A high-dimensional feature selection method and system for CAE simulation

Abstract

The application relates to a high-dimensional feature selection method and system for CAE simulation, and belongs to the technical field of CAE simulation. The method solves the problems of low calculation efficiency and difficulty in balancing precision and complexity in the prior art high-dimensional feature selection. The method comprises the following steps: obtaining an original sample set of a CAE simulation task; constructing a target function according to a prediction error and the number of selected parameter features; iteratively optimizing an initialized mask vector; in each iteration, a neighborhood search strategy is adopted to generate a candidate mask vector from the current mask vector, a sample subset is extracted from the original sample set to train a corresponding proxy model, and then the current optimal candidate mask vector is obtained by calculating the target function value; the global optimal mask vector is updated and used for the next iteration; when a preset convergence condition is met, the iteration optimization is terminated, and the global optimal mask vector is output; and the feature subset corresponding to the global optimal mask vector is the selected CAE simulation key parameter feature. Efficient and accurate selection of key features is realized.

Description

Technical Field

[0001] This invention relates to the field of CAE simulation technology, and in particular to a high-dimensional feature selection method and system for CAE simulation. Background Technology

[0002] In the field of computer-aided engineering (CAE) simulation-driven design and optimization, as the complexity of engineering systems continues to increase, the input feature dimensions of simulation models, such as design parameters, material properties, and boundary conditions, often reach hundreds or even thousands of dimensions. Selecting the key parameters that have the greatest impact on target performance from this high-dimensional feature space is of great significance for building efficient surrogate models and guiding subsequent optimization design.

[0003] Existing feature selection methods, such as filtering, wrapping, and embedding methods, face significant limitations when processing such high-dimensional data: Filtering methods (such as chi-square test, mutual information, correlation coefficient) rely solely on statistical indicators to assess the correlation between a single feature and the response, completely ignoring the interaction effects between features and the association between feature subsets and the subsequent modeling process. This can easily lead to the selection of statistically relevant feature combinations that have poor joint modeling performance. While wrapper methods (such as combinations of genetic algorithms, particle swarm optimization, support vector machines, and neural networks) can consider the interaction between features and models through iterative search, their search strategies are mostly global random sampling, requiring the evaluation of a large number of feature combinations to converge, resulting in high computational costs and a tendency to get trapped in local optima.

[0004] Embedded methods (such as Lasso regularization and random forest importance scoring) embed feature selection into the model training process. While they have a certain computational efficiency, their selection logic depends on the assumptions of a specific model and they can usually only handle linear relationships or specific types of nonlinearity. They lack the ability to model strong nonlinearity and multimodal responses commonly found in CAE simulations.

[0005] Furthermore, existing methods often focus on a single objective, making it difficult to balance the relationship between prediction error and model complexity. This is especially true in small-sample, high-dimensional nonlinear problems in CAE simulations, which can easily lead to overfitting or decreased generalization ability. At the same time, existing methods cannot provide quantitative estimates of the uncertainty of prediction results, which constitutes a significant application bottleneck in high-risk decision-making scenarios such as aerospace and energy equipment. Summary of the Invention

[0006] Based on the above analysis, the embodiments of the present invention aim to provide a high-dimensional feature selection method and system for CAE simulation, in order to solve the problems of difficulty in balancing accuracy and complexity and low computational efficiency in high-dimensional feature selection in existing CAE simulations.

[0007] On one hand, embodiments of the present invention provide a high-dimensional feature selection method for CAE simulation, comprising the following steps: Obtain the original sample set of the CAE simulation task, where each sample includes multiple parameter features and the corresponding simulation response value; An objective function is constructed based on the prediction error and the number of selected parameter features. The prediction error is calculated based on the simulation response value and the predicted value output by the surrogate model. Based on the original sample set and the objective function, the initialized mask vector is iteratively optimized. Each iteration includes: generating multiple candidate mask vectors using a neighborhood search strategy for the current mask vector; selecting parameter features based on each candidate mask vector; extracting a subset of samples from the original sample set; training the corresponding surrogate model; obtaining the current optimal candidate mask vector by calculating the objective function value; and updating the globally optimal mask vector for use in the next iteration. When the preset convergence condition is met, the iterative optimization is terminated and the globally optimal mask vector is output. The corresponding feature subset is the selected CAE simulation key parameter feature.

