Simulation agent model recommendation method based on multi-dimensional feature fusion

Abstract

The invention discloses a simulation agent model recommendation method based on multi-dimensional feature fusion, and the method comprises the steps: carrying out the feature extraction of sample data used for training a model, obtaining the dimension feature, the quantity feature, the spatial distribution feature and the nonlinear feature of the sample data, and forming a data fingerprint of the sample data: a fingerprint vector phi = [dim, N, h, S]; obtaining a calculation function corresponding to each feature of the current fingerprint vector according to a preset corresponding relationship between the fingerprint vector and the calculation function, and then respectively scoring the candidate proxy models; the agent models with high scores are recommended, and the agent models with low scores are not recommended. According to the method, a user can select a proper agent model method according to a priori criterion result before the agent model is really used for training, and manual trial and error are avoided.

Description

Technical Field

[0001] This invention belongs to the field of computer simulation technology and relates to a simulation agent model recommendation method based on multi-dimensional feature fusion. Background Technology

[0002] To ensure the reliability and accuracy of engineering design and analysis results, modern simulation models are increasingly pursuing higher levels of detail. This extreme pursuit of fidelity leads to an exponential increase in model complexity. As model accuracy improves, the required computational resources and time costs also rise sharply, especially in complex systems engineering such as aerospace and new energy equipment. To address the high computational costs associated with high-fidelity models, the data-driven, rapid computation paradigm—the surrogate model—has become a key technological path to overcome computational bottlenecks.

[0003] A surrogate model is a simplified model constructed in simulation computation and engineering optimization. Its core is to establish a mapping relationship between input and output through data-driven methods, replacing the computationally expensive or complex high-precision original model. Surrogate models have many names, such as approximate models and meta-models. Despite the differences in terminology, their technical essence all points to a data-driven modeling methodology based on sample space, and their core meaning is highly unified: using the input-output dataset obtained from a finite number of high-precision model calculations, a lightweight mathematical representation capable of reproducing the behavior of the original model is constructed, ultimately achieving an optimal balance between accuracy and efficiency in engineering.

[0004] Over the past half-century, surrogate modeling techniques have experienced vigorous development and progress, giving rise to several classic single-model methods, such as Response Surface Methodology (PRS), Kriging, Radial Basis Function (RBF), Support Vector Regression (SVR), and Artificial Neural Networks (ANN). These methods have been widely applied in multiple disciplines (such as mechanics, biology, chemistry, and fluid dynamics) and multiple fields (such as aerospace, geological exploration, motor vehicles, and data processing).

[0005] However, different single models are applicable to problems of different dimensions, orders, and degrees of nonlinearity. They also usually exhibit different levels of fitting characteristics for the same engineering problem, and no single model is applicable to all problems.

[0006] The shortcomings and deficiencies of existing technologies are as follows:

[0007] Shortcoming 1: Lack of decision-making factors for selecting the proxy model

[0008] Currently, there are no good standards or specifications for selecting surrogate model methods. Engineers rely heavily on subjective experience when choosing surrogate models, iterating repeatedly through trial and error, which is laborious and time-consuming. Often, it is necessary to go through all surrogate model methods and complete the verification before selecting a relatively suitable surrogate model construction method based on the verification results. It is impossible to achieve prior knowledge, which is very time-consuming when the sample data volume is large.

[0009] Shortcoming 2: Differences in professional background lead to decision-making bias

[0010] Due to the lack of a unified and standardized decision-making mechanism, different professional backgrounds have led to fixed thinking paradigms and decision-making paths. For example, when there is an overemphasis on the analytical and smooth properties of the model, multinomial response surface (PRS) tends to be used; when the generalization ability of the algorithm is emphasized, machine learning models such as support vector regression (SVR) are preferred; the assumption of spatial correlation is presupposed, and the universality of the Kriging method is insisted upon; and the ease of operation is relied upon, and radial basis function (RBF) interpolation is commonly used. Summary of the Invention

[0011] This invention aims to eliminate the inefficiency of relying on subjective experience and trial-and-error exploration in the field of engineering simulation for the selection of surrogate models. By providing a simulation surrogate model recommendation method based on multi-dimensional feature fusion, it realizes prior evaluation and automated decision-making based on sample data features, quantitatively and systematically provides recommended surrogate models, avoids manual trial-and-error processes, and improves decision-making efficiency and accuracy.

