simultaneously take into account and maintain the correlation and condition constraints of experimental factors when generating and recombining experimental samples for complex simulation systems, resulting in serious deviations in the calculation of sensitivity influence coefficients.

[0005] To achieve the above objectives, the present disclosure adopts the following technical solution: This disclosure provides a method for determining key influencing factors based on complex simulation systems, including: In response to the factor analysis request command from the simulation system, multiple experimental factors and condition constraint rules characterizing the logical restrictions between the experimental factors are obtained, and a correlation coefficient matrix characterizing the dependency relationship between the experimental factors is constructed. An initial uniform sample set is generated, and based on the correlation coefficient matrix, the initial uniform sample set is subjected to correlation feature mapping processing to obtain a first uniform sample set; The first uniform sample set is split and reorganized into a combined sample matrix for sensitivity analysis by nonlinear constraint optimization using the interior point method; wherein, the nonlinear constraint optimization includes: constructing an optimization objective function with target mean and target variance as metrics and constructing constraints including correlation error tolerance; solving the optimization objective function based on the constraints to obtain an optimization column vector, and combining the optimization column vectors to obtain the combined sample matrix; The combined sample matrix is ​​mapped to the actual value range of each experimental factor, and the mapped combined sample matrix is ​​subjected to condition constraint processing based on the condition constraint rules to obtain the second uniform sample set. The second uniform sample set is input into the simulation system to obtain simulation results. Based on the second uniform sample set and the simulation results, the influence coefficient of each experimental factor on the simulation results is calculated by sensitivity analysis.

[0006] The beneficial effects of this disclosure are as follows: In response to a factor analysis request instruction, the embodiments of this disclosure construct a correlation coefficient matrix and perform correlation feature mapping on an initial uniform sample set accordingly, so that the first uniform sample set objectively possesses a preset numerical dependency structure between experimental factors. In the process of splitting and recombining the first uniform sample set into a combined sample matrix for sensitivity analysis, embodiments of this disclosure perform nonlinear constraint optimization using the interior-point method. An optimization objective function is constructed using the target mean and target variance as metrics, and constraints are established using correlation error tolerance to solve for the optimized column vectors. This nonlinear constraint optimization mechanism ensures that when the recombined combined sample matrix performs the matrix permutation required for sensitivity analysis, the statistical distribution characteristics of its replaced columns are forcibly locked within the target mean and variance range. Simultaneously, the error between its actual correlation coefficient and the target correlation coefficient is limited to within the tolerance threshold, thus mathematically preventing the matrix recombination operation from doubly damaging the original correlation structure and uniform distribution characteristics of the samples. Furthermore, embodiments of this disclosure map the recombined combined sample matrix to the actual value range and perform filtering based on conditional constraint rules to remove samples that do not meet the logical constraints.

[0007] The sequential combination and interaction of the above features effectively solve the technical defects of existing technologies in constructing special matrices for sensitivity analysis of complex simulation systems, which cannot simultaneously take into account and maintain the correlation structure of experimental factors and the uniformity of sample spatial distribution. It eliminates the structural distortion caused by mechanical splicing of matrices and the contamination of simulation results by illegal boundary samples. As a result, the influence coefficients calculated based on the combined sample matrix and variance decomposition can objectively and unbiasedly reflect the actual impact of each experimental factor on the simulation results. Attached Figure Description

[0008] The specific embodiments of this disclosure will be described in further detail below with reference to the accompanying drawings.

[0009] Figure 1 The flowchart of a method for determining key influencing factors based on a complex simulation system disclosed herein is shown.

[0010] Figure 2 A schematic diagram of the structure of a computer system for implementing the apparatus provided in the embodiments of this disclosure is shown. Detailed Implementation

[0011] To more clearly illustrate this disclosure, the following description, in conjunction with embodiments and accompanying drawings, provides further insight. Similar components in the drawings are indicated by the same reference numerals. Those skilled in the art should understand that the specific description below is illustrative rather than restrictive and should not be construed as limiting the scope of protection of this disclosure.

[0012] In complex simulation system applications, system analysis often relies on sensitivity analysis methods, such as Sobol parameter sensitivity analysis based on variance decomposition, to quantify the actual contribution of each experimental factor to the simulation results. To achieve efficient variance decomposition, such methods employ specific matrix reconstruction specifications at the underlying mathematical framework. This requires cross-permutation and recombination of specific sample columns between different basic sample matrices to construct a dedicated combined matrix as simulation input. However, this traditional matrix construction and recombination mechanism reveals a mismatch between the underlying theoretical assumptions and actual operating conditions when applied to real engineering systems containing non-independent factors.

[0013] In real-world complex engineering structures or simulation scenarios, deep numerical dependencies and physical correlations are prevalent among various experimental factors. Conventional sampling and analysis processes, when faced with such correlated variables, fail to maintain the original correlation structure during the dynamic flow of matrix permutations, leading to severe mathematical distortions. Specifically, when a sensitivity analysis model mechanically permutes the sample columns of the base matrix to calculate the total sensitivity index of a single factor, this abrupt column insertion directly blocks and tears apart the original parameter correlation network, resulting in data structure distortion in the recombined matrix. Furthermore, attempting to forcibly distort the samples to match the target correlation using conventional methods such as numerical translation, spatial projection, or boundary correction after matrix reconstruction directly disrupts the original spatial filling and uniform distribution characteristics of the samples in the multidimensional parameter space, causing local clustering, overlap, or sampling blind spots. This fundamental contradiction—the inability to simultaneously consider and maintain the correlation structure of experimental factors and the uniformity of sample spatial distribution during matrix cross-recombination—directly results in the recombined sample matrix input into the simulation system failing to accurately reproduce the true coupling environment within the complex system. The simulation system performs calculations based on these distorted or non-compliant sample data, which inevitably leads to error contamination in the output simulation results. Consequently, the sensitivity influence coefficients calculated in the variance decomposition stage will have serious numerical deviations, making it impossible to provide accurate key influence factor identification support for the optimization design of complex engineering systems.