[0008] Based on the above method, a further improvement is made, and the objective function is constructed according to the prediction error and the number of selected parameter features, using the following formula: , in, Representation based on mask vector The objective function; Represents the mask vector It is A binary vector of dimension 1 This indicates the number of selected parameter features, i.e., the number of non-zero elements in the mask vector; Representation based on mask vector The prediction error calculated by the corresponding surrogate model; This represents the regularization coefficient.

[0009] Based on the further improvement of the above method, the neighborhood search strategy includes: an addition operation and a deletion operation; wherein, the addition operation is used to set the mask value of the position corresponding to a currently unselected parameter feature from 0 to 1 based on the current mask vector, so as to generate a candidate mask vector; the deletion operation is used to set the mask value of the position corresponding to a currently selected parameter feature from 1 to 0 based on the current mask vector, so as to generate a candidate mask vector.

[0010] Based on the further improvement of the above method, the globally optimal mask vector is the mask vector that minimizes the objective function value found up to the current iteration. Each iteration also includes: identifying whether the relative improvement of the objective function value corresponding to the globally optimal mask vector in multiple consecutive iterations is less than a preset improvement ratio threshold. If it is less, the forward search strategy is used in the current iteration to expand the neighborhood search space of the current mask vector to generate candidate mask vectors. Otherwise, the next iteration is executed and the neighborhood search strategy is used to continue generating candidate mask vectors.

[0011] A further improvement to the above method is to expand the neighborhood search space of the current mask vector by adopting a forward search strategy. This involves changing the mask values ​​of the two parameter feature positions on the basis of the current mask vector.

[0012] Based on the above method, after expanding the neighborhood search space using a forward search mechanism in one iteration, the neighborhood search strategy is resumed to generate candidate mask vectors in the next iteration.

[0013] Based on the further improvement of the above method, the surrogate model is a Gaussian process surrogate model; the training set and validation set are obtained according to the sample subset; the corresponding surrogate model is trained by optimizing the kernel function hyperparameter of the Gaussian process by maximizing the marginal likelihood function based on the training set, so as to obtain the Gaussian process surrogate model corresponding to the candidate mask vector.

[0014] Based on a further improvement to the above method, the prediction error is calculated based on the simulation response value and the predicted value output by the surrogate model, including: Based on the trained surrogate model, the posterior prediction distribution of each sample in the validation set is calculated, and the mean of the distribution is used as the predicted value of that sample. The mean squared error is calculated as the prediction error based on the predicted value of each sample in the validation set and its corresponding simulation response value.

[0015] Further improvements to the above method involve simultaneously changing the mask values ​​at the feature positions of both parameters, including: Set the mask value of the corresponding positions of two currently unselected parameter features from 0 to 1, or set the mask value of the corresponding positions of two currently selected parameter features from 1 to 0, or set the mask value of the corresponding position of one currently unselected parameter feature from 0 to 1 and set the mask value of the corresponding position of one currently selected parameter feature from 1 to 0.

[0016] On the other hand, embodiments of the present invention provide a high-dimensional feature selection system for CAE simulation, comprising: The data acquisition module is used to acquire the original sample set of the CAE simulation task, where each sample includes multiple parameter features and the corresponding simulation response value; The feature selection module is used to construct an objective function based on the prediction error and the number of selected parameter features. The prediction error is calculated based on the simulation response value and the predicted value output by the surrogate model. Based on the original sample set and the objective function, the initialized mask vector is iteratively optimized. Each iteration includes: generating multiple candidate mask vectors using a neighborhood search strategy for the current mask vector; selecting parameter features based on each candidate mask vector; extracting a sample subset from the original sample set; training the corresponding surrogate model; obtaining the current optimal candidate mask vector by calculating the objective function value; and updating the globally optimal mask vector for use in the next iteration. The feature output module is used to terminate iterative optimization and output the globally optimal mask vector when the preset convergence condition is met. The corresponding feature subset is the selected CAE simulation key parameter feature.

[0017] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. By constructing an objective function that balances prediction error and feature quantity, and adopting an iterative optimization strategy based on neighborhood search, the key parameter features that have the most significant impact on simulation response are automatically selected while ensuring model accuracy. This significantly reduces the feature dimension and effectively improves the construction efficiency and interpretability of subsequent proxy models, providing more concise and reliable design variables for CAE simulation-driven design.

[0018] 2. Improve the neighborhood search strategy (add add and delete operations) and introduce a forward search mechanism to achieve a clever balance between local search and global exploration; by continuously monitoring the relative improvement of the objective function value corresponding to the global optimal mask vector, when trapped in a local optimum, the search space is adaptively expanded to simultaneously change the states of two features, effectively avoiding premature convergence and improving the global optimization capability.

