Aerodynamic optimization method based on multi-element model adaptation and improved particle swarm

Abstract

The application provides an aerodynamic optimization method based on a multi-model self-adaption and improved particle swarm, which comprises the following steps: obtaining influence factors related to target values, collecting a plurality of groups of independent influence factors and target data satisfying normal distribution, dividing the data set into a training set and a test set after preprocessing and normalization; establishing a plurality of meta-models through a machine learning method, saving parameter files of each trained meta-model and average evaluation indexes of the meta-models; establishing a particle swarm optimization algorithm which is improved in initialization, arithmetic crossover, natural selection and adaptive inertia weight; taking the saved meta-model parameter files as fitness calculation functions of the improved particle swarm optimization algorithm, and outputting optimized results from the optimized fitness. The optimization method of the application is combined with the meta-model and the improved meta-heuristic optimization algorithm, can reduce the simulation times of optimization iteration without affecting the precision of a simulation target model, thereby reducing the consumption of computing resources, improving the optimization efficiency, and the self-adaptive multi-model has flexibility and scalability, can self-adaptively select the optimal meta-model suitable for the optimization algorithm under small sample size, and further obtain a more optimal optimization target value.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic optimization technology, and in particular to an aerodynamic optimization method based on multivariate model adaptive and improved particle swarm optimization. Background Technology

[0002] Aerodynamic optimization design refers to the technology of optimizing the aerodynamic characteristics of objects such as automobiles, aircraft, and buildings to improve their performance, reduce drag, and enhance stability.

[0003] Currently, the most widely used optimization algorithms in the field of aerodynamic optimization are mainly divided into evolutionary algorithms and swarm intelligence algorithms. These algorithms employ different mechanisms and strategies during the optimization process to achieve the goal of finding the optimal solution. The selection of these algorithms is often based on factors such as the nature of the specific application problem, constraints, solution objectives, and computational resources.

[0004] Although these algorithms have the ability to search globally, they also have problems such as slow convergence speed, a large number of hyperparameters that need to be adjusted for some algorithms, and poor optimization performance when the amount of data is small. Therefore, the development of aerodynamic optimization algorithms that can be efficient and adaptable to small sample aerodynamic data optimization is of great significance. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide an aerodynamic optimization method based on multivariate model adaptive and improved particle swarm optimization, which improves the optimization effect of traditional optimization methods, provides a better combination of design parameters, makes progress in improving aerodynamic performance, establishes the overall structure of the aerodynamic optimization model, and achieves the same high efficiency and stability for optimization of small sample aerodynamic data, providing important basic data for improving aerodynamic performance and engineering efficiency.

[0006] This invention provides an aerodynamic optimization method based on multivariate model adaptive and improved particle swarm optimization, comprising the following steps:

[0007] Step S1: Collect aerodynamic data and influencing factor data, using the aerodynamic data as the target value to be optimized. Preprocess the target value and influencing factor data, including outlier removal: using statistical methods, if a data point significantly deviates from the standard deviation or mean, it is removed; thus reducing interference data. Secondly, normalize the data to eliminate scale differences, which helps improve the stability and accuracy of the model.

[0008] Step S2: Use the preprocessed data to train multiple prediction models established using machine learning methods as meta-models for the optimization process, and save the parameter file of each trained meta-model and the average evaluation index of each meta-model; the parameters are hyperparameters, including: weights, number of iterations, and kernel function;

[0009] Step S3: The meta-model outputs the optimization results. Based on the optimization results and the average evaluation index, the optimal meta-model is adaptively selected. The optimization results are the optimized aerodynamic data values ​​output after the meta-model is trained.

[0010] Step S4: Load the parameter file of the meta-model and encapsulate it into a fitness calculation function of the particle swarm algorithm to optimize the fitness, output the optimized output result, and then inverse normalize the output result to obtain the optimal aerodynamic data value.

[0011] Furthermore, the step of using visualization analysis methods to draw a scatter plot of the data includes: using the pairplot function from Python's seaborn library to plot the dataset X. n ={(x1,y1),(x2,y1),…,(x n Draw a scatter plot of x points (y1) and x points (y1) n y1 represents the data for the nth influencing factor, and y1 represents the aerodynamic data.