[0014] In view of this, embodiments of this disclosure provide a method for determining key influencing factors based on complex simulation systems, such as... Figure 1 As shown, the method includes S10-S50, specifically: S10. In response to the factor analysis request command of the simulation system, obtain multiple experimental factors and condition constraint rules characterizing the logical restrictions between the experimental factors, and construct a correlation coefficient matrix characterizing the dependency relationship between the experimental factors. In this embodiment, the correlation coefficient matrix refers to a mathematical tool used to quantify the interdependence between multiple experimental factors in a complex simulation system, which ensures that the generated samples can truly reproduce the coupling state of each variable in the physical world in numerical space.

[0015] S20. Generate an initial uniform sample set. Based on the correlation coefficient matrix, perform correlation feature mapping processing on the initial uniform sample set to obtain a first uniform sample set. S30. The first uniform sample set is split and reorganized into a combined sample matrix for sensitivity analysis using interior point method nonlinear constraint optimization. The nonlinear constraint optimization includes: constructing an optimization objective function with target mean and target variance as metrics, and constructing constraints including correlation error tolerance; solving the optimization objective function based on the constraints to obtain optimized column vectors; and combining the optimized column vectors to obtain the combined sample matrix. In this embodiment, nonlinear constraint optimization specifically refers to a mathematical programming process introduced to solve the structural tearing problem caused by traditional column permutation operations when reconstructing the combined sample matrix for sensitivity analysis, seeking the optimal sample column vectors under various statistical constraints.

[0016] S40. Map the combined sample matrix to the actual value range of each experimental factor, and perform condition constraint processing on the mapped combined sample matrix based on the condition constraint rules to obtain the second uniform sample set; in this embodiment, the condition constraint rules refer to the hard physical or logical boundary restrictions that the experimental factors must comply with in actual engineering applications, such as exclusivity or value range reduction under a specific combination of variables.

[0017] S50. Input the second uniform sample set into the simulation system to obtain simulation results. Based on the second uniform sample set and the simulation results, calculate the influence coefficient of each experimental factor on the simulation results using sensitivity analysis.

[0018] In this embodiment, the correlation coefficient matrix is ​​constructed through steps S10-S20, and the initial uniform sample set is processed by correlation feature mapping based on it. This changes the distribution state of traditional random sampling, so that the generated first uniform sample set objectively has a numerical dependency structure corresponding to the engineering system, and reduces the distribution bias of the input samples.

[0019] To address the matrix column rearrangement operation required in sensitivity analysis, this embodiment introduces a nonlinear constraint optimization mechanism based on the interior-point method in step S30. By setting the target mean and target variance as the objective function and the correlation error tolerance as the constraint condition, the calculated optimized column vectors, when concatenated into the combined sample matrix, have their statistical distribution characteristics and correlation errors forcibly limited to a preset threshold range. This process, at the mathematical calculation level, prevents the matrix rearrangement operation from disrupting the original correlation structure and uniform distribution characteristics of the samples.

[0020] Furthermore, step S40 maps the recombined combined sample matrix to the actual value range and introduces conditional constraint rules to perform filtering, eliminating boundary samples that do not meet the logical constraints, thus ensuring that the second uniform sample set conforms to the actual engineering constraints.

[0021] In summary, this embodiment effectively addresses the technical shortcomings of existing technologies in constructing sensitivity analysis matrices, which cannot simultaneously consider the correlation structure and distribution uniformity of experimental factors. By eliminating structural distortion caused by matrix recombination and the influence of non-compliant samples, the influence coefficients calculated based on variance decomposition in S50 can more objectively reflect the actual impact of each experimental factor on the simulation results.

[0022] In a specific example, experimental factors, also known as input variables or system parameters, refer to underlying parameters input into a complex simulation system model whose changes in numerical or logical states can directly or indirectly drive the corresponding evolution of the simulation system's output results. In practical complex engineering applications, such as system simulations in aerospace and complex equipment control, experimental factors are typically characterized as parameters with specific physical dimensions, such as ambient temperature, stress limits, or control logic parameters, such as switch states or gear indicators. In the embodiments of this disclosure, based on the dual dimensions of data structure and physical constraints, the experimental factors are finely defined: in terms of data distribution, they include continuous factors that can take values ​​within a preset range and discrete factors constrained by a specific set; in terms of engineering constraint attributes, they include unconditionally constrained factors that take values ​​independently and conditionally constrained factors whose legal value space is controlled by the evolution of other factors' states. The core purpose of sensitivity analysis is to quantify and screen out the key influencing factors that contribute the most to the global variance of the simulation results, while fully preserving the true correlation between each experimental factor.

[0023] In one possible implementation, after calculating the influence coefficients of each experimental factor on the simulation results using sensitivity analysis based on the second uniform sample set and the simulation results, the method further includes sorting the influence coefficients of each experimental factor in descending order to obtain the experimental factors corresponding to the top q influence coefficients, where q is an integer greater than 0. Since the influence coefficient of an experimental factor is proportional to its degree of influence on the simulation results, these experimental factors with larger influence coefficients are the key influencing factors.

[0024] In one possible implementation, generating the initial uniform sample set includes: An initial uniform sample set is generated using the maximum-minimum distance Latin hypercube sampling algorithm; The step of performing correlation feature mapping processing on the initial uniform sample set based on the correlation coefficient matrix to obtain the first uniform sample set includes: The first uniform sample set is obtained by using the initial uniform sample set as input to the Gaussian Copula function.

[0025] In a specific example, the inter-factor dependency refers to a quantitative index used to describe the dependency relationship between multiple experimental factors, specifically a correlation coefficient matrix; this correlation coefficient matrix is ​​used as the input parameter of the Gaussian Copula function in step S22 to generate experimental samples that can accurately reflect the inter-factor dependency structure.