[0019] 3. Improved CAE simulation modeling process. By intelligently filtering key design parameters, the input dimensions of the simulation model are significantly reduced, the complexity of high-fidelity simulation calculation is reduced, the prediction accuracy and reliability of the simulation model are improved, unnecessary computing resource consumption is reduced, and engineering design iteration is accelerated. It is applicable to CAE simulation optimization problems in aerospace, automotive engineering, energy equipment and other fields.

[0020] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0021] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a flowchart of a high-dimensional feature selection method for CAE simulation in Embodiment 1 of the present invention. Detailed Implementation

[0022] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0023] Example 1 A specific embodiment of the present invention discloses a high-dimensional feature selection method for CAE simulation, such as... Figure 1 As shown, it includes steps S1-S3.

[0024] S1. Obtain the original sample set of the CAE simulation task, where each sample includes multiple parameter features and corresponding simulation response values.

[0025] It should be noted that the CAE simulation task in step S1 is carried out for the target engineering system, such as aerodynamic characteristic analysis in the aerospace field, structural optimization in automotive engineering, performance prediction of energy equipment, and parameter inversion in material design. Parametric simulation is performed by CAE simulation software, and the parameter feature dimensions often reach hundreds or even thousands of dimensions.

[0026] Specifically, methods such as Latin Hypercube Sampling (LHS) are used to generate multiple sampling points in a high-dimensional parametric feature space, with each sampling point corresponding to a specific combination of high-dimensional parametric features. For each sampling point, a CAE simulation solver is run to calculate its corresponding simulation response value.

[0027] The parameter characteristics in CAE simulation include at least one of the following: geometric dimension parameters, material property parameters, load condition parameters, or boundary condition parameters; the simulation response values ​​include at least one of the following: structural mass properties, mechanical response, thermal response, fluid dynamics response, or multidisciplinary coupled response.

[0028] Taking the aerodynamic shape optimization design of aero-engine turbine blades as an example, the high-dimensional parameters that need to be considered in the aerodynamic performance simulation include: geometric parameters, material property parameters, and boundary condition parameters. Geometric parameters include: blade leading edge radius (mm), maximum blade thickness (mm), blade installation angle (degrees), airfoil chord length (mm), and trailing edge radius (mm); material property parameters include: material density (kg / m³) and elastic modulus (GPa); boundary condition parameters include: inlet total pressure (Pa) and inlet total temperature (K). The simulation response value is the total pressure loss coefficient of the turbine blade; the smaller this coefficient, the better the aerodynamic performance of the blade.

[0029] The high-dimensional parameter features of each sampling point and the corresponding simulation response value are used as a sample to form the original sample set. ,in, Indicates the first The parameter feature vector of each sample contains all The values ​​of each parameter feature, i.e. This represents the total number of parametric features; express The corresponding simulation response value; This indicates the total number of samples.

[0030] S2. Construct an objective function based on the prediction error and the number of selected parameter features. The prediction error is calculated based on the simulation response value and the predicted value output by the surrogate model. Based on the original sample set and the objective function, iteratively optimize the initialized mask vector. Each iteration includes: generating multiple candidate mask vectors using a neighborhood search strategy for the current mask vector; selecting parameter features based on each candidate mask vector; extracting a subset of samples from the original sample set; training the corresponding surrogate model; obtaining the current optimal candidate mask vector by calculating the objective function value; and updating the globally optimal mask vector for use in the next iteration.

[0031] It should be noted that this embodiment utilizes a mask vector. to indicate The selection state of each parameter feature, mask vector It is A binary vector of dimension, where, Represents the nth element in the mask vector The mask value at position 1 means that position 1 is selected. Individual parameter features; Represents the nth element in the mask vector The mask value at position i is 0, meaning the position i is removed. Features of each parameter.

[0032] To ensure prediction accuracy while selecting a concise subset of parameters and features, thus achieving a balance between accuracy and simplicity, the multi-objective feature selection problem is transformed into an operational optimization framework.

[0033] Optionally, this multi-objective feature selection problem can be transformed into a constrained optimization problem: ensuring the number of features does not exceed a preset upper limit. Under the given conditions, the constrained optimization problem of minimizing the prediction error is expressed as follows: , in, Representation based on mask vector The prediction error calculated by the corresponding surrogate model is used to represent the accuracy of the prediction; It is done by calculating the mask vector The L0 norm is used to obtain the number of non-zero elements in the mask vector, which is used to represent the number of selected parameter features.