[0012] The data normalization process involves using the MinMaxScaler() function of the preprocessing module in the sklearn library to map data of different scales and ranges to a unified range of [0,1].

[0013] The preprocessing also includes:

[0014] A scatter matrix of data was plotted using visualization analysis methods to analyze whether there is a significant linear correlation between different influencing factors and the target value, as well as the distribution of the data. The linear trend and clustering characteristics among the variables were discovered. Through the analysis of the linear trend and clustering characteristics, the initial selection of the model was completed.

[0015] The analysis of whether there is a significant linear correlation between different influencing factors and the target value, and the distribution of the data, includes:

[0016] Based on the linear trends of the independent and dependent variables in the scatter plot (represented by a straight line or near-straight line), a linear relationship is analyzed to determine the existence of the data, thus performing the first preliminary screening: If the data shows a clear linear trend, a linear regression model is selected, including gradient descent linear regression and ridge regression models; these can fit the linear relationship well. For non-linear trends, more complex models are considered, such as multilayer perceptron models, random forest models, decision tree models, extreme gradient boosting models, and BP neural network models; thus completing the first preliminary screening.

[0017] The clustering characteristics of a scatter plot are determined by the fact that data points in the scatter plot tend to cluster or group together, indicating a certain similarity or group structure among the data points. When the data shows obvious clustering characteristics, i.e., the distance between the scatter points is less than a set distance threshold, the initial model selection involves adding a clustering algorithm (e.g., hierarchical clustering or k-means clustering) to the predictive model obtained from the first preliminary screening. When the distance between the scatter points is large and the distribution is sparse, the clustering characteristics are not obvious, and the predictive model obtained from the first preliminary screening is the initial model selection.

[0018] Furthermore, the step of using visualization analysis methods to draw a scatter plot of the data includes: using the pairplot function from Python's seaborn library to plot the dataset X. n ={(x1,y1),(x2,y1),…,(x n Draw a scatter plot of x points (y1) and x points (y1) n y1 represents the data of the nth influencing factor, and y1 represents the aerodynamic data.

[0019] Furthermore, the prediction models include: multilayer perceptron (MLP) model, gradient descent linear regression model, random forest model, decision tree model, extreme gradient boosting model (XGBoost), Bp neural network model, and ridge regression model;

[0020] The formula for the multilayer perceptron is:

[0021]

[0022] Where x i This represents the training set data;

[0023] w i Represents the weights during the training process;

[0024] f represents the output of a neural network-based machine learning model;

[0025] For activation functions;

[0026] The preprocessed data is used to train multiple prediction models built using machine learning methods as meta-models for the optimization process. The parameter files of each trained meta-model and the average evaluation index of each meta-model are saved. During model training, the Rectified Linear Unit (ReLU) function is used as a regularization term to avoid overfitting. Simultaneously, the model uses MSE to calculate the Euclidean distance between the true and predicted values, which is used as the loss function for model training. The calculation formula is as follows:

[0027]

[0028]

[0029] Where x is the output value of the neuron in the previous layer;

[0030] e is the natural base;

[0031] y i Represents the actual value;

[0032] Indicates the predicted value;

[0033] n samples The sample size of the training set;

[0034] Then, several evaluation metrics are used: root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination R. 2 (R-Squared) evaluates the performance of each model;

[0035] The formula is:

[0036]

[0037] Where ε represents a small positive number, usually used to avoid the denominator being zero, |y i | is the absolute value of the true value;

[0038] When the metamodel is a multilayer perceptron model, its evaluation metrics are RMSE and R. 2 ,

[0039] When the metamodel is a linear regression model, its evaluation indicators are MAPE and R. 2 ,

[0040] When the meta-model is a random forest model, its evaluation metrics are MAPE and R. 2 ,

[0041] When the meta-model is a decision tree model, its evaluation metrics are MAPE and R. 2 ,

[0042] When the metamodel is an XGBoost model, its evaluation metrics are MAPE and R. 2 ,

[0043] When the metamodel is a Bp neural network model, its evaluation metrics are MAPE and R. 2 ,

[0044] When the meta-model is a ridge regression model, its evaluation index is R0. 2 ;

[0045] Input the data into the model and train it at least three times to ensure the reliability of the training results. Each training iteration yields an evaluation metric value. The average of these performance metrics is then calculated to obtain the average evaluation metric.