[0012] This invention is achieved through the following technical solution:

[0013] A simulation agent model recommendation method based on multi-dimensional feature fusion extracts features from the sample data used to train the model, obtaining the dimensional features, quantity features, spatial distribution features and nonlinear features of the sample data, and constructs the data fingerprint of the sample data: fingerprint vector Φ=[dim,N,h,S];

[0014] Where dim is the dimension of the control variable of the sample data, N is the number of data points, h is the Hopkins statistic that reflects the spatial distribution of the sample data, and S is the curvature entropy that reflects the nonlinearity of the sample data.

[0015] Based on the pre-defined correspondence between fingerprint vectors and calculation functions, the calculation functions corresponding to each feature of the current fingerprint vector are obtained, and then the candidate proxy models are scored respectively; the proxy model with a high score is recommended, and the proxy model with a low score is not recommended.

[0016] The rating results for the proxy model are as follows:

[0017] S m =f dim (f N (fh (f S (B m )))),0<S m <10

[0018] Among them, S m For the scoring result; B m Basic score; f dim Calculate the function for the control variable dimensions;

[0019] f N The function for calculating the sample size; f h The function to calculate the Hopkins statistic; f S This is the function for calculating curvature entropy.

[0020] Furthermore, a data point is defined as a set of data that includes both input and output.

[0021] The sample data used for training the model were also preprocessed as follows: outlier data were removed, and duplicate data points were merged, keeping only one set.

[0022] Outlier data: When a set of data contains data types other than real numbers, the set of data is considered outlier data;

[0023] The repeated data points: When two sets of data are completely identical and both are non-outlier data points, then these two sets of data are considered to be repeated data points.

[0024] The dim, N, and h in the fingerprint vector are obtained as follows:

[0025] When the control variable of the dataset used as sample data has a dimension of d and a length of n, it is considered to have n data points, and each data point has a dimension of d.

[0026] Then the control variable dimension dim of the sample data is d, and the number of data points N is n;

[0027] With x ij Let x represent the j-th dimension control variable of the i-th data point, and transpose it to obtain x. i =[x i1 ,x i2 ,...x id ] T ;

[0028] Generate a space D:

[0029] D = {x1, x2, ... x} n}

[0030] And in space D, x i ∈R d i = 1, 2, ..., n;

[0031] m points P1, P2, ... P are randomly selected from D in sequence. m And for each point P i Before extraction, 1≤i≤m<n, find P. i Remove itself from the nearest neighbor v in D, and let X i For P i The Euclidean distance between v and v is:

[0032]

[0033] In space D, m points Q1, Q2, ... Q are randomly generated again in a uniform manner. n And for each point Q i Given that 1 ≤ i ≤ m < n, find Q. i Find the nearest neighbor w point in D, and let Y i For Q i The Euclidean distance between w and w is:

[0034]

[0035] Then the Hopkins statistic h is:

[0036]

[0037] The range of h values ​​is [0,1]. The larger the h value, the worse the uniformity of the data distribution; the smaller the h value, the better the uniformity of the data distribution.

[0038] The curvature entropy S in the fingerprint vector is the globally normalized curvature entropy, which is obtained as follows:

[0039] ① Construct a local quadratic surface based on data points in the sample data;

[0040] For the current data point y i Select k y values ​​within its neighborhood. i Data points other than those mentioned above, and denoted as y. j Then, based on the weighted least squares method, a system of equations for the quadratic surface is constructed:

[0041]

[0042] Where c is a constant term, T denotes transpose; g is the gradient vector, and H is the Hessian matrix representing the curvature of the local surface. Both are derived from f at the current data point y. i The definition of partial derivatives at point A;

[0043] ② Calculate the eigenvalues ​​of the Hessian matrix and perform eigenvalue decomposition on H to obtain curvature information in different directions:

[0044] H = QΛQ T Λ=diag(λ1,λ2,…,λ d )

[0045] Where Q represents the matrix composed of unit eigenvectors obtained by eigenvalue decomposition of matrix H, T represents the transpose of a vector or matrix, λ represents the eigenvalues ​​of matrix H, and λ1~λ2 d Represents the eigenvalues ​​from 1 to d;

[0046] ③ Take the absolute value of the eigenvalues ​​of the H matrix to characterize the magnitude of the curvature:

[0047]

[0048] Where λ k For the k-th eigenvalue obtained from the decomposition, p k For λ k Weights among all eigenvalues;

[0049] ④ Calculate the normalized curvature entropy:

[0050]

[0051] Where Si is p k Information entropy;

[0052] ⑤ Calculate the normalized curvature entropy of all valid points in the neighborhood for each of steps ① to ④. Average the normalized curvature entropy of all data points to obtain the global normalized curvature entropy.

[0053]

[0054] The correspondence between the preset fingerprint vector and the calculation function is as follows:

[0055]

[0056] Apart from the cases listed above, in all other cases, f of all candidate proxy models dim f N f h f S All are: ×1.

[0057] The recommendation decision for a candidate agent model is based on the following:

[0058] ①7 ≤ rating ≤ 10: Recommended for use;

[0059] ②6 ≤ rating ≤ 7: The effect is average, but it can be used;

[0060] ③ 0 ≤ rating ≤ 6: Not recommended;

[0061] ④ If all algorithms score less than 6 points, it indicates that further sample data is needed for re-evaluation.

[0062] Compared with the prior art, the present invention has the following beneficial technical effects:

[0063] To address the shortcomings and deficiencies of current surrogate model selection decision-making mechanisms, this invention focuses on constructing decision elements from sample data features to form data fingerprints, and then using these fingerprints to quantify recommendation strategies. This allows users to select an appropriate surrogate model method based on prior criteria before actually training the surrogate model, avoiding manual trial and error.

[0064] The main factors affecting the applicable scenarios of the proxy model include: the dimension of the control variables, the number of data samples (i.e., the number of points), the sparsity of the data, and the degree of nonlinearity. This invention conducts prior evaluation of the sample data from four dimensions: the dimension of the control variables, the number of samples, the Hopkins statistic, and the curvature entropy, and constructs a data fingerprint.

[0065] Among these factors, the dimensionality and sample length of the sample data are two relatively clear factors. Secondly, the calculation time for the Hopkins statistic and curvature entropy parameters is not very long, and the time complexity is not high. The control variable dimensionality (dim) and sample size (N) comprehensively reflect the size of the dataset, corresponding to scoring indicators such as modeling efficiency, prediction efficiency, and high-dimensionality capability of the model. The Hopkins statistic reflects the uniformity of data distribution, corresponding to the model's data sparsity capability. Curvature entropy reflects the nonlinearity of the data, corresponding to the model's nonlinear capability. Based on these indicators, a preliminary judgment can be made to identify which surrogate models are suitable and which are not for the dataset. This allows for a preliminary understanding of which algorithms are suitable and unsuitable without having to actually test each one, avoiding wasting time in the wrong direction. Therefore, by constructing data fingerprints, prior evaluation can replace subsequent verification, transforming decision-making from traditional trial-and-error methods to prior recommendation methods, significantly improving decision-making efficiency.

[0066] The quantitative recommendation strategy of this invention is based on a data-driven, interdisciplinary agent model recommendation scoring mechanism. It comprehensively scores candidate agent model methods by combining data fingerprints and recommendation scoring mechanisms. Models with high scores can be recommended for use, while methods with low scores are not recommended. Based on quantitative multi-feature fusion for decision-making, the decision accuracy has achieved a leapfrog breakthrough. The decision-making process is traceable and avoids decision bias caused by personal preferences and experience. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the process of the present invention.

[0068] Figure 2 This is a schematic diagram of the characteristics of an aircraft engine fan. Detailed Implementation

[0069] The present invention will be further described in detail below with reference to embodiments. These descriptions are for illustrative purposes only and are not intended to limit the scope of the invention.

[0070] This invention provides a simulation agent model recommendation method based on multi-dimensional feature fusion. The selection of candidate models is based on the analysis of each individual model and the summary of engineering application experience, resulting in the candidate models and their characteristics shown in Table 1.

[0071] Table 1. Comprehensive Comparison of Four Candidate Agent Models

[0072] characteristic PRS Kriging RBF SVR Modeling efficiency ★☆☆☆ ★★★☆ ★★☆☆ ★★★★ Prediction efficiency ★★★★ ★★☆☆ ★★★☆ ★★★★ High-dimensional capabilities ★☆☆☆ ★★☆☆ ★★★☆ ★★★★ noise reduction capability ★★★☆ ★☆☆☆ ★★☆☆ ★★★★ accuracy ★★☆☆ ★★★★ ★★★★ ★★★☆ Data sparsity capability ★☆☆☆ ★★★★ ★★★☆ ★★☆☆ Nonlinear capability ★★☆☆ ★★★★ ★★★★ ★★★★

[0073] Modeling efficiency refers to the time cost of building a surrogate model using the current surrogate modeling method, which can also be understood as training time. Because the SVR algorithm requires least-squares optimization during training, involving an iterative process, its time cost is relatively high. The PRS algorithm, on the other hand, only requires performing a matrix inversion once, so its time cost is the lowest.

[0074] Prediction efficiency refers to the execution efficiency of the surrogate model after training. Since PRS and SVR are both regression algorithms, they perform deterministic algebraic equation operations during prediction, resulting in high prediction efficiency. Kriging and RBF are essentially interpolation algorithms, so they involve reading sample data, making them less efficient than the two regression algorithms mentioned above.

[0075] High-dimensionality capability refers to whether it is suitable for data samples with high control variable dimensions. According to relevant literature, RBF and SVR perform better in this regard.

[0076] Noise robustness refers to whether the current surrogate model can make accurate predictions when the sample data is not faithful (e.g., the input control variables are not significantly different, but the single output variable oscillates significantly). Since PRS and SVR are both regression algorithms, they are better able to reflect global characteristics and have better noise robustness than interpolation algorithms, but the accuracy of regression algorithms is relatively worse than that of interpolation.

[0077] Data sparsity is a concern for current surrogate model methods, which are affected by the uniformity of data distribution. When the uniformity of sample data distribution is poor, it becomes difficult to calculate accurate results in regions far from data points. Based on past experience, the Kringing algorithm performs well in terms of data sparsity, followed by RBF, while regression algorithms such as PRS and SVR perform poorly in this regard.

[0078] Nonlinearity capability refers to whether the surrogate model's predictive ability can be guaranteed when the data distribution is highly nonlinear. Overall, except for PRS, all other methods can accurately predict highly nonlinear sample data.

[0079] like Figure 1 As shown, the simulation agent model recommendation method based on multi-dimensional feature fusion of the present invention includes the following operations:

[0080] Feature extraction is performed on the sample data used to train the model to obtain the dimensional features, quantity features, spatial distribution features and nonlinear features of the sample data, and to form the data fingerprint of the sample data: fingerprint vector Φ=[dim,N,h,S];

[0081] Where dim is the dimension of the control variable of the sample data, N is the number of data points, h is the Hopkins statistic that reflects the spatial distribution of the sample data, and S is the curvature entropy that reflects the nonlinearity of the sample data.

[0082] Based on the pre-defined correspondence between fingerprint vectors and calculation functions, the calculation functions corresponding to each feature of the current fingerprint vector are obtained, and then the candidate proxy models are scored respectively; the proxy model with a high score is recommended, and the proxy model with a low score is not recommended.

[0083] The rating results for the proxy model are as follows:

[0084] S m =f dim (f N (f h (f S (B m )))),0<S m <10

[0085] Among them, S m For the scoring result; B m Basic score; f dim Calculate the function for the control variable dimensions;

[0086] f N The function for calculating the sample size; f h The function to calculate the Hopkins statistic; f S This is the function for calculating curvature entropy.

[0087] The sample data, data fingerprints, and recommendation decisions will be explained in detail below.

[0088] 1. Data Sample Preprocessing

[0089] A data point is defined as a set of data containing both input and output.

[0090] Iterate through the original data samples used to train the model, remove outlier data (delete outlier data), and merge duplicate data points (keep only one set);

[0091] Outlier data: When a set of data contains data types other than real number types, such as Inf, NaN, Chinese characters, symbols, strings, etc., the set of data is considered outlier data.

[0092] The repeated data points: When two sets of data are completely identical and both are non-outlier data points, then these two sets of data are considered to be repeated data points.

[0093] 2. Extract data fingerprints

[0094] Feature extraction is performed on the preprocessed sample data to obtain four dimensions of features: dimensionality, quantity, spatial distribution, and nonlinearity. These features together form a fingerprint vector, which is the data fingerprint of the data sample.

[0095] Fingerprint vector Φ = [dim, N, h, S];

[0096] Where: dim represents the dimension of the control variables in the sample data (for example, if the input of the sample data is two variables, then the dimension of the control variables is two-dimensional), N represents the number of sample data (number of data points), h represents the Hopkins statistic of the sample data, and S represents the curvature entropy of the sample data.

[0097] The following provides the methods for calculating the control variable dimension dim, the number of data points N and h, the Hopkins statistic h, and the curvature entropy S in the fingerprint vector of a data fingerprint:

[0098] 1) A data point is defined as a set of data containing both input and output.

[0099] When the control variable of the dataset used as sample data has a dimension of d and a length of n, it is considered to have n data points, and each data point has a dimension of d.

[0100] Then the control variable dimension dim of the sample data is d, and the number of data points N is n;

[0101] 2) The Hopkins statistic is a spatial statistic used to test the spatial randomness of spatially distributed variables, thereby determining whether the data can be clustered. Its acquisition steps are as follows:

[0102] With x ij Let x represent the j-th dimension control variable of the i-th data point, and transpose it to obtain x. i =[x i1 ,x i2 ,...x id ] T ;

[0103] Generate a space D:

[0104] D = {x1, x2, ... x} n}

[0105] And in space D, x i ∈R d , i = 1, 2,..., n;

[0106] Uniformly extract m points P1, P2,... P m from D in sequence, and for each point P i Before extraction, 1 ≤ i ≤ ≤ m < n, find the nearest neighbor v point of P i in D excluding itself, and let X i be the Euclidean distance between P i and v, that is:

[0107]

[0108] Randomly generate m points Q1, Q2,... Q n again uniformly in space D, and for each point Q i , 1 ≤ i ≤ ≤ m < n, find the nearest neighbor w point of Q i in D, and let Y i be the Euclidean distance between Q i and w, that is:

[0109]

[0110] Then the Hopkins statistic h is:

[0111]

[0112] The range of h value is [0, 1]. The larger h is, the worse the data distribution uniformity is, and the smaller h is, the better the data uniformity is.

[0113] Furthermore, the evaluation criterion of the Hopkins statistic h is:

[0114] When h ≤ 0.4, the data distribution uniformity: completely uniform distribution;

[0115] When 0.4 < h ≤ 0.5, the data distribution uniformity is good, with local slight clustering;

[0116] When 0.5 < h ≤ 0.55, the data distribution is relatively uniform, with a certain clustering trend;

[0117] When 0.55 < h ≤ 0.6, the data distribution uniformity is average, with a strong clustering trend;

[0118] When 0.6 < h ≤ 0.75, the data distribution uniformity is poor, showing significant clustering characteristics;

[0119] When 0.75 < h ≤ 1.0, the data distribution uniformity is very poor, and there are strong clustering characteristics.

[0120] 3) Curvature Entropy is an information - theoretic index that quantifies the local bending complexity of a curve or surface, originating from the measurement of the disorder of geometric shapes. Its core idea is to regard the curvature change of a curve as a random process and reflect the regularity of the shape through the entropy value. This concept was proposed by Japanese scholars when analyzing the cognitive experiments of human perception of curve shapes, combining differential geometry (curvature) and information theory (Shannon entropy). Curvature Entropy describes the uncertainty of the probability distribution of the angle change of the curve tangent direction. The higher the entropy value, the more random the curvature change (the more complex the shape); the lower the entropy value, the more ordered the curvature change (the smoother the shape).

[0121] The curvature entropy is obtained by calculating the global normalized curvature entropy:

[0122] ① Construct a local quadratic surface based on the data points in the sample data. For the current data point y i , select k data points outside its neighborhood and denote them as y i , and then construct a system of quadratic surface equations based on the weighted least - squares method: <> j

[0123]

[0124]

[0125] i where c is a constant term, T represents the transpose of a vector or matrix; g is the gradient vector, and H is the Hessian matrix (reflecting the bending degree of the local surface), and both (g, H) are defined by the partial derivatives of f at the current data point x

[0126] ② Calculate the eigenvalues of the Hessian matrix. Since the curvature of the surface is captured by the Hessian matrix H, after performing eigenvalue decomposition on H, curvature information in different directions can be obtained: <000>

[0127] H = QΛQ T , Λ = diag(λ1, λ2, …, λ d )

[0128] where Q represents the matrix composed of unit eigenvectors obtained after eigenvalue decomposition of the H matrix, T represents the transpose of a vector or matrix, λ represents the eigenvalue of the matrix H, and λ1 ~ λ d represents the 1st to dth eigenvalues, and d is the variable dimension of the input data.

[0128] ③ Calculate the curvature probability distribution in each direction. Since the H matrix is a real - symmetric matrix, its eigenvalues are all real numbers. Since the orientation of the surface bend is not concerned when calculating the curvature, the absolute values of the eigenvalues of the H matrix are taken to represent the magnitude of the curvature.

[0129]

[0130] Where λ k Let p represent the k-th eigenvalue obtained from the decomposition (there are d eigenvalues ​​in total). Each eigenvalue is calculated separately. k λ represents the k-th eigenvalue. k The weights among all eigenvalues ​​range from a maximum of 1 to a minimum of 0.

[0131] ④ Calculate the normalized curvature entropy. The normalized curvature entropy is distributed between 0 and 1. The closer it is to 0, the better the linearity of the data distribution. The closer it is to 1, the stronger the nonlinearity.

[0132]

[0133] Si is the weight p corresponding to the k-th eigenvalue. k Information entropy;

[0134] ⑤ Repeat the above process (①~④) to calculate the global normalized curvature entropy of all valid points in the neighborhood:

[0135] Get the current data point x i After obtaining the corresponding curvature entropy, change the data point and repeat the above steps until all data points are calculated. Take the average of the normalized curvature entropy of all data points (N) to obtain the global normalized curvature entropy of all data points.

[0136]

[0137] If we consider that due to the distribution of data points, not all data points can be used to calculate curvature entropy, then N iterations here represent the number of all data points (valid data points) from which curvature entropy can be calculated.

[0138] 3. Implement the recommendation rating strategy

[0139] The recommendation scoring strategy is based on the current data fingerprint, which scores the four candidate surrogate model methods (PRS, Kriging, RBF, and SVR). The one with the higher score is recommended, and the one with the lower score is not recommended.

[0140] The total score for the proxy model is:

[0141] S m =f dim (f N (f h (f S (B m )))),0<S m <10

[0142] Among them, S m For the scoring result; B m Basic score; f dim Calculate the function for the control variable dimensions;

[0143] f N The function for calculating the sample size; f h The function to calculate the Hopkins statistic; f S This is the function for calculating curvature entropy.

[0144] The pre-defined correspondence between fingerprint vectors and calculation functions is as follows:

[0145]

[0146]

[0147] Apart from the cases listed above, in all other cases, f of all candidate proxy models dim f N f h f S All are: ×1.

[0148] The recommendation decision for a candidate agent model is based on the following:

[0149] ①7 ≤ rating ≤ 10: Recommended for use;

[0150] ②6 ≤ rating ≤ 7: The effect is average, but it can be used;

[0151] ③ 0 ≤ rating ≤ 6: Not recommended;

[0152] ④ If all algorithms score less than 6 points, it indicates that further sample data is needed for re-evaluation.

[0153] Specific implementation examples are given below.

[0154] Example 1: Typical fingerprints for which Kriging is applicable: High spatial correlation scenarios

[0155] Applicable scenarios: geostatistics, spatial interpolation

[0156] Data fingerprint: [dim=8, N=500, h=0.85, S=0.55]

[0157] Kriging score result: S m ={[(7.0×1)+1.0]×1}+1.5=9.5;

[0158] RBF score result: S m ={[(7.0×1)×1]+0.8}+1.2=9.0;

[0159] SVR rating result: S m ={[(6.5×1)×1]×1}+0.5=7.0;

[0160] PRS score result: S m ={[(6.0×1)×1]×1}×1=6.0;

[0161] Rating results: 10 (Kriging) > 9.0 (RBF) > 7.0 (SVR) > 6.0 (PRS)

[0162] Recommendation: Higher scores are more recommended. Which option to use is up to the user; users are not prevented from choosing lower-scoring options.

[0163] Feature description: A high h value (0.85) indicates strong spatial clustering; a medium S value (0.55) indicates moderate nonlinearity, but does not exceed Kriging's trend fitting ability; the sample size is moderately small (N=500), suitable for most interpolation or regression algorithms.

[0164] Example 2: Typical fingerprints applicable to SVR: high-dimensional, strongly nonlinear scenarios

[0165] Data fingerprint: [dim=18, N=3000, h=0.45, S=0.78]

[0166] Kriging score result: S m ={[(7.0×1)×1]×1}×1=7.0;

[0167] RBF score result: S m ={[(7.0×1)×1]+0.8}+0.7=8.5;

[0168] SVR rating result: S m ={[(6.5+2.0)×1]×1}+2.0=10.5;

[0169] PRS score result: S m ={[(6.0×0.5)×1]×1}×0.5=1.5;

[0170] Scoring results: 10.5 (SVR) > 8.5 (RBF) > 7.0 (Kriging) > 1.5 (PRS)

[0171] Applicable scenarios: Nonlinear dynamic processes of mechanisms, such as contact collisions, landing gear retraction and extension, etc.

[0172] Feature description:

[0173] A high dim value (18) will trigger the "curse of dimensionality". The kernel function of SVR has a stronger generalization ability in high-dimensional space and is more suitable for the current scenario. A high S value (0.78) reflects strong nonlinearity. The kernel trick of SVR can be used to map complex relationships. A low h value (0.45) indicates that the data distribution is relatively uniform and is suitable for most proxy model algorithms.

[0174] Example 3: Typical fingerprints applicable to RBF: Large-scale uniform data scenarios

[0175] Data fingerprint: [dim=12, N=15000, h=0.52, S=0.35]

[0176] Applicable scenarios: Spatial signal processing, scattered data point interpolation

[0177] Scoring results: SVR = RBF > Kriging > PRS

[0178] Feature description:

[0179] The low S value (0.35) reflects weak nonlinearity, which can give full play to the advantages of RBF in fitting smooth surfaces; the sample data is close to uniform distribution (h=0.52), which is particularly suitable for interpolation algorithms.

[0180] Example 4: PRS model applicable vectors: low-dimensional, linear scenes

[0181] Data fingerprint: [dim=3, N=200, h=0.25, S=0.15]

[0182] Applicable scenarios: rapid conceptual design, rapid estimation with few samples

[0183] Rating results: Kriging > PRS > RBF > SVR

[0184] Feature description:

[0185] The low d value (3) avoids the explosion of polynomial terms and keeps the model simple; the low S value (0.15) reflects the near-linear relationship and matches the linear / quadratic basis functions of PRS; the low h value (0.25) indicates that the sample points are very evenly distributed. Kriging has a slight advantage over PRS, but PRS is simple and has strong interpretability.

[0186] Example 5: Selection of a surrogate model for the characteristic curve of an aero-engine compressor

[0187] Taking the characteristic curve of an aero-engine fan as an example, the relationship between its normalized mass flow rate, normalized pressure ratio, and normalized speed is as follows: Figure 2As shown. In actual modeling, it is generally necessary to calculate the normalized mass flow rate based on the normalized pressure ratio and normalized rotational speed. Since the data points are scattered, they cannot be calculated using conventional interpolation methods. Therefore, a surrogate model needs to be constructed to achieve the above purpose.

[0188] Construct a set of sample data, including normalized mass flow rate, normalized pressure ratio, and normalized rotational speed. After preprocessing, remove outlier and duplicate data to obtain Data = [rpm, Pi, w].

[0189] Data fingerprint: [dim=2, N=150, h=0.787969, S=0.585079]

[0190] Kriging score result: S m ={[(7.0×1)+1.0]×1}×1=8.0;

[0191] RBF score result: S m ={[(7.0×1)×1]+0.8}+1.2=9.0;

[0192] SVR rating result: S m ={[(6.5×1)×1]×1}+0.5=7.5;

[0193] PRS score result: S m ={[(6.0+1.0)×1]×1}×1=7.0;

[0194] Rating results: 9 (RBF) > 8.0 (Kriging) > 7.5 (SVR) > 7.0 (PRS)

[0195] Feature description:

[0196] The high h-value (0.787969) indicates that the sample data is highly unevenly distributed, with significant local clustering. Figure 2 As can be seen from the results, the PRS method is clearly unsuitable; a moderate S-value (0.585079) indicates moderate nonlinearity, and all methods can be used; for small sample sizes (N=150), interpolation methods are preferred, and the scoring results also show that RBF and Kriging are highly recommended, while SVR can be used but is not a high priority. The scoring results proposed in this invention are consistent with the observations of the data characteristics.

[0197] The embodiments given above are preferred examples for implementing the present invention, and the present invention is not limited to the above embodiments. Any non-essential additions or substitutions made by those skilled in the art based on the technical features of the present invention are within the protection scope of the present invention.

Claims

1. A recommendation method for a simulation agent model based on multi-dimensional feature fusion, characterized in that, Includes the following operations: Feature extraction is performed on the sample data used to train the model to obtain the dimensional features, quantity features, spatial distribution features and nonlinear features of the sample data, and to form the data fingerprint of the sample data: fingerprint vector Φ=[dim,N,h,S]; Where dim is the dimension of the control variable of the sample data, N is the number of data points, h is the Hopkins statistic that reflects the spatial distribution of the sample data, and S is the curvature entropy that reflects the nonlinearity of the sample data. Based on the pre-defined correspondence between fingerprint vectors and calculation functions, the calculation functions corresponding to each feature of the current fingerprint vector are obtained, and then the candidate proxy models are scored respectively; the proxy model with a high score is recommended, and the proxy model with a low score is not recommended. The rating results for the proxy model are as follows: S m =f dim (f N (f h (f S (B m )))),0<S m <10 Among them, S m For the scoring result; B m Basic score; f dim Calculate the function for the control variable dimensions; f N The function for calculating the sample size; f h The function to calculate the Hopkins statistic; f S This is the function for calculating curvature entropy.

2. The simulation agent model recommendation method based on multi-dimensional feature fusion as described in claim 1, characterized in that, A data point is defined as a set of data containing both input and output. The sample data used for training the model were also preprocessed as follows: outlier data were removed, and duplicate data