[0034] The value of is set based on the computing resource capacity or prior knowledge of the domain. For example, it can be set between 15 and 30 features. Then, under the constraint that the number of selected parameter features does not exceed this upper limit, a search is performed to minimize the prediction error. The smallest feature subset.

[0035] Optionally, a regularization method is used to fuse the prediction accuracy and the number of selected parameter features into a comprehensive objective, and the constructed objective function is shown below: , in, Representation based on mask vector The objective function; represents the regularization coefficient, a non-negative real number used to balance the trade-off between prediction accuracy and feature simplicity. When When the value is large (e.g.) The penalty for the number of features is increased in the objective function, and the iterative optimization process will tend to choose a simpler model with fewer features, even if this may sacrifice some prediction accuracy; when When the value is small (e.g.) With the penalty weight for the number of features reduced, the iterative optimization process will focus more on improving prediction accuracy, allowing for the selection of more parameter features.

[0036] It should be noted that, The value is determined through cross-validation on independent validation sets. For example, try... Multiple candidate values, such as 0.001, 0.005, 0.01, 0.05, and 0.1, were selected, and the feature selection algorithm was run for each value. The performance of the final model was then evaluated, and the model with the best generalization ability was chosen. value.

[0037] It should be noted that, depending on the actual application requirements, either the constraint optimization form or the regularization form can be selected. Alternatively, both methods can be provided simultaneously, and the optimal feature subset can be chosen by comparing the results. This implementation method ensures both mathematical rigor and flexibility and operability in engineering practice.

[0038] Compared with existing technologies, this embodiment searches for a mask vector in binary space that minimizes the objective function. This direct optimization of the number of selected parameter features makes it easier to obtain a sparser and more interpretable subset of features.

[0039] Before starting iterative optimization, first initialize a mask vector. As the starting point for the search, the initialization strategy employs empty set initialization, random initialization, or specified initialization. Empty set initialization sets all mask values ​​in the mask vector to 0, indicating that no parametric features are initially selected. Random initialization randomly selects a small number of parametric features (e.g., 3-5 random parametric features) and sets the mask values ​​at their corresponding positions to 1, while setting the rest to 0, resulting in an initial mask vector containing a small number of non-zero bits. Specified initialization is based on prior knowledge, specifying certain features that have a significant impact on the simulation response value, setting the mask values ​​at their corresponding positions to 1, and setting the rest to 0.

[0040] Furthermore, parameters such as the maximum number of iterations and the convergence threshold are set; the initialized mask vector is the current mask vector in the first iteration.

[0041] In each iteration In the process, the following steps are performed based on the current mask vector: ① Use a neighborhood search strategy to generate multiple candidate mask vectors for the current mask vector.

[0042] It should be noted that the neighborhood search strategy includes two neighborhood search operators: an addition operation and a deletion operation. The addition operation is used to set the mask value of the position corresponding to a currently unselected parameter feature from 0 to 1 based on the current mask vector, generating multiple candidate mask vectors. The deletion operation is used to set the mask value of the position corresponding to a currently selected parameter feature from 1 to 0 based on the current mask vector, generating multiple candidate mask vectors.

[0043] Based on the current mask vector The following formulas represent the addition operations respectively. and delete operations Generated candidate mask vector : , .

[0044] For example, if the currently unselected features include leading edge radius, maximum thickness, mounting angle, etc., then the mask value of the position corresponding to each unselected feature is changed from 0 to 1 in turn to generate multiple candidate vectors obtained through the addition operation; the mask value of the position corresponding to each selected feature is changed from 1 to 0 in turn to generate multiple candidate vectors obtained through the deletion operation.

[0045] For the current mask vector The candidate mask vectors generated by the two operations described above together constitute the neighborhood candidate set in each iteration. .

[0046] The neighborhood search strategy in this embodiment can improve accuracy by adding features and eliminating redundant features by deleting them. It effectively controls computational complexity while ensuring the quality of the solution, making it particularly suitable for handling high-dimensional feature selection problems.

[0047] Preferably, to control computational cost while ensuring solution quality, the neighborhood search strategy does not need to evaluate all possible candidate mask vectors generated by addition and deletion operations in each iteration. Specifically, based on pre-computed feature importance scores (such as mutual information, Pearson correlation coefficient, etc.), each iteration only evaluates the mask vectors with the highest importance. The unselected features are evaluated by performing an addition operation, and the least important features are evaluated. The selected features are evaluated for deletion, among which... The preset search width parameter is selected, ranging from 5 to 50 depending on computational resources. This heuristic sampling strategy reduces the computational complexity of a single iteration while maintaining search effectiveness. Reduce to This significantly improves the practicality of the method in this embodiment in high-dimensional scenarios.