[0046] Save the trained meta-model parameter file and average evaluation index to establish an adaptive selection model.

[0047] Furthermore, if there is an initial selection of models, then the prediction model is the model selected in the initial selection.

[0048] Furthermore, adaptive selection of the optimal metamodel includes:

[0049] The optimal model is selected by dynamically choosing different models based on the performance of the data size (i.e., sample size) in prediction and optimization, and the minimum value of the product of the optimization result and the indicator weight is chosen.

[0050]

[0051] Where j is the j-th meta-model, y j It is the optimized result value; A j A represents the performance metric for each meta-model. j In this article, R 2 It can also be extended to take positively correlated evaluation indicators, where ρ is the number of meta-models.

[0052] Furthermore, the particle swarm optimization algorithm is an improved particle swarm optimization algorithm. This improved algorithm employs K-means clustering for improved initialization, introduces arithmetic crossover and natural selection from a genetic algorithm, and incorporates adaptive inertia weights. By iteratively updating the velocity and position of the particles, the particle swarm gradually searches for the optimal solution. This includes improvements to initialization, incorporating one or two of arithmetic crossover and natural selection.

[0053] The initialization improvement utilizes the K-means clustering method to randomly generate particle positions in the data in the original initialization manner, and then divides the generated samples into different clusters, each cluster representing a specific region or solution space, with the cluster center as the initial position;

[0054] Randomly generated particle positions:

[0055] [|P1|,|P2|,…,|P N |] (6)

[0056] Among them, P N It is the position of the Nth particle, where N represents the total number of particles;

[0057] The method for determining the cluster center is as follows:

[0058] [|P1|,|P2|,…,|P N |],[|P1|,|P2|,…,|P N |],…,[|P1|,|P2|,…,|P N |] (7)

[0059]

[0060] Choose K cluster centers. When K = j, obtain j cluster center locations from N randomly generated particle locations P.

[0061] Formula (7) represents the positions of multiple particles generated through multiple iterations; Formula (8) represents dividing the newly generated particle positions according to K cluster centers in each iteration until all particles are divided. The particle division in Formula (8) is just an example.

[0062] The improved arithmetic crossover and natural selection are as follows: After updating the individual and global historical best positions and fitness values, a sampling interval is constructed centered on the optimal solution of the current particle swarm cycle. Two particles at the newly sampled positions are randomly selected for arithmetic crossover. Then, after updating all particles, natural selection is added to select the optimal particle position, velocity, individual best position, and individual best fitness value based on survival of the fittest. This increases the diversity of the particle swarm distribution while also obtaining high-quality particles. The velocity and position updates are calculated using the following formulas:

[0063]

[0064] In the formula: i and j represent the i-th particle and the j-th dimension, where i = 1, 2, ..., N; j = 1, 2, ..., n; v represents the particle velocity;

[0065] Let represent the particle velocity of the i-th particle in the j-th dimension during the it-th iteration;

[0066] ω is the inertia weight, a parameter that is set to dynamically change between [0.1, 0.65], which determines the speed and direction of the particle's movement in the search space;

[0067] c1 and c2 are the learning factors of the algorithm, namely the individual learning factor and the swarm learning factor. They determine the degree of trade-off between the individual optimal solution and the global optimal solution, and are mainly used to adjust the parameters of the particle swarm step size.

[0068] r1 and r2 are random numbers between (0,1), and it is the number of particle swarm iterations;

[0069] This represents the individual optimal solution for the i-th particle in the j-th dimension during the it-th iteration;

[0070] This represents the value after updating the velocity of the i-th particle in the j-th dimension in the it-th iteration;

[0071] This represents the global optimal solution for the i-th particle in the j-th dimension during the it-th iteration;

[0072] c 1up This represents the constraint on the maximum value of the individual learning factor;

[0073] c 2up This represents a constraint on the maximum value of the group learning factor;

[0074] c 1low This represents a minimum constraint on the individual learning factor;

[0075] c 2low This represents a constraint on the minimum value of the group learning factor.