[0026] The embodiments of this application generate an initial uniform sample set through the maximum-minimum distance Latin hypercube sampling algorithm. By calculating and iteratively replacing to maximize the minimum Euclidean distance between sample points, the local clustering of sample points in the multidimensional parameter space is eliminated, so that the generated initial uniform sample set achieves the preset distribution uniformity. Furthermore, embodiments of this disclosure use the correlation coefficient matrix characterizing the dependency relationship between experimental factors as the input parameter of the Gaussian Copula function to transform the initial uniform sample set, converting independent uniformly distributed samples into samples with the dependency distribution corresponding to the correlation coefficient matrix, so that the generated first uniform sample set objectively contains the nonlinear numerical dependency structure between experimental factors, solving the problem that the sample distribution does not match the actual situation due to the traditional sampling assumption of independent factors. Furthermore, the embodiments of this disclosure perform nonlinear constraint optimization on the first uniform sample set using the interior point method, incorporating the target correlation as an equality constraint into the optimization objective function for solution. This enables the error between the actual correlation coefficient of the replaced sample column and the target correlation coefficient to be forcibly limited within a preset threshold range when dealing with the sample matrix column replacement operation required for subsequent sensitivity analysis, thereby preventing the matrix reconstruction operation from destroying the original correlation structure of the samples.

[0027] In one possible implementation, generating the initial uniform sample set using the maximum-minimum distance Latin hypercube sampling algorithm includes: S211. For each experimental factor, generate a random permutation from 1 to 2n; S212, According to the formula

[0028] The value of the k-th sample in the standard Latin hypercube sampling uniform sample under the i-th test factor is obtained. To construct a standard uniform sample set; where, The total number of samples in the standard uniform sample set. It is the k-th value in the random permutation corresponding to the i-th experimental factor; In order to be in Random numbers drawn from a uniform distribution within an interval; S213. For the standard uniform sample set, calculate the Euclidean distance between any two samples under all experimental factors, and extract the minimum distance to obtain the first distance. As an initial evaluation index for the uniformity of sample distribution; S214. Iteratively execute the following operations until the current iteration number is greater than or equal to the first preset iteration threshold or the second distance. and first distance If the absolute value of the difference is less than the first preset convergence threshold, the standard uniform sample set of this iteration is output as the initial uniform sample set. S215. Randomly adjust each standard uniform sample set A random number is generated to create a candidate sample set. The Euclidean distance between any two samples in the candidate sample set is calculated under all experimental factors, and the minimum distance is extracted to obtain the second distance. Calculate the second distance and first distance The difference; S216, Determine the second distance Is it greater than the first distance? If the value is greater than 0, the candidate sample set is used to replace the standard uniform sample set; otherwise, the standard uniform sample set is retained.

[0029] It should be noted that in this embodiment, the first preset iteration threshold refers to the maximum allowed number of iterations set to prevent the algorithm from getting stuck in an infinite loop while optimizing the Euclidean distance in the sample space. Its value is determined by the balance between the actual available computing resources and the requirement for uniformity of sample distribution. For example, it can be 100 or 500. The first preset convergence threshold refers to the lower limit of the absolute value of the difference between the second distance and the first distance in the sample set in two consecutive iterations. Specifically, it is used to judge whether the distribution of samples in the multidimensional parameter space has reached a stable and uniform stopping point. Its value depends on the sensitivity of the complex simulation system to the accuracy of the input parameter space distribution. It is usually a very small positive real number, such as 10. -4 10 -5 or The minimum Euclidean distance change is the absolute value of the difference between the second distance and the first distance.

[0030] In a specific example, for the standard uniform sample set, calculating the Euclidean distance between any two samples under all trial factors includes: For any two standard uniform sample sets and The formula for calculating its Euclidean distance is:

[0031] in, The total number of experimental factors. and They are respectively and The value of the i-th experimental factor.

[0032] In one possible implementation, constructing the correlation coefficient matrix characterizing the dependencies between the experimental factors includes: Obtain the historical sample set saved by the simulation system during the actual test process and use it as historical data, wherein the historical sample set includes the actual value data of each experimental factor under multiple historical runs; Based on historical data, the correlation coefficients between the experimental factors are calculated using the Pearson correlation coefficient, and a correlation coefficient matrix R for each experimental factor is constructed. It should be noted that, in this embodiment, historical data specifically refers to the historical sample set accumulated by the simulation system during its initial testing or actual operation. This historical sample set constitutes the data foundation for the experimental factors, containing the actual value records of each experimental factor under multiple historical operating conditions. Based on these specific value records, i.e., the numerical fluctuations and co-occurrence of each factor in the real environment, the Pearson correlation coefficients between the experimental factors are calculated, thereby deriving a correlation coefficient matrix that objectively represents their dependency relationship.

[0033] The step of using the initial uniform sample set as input to the Gaussian Copula function to obtain the first uniform sample set includes: S221. Define the initial uniform sample set as... ,in, The total number of samples in the initial uniform sample set. The total number of experimental factors. Let be the value of the k-th sample in the initial uniform sample set under the j-th experimental factor, where ; S222, According to the formula

[0034] The independent standard normal variable values ​​of the k-th sample in the initial uniform sample set under the j-th experimental factor were calculated. , so as to pass all The independent standard normal sample matrix is ​​constructed. , ;in, It is the inverse cumulative distribution function of the standard normal distribution (CDF). S223, According to the formula

[0035] For independent standard normal sample matrix After transformation, we obtain the matrix of correlated normally distributed random variables. ; in It is the correlation coefficient matrix The Cholesky decomposition (Cholesky) results; S224. The matrix of correlated normally distributed random variables... The first uniform sample set is obtained by transforming the standard normal distribution using the inverse cumulative distribution function. . The variables are evenly distributed within the interval, capturing the dependencies between them.

[0036] In a specific example, before S221, the method also includes: In response to the user's settings, a Gaussian Copula function suitable for linearly dependent and tail-independent structures is selected based on the data dependency structure, as shown in the following formula:

[0037] in, For an M-dimensional Gaussian Copula function that has the aforementioned correlation coefficient matrix R, It is the inverse function of the standard normal distribution; For the initial uniform sample set Obedience Variables that are uniformly distributed across an interval. express The cumulative distribution function of the joint normal distribution; M is the total number of experimental factors; It should be noted that, in this embodiment, the multiple formulas in S221-S224 collectively constitute the theoretical joint distribution model of the Gaussian Copula function. To generate random samples conforming to this theoretical model in computer simulation, this disclosure specifically implements the sample sampling of the Gaussian Copula function through the equivalent algorithm logic described in steps S221 to S223.