[0048] In addition, during the iteration process, the improvement of the objective function value after each parameter feature is added or removed is recorded. For parameter features that frequently bring improvements in historical iterations, their evaluation weight is increased in subsequent iterations; for features that have not brought improvements for a long time, their evaluation priority is reduced, thereby focusing computational resources on more promising search directions.

[0049] ② After selecting parameter features based on each candidate mask vector, extract a subset of samples from the original sample set and train the corresponding surrogate model.

[0050] First, based on the positions in the candidate mask vector where the mask value is 1, the corresponding parameter feature values ​​are extracted from the original sample set to form a dimensionality-reduced sample subset.

[0051] Specifically, for each sample in the original sample set Feature subset selected based on candidate mask vector Extract sub-feature vectors The resulting sample subset is .

[0052] Then, the training set is obtained based on the sample subset. (The number of training samples is) ) and validation set (The number of validation samples is) The training set is used to train the proxy model, and the validation set is used to evaluate the prediction error of the proxy model.

[0053] It should be noted that this embodiment does not limit the method of obtaining the training set and validation set. The training set and validation set can be obtained by randomly dividing the sample subsets according to the ratio of 80%:20%, or the sample subsets can be subjected to k-fold cross-validation, that is, the sample subsets are divided into k parts, one part is used as the validation set and the remaining k-1 parts are used as the training set.

[0054] Furthermore, the surrogate model in this embodiment is a Gaussian process surrogate model. As a powerful nonparametric Bayesian model, the Gaussian process is particularly suitable for modeling small samples and high-dimensional data. It is entirely defined by the mean function and covariance function (kernel function), and can also obtain the posterior variance of the prediction results, i.e., a quantitative estimate of uncertainty. This characteristic allows for the simultaneous determination of the confidence level of the prediction results when using selected key parameter features for performance prediction. This provides important risk assessment basis for high-risk engineering decisions such as aero-engine blade design, overcoming the deficiency of traditional feature selection methods that can only output point predictions and cannot quantify uncertainty.

[0055] For feature subsets Given a defined input space, establish the following Gaussian process surrogate model. : , in, This represents the mean function, usually set as a constant function, which takes the average of the response values ​​in the training set. The covariance function (also known as the kernel function) is used to describe the training samples. and Similarity between (different input points).

[0056] In this embodiment, the kernel function is a radial basis function. The process of training the surrogate model is to optimize the hyperparameters of the kernel function (signal variance, length scale parameters of each feature, and noise variance) by maximizing the marginal likelihood function. This optimization process is usually implemented using gradient-based optimization algorithms (such as the conjugate gradient method or the quasi-Newton method).

[0057] ③ Obtain the optimal candidate mask vector for the current iteration by calculating the objective function value.

[0058] After the Gaussian process surrogate model is trained, the posterior prediction distribution of each sample in the validation set is first calculated, as shown in the following expression: , in, Represents the samples in the validation set The potential function value; Represents the latent function value The posterior mean; Represents the latent function value The posterior variance is used as an estimate of the uncertainty of the prediction; the larger the value, the lower the reliability of the prediction.

[0059] It should be noted that the posterior mean and posterior variance The results are calculated using the following formulas: , , in, It is The training set kernel matrix, whose elements are composed of Composition, representing the kernel matrix between training samples; It is The vector represents the covariance vector between the validation sample and all training samples; A vector representing the simulated response values ​​of the training samples; Noise variance represents the random error in the observed data, which is automatically determined during training by maximizing the marginal likelihood function; It is The identity matrix is ​​used to ensure the positive definiteness and numerical stability of the matrix; This indicates the calculation of the inverse matrix. This indicates the matrix transpose.

[0060] Furthermore, the mean of the posterior prediction distribution for each sample is used as the predicted value for that sample; based on the predicted value of each sample in the validation set and its corresponding simulated response value, the mean squared error is calculated as a candidate mask vector. Corresponding prediction error The formula is shown below: , in, This indicates the number of samples in the validation set. Indicates the first in the verification set The predicted value for each sample, Indicates the first in the verification set The true simulated response value of each sample.

[0061] Furthermore, the candidate mask vector is calculated using the following formula. The corresponding objective function value: .

[0062] Finally, for the neighborhood candidate set After evaluating all candidate mask vectors, the candidate mask vector that minimizes the objective function value is selected as the optimal candidate mask vector for the current iteration. The formula is expressed as follows: .