[0076] rd represents a random number;

[0077] exp() represents the exponential function.

[0078] Furthermore, the improved particle swarm optimization algorithm also includes improvements to the adaptive inertia weight: a linear variation strategy is adopted, which reduces the number of parameter adjustments. The formula for the adaptive inertia weight is:

[0079]

[0080] Where ω represents the inertia weight, it represents the current iteration number, and MaxIt is the maximum number of iterations. max and ω min These represent the upper and lower limits of the inertia weight, respectively.

[0081] Compared with existing methods, this invention can efficiently process small sample aerodynamic data and quickly obtain optimized aerodynamic data values. Specifically, it has a fast convergence speed and requires fewer hyperparameters to be adjusted, offering the following advantages:

[0082] ① This invention designs an aerodynamic optimization method based on multivariate model adaptation and improved particle swarm optimization. This method combines multivariate model adaptive selection, improved particle swarm optimization (in which each solution is called a particle, and all particles have a position and a velocity. Each particle adjusts its position and velocity based on its own experience and the experience of the group, thus gradually approaching the optimal solution), and data preprocessing techniques. This combined model achieves better and more efficient optimization results, even in optimization designs with small aerodynamic data scales. It also provides important basic data for improving aerodynamic performance and engineering efficiency.

[0083] ② Data preprocessing techniques were employed to comprehensively analyze the input data before model training. A scatter plot was created using visualization analysis methods to analyze whether there was a significant linear correlation between different influencing factors and the target value, as well as the data distribution. This helped identify linear trends, outliers, and clustering characteristics among variables, providing a basis for subsequent multivariate model selection. Secondly, data normalization was performed to eliminate scale differences, improving the model's stability and accuracy.

[0084] ③ An adaptive model selection method is proposed, which uses the coefficient of the average evaluation index of each model in the total evaluation index as the weight of the fitness value, and outputs the model with the smallest fitness value under the weight coefficient, providing flexible optimization selection for datasets of various sizes.

[0085] ④ An improved particle swarm optimization (PSO) algorithm and a multivariate model are used as its proxy. Based on the traditional PSO algorithm, particles are reinitialized using K-means clustering, and arithmetic crossover and natural selection from a genetic algorithm are introduced. Adaptive inertia weights are added, reducing the number of hyperparameter adjustments, increasing the diversity of the particle swarm, and improving the optimization convergence speed and global search capability of the PSO algorithm. Combining this with an adaptive selection multivariate model improves the optimization results and allows for flexible adaptation to data of different scales. Attached Figure Description

[0086] Figure 1 This is a technical flowchart of the present invention;

[0087] Figure 2 This is a neural network structure diagram of the meta-model of the present invention, the multilayer perceptron;

[0088] Figure 3 This is an overall structural diagram of the present invention;

[0089] Figure 4 This is a scatter matrix diagram of an embodiment of the present invention. Detailed Implementation

[0090] With the development of industrial technology, aerodynamic optimization design technology has gradually become an important industrial design method. This technology utilizes the characteristics of airflow to improve product performance and efficiency, thereby enhancing product quality and competitiveness. It is commonly applied in various industrial fields such as aircraft, automobiles, wind turbines, and rocket engine nozzles. This invention uses the automotive industry as an example. Automotive aerodynamic design mainly includes the aerodynamic design of components such as the body, contours, rearview mirrors, and wheel hubs. The automotive wheel hub is used as the implementation data for aerodynamic optimization design in this example. The aerodynamic optimization design of the automotive wheel hub uses the drag coefficient as aerodynamic data for optimization. After optimization, air resistance can be reduced, stability improved, noise and vibration reduced, etc., while also promoting the development of automotive engineering technology, and having a positive impact on improving vehicle performance, reducing energy consumption, enhancing ride comfort, and improving the driving experience.