[0038] In a specific example, the Pearson correlation coefficient is calculated using the following methods:

[0039] in, It is a test factor and test factors The correlation coefficient, and They are the first The first experimental factor and the first The mean of each experimental factor; the correlation coefficients among all experimental factors are calculated and then filled into the correlation coefficient matrix. H is the total number of historical data samples. For the i-th sample in the historical data at the th... Values ​​under each experimental factor; For the i-th sample in the historical data at the th... The values ​​taken under each experimental factor.

[0040] In one possible implementation, splitting the first uniform sample set and recombining it into a combined sample matrix for sensitivity analysis through nonlinear constraint optimization using the interior-point method includes: Construct a first sample matrix based on the first uniform sample set. , Let M be the value of the k-th sample in the j-th experimental factor within the first uniform sample set; M is the total number of experimental factors. This represents the total number of samples in the first sample matrix; The first sample matrix The former Rows as the second sample matrix ,the remaining Rows as the third sample matrix ; where the second sample matrix for

[0041] Third Sample Matrix for

[0042] Traverse the correlation coefficient matrix and select the set of factor indices that have a non-zero correlation with the c-th column and are not themselves. Specifically, if targeting the first If there are several experimental factors, then c equals j; judge If the column is empty, extract the c-th column of the third sample matrix as the c-th column of the fourth sample matrix to obtain the optimized column vector that satisfies the statistical properties and correlation constraints. ; Otherwise, construct a nonlinear constrained optimization model, using the c-th column of the third sample matrix as the initial value, and solve for the optimal column vector that satisfies the statistical properties and correlation constraints. ; Obtain M optimized column vectors that satisfy statistical properties and correlation constraints. , As the fourth sample matrix Column c, all The fourth sample matrix is ​​obtained by combining and constructing. ; for , build indivual The fifth sample matrix Among them, the fifth sample matrix The c-th column equals the fourth sample matrix The c-th column, and the remaining columns are respectively equal to the second sample matrix. The corresponding column; The second sample matrix Third sample matrix and The fifth sample matrix This combination yields a combined sample matrix used for sensitivity analysis of the input simulation system. ; The method uses the c-th column of the third sample matrix as the initial value to solve for the optimal column vector that satisfies the statistical properties and correlation constraints. include: Construct the optimization objective function:

[0043] in, This represents the value of the objective function to be optimized. This represents the specific element value in the r-th row of the c-th column after optimization; This represents the weighting coefficient of the mean constraint in the optimization objective. This represents the weighting coefficient of the variance constraint in the optimization objective. To set a target mean, The target variance is preset; Among them, the preset target mean and preset target variance refer to the ideal statistical moment parameters that the generated sample column vector must reach in the multidimensional parameter space in order to lock the sample distribution characteristics when performing nonlinear constraint optimization and recombination on the sample matrix. Specifically, they are the core mathematical benchmarks for judging whether the recombined sample column can maintain the original space filling and uniform distribution characteristics. Their value logic is strictly based on the theoretical statistical properties of the standard uniform distribution adopted in this application, rather than empirical settings.

[0044] Specifically, in the embodiments of this disclosure, when constructing the basis matrix for Copula transformation and sensitivity analysis, the sample data are all mapped to the standard interval [0,1]. To ensure that the generated samples are still perfectly uniformly distributed within this interval, according to the principles of probability theory and mathematical statistics, the theoretical expected value of the standard uniform distribution U(0,1) is 0.5, and the theoretical variance is 1 / 12. Therefore, the preset target mean is... Strictly set to 0.5, the preset target variance will be... The target value is set to 1 / 12. These two preset target values ​​serve as mathematical anchors in the optimization objective function, ensuring that even if the algorithm makes non-linear adjustments to the sample values ​​to meet correlation constraints, the distribution of samples in each single dimension will not be biased or produce local clustering.

[0045] Construct correlation inequality constraints:

[0046] in, express With the p-th column vector of the second sample matrix The actual correlation coefficient; The first in the target correlation coefficient matrix The value in row p; To preset the correlation error tolerance, construct variable boundary constraints:

[0047] The preset correlation error tolerance refers to the maximum absolute error limit allowed in the nonlinear constraint optimization process, where the actual correlation coefficient between the optimized sample column and the reference sample column deviates from the corresponding target value in the target correlation coefficient matrix. Specifically, it mathematically defines the acceptable range of correlation structure distortion after sample recombination, serving as a stopping criterion for the algorithm iteration to satisfy the correlation constraints. The logic for determining this tolerance is based on a balance between maintaining the strictness of the true correlation structure of the experimental factors and the convergence of the numerical solution of the nonlinear optimization algorithm: a value that is too small will lead to an excessively narrow feasible region for the optimization model, making it difficult for the algorithm to converge or resulting in excessively high computational costs; a value that is too large will lead to severe distortion of the correlation of the recombinated samples, making it impossible to recreate the true coupling environment in the physical system. Typically, based on the engineering accuracy requirements of actual complex simulation systems, it is set to a decimal between 0.01 and 0.1, for example, preferably 0.05 in this embodiment.

[0048] By incorporating correlation inequality constraints and variable boundary constraints into the objective function using a logarithmic barrier function, and then iteratively updating it using Newton's method. until the objective function is optimized. Once convergence is achieved or the preset number of iterations is reached, the optimized column vector that currently satisfies the statistical properties and correlation constraints is output. , which is the c-th column of the fourth sample matrix.

[0049] The core function of this embodiment, which uses the interior-point method for nonlinear constraint optimization and constructs the objective optimization function, is to perform a dual correction of statistical and correlational properties on the newly generated sample columns when replacing columns in the recombined sample matrix for sensitivity analysis. By constructing the objective optimization function and introducing objective mean and objective variance as metrics, combined with constraints such as correlation error tolerance, the achieved technical effect is that the algorithm, during the solution process, can both forcibly limit the error between the actual correlation coefficient of the replaced sample column and the target correlation coefficient within a safe range to ensure that the true correlation structure between factors is not destroyed, and perfectly lock the uniform distribution characteristics of the new sample column. This solves the underlying contradiction that the Sobol sensitivity analysis method cannot simultaneously consider sample correlation and distribution uniformity when constructing column replacements for a specific sample matrix.

