Multivariable parameter optimization analysis method based on orthogonal test and proxy model

Abstract

The invention belongs to the technical field of electric data processing, and particularly relates to a multivariable parameter optimization analysis method based on an orthogonal test and an agent model, and the method comprises the steps: determining an initial training data set of a to-be-optimized aircraft wing; constructing two different types of agent models for establishing an approximate mapping relationship between the design variable and the fatigue crack life; utilizing a cross validation method to evaluate the prediction precision of the two proxy models on the fatigue crack life, and selecting a model with higher precision as a main optimization proxy model according to an evaluation result; carrying out global optimization by adopting a mixed strategy combining two optimization algorithms; and outputting the optimal design variable combination, and verifying the optimal design variable combination. According to the method, the required initial test or simulation frequency is remarkably reduced through the orthogonal test design, and meanwhile, the proxy model is used for replacing an original target function with high calculation cost, so that frequent calling of the original target function is avoided, and the overall optimization efficiency is greatly improved.

Description

Technical Field

[0001] This application belongs to the field of electrical data processing technology, and specifically relates to a multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model. Background Technology

[0002] In many engineering fields, such as engineering design, materials research and development, and process optimization, there is a common need to synergistically optimize multiple influencing factors (i.e., variables) in order to obtain the best performance indicators. Traditional parameter optimization methods, such as full factorial testing or experience-based trial-and-error methods, usually require a large number of experiments, resulting in high optimization costs and long cycles, which are difficult to meet the urgent efficiency requirements of modern engineering practice.

[0003] To reduce the number of trials, orthogonal experimental design is widely used as an efficient experimental design method. It can comprehensively cover multiple levels of design variables with a fewer number of trials, thus effectively analyzing the main effects of each variable. However, orthogonal experimental design itself is primarily a sample point arrangement strategy and lacks the ability to predict unexperimented points, and it is also difficult to accurately characterize complex nonlinear response relationships. Furthermore, when the objective function upon which optimization depends (such as high-fidelity simulation calculations) is computationally expensive, even with a reduced number of trials, direct iterative optimization remains inefficient.

[0004] Surrogate models offer a solution to computationally expensive problems. This technique constructs an approximate mathematical model of the objective function based on finite sample data, replacing the costly original computational process and significantly reducing computational overhead in the optimization process. Among various surrogate models, polynomial response surface models are widely used due to their simplicity and clear physical meaning; Kriging models, as a spatial interpolation method, exhibit higher accuracy when fitting response surfaces with local fluctuations and nonlinear characteristics. However, single surrogate models have limitations in adaptability: polynomial response surface models often struggle to accurately capture higher-order nonlinear relationships; and Kriging models may suffer from overfitting or extrapolation instability in regions with sparse sample points.

[0005] After obtaining the surrogate model, the choice of optimization algorithm is equally crucial. Traditional gradient-based optimization algorithms are prone to getting trapped in local optima. While intelligent optimization algorithms such as genetic algorithms and particle swarm optimization have stronger global search capabilities, they also have their shortcomings, such as slower convergence speed or insufficient optimization accuracy in the later stages.

[0006] In summary, existing technologies often use experimental design methods, surrogate modeling techniques, and optimization algorithms independently or in simple series, lacking a comprehensive analytical approach that systematically integrates efficient experimental design, complementary construction of multiple surrogate models, and hybrid intelligent optimization strategies. This fragmentation makes it difficult to simultaneously achieve high efficiency, high accuracy, and strong robustness when facing complex multivariate parameter optimization problems. Therefore, there is an urgent need in this field for a generalized parameter optimization analysis framework that can integrate these advantages. Summary of the Invention

[0007] To address the aforementioned problems, this application provides a multivariate parameter optimization analysis method based on orthogonal experiments and surrogate models, including:

[0008] Step 1: Determine multiple design variables and their value ranges for the aircraft wing to be optimized. Generate a set of sample points covering the value ranges of the design variables based on the orthogonal experimental design method, and obtain the wing fatigue crack life value corresponding to each sample point to form an initial training dataset.

[0009] Step 2: Based on the initial training dataset, construct two different types of surrogate models in parallel to establish an approximate mapping relationship between design variables and fatigue crack life;

[0010] Step 3: Use cross-validation to evaluate the prediction accuracy of the two surrogate models constructed in Step 2 for fatigue crack life, and select the model with higher accuracy as the main optimization surrogate model based on the evaluation results.

[0011] Step 4: With maximizing fatigue crack life as the optimization objective, the main optimization surrogate model selected in Step 3 is used as the alternative prediction model for this optimization objective. A hybrid strategy combining two optimization algorithms is adopted to perform global optimization and obtain the optimal combination of design variables.

[0012] Step 5: Output the optimal combination of design variables obtained in Step 4, and verify the optimal combination of design variables through actual experiments or high-precision simulations.

[0013] Preferably, the design variables include geometric parameters and material property parameters.

[0014] Preferably, the wing fatigue crack life value corresponding to each sample point is obtained through finite element analysis or fatigue testing.

[0015] Preferably, the two surrogate models include the polynomial response surface model and the Kriging model.