[0091] This invention, based on multivariate model adaptation and improved particle swarm optimization, combined with data preprocessing techniques, achieves high efficiency, stability, and adaptability in aerodynamic optimization design. The technical solution of this invention will be clearly and thoroughly described below with reference to embodiments. The described embodiments are only a portion of the embodiments of this invention.

[0092] The aerodynamic optimization method based on multivariate model adaptive and improved particle swarm optimization provided by this invention has the following overall technical process: Figure 1 As shown, it includes the following steps:

[0093] Step S1: Preprocess the collected target values ​​and influencing factors data: First, use visualization analysis methods to draw a scatter matrix of the data, analyze whether there is a significant linear correlation between different influencing factors and the target value, and analyze the distribution of the data. This helps to discover linear trends, outliers, and clustering characteristics among variables, complete the removal of outliers, and perform preliminary model screening, providing a basis for subsequent multivariate model selection. Second, normalize the data to eliminate scale differences and improve the stability and accuracy of the model.

[0094] Step S2: Use the preprocessed data to train multiple prediction models built using machine learning methods as meta-models for the optimization process, and save the parameter file of each trained meta-model and the average evaluation index of each meta-model.

[0095] The models include: Multilayer Perceptron (MLP), Linear Regression of Gradient Descent, Random Forest, Decision Tree, Extreme Gradient Boosting (XGBoost), BP Neural Network, and Ridge Regression. The formula for the Multilayer Perceptron is:

[0096]

[0097] Where x i w represents the training set data. i Let f represent the weights during the training process, and let f represent the output of the neural network-based machine learning model. Figure 2 The structure shown. The activation function used is the Rectified Linear Unit (ReLU). Simultaneously, the model uses the MSE to calculate the Euclidean distance between the true and predicted values, which is then used as the loss function for model training. The calculation formula is as follows:

[0098]

[0099]

[0100] y i Represents the actual value. n represents the predicted value. samples The size of the training set is specified. Finally, several evaluation metrics are used: Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination R0. 2 R-squared (R-Squared) evaluates the performance of each model. The formula is:

[0101]

[0102] Step S3: Establish an improved particle swarm optimization algorithm with improved initialization, incorporating arithmetic crossover, natural selection, and adaptive inertia weights;

[0103] Step S4: Use the saved meta-model parameter file as the fitness calculation function of the improved particle swarm algorithm, and optimize the fitness output to get the optimized output result.

[0104] In this embodiment of the invention, the collected aerodynamic data is wind resistance data, and the influencing factor data is wheel hub data with each axis system affecting wind resistance. The six parameters (influencing factors) affecting the target value of the wheel hub data for a certain SUV model are respectively two parameters PXZ1 and PXZ2 with a system in the XZ plane, and four parameters PY1, PY2, PY3, and PY4 with a system in the Y-axis direction. The wind resistance coefficient is the target optimization value (aerodynamic data), aiming to minimize the wind resistance coefficient and obtain the corresponding parameter values ​​at the minimum wind resistance coefficient. The maximum and minimum values ​​of each parameter affecting the wind resistance coefficient are set as shown in Table 1.

[0105] Table 1. Maximum and minimum values ​​of various parameters affecting the drag coefficient.

[0106]

[0107] The specific implementation process is as follows: Figure 3 As shown, it includes the following steps:

[0108] Step 1: Preprocess the collected drag coefficient values ​​and corresponding influencing factor wheel hub data: First, use visualization analysis methods to draw a scatter matrix plot of the data, as shown below. Figure 4 As shown, this study analyzes whether there is a significant linear correlation between different influencing factors and the drag coefficient value, and examines the distribution of the data. Figure 4 The last column or row represents the linear relationship and distribution between the influencing factors and the drag coefficient values. Most of these influencing factors and the drag coefficient exhibit a linear correlation; therefore, classic machine learning models such as linear regression, decision trees or neural networks, random forests, and XGBoost can be considered. Figure 4 Regarding the distribution of scattered points, outliers are considered abnormal and removed. It can also be seen that the clustering degree between the various variables and the drag coefficient is not high; therefore, clustering algorithms like k-means will not be considered for prediction. In summary, through the analysis of… Figure 4 The analysis revealed weak linear relationships among the parameter variables, indicating they were independent of each other, but exhibited a significant linear correlation with the drag coefficient (cd). Furthermore, most variables showed negative correlations, providing a basis for subsequent multivariate model selection. Secondly, the data were normalized.