[0063] ④ Compare the current best candidate mask vector with the global best mask vector, and update the global best mask vector for use in the next iteration.

[0064] Global optimal mask vector It is the mask vector that minimizes the objective function value found up to the current iteration; if the objective function value of the current optimal candidate mask vector is... The objective function value is less than the globally optimal mask vector. Then the globally optimal mask vector will be updated to the currently optimal candidate mask vector. The updated global optimal mask vector is used in the next iteration (i.e., the updated global optimal mask vector is used as the current mask vector in the next iteration); otherwise, the global optimal mask vector is kept unchanged and used in the next iteration.

[0065] It should be noted that the globally optimal mask vector in the first iteration is the initialized mask vector. If the initialization strategy uses an empty set, the mean of the true simulation response values ​​in the training set is directly used as the predicted value for each validation sample in the validation set. The mean squared error on the validation set is calculated as the prediction error, and then the objective function value corresponding to the globally optimal mask vector is calculated. .

[0066] To avoid getting trapped in local optima, each iteration also includes: identifying whether the relative improvement of the objective function value corresponding to the globally optimal mask vector in multiple consecutive iterations is less than a preset improvement ratio threshold. If it is less, a forward search strategy is used in the current iteration to expand the neighborhood search space of the current mask vector and generate candidate mask vectors. Otherwise, the next iteration is executed and the neighborhood search strategy is used to continue generating candidate mask vectors.

[0067] Among them, the Relative improvement in the next iteration It is calculated using the following formula: , in, and They represent up to the number Second and third The objective function value corresponding to the globally optimal mask vector at the end of the next iteration.

[0068] This embodiment uses a counter to monitor whether the relative improvement amount is continuously less than a preset improvement ratio threshold. The number of iterations is initially 0, and after each iteration: if If the value is 0, it means that the iteration has achieved significant improvement, and the counter value is reset to 0. if If the result is not significant, it indicates that the improvement in this iteration is not significant. The counter value is then incremented by 1 to determine whether the counter value has reached the forward depth configured in the forward search strategy. : If the target is not reached, proceed to the next iteration and continue to use the neighborhood search strategy to generate candidate mask vectors. If it has been reached, it means that it has been continuous. If the next iteration does not show significant improvement, it may be trapped in a local optimum. In this case, a forward search strategy should be immediately triggered in the current iteration to optimize the current mask vector. The neighborhood search space is expanded to generate candidate mask vectors.

[0069] It should be noted that the forward depth in the forward search strategy The value range is [3, 10]; Improved proportional threshold It is usually set to a small positive number, such as 0.01, which means that an improvement is considered effective only when the relative improvement of the objective function value reaches or exceeds 1%.

[0070] Expanding the neighborhood search space of the current mask vector using a forward search strategy involves simultaneously changing the mask values ​​at the feature positions of two parameters based on the current mask vector. This includes the following three cases: Double Addition: Sets the mask value of the corresponding positions of two currently unselected parameter features from 0 to 1; Double deletion: Sets the mask value of the corresponding positions of the two currently selected parameter features from 1 to 0; Add and delete: Set the mask value of the position corresponding to a currently unselected parameter feature from 0 to 1, and set the mask value of the position corresponding to a currently selected parameter feature from 1 to 0.

[0071] The expanded neighborhood search space is represented as: After selecting parameter features based on the candidate mask vectors, a subset of samples is extracted from the original sample set to train the corresponding surrogate model, and then the objective function value corresponding to each candidate mask vector is calculated. If there is an objective function value smaller than that corresponding to the current global optimal mask vector, the global optimal mask vector is updated to the candidate mask vector corresponding to the smallest objective function value.

[0072] It is important to note that after expanding the neighborhood search space using the forward search mechanism in one iteration, the counter value is reset to 0 regardless of whether a better mask vector is found. In the next iteration, the neighborhood search strategy is resumed to generate candidate mask vectors, thus achieving a balance between global exploration and local refinement.

[0073] S3. When the preset convergence condition is met, terminate the iterative optimization and output the global optimal mask vector. The corresponding feature subset is the selected CAE simulation key parameter feature.

[0074] It should be noted that after each iteration, the convergence condition is checked to see if it is satisfied: ① Reaching the target error: If the prediction error corresponding to the current optimal mask vector is less than or equal to the preset error threshold, it indicates that the accuracy of the surrogate model has met the engineering requirements, and the iteration terminates. The error threshold is set according to the accuracy requirements of the specific application scenario; for example, it can be set to 0.01 or 0.001.

[0075] ② The relative improvement amount is too small: if continuous If the relative improvement in each iteration is less than the preset minimum improvement threshold, it indicates that the solution has converged to the vicinity of the optimal solution, and the space for further improvement is minimal, thus terminating the iteration. The minimum improvement threshold is set to a very small positive number, such as 0.0001.

[0076] ③ Reaching the maximum number of iterations: To prevent infinite iteration loops, a maximum number of iterations is set. When the number of iterations reaches this limit, the iteration is forcibly terminated. The maximum number of iterations is set to a value between 100 and 1000, depending on the problem size.

[0077] When any convergence condition is met, the iterative optimization process terminates, and the current globally optimal mask vector is the final feature selection scheme.

[0078] For example, in the simulation scenario of aero-engine turbine blade aerodynamic performance, the key parameter features selected based on the final output global optimal mask vector include: blade leading edge radius, blade maximum thickness, blade installation angle, inlet total pressure and inlet total temperature, while other features are removed.

[0079] Compared with existing technologies, this embodiment provides a high-dimensional feature selection method for CAE simulation. By constructing an objective function that balances prediction error and feature quantity, and employing an iterative optimization strategy based on neighborhood search, it automatically selects the key parameter features that have the most significant impact on the simulation response while ensuring model accuracy. This significantly reduces the feature dimensionality, effectively improves the construction efficiency and interpretability of subsequent proxy models, and provides more concise and reliable design variables for CAE simulation-driven design. The improved neighborhood search strategy (adding add and delete operations) and the introduction of a forward search mechanism achieve a clever balance between local search and global exploration. By continuously monitoring the relative improvement of the objective function value corresponding to the globally optimal mask vector, the search space is adaptively expanded to simultaneously change the states of two features when trapped in a local optimum, effectively avoiding premature convergence and improving global optimization capabilities. The modeling process of CAE simulation has been improved. By intelligently filtering key design parameters, the input dimensions of the simulation model have been significantly reduced, the complexity of high-fidelity simulation calculations has been lowered, the prediction accuracy and reliability of the simulation model have been improved, unnecessary consumption of computing resources has been reduced, and engineering design iterations have been accelerated. It is applicable to CAE simulation optimization problems in aerospace, automotive engineering, energy equipment and other fields.

[0080] Example 2 Another embodiment of the present invention discloses a high-dimensional feature selection system for CAE simulation, thereby implementing the high-dimensional feature selection method for CAE simulation in Embodiment 1. The specific implementation of each module is described in the corresponding description in Embodiment 1. The system includes: The data acquisition module is used to acquire the original sample set of the CAE simulation task, where each sample includes multiple parameter features and the corresponding simulation response value; The feature selection module is used to construct an objective function based on the prediction error and the number of selected parameter features. The prediction error is calculated based on the simulation response value and the predicted value output by the surrogate model. Based on the original sample set and the objective function, the initialized mask vector is iteratively optimized. Each iteration includes: generating multiple candidate mask vectors using a neighborhood search strategy for the current mask vector; selecting parameter features based on each candidate mask vector; extracting a sample subset from the original sample set; training the corresponding surrogate model; obtaining the current optimal candidate mask vector by calculating the objective function value; and updating the globally optimal mask vector for use in the next iteration. The feature output module is used to terminate iterative optimization and output the globally optimal mask vector when the preset convergence condition is met. The corresponding feature subset is the selected CAE simulation key parameter feature.

[0081] Since the high-dimensional feature selection system for CAE simulation described in this embodiment and the aforementioned high-dimensional feature selection method for CAE simulation are related and can be mutually referenced, this description is redundant and will not be repeated here. Because this system embodiment shares the same principle as the aforementioned method embodiment, it also possesses the corresponding technical effects of the aforementioned method embodiment.

[0082] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0083] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A high-dimensional feature selection method for CAE simulation, characterized in that, Includes the following steps: Obtain the original sample set of the CAE simulation task, where each sample includes multiple parameter features and the corresponding simulation response value; An objective function is constructed based on the prediction error and the number of selected parameter features, wherein the prediction error is calculated based on the simulation response value and the predicted value output by the surrogate model. Based on the original sample set and the objective function, the initialized mask vector is iteratively optimized; in Each iteration includes: The neighborhood search strategy is used to generate multiple candidate mask vectors for the current mask vector. After selecting parameter features for each candidate mask vector, a subset of samples is extracted from the original sample set to train the corresponding surrogate model. Then, the current optimal candidate mask vector is obtained by calculating the objective function value, and the global optimal mask vector is updated for use in the next iteration. When the preset convergence condition is met, the iterative optimization is terminated and the globally optimal mask vector is output. The corresponding feature subset is the selected CAE simulation key parameter feature.

2. The high-dimensional feature selection method for CAE simulation according to claim 1, characterized in that, Based on the prediction error and the number of selected parameter features, the objective function is constructed using the following formula: ， in, Representation based on mask vector The objective function; Represents the mask vector It is A binary vector of dimension 1 This indicates the number of selected parameter features, i.e., the number of non-zero elements in the mask vector; Representation based on mask vector The prediction error calculated by the corresponding surrogate model; This represents the regularization coefficient.

3. The high-dimensional feature selection method for CAE simulation according to claim 1, characterized in that, The neighborhood search strategy includes an add operation and a delete operation; wherein, the add operation is used to set the mask value of the position corresponding to a currently unselected parameter feature from 0 to 1 based on the current mask vector, to generate a candidate mask vector; the delete operation is used to set the mask value of the position corresponding to a currently selected parameter feature from 1 to 0 based on the current mask vector, to generate a candidate mask vector.

4. The high-dimensional feature selection method for CAE simulation according to claim 1, characterized in that, The globally optimal mask vector is the mask vector that minimizes the objective function value found up to the current iteration; Each iteration further includes: identifying whether the relative improvement of the objective function value corresponding to the globally optimal mask vector in multiple consecutive iterations is less than a preset improvement ratio threshold. If it is less, a forward search strategy is used in the current iteration to expand the neighborhood search space of the current mask vector and generate a candidate mask vector. Otherwise, the next iteration is executed and the neighborhood search strategy is used to continue generating candidate mask vectors.

5. The high-dimensional feature selection method for CAE simulation according to claim 4, characterized in that, The method of expanding the neighborhood search space of the current mask vector by adopting a forward search strategy involves changing the mask values ​​of the two parameter feature positions simultaneously based on the current mask vector.

6. The high-dimensional feature selection method for CAE simulation according to claim 4, characterized in that, After expanding the neighborhood search space using a forward search mechanism in one iteration, the neighborhood search strategy is resumed in the next iteration to generate candidate mask vectors.

7. The high-dimensional feature selection method for CAE simulation according to claim 1, characterized in that, The surrogate model is a Gaussian process surrogate model; a training set and a validation set are obtained based on a subset of samples; the surrogate model corresponding to the training is trained by optimizing the kernel function hyperparameter of the Gaussian process by maximizing the marginal likelihood function based on the training set, so as to obtain the Gaussian process surrogate model corresponding to the candidate mask vector.

8. The high-dimensional feature selection method for CAE simulation according to claim 7, characterized in that, The prediction error is calculated based on the simulation response value and the predicted value output by the surrogate model, including: Based on the trained surrogate model, the posterior prediction distribution of each sample in the validation set is calculated, and the mean of the distribution is used as the predicted value of that sample. The mean squared error is calculated as the prediction error based on the predicted value of each sample in the validation set and its corresponding simulation response value.

9. The high-dimensional feature selection method for CAE simulation according to claim 5, characterized in that, The mask value that simultaneously changes the feature positions of two parameters includes: Set the mask value of the corresponding positions of two currently unselected parameter features from 0 to 1, or set the mask value of the corresponding positions of two currently selected parameter features from 1 to 0, or set the mask value of the corresponding position of one currently unselected parameter feature from 0 to 1 and set the mask value of the corresponding position of one currently selected parameter feature from 1 to 0.

10. A high-dimensional feature selection system for CAE simulation, characterized in that, include: The data acquisition module is used to acquire the original sample set of the CAE simulation task, where each sample includes multiple parameter features and the corresponding simulation response value; The feature selection module is used to construct an objective function based on the prediction error and the number of selected parameter features, wherein the prediction error is calculated based on the simulation response value and the prediction value output by the surrogate model. Based on the original sample set and the objective function, the initialized mask vector is iteratively optimized; in Each iteration includes: generating multiple candidate mask vectors using a neighborhood search strategy on the current mask vector; selecting parameter features based on each candidate mask vector and extracting a subset of samples from the original sample set; training the corresponding surrogate model; obtaining the current optimal candidate mask vector by calculating the objective function value; and updating the globally optimal mask vector for use in the next iteration. The feature output module is used to terminate iterative optimization and output the globally optimal mask vector when the preset convergence condition is met. The corresponding feature subset is the selected CAE simulation key parameter feature.

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