[0050] In a specific example, the specific execution process of the above steps is as follows: for the first... The test factor is traversed through the correlation coefficient matrix, and the factors that are most similar to the first test factor are selected. The column has a set of factor indices that are not zero-correlation and are not themselves. The set The column corresponding to the second sample matrix is ​​the reference object that the c-th column must satisfy the correlation constraint during adjustment; Setting the correlation error tolerance: Define the correlation error tolerance =0.05, specifying the optimized i-th Columns and The absolute error between the actual correlation coefficient and the target correlation coefficient in each column must not exceed [a certain value]. To balance the satisfaction of correlation constraints with the convergence of numerical computation; Set the target parameters for the distribution characteristics: to ensure that the adjusted data in column c strictly follow... Based on the uniform distribution characteristics of the interval, the following statistical moment target parameters are set: Target mean: ; Objective variance: ; Nonlinear optimization based on uniformity preservation and correlation reconstruction: For column c, according to the set Whether it is empty, use a differential adjustment strategy to generate the c-th column of the fourth sample matrix: If set An empty value indicates that the factor is not correlated with other factors, and the third sample matrix is ​​directly extracted (matrix). ) Column c is the c-th column of the fourth sample matrix; If set For non-empty samples, construct a nonlinear constrained optimization model, using the c-th column of the third sample matrix as the initial value, and solve for the optimal column vector that satisfies the statistical properties and correlation constraints. , dimension ; Construct the optimization objective function:

[0051] This represents the objective function value for optimization. The smaller the value, the closer the sample distribution is to the ideal uniform distribution. This represents the specific element value in the r-th row of the c-th column after optimization; , This represents the weighting coefficient, used to balance the importance of the mean constraint and the variance constraint in the optimization objective; here, both are set to 0.5. Specifically, in this optimization objective function, the weight coefficients and The value of is based on balancing the relative importance of mean deviation and variance deviation in the optimization iteration process, as well as the normalization of the dimensions of different statistics. Specifically, since the sample mean and variance terms are usually on different orders of magnitude in numerical calculations, to avoid the objective function being absolutely dominated by the larger term when solving nonlinear optimizations using the interior point method, it is necessary to introduce . and Perform numerical scaling and leveling.

[0052] In practical value selection logic, if the current simulation system has stricter requirements on the central tendency of the input samples, then increase... The value of is determined by the requirement for higher preservation of sample dispersion; if a higher degree of preservation is required, then the value of is increased. The value of is determined according to the principle of equal penalty in the absence of specific preferences, and is usually set to . =0.5 and =0.5.

[0053] The constraints include correlation inequality constraints and variable boundary constraints; The correlation inequality constraints include:

[0054] in, express With the p-th column vector of the second sample matrix The actual correlation coefficient; The first in the target correlation coefficient matrix The value in row p; To predetermine the correlation error tolerance; variable boundary constraints include:

[0055] Introducing a logarithmic barrier function integrates inequality constraints into the objective function, transforming it into an unconstrained optimization subproblem. The vector values ​​are then iteratively updated using Newton's method until convergence or the preset number of iterations (100) is reached, outputting the optimized column vector. As the fourth sample matrix Column. Ultimately composed of all The optimized columns form the complete fourth sample matrix. ; Build indivual The fifth sample matrix This makes the fifth sample matrix The c-th column equals the fourth sample matrix The c-th column, and the remaining columns are respectively equal to the second sample matrix. The corresponding column; The second sample matrix Third sample matrix and The fifth sample matrix The combined samples are used to obtain a combined sample matrix for sensitivity analysis of the simulation system. .

[0056] In one possible implementation, mapping the combined sample matrix AB to the actual value range of each experimental factor includes: This step is defined as the basic mapping, specifically including: If the i-th experimental factor is a continuous factor, then obtain the actual value range of the i-th experimental factor. ,in, The minimum value within the actual range of values. This is the maximum value within the actual range of values; According to the formula

[0057] After calculating the combined sample matrix mapping, the actual value of the k-th sample under the i-th experimental factor is obtained. To construct the second uniform sample set ;in The element value of the k-th sample under the ith experimental factor before the combined sample matrix is ​​mapped; If the i-th experimental factor is an unconstrained discrete factor, obtain the set of discrete values ​​for the i-th experimental factor.

[0058] According to the formula

[0059] The position index of the discrete value set is calculated. ,in, To round down, The element value of the i-th experimental factor under the k-th sample before the combined sample matrix mapping; m is the total number of the discrete value set; Then the actual value of the k-th sample under the i-th experimental factor after the combined sample matrix mapping. for: .

[0060] In one possible implementation, the conditional constraint processing of the mapped combined sample matrix based on conditional constraint rules to obtain the second uniform sample set includes: This step is defined as conditional mapping, specifically as follows: If the i-th experimental factor is a conditionally constrained discrete factor, then the conditional constraint rules are parsed to obtain the preset trigger conditions and the constraint set. Specifically, the preset triggering condition is a logical equality or logical inequality constraint condition existing between each of the experimental factors; that is, if the first... The values ​​of each experimental factor are: Then the first The values ​​of each experimental factor must be from a limited set. In the meantime, targeted adjustments need to be made after the basic mapping to ensure that the constraints are strictly enforced; In this embodiment, the preset trigger condition refers to the logic activation threshold or prerequisite event used to determine whether a mandatory value restriction needs to be applied to a specific sample when performing actual physical space mapping on discrete experimental factors containing conditional constraints; its specific meaning is to objectively characterize the deep coupling relationship and exclusive constraint boundary between various physical variables or control logics within a complex simulation system. For example, when the control parameters of the simulation system are in the on state, the controlled parameters can only take values ​​in a specific subset.