[0109] The dataset was plotted using the `pairplot` function from Python's seaborn library. Data normalization was achieved by using the `MinMaxScaler()` function from the `preprocessing` library of the sklearn library to map data of different scales and ranges to a uniform range of [0,1]. This eliminated scale differences and improved the model's stability and accuracy.

[0110] Step 2: Train the preprocessed data on multiple prediction models built using machine learning methods as meta-models for the optimization process. Save the parameter file of each trained meta-model and the average evaluation index of each meta-model after five training iterations. The average evaluation index results of the multivariate models are shown in Table 2.

[0111] Table 2. Results of Average Evaluation Indicators for the Multivariate Model

[0112]

[0113] Each model has many different metrics, but to compare the performance of different models, the same metrics must be used for evaluation.

[0114] As shown in Table 2, when the dataset size is 69, the gradient descent linear regression model performs well on the evaluation metric R. 2 The best performance was achieved with a score of 0.936, followed by Ridge Regression, which performed similarly. The Bp network model had the lowest performance. Therefore, the Bp network should be avoided as a surrogate model for optimization with small datasets. These metrics are saved, and the average percentage of each model's performance across all models is calculated as a weighting factor for the fitness values ​​in subsequent optimization steps.

[0115] Step 3: Improve the Particle Swarm Optimization (PSO) algorithm. The specific process is as follows: Figure 3 As shown. An improved particle swarm optimization algorithm with improved initialization, arithmetic crossover, natural selection, and adaptive inertia weights is established. Specifically: First, an adaptive selection multivariate model is established. These meta-models are constructed using machine learning methods. Then, L2 regularization can be added to prevent overfitting based on the prediction results. Next, the parameter files of these meta-models are saved, and the average evaluation performance index of each meta-model is calculated. At the same time, an improved particle swarm algorithm model is established. Through initialization, the particle swarm size, initial position, velocity, and improved method are set to establish this optimization model. Then, the parameter files of each meta-model and the average performance index are used to adaptively select the objective function of the optimization model according to formula (5) to obtain the individual and global optimal solutions of the current particles. Then, the velocity and position of each particle are updated. During the update process, the adaptive inertia weight method is set and arithmetic crossover and natural selection are added. The cyclic particle swarm optimization algorithm outputs the optimal solution when the number of iterations is reached (i.e., the termination condition).

[0116] Step 4: Use the saved meta-model parameter file as the fitness calculation function of the improved particle swarm optimization algorithm, optimize the fitness output, and obtain the optimal drag coefficient. Specifically, the optimal meta-model is the model selected by taking the minimum value of the product of the optimized optimal drag coefficient value and the index weight, as shown in formula (5):

[0117]

[0118] Where j is the j-th meta-model, y j It is the optimized result value; A j A represents the performance metric for each meta-model. j In this article, R 2 It can also be extended to take positively correlated evaluation indicators, where ρ is the number of meta-models.

[0119] The optimization results after inverse normalization are shown in Table 3. The optimization results of commonly used models that simultaneously satisfy the normal distribution but with different sample sizes (Kriging as a surrogate optimization model for Multi-Island Genetic Algorithm (MIGA), Kriging as a surrogate optimization model for Particle Swarm Optimization (Kriging+PSO), multivariate model as a surrogate optimization model for Particle Swarm Optimization (multivariate model+PSO), and the optimization design method proposed in this invention) are shown in Table 3.

[0120] Table 3 compares the optimization results with other optimization design methods.

[0121]

[0122] As shown in Table 3, the proposed optimization design for automotive wheel hub aerodynamics, based on data preprocessing techniques, an adaptive selection multivariate model, and an improved particle swarm optimization algorithm, significantly outperforms other models mentioned above in terms of optimized values. Compared to the optimal values ​​of Kriging+MIGA and Kriging+PSO optimization designs, the optimized values ​​are reduced by 0.0012 and 0.00126, respectively, with a minimum drag coefficient of 0.33458. The optimization performance with gradually decreasing sample sizes is also superior to other models. This example demonstrates that the proposed optimization design, which combines an adaptive selection multivariate model built using machine learning with an improved particle swarm optimization algorithm, can achieve optimal aerodynamic design and is adaptable to aerodynamic data of varying scales.

Claims

1. A method for aerodynamic optimization based on multi-model adaptive and improved particle swarm, characterized in that, The method comprises the following steps: Step S1: collecting aerodynamic data and data of influencing factors, taking the aerodynamic data as a target value to be optimized, and pre-processing the target value and the data of influencing factors, the pre-processing comprising eliminating abnormal values: using a statistical method, if a data point deviates from a standard deviation or a mean value, the data point is eliminated; Secondly, the data is normalized to eliminate scale differences; Step S2: using the pre-processed data to train a plurality of prediction models established by using a machine learning method as meta-models of an optimization process, saving a parameter file of each trained meta-model and an average evaluation index of each meta-model; The parameters are hyperparameters, including: weight, iteration number, kernel function; Step S3: the meta-model outputs an optimization result, and the optimal meta-model is adaptively selected according to the optimization result and the average evaluation index; the optimization result is an optimized aerodynamic data value output by the meta-model after training; Step S4: loading the parameter file of the meta-model and encapsulating the parameter file as a fitness calculation function of a particle swarm optimization algorithm, thereby optimizing the fitness, outputting an optimized output result, and then obtaining optimal aerodynamic data values by reverse normalizing the output result, the particle swarm optimization algorithm is an improved particle swarm optimization algorithm, comprising: initialization, addition of one or both of arithmetic crossover and natural selection, and improvement: The initialization improvement uses a K-means clustering method to randomly generate particle positions in an original initialization manner, and then divides the generated samples into different clusters, and each cluster represents a specific area or solution space, and the cluster center is used as an initial position; Randomly generated particle positions: ， where P N is the position of the Nth particle, N representing the total number of particles; The position points of the cluster centers are taken, and the method is as follows: a plurality of particle positions generated by multiple iterations; in each iteration, the newly generated particle positions are divided according to the K cluster center points until all the particles are divided; The arithmetic crossover and natural selection improvement is as follows: after updating the individual and global historical optimal position and fitness value, a sampling interval is constructed with the optimal solution of the current particle swarm cycle as the center, and two particles are randomly selected for arithmetic crossover, and then after updating all the particles, natural selection is added, and the optimal particle position, speed, individual optimal position and individual optimal fitness value are selected according to the survival of the fittest, thereby increasing the diversity distribution of the particle swarm and obtaining high-quality particles; the speed and position are updated, and the formula is as follows: ， wherein, represents the first iteration of the particle the dimensional particle velocity; is the inertia weight, set to vary dynamically between 0.9 and 0.4 which determines the velocity and direction of the particle in the search space; , are the individual learning factor and the group learning factor, respectively; , For a random number between 0 and 1, it is the number of iterations of the particle swarm. Xi,jitdenotes the individual optimal solution of the jthdimension of the ithparticle at the itthiteration; vi,j represents the updated value of the velocity of the ith particle in the jth dimension at the it iteration; Xi,jitdenotes the global optimal solution of the ith particle in the jth dimension at the it iteration; denotes the individual learning factor maximum constraint; denotes the group learning factor maximum constraint; denotes the individual learning factor minimum constraint; denotes the group learning factor minimum constraint; represents a random number; exp() represents an exponential function; represents the first +1 iteration the particle the dimensional particle velocity; vi+1j represents the updated value of the jth dimension of the ith particle at the (it+1)th iteration; is the maximum number of iterations; represents the current iteration number.

2. The aerodynamic optimization method based on multi-element model adaptive and improved particle swarm according to claim 1, characterized in that, The normalization of the data is to map the data of different scales and ranges into a uniform range using the MinMaxScaler() function of preprocessing in the sklearn library.

3. The aerodynamic optimization method based on multi-model adaptive and improved particle swarm of claim 1, wherein, The pre-processing further comprises: A scatter matrix diagram of the data is drawn by using a visual analysis method to analyze whether there is a significant linear correlation between different influencing factors and the target value and the distribution of the data, find the linear trend and clustering characteristics between variables, and complete preliminary selection of the model through analysis of the linear trend and the clustering characteristics; The analysis of whether there is a significant linear correlation between different influencing factors and the target value and the distribution of the data comprises: According to the linear trend of each independent variable and dependent variable in the scatter plot matrix, the linear relationship between the data is analyzed, so as to carry out the first preliminary screening: if the data shows obvious linear trend, the linear regression model is selected, which includes the gradient descent linear regression model, the ridge regression model; for non-linear trend, the multilayer perception model, the random forest model, the decision tree model, the extreme gradient boosting model and the Bp neural network model are selected; so as to complete the first preliminary screening; The clustering characteristics of the scatter plot matrix are judged, when the data shows obvious clustering characteristics, that is, the distance between each scatter point is less than the set distance threshold, the preliminary selection of the model is the prediction model obtained in the first preliminary screening and the clustering algorithm; when the distance between each scatter point is large and sparse, the clustering characteristics are not obvious, and the prediction model obtained in the first preliminary screening is the preliminary selection of the model.

4. The aerodynamic optimization method based on multi-model adaptive and improved particle swarm according to claim 3, characterized in that, The scatter matrix plot of the data drawn by the visual analysis method comprises: using the pairplot function in the seaborn library of Python on the data set drawing a scatter matrix plot, representing the nth influencing factor data, representing the aerodynamic data.

5. The aerodynamic optimization method based on multi-model adaptive and improved particle swarm according to claim 1, characterized in that, The prediction model includes: multilayer perception model, gradient descent linear regression model, random forest model, decision tree model, extreme gradient boosting model, Bp neural network model and ridge regression model; The preprocessed data is used to train a plurality of prediction models established by using a machine learning method as a meta-model of an optimization process, and a parameter file of each trained meta-model and an average evaluation index of each meta-model are saved; wherein a linear rectification function is used as a regularization term in the model training process to avoid overfitting; and the model uses The Euclidean distance between the true value and the predicted value is calculated and used as the loss function of the model training. Then several evaluation metrics are used: root mean square error, mean absolute percentage error and coefficient of determination The performance of each model is evaluated; When the meta-model is a multi-layer perceptron model, the evaluation index is RMSE, , When the meta-model is a linear regression model, the evaluation index is MAPE, , When the meta-model is a random forest model, the evaluation index is MAPE, , When the meta-model is a decision tree model, the evaluation index is MAPE, , When the meta-model is an XGBoost model, the evaluation index is MAPE, , When the meta-model is a Bp neural network model, the evaluation index is MAPE, , When the meta-model is a ridge regression model, the evaluation index is ; The data is input into the model, and the training is carried out at least three times, each time obtaining an evaluation index value, taking the average value of several performance evaluation indexes to obtain the average evaluation index; The trained meta-model parameter file and the average evaluation index are saved, and the self-adaptive selection model is established.

6. The aerodynamic optimization method based on multi-model adaptive and improved particle swarm of claim 4, wherein, When there is a preliminary selection of the model, the prediction model is the model after the preliminary selection.

7. The aerodynamic optimization method based on multi-model adaptive and improved particle swarm of claim 1, wherein, The self-adaptive selection of the optimal meta-model includes: The optimal model is selected according to the minimum value of the product of the optimization result and the index weight: ， wherein j is the jth metamodel, is the optimization result value; denotes the performance indicator of each metamodel, is the number of metamodels.

8. The aerodynamic optimization method based on multi-model adaptive and improved particle swarm of claim 7, wherein, The improved particle swarm optimization algorithm also includes the improvement of the adaptive inertia weight: the linear change strategy is adopted, and the formula of the adaptive inertia weight is: ， wherein denotes an inertia weight denotes the current iteration number, is the maximum iteration number, and denote the upper and lower limits of the inertia weight, respectively.

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