[0016] Preferably, the geometric parameters include, but are not limited to, relative airfoil thickness, chord length, sweep angle, aspect ratio, and root-to-tip ratio; the material property parameters include, but are not limited to, elastic modulus, Poisson's ratio, material density, and fatigue strength coefficient.

[0017] Preferably, a hybrid strategy combining particle swarm optimization and genetic algorithm is used for global optimization.

[0018] Preferably, the specific steps for global optimization using a hybrid strategy combining particle swarm optimization and genetic algorithms are as follows:

[0019] First, run the particle swarm optimization algorithm to quickly explore the global environment and obtain a high-quality combination of design variables;

[0020] The optimal combination of design variables obtained by the particle swarm optimization algorithm is used as the initial combination of design variables for the genetic algorithm. The genetic algorithm is then started to perform a subsequent global search to obtain the optimal combination of design variables.

[0021] Preferably, if the verification result in step 5 does not meet the expected life target, the design variable combination and fatigue crack life value in the verification are added to the initial training dataset, the surrogate model is updated, and steps 2 to 5 are repeated until the verification result meets the expected life target.

[0022] This application offers the following significant advantages: Orthogonal experimental design significantly reduces the number of initial experiments or simulations required; surrogate models replace the computationally expensive original objective function, avoiding frequent calls to it and thus greatly improving overall optimization efficiency. The use of a dual surrogate model, combining a multinomial response surface methodology and a Kriging model, effectively captures both the global trend of the response and finely fits local nonlinear characteristics, significantly improving the prediction accuracy of the response surface. The optimization phase employs a hybrid strategy combining particle swarm optimization and genetic algorithms, balancing the advantages of global exploration and local search, effectively avoiding premature convergence and increasing the probability of finding the global optimum. This method is independent of specific physical systems or simulation programs; its framework is applicable to various multivariate parameter optimization scenarios such as structural design, process parameter control, and formulation optimization, demonstrating strong universality. Orthogonal experimental design facilitates the analysis of the main effects of each design variable and the interactions between variables, enhancing the understandability and engineering insight of the entire optimization process. Attached Figure Description

[0023] Figure 1 This is a flowchart of the multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model in this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0025] To address the aforementioned problems, this application provides a multivariate parameter optimization analysis method based on orthogonal experiments and surrogate models, such as... Figure 1 As shown: including:

[0026] Step 1: Determine multiple design variables and their value ranges for the aircraft wing to be optimized. Generate a sample point set covering the value ranges of the design variables using orthogonal experimental design, and obtain the wing fatigue crack life value corresponding to each sample point to form an initial training dataset. The design variables include geometric parameters and material property parameters. In some optional embodiments, the geometric parameters include, but are not limited to, relative airfoil thickness, chord length, sweep angle, aspect ratio, and root-to-tip ratio; the material property parameters include, but are not limited to, elastic modulus, Poisson's ratio, material density, and fatigue strength coefficient.

[0027] This embodiment selects five key design variables: airfoil relative thickness x1, ranging from 12% to 18%; aspect ratio x2, ranging from 8 to 12; quarter-chord sweep angle x3, ranging from 25° to 35°; elastic modulus of the aluminum alloy used x4, ranging from 68 to 72 GPa; and fatigue strength coefficient x5, ranging from 800 to 1200 MPa. An orthogonal array is used to arrange the experiment, generating 25 sets of parameter combinations. Parametric finite element analysis software is then used to simulate fatigue crack initiation life, obtaining the fatigue crack life value y (unit: flight hours) corresponding to each set of design variables, forming an initial training dataset. In some optional embodiments, the wing fatigue crack life value corresponding to each sample point is obtained through finite element analysis or fatigue testing.

[0028] Step 2: Based on the initial training dataset, construct two different types of surrogate models in parallel to establish an approximate mapping relationship between design variables and fatigue crack life;

[0029] In some alternative implementations, the two proxy models include a polynomial response surface model and a Kriging model.

[0030] Polynomial response surface model: A second-order complete polynomial containing constant, linear, quadratic, and cross terms is used for fitting. The model form is as follows:

[0031] ;

[0032] The polynomial response surface model is used to predict the fatigue crack life of the design variable x.

[0033] This represents the constant term in the polynomial model. For the i-th design variable x i The coefficients of the first-order terms in a first-order correlation; Represents the cross term coefficient related to the product of the i-th and j-th design variables; The coefficient of the quadratic term related to the square of the i-th design variable is represented by k; k is the total number of design variables, and x represents the coefficient of the quadratic term related to the square of the i-th design variable. i For the i-th design variable, x j Let j be the j-th design variable.

[0034] Step 3: Use cross-validation to evaluate the prediction accuracy of the two surrogate models constructed in Step 2 for fatigue crack life, and select the model with higher accuracy as the main optimization surrogate model based on the evaluation results.

[0035] Step 4: With maximizing fatigue crack life as the optimization objective, the main optimization surrogate model selected in Step 3 is used as the alternative prediction model for this optimization objective, and a hybrid strategy combining two optimization algorithms is adopted for global optimization.