[0061] Its setting and analysis logic are not based on random assignment by the algorithm, but are strictly mapped from the conditional constraints of actual engineering conditions. Mathematically, this is specifically manifested as pre-established logical equations or logical inequalities between experimental factors.

[0062] At the algorithm execution level, this condition acts as a switch for sample data filtering and intervention: when a sample feature in the combined sample matrix is ​​found during traversal, such as the i-th factor having a specific value v, and this preset trigger condition is met, the system is explicitly informed that the sample has reached the boundary of the engineering logic. This forces a targeted mapping adjustment to the associated experimental factor, i.e., the j-th factor, strictly locking its value within the legally defined set S. This mechanism completely eliminates the contamination of the simulation environment by non-compliant boundary samples from the data level, ensuring the absolute legality and compliance of the final generated second uniform sample set in engineering application logic.

[0063] Iterate through all samples in D and select those that meet the preset triggering conditions; that is, the value of the i-th experimental factor is... The sample, the index set of the sample is defined as ; For samples in K, readjust the value of the j-th experimental factor so that it only comes from the limited set. Select from; For the samples in K, the value of the j-th experimental factor is readjusted so that it only comes from the limited set. The selection process specifically includes: based on The value at the corresponding position in First, according to the formula

[0064] Calculated Position index in , for The total number of elements in the middle, then The actual value of the k-th sample under the j-th experimental factor Updated to , for The Middle Each element.

[0065] In one possible implementation, after inputting the second uniform sample set into the simulation system to obtain simulation results, the method further includes: The simulation result data is split according to the source of the corresponding sample matrix, and the simulation results corresponding to the mapped second sample matrix are obtained respectively. The simulation results corresponding to the mapped third sample matrix And the simulation results corresponding to each of the mapped fifth sample matrices. ;in, , For the total number of experimental factors, the aforementioned The above and each of the above By combining in sequence, we can construct a... The column matrix result is column matrix Y, and its formula is: .

[0066] In one possible implementation, calculating the influence coefficients of each experimental factor on the simulation results using sensitivity analysis, based on the second uniform sample set and the simulation results, includes: Since there is correlation among the experimental factors, the generalized Sobol method, which is applicable to dependent variables, is used to calculate the total sensitivity index of each experimental factor. According to the formula:

[0067] Calculate the total variance of the simulation system output. , The simulation result vector The mean, The second sample matrix The simulation result vector, The second sample matrix The The simulation result values ​​corresponding to each sample, where n is the second sample matrix. The total number of samples; According to the formula:

[0068] Calculate the first The overall sensitivity index of each experimental factor To obtain the first The influence coefficient of each experimental factor To use the fifth sample matrix The The simulation results are obtained by running the simulation on a sample.

[0069] It should be noted that the simulation system can be equipped with various models, such as prediction models, and this embodiment does not impose any restrictions on this.

[0070] In summary, by using Copula theory and correlation coefficient matrix, the experimental samples generated by this invention can accurately reproduce the true correlation between experimental factors, overcoming the shortcomings of traditional sampling that assumes factor independence.

[0071] By defining conditional constraints and performing targeted conditional mapping based on these constraints, this invention ensures that the final sample strictly satisfies complex if-then logic restrictions, thus guaranteeing the validity of the sample.

[0072] This invention innovatively uses interior-point nonlinear constraint optimization. When constructing column replacements for a specific sample matrix for the Sobol method, this method uses the target correlation as a strict constraint condition, ensuring that the correlation structure of the factors is not destroyed while meeting the Sobol calculation requirements, thus solving the problem that existing technologies cannot achieve both.

[0073] The samples of this invention simultaneously satisfy space-filling requirements, correlations between experimental factors, and conditional constraints between experimental factors, while maintaining correlation in the Sobol construction. Therefore, the Sobol total sensitivity index and normalized influence coefficient calculated by running the simulation system using the samples generated by this invention can more accurately and reliably reflect the true impact of each experimental factor on the system results, providing a solid foundation for identifying key factors.

[0074] like Figure 2 As shown, a computer system suitable for implementing the method for determining key influence factors based on a complex simulation system provided in the above embodiments includes a central processing module (CPU), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) or a program loaded from a storage portion into a random access memory (RAM). The RAM also stores various programs and data required for the operation of the computer system. The CPU, ROM, and RAM are connected via a bus. An input / output (I / O) interface is also connected to the bus.

[0075] The following components are connected to the I / O interface: input sections including keyboards, mice, etc.; output sections including liquid crystal displays (LCDs) and speakers, etc.; storage sections including hard disks, etc.; and communication sections including network interface cards such as LAN cards and modems. The communication sections perform communication processing via networks such as the Internet. Drives are also connected to the I / O interface as needed. Removable media, such as disks, optical disks, magneto-optical disks, semiconductor memories, etc., are installed on the drive as needed so that computer programs read from them can be installed into the storage section as required.

[0076] Specifically, according to this embodiment, the process described in the flowchart above can be implemented as a computer software program. For example, this embodiment includes a computer program product comprising a computer program tangibly embodied on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium.

[0077] The flowcharts and schematic diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of the system, method, and computer program product of this embodiment. In this regard, each block in the flowchart or schematic diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the schematic diagram and / or flowchart, and combinations of blocks in the schematic diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0078] This embodiment also provides a non-volatile computer storage medium. This non-volatile computer storage medium can be the non-volatile computer storage medium included in the above-described device, or it can be a separate non-volatile computer storage medium not installed in the terminal. The non-volatile computer storage medium stores one or more programs. When these programs are executed by a device, the device S10, in response to a factor analysis request instruction from the simulation system, acquires multiple experimental factors and condition constraint rules characterizing the logical limitations between the experimental factors, and constructs a correlation coefficient matrix characterizing the dependencies between the experimental factors. In this embodiment, the correlation coefficient matrix is ​​a mathematical tool used to quantify the interdependencies between multiple experimental factors in a complex simulation system, ensuring that the generated samples can realistically reproduce the coupling state of variables in the physical world in numerical space. S20. Generate an initial uniform sample set. Based on the correlation coefficient matrix, perform correlation feature mapping on the initial uniform sample set to obtain a first uniform sample set. S30. Split the first uniform sample set and reorganize it into a combined sample matrix for sensitivity analysis using interior point method with nonlinear constraints. The nonlinear constraint optimization includes: constructing an optimization objective function with target mean and target variance as metrics and constructing constraints including correlation error tolerance; solving the optimization objective function based on the constraints to obtain optimized column vectors; and combining the optimized column vectors to obtain the combined sample matrix. In this embodiment, nonlinear constraint optimization specifically refers to a mathematical programming process introduced to solve the structural tearing problem caused by traditional column permutation operations when reconstructing the combined sample matrix for sensitivity analysis, which seeks the optimal sample column vector under various statistical constraints. S40. Map the combined sample matrix to the actual value range of each experimental factor, and perform condition constraint processing on the mapped combined sample matrix based on condition constraint rules to obtain a second uniform sample set. In this embodiment, the condition constraint rules refer to the hard physical or logical boundary restrictions that the experimental factors must comply with in actual engineering applications, such as exclusivity or value range reduction under a specific combination of variables. S50. Input the second uniform sample set into the simulation system to obtain simulation results. Based on the second uniform sample set and the simulation results, calculate the influence coefficient of each experimental factor on the simulation results using sensitivity analysis.

[0079] In the description of this disclosure, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this disclosure and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this disclosure. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly, for example, they can be fixed connections, detachable connections, or integral connections; they can be mechanical connections or electrical connections; they can be direct connections or indirect connections through an intermediate medium; they can be internal connections between two elements. For those skilled in the art, the specific meaning of the above terms in this disclosure can be understood according to the specific circumstances.

[0080] It should also be noted that, in the description of this disclosure, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0081] Obviously, the above embodiments of this disclosure are merely examples for clearly illustrating this disclosure, and are not intended to limit the implementation of this disclosure. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all implementation methods here. Any obvious variations or modifications derived from the technical solutions of this disclosure are still within the protection scope of this disclosure.

Claims

1. A method for determining key influencing factors based on complex simulation systems, characterized in that, include: In response to the factor analysis request command from the simulation system, multiple experimental factors and condition constraint rules characterizing the logical restrictions between the experimental factors are obtained, and a correlation coefficient matrix characterizing the dependency relationship between the experimental factors is constructed. An initial uniform sample set is generated, and based on the correlation coefficient matrix, the initial uniform sample set is subjected to correlation feature mapping processing to obtain a first uniform sample set; The first uniform sample set is split and reorganized into a combined sample matrix for sensitivity analysis by nonlinear constraint optimization using the interior point method; wherein, the nonlinear constraint optimization includes constructing an optimization objective function with target mean and target variance as metrics and constructing constraints including correlation error tolerance; solving the optimization objective function based on the constraints to obtain an optimization column vector, and combining the optimization column vectors to obtain the combined sample matrix; The combined sample matrix is ​​mapped to the actual value range of each experimental factor, and the mapped combined sample matrix is ​​subjected to condition constraint processing based on the condition constraint rules to obtain the second uniform sample set. The second uniform sample set is input into the simulation system to obtain simulation results. Based on the second uniform sample set and the simulation results, the influence coefficient of each experimental factor on the simulation results is calculated by sensitivity analysis.

2. The method for determining key influencing factors based on complex simulation systems according to claim 1, characterized in that, Based on the second uniform sample set and the simulation results, after calculating the influence coefficient of each experimental factor on the simulation results using the sensitivity analysis method, the method further includes sorting the influence coefficients of each experimental factor in descending order to obtain the experimental factors corresponding to the first q influence coefficients, where q is an integer greater than 0.

3. The method for determining key influencing factors based on complex simulation systems according to claim 1, characterized in that, The generation of the initial uniform sample set includes: An initial uniform sample set is generated using the maximum-minimum distance Latin hypercube sampling algorithm; The step of performing correlation feature mapping processing on the initial uniform sample set based on the correlation coefficient matrix to obtain the first uniform sample set includes: The first uniform sample set is obtained by using the initial uniform sample set as input to the Gaussian Copula function.

4. The method for determining key influencing factors based on complex simulation systems according to claim 3, characterized in that, The generation of the initial uniform sample set using the maximum-minimum distance Latin hypercube sampling algorithm includes: For each experimental factor, generate a random permutation from 1 to 2n; According to the formula The value of the k-th sample in the standard Latin hypercube sampling uniform sample under the i-th test factor is obtained. To construct a standard uniform sample set; where, The total number of samples in the standard uniform sample set. It is the k-th value in the random permutation corresponding to the i-th experimental factor; In order to be in Random numbers drawn from a uniform distribution within an interval; For the standard uniform sample set, calculate the Euclidean distance between any two samples under all experimental factors, and extract the minimum distance to obtain the first distance. ; The following operation is performed iteratively until the current iteration number is greater than or equal to the first preset iteration threshold or the second distance. and first distance If the absolute value of the difference is less than the first preset convergence threshold, the standard uniform sample set of this iteration is output as the initial uniform sample set. Randomly adjust each standard uniform sample set A random number is generated to create a candidate sample set. The Euclidean distance between any two samples in the candidate sample set is calculated under all experimental factors, and the minimum distance is extracted to obtain the second distance. Calculate the second distance and first distance The difference; Determine the second distance Is it greater than the first distance? If the value is greater than 0, the candidate sample set is used to replace the standard uniform sample set; otherwise, the standard uniform sample set is retained.

5. The method for determining key influencing factors based on complex simulation systems according to claim 3, characterized in that, The construction of the correlation coefficient matrix characterizing the dependency relationship among the experimental factors includes: Obtain the historical sample set saved by the simulation system during the actual test process and use it as historical data; Based on the historical data, the correlation coefficients between the experimental factors are calculated using the Pearson correlation coefficient, and a correlation coefficient matrix R for each experimental factor is constructed. The step of using the initial uniform sample set as input to the Gaussian Copula function to obtain the first uniform sample set includes: Define the initial uniform sample set as ,in, The total number of samples in the initial uniform sample set. The total number of experimental factors. Let be the value of the k-th sample in the initial uniform sample set under the j-th experimental factor, where ; According to the formula The independent standard normal variable values ​​of the k-th sample in the initial uniform sample set under the j-th experimental factor were calculated. To construct an independent standard normal sample matrix ;in, This is the inverse cumulative distribution function of the standard normal distribution; According to the formula For independent standard normal sample matrix After transformation, we obtain the matrix of correlated normally distributed random variables. ,in It is the correlation coefficient matrix The Cholesky decomposition results; The matrix of correlated normally distributed random variables The first uniform sample set is obtained by transforming the standard normal distribution using the inverse cumulative distribution function.

6. The method for determining key influencing factors based on complex simulation systems according to claim 3, characterized in that, The step of splitting the first uniform sample set and recombining it into a combined sample matrix for sensitivity analysis by nonlinear constraint optimization using the interior point method includes: Construct a first sample matrix based on the first uniform sample set. , Let M be the value of the k-th sample in the j-th experimental factor within the first uniform sample set; M is the total number of experimental factors. This represents the total number of samples in the first sample matrix; The first sample matrix The former Rows as the second sample matrix ,the remaining Rows as the third sample matrix ; where the second sample matrix for Third Sample Matrix for Traverse the correlation coefficient matrix and select the set of factor indices that have a non-zero correlation with the c-th column and are not themselves. ; judge If the column is empty, extract the c-th column of the third sample matrix as the c-th column of the fourth sample matrix to obtain the optimized column vector that satisfies the statistical properties and correlation constraints. ; Otherwise, construct a nonlinear constrained optimization model, using the c-th column of the third sample matrix as the initial value, and solve for the optimal column vector that satisfies the statistical properties and correlation constraints. ; Obtain M optimized column vectors that satisfy statistical properties and correlation constraints. , As the fourth sample matrix Column c, all The fourth sample matrix is ​​obtained by combining and constructing. ; Build indivual The fifth sample matrix Among them, the fifth sample matrix The c-th column equals the fourth sample matrix The c-th column, and the remaining columns are respectively equal to the second sample matrix. The corresponding column; The second sample matrix Third sample matrix and The fifth sample matrix This combination yields a combined sample matrix used for sensitivity analysis of the input simulation system. ; The method uses the c-th column of the third sample matrix as the initial value to solve for the optimal column vector that satisfies the statistical properties and correlation constraints. include: Construct the optimization objective function: in, This represents the value of the objective function to be optimized. This represents the specific element value in the r-th row of the c-th column after optimization; This represents the weighting coefficient of the mean constraint in the optimization objective. This represents the weighting coefficient of the variance constraint in the optimization objective. To set a target mean, The target variance is preset; Construct correlation inequality constraints: in, express With the p-th column vector of the second sample matrix The actual correlation coefficient; The first in the target correlation coefficient matrix The value in row p; To preset the correlation error tolerance; Constructing variable boundary constraints: By incorporating correlation inequality constraints and variable boundary constraints into the objective function using a logarithmic barrier function, and then iteratively updating it using Newton's method. until the objective function is optimized. Once convergence is achieved or the preset number of iterations is reached, output the current optimized column vector. As the fourth sample matrix List.

7. The method for determining key influencing factors based on complex simulation systems according to claim 6, characterized in that, The process of mapping the combined sample matrix to the actual value range of each experimental factor includes: If the i-th experimental factor is a continuous factor, then obtain the actual value range of the i-th experimental factor. ,in, The minimum value within the actual range of values. This is the maximum value within the actual range of values; According to the formula After calculating the combined sample matrix mapping, the actual value of the k-th sample under the i-th experimental factor is obtained. To construct the second uniform sample set ;in The element value of the k-th sample under the ith experimental factor before the combined sample matrix is ​​mapped; If the i-th experimental factor is an unconstrained discrete factor, obtain the set of discrete values ​​for the i-th experimental factor. According to the formula The position index of the discrete value set is calculated. ,in, To round down, The element value of the i-th experimental factor under the k-th sample before the combined sample matrix mapping; m is the total number of the discrete value set; Then the actual value of the k-th sample under the i-th experimental factor after the combined sample matrix mapping. for 。 8. The method for determining key influencing factors based on complex simulation systems according to claim 7, characterized in that, The conditional constraint processing of the mapped combined sample matrix based on conditional constraint rules to obtain the second uniform sample set includes: If the i-th experimental factor is a conditionally constrained discrete factor, then the conditional constraint rules are parsed to obtain the preset trigger conditions and the constraint set. ; Traversing the second uniform sample set From all samples, filter out those that meet the preset trigger conditions; According to the formula Calculate the qualified set Position index in , For a limited set Total number of elements in the middle; The second uniform sample set The actual value of the k-th sample under the j-th experimental factor Updated to , for The Middle Each element.

9. The method for determining key influencing factors based on complex simulation systems according to claim 8, characterized in that, After inputting the second uniform sample set into the simulation system to obtain simulation results, the method further includes: The simulation result data is split according to the source of the corresponding sample matrix, and the simulation results corresponding to the mapped second sample matrix are obtained respectively. The simulation results corresponding to the mapped third sample matrix And the simulation results corresponding to each of the mapped fifth sample matrices. ;in, , The total number of experimental factors will be used to calculate the simulation results. Simulation results and various simulation results By combining them in sequence, we can construct the resulting column matrix Y, whose formula is as follows: 。 10. The method for determining key influencing factors based on complex simulation systems according to claim 9, characterized in that, The influence coefficients of each experimental factor on the simulation results, calculated using sensitivity analysis based on the second uniform sample set and the simulation results, include: According to the formula: Calculate the total variance of the simulation system output. , The simulation result vector The mean, The second sample matrix The simulation result vector, The second sample matrix The The simulation result values ​​corresponding to each sample, where n is the second sample matrix. The total number of samples; According to the formula: Calculate the first The overall sensitivity index of each experimental factor To obtain the first The influence coefficient of each experimental factor To use the fifth sample matrix The The simulation results are obtained by running the simulation on a sample.

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