[0036] A hybrid strategy combining particle swarm optimization and genetic algorithms is adopted:

[0037] Particle Swarm Optimization (PSO) Phase: The PSO population size is set to 50, and the algorithm iterates for 100 generations. The algorithm quickly searches the variable space and converges to a batch of relatively optimal solutions (designing high-quality combinations of variables).

[0038] Genetic Algorithm Stage: The top 30% of elite individuals (high-quality combinations of design variables) obtained in the particle swarm optimization stage are directly used as the initial combination of design variables for the genetic algorithm. Starting from this initial combination of design variables, the genetic algorithm continues to run for 200 generations of optimization, using its selection, crossover, and mutation operations to perform more refined local development and global exploration, avoiding premature convergence, and finally finding the optimal combination of design variables, i.e., the globally optimal solution or a near-optimal solution combination.

[0039] Step 5: Output the optimal design variable combination obtained in Step 4, and verify the optimal design variable combination through actual experiments or high-precision simulations. Specifically, perform high-precision, high-fidelity finite element fatigue analysis on the optimal design variable combination, and compare the verified actual life with the model prediction value. If the expected life target is achieved and the error with the prediction value is within an acceptable range (e.g., <5%), the optimization is considered successful, and the process ends. If the target is not achieved or the error is too large, add new sample points to the initial training dataset, return to Step 2, rebuild and verify the surrogate model, and then perform a new round of optimization and verification.

[0040] This application offers the following significant advantages: Orthogonal experimental design significantly reduces the number of initial experiments or simulations required; surrogate models replace the computationally expensive original objective function, avoiding frequent calls to it and thus greatly improving overall optimization efficiency. The use of a dual surrogate model, combining a multinomial response surface methodology and a Kriging model, effectively captures both the global trend of the response and finely fits local nonlinear characteristics, significantly improving the prediction accuracy of the response surface. The optimization phase employs a hybrid strategy combining particle swarm optimization and genetic algorithms, balancing the advantages of global exploration and local search, effectively avoiding premature convergence and increasing the probability of finding the global optimum. This method is independent of specific physical systems or simulation programs; its framework is applicable to various multivariate parameter optimization scenarios such as structural design, process parameter control, and formulation optimization, demonstrating strong universality. Orthogonal experimental design facilitates the analysis of the main effects of each design variable and the interactions between variables, enhancing the understandability and engineering insight of the entire optimization process.

[0041] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model, characterized in that, include: Step 1: Determine multiple design variables and their value ranges for the aircraft wing to be optimized. Generate a set of sample points covering the value ranges of the design variables based on the orthogonal experimental design method, and obtain the wing fatigue crack life value corresponding to each sample point to form an initial training dataset. Step 2: Based on the initial training dataset, construct two different types of surrogate models in parallel to establish an approximate mapping relationship between design variables and fatigue crack life; Step 3: Use cross-validation to evaluate the prediction accuracy of the two surrogate models constructed in Step 2 for fatigue crack life, and select the model with higher accuracy as the main optimization surrogate model based on the evaluation results. Step 4: With maximizing fatigue crack life as the optimization objective, the main optimization surrogate model selected in Step 3 is used as the alternative prediction model for this optimization objective. A hybrid strategy combining two optimization algorithms is adopted to perform global optimization and obtain the optimal combination of design variables. Step 5: Output the optimal combination of design variables obtained in Step 4, and verify the optimal combination of design variables through actual experiments or simulations.

2. The multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model as described in claim 1, characterized in that, The design variables include geometric parameters and material property parameters.

3. The multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model as described in claim 1, characterized in that, The fatigue crack life value of the wing corresponding to each sample point is obtained through finite element analysis or fatigue testing.

4. The multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model as described in claim 1, characterized in that, Two proxy models include the polynomial response surface model and the Kriging model.

5. The multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model as described in claim 2, characterized in that, The geometric parameters include, but are not limited to, relative airfoil thickness, chord length, sweep angle, aspect ratio, and root-to-tip ratio; the material property parameters include, but are not limited to, elastic modulus, Poisson's ratio, material density, and fatigue strength coefficient.

6. The multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model as described in claim 1, characterized in that, A hybrid strategy combining particle swarm optimization and genetic algorithm is adopted for global optimization.

7. The multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model as described in claim 6, characterized in that, The specific steps for global optimization using a hybrid strategy combining particle swarm optimization and genetic algorithm are as follows: First, run the particle swarm optimization algorithm to quickly explore the global environment and obtain a high-quality combination of design variables; The optimal combination of design variables obtained by the particle swarm optimization algorithm is used as the initial combination of design variables for the genetic algorithm. The genetic algorithm is then started to perform a subsequent global search to obtain the optimal combination of design variables.

8. The multivariate parameter optimization analysis method based on orthogonal experiment and surrogate model as described in claim 1, characterized in that, If the verification result in step 5 does not meet the expected life target, the design variable combination and fatigue crack life value in the verification are added to the initial training dataset, the surrogate model is updated, and steps 2 to 5 are repeated until the verification result meets the expected life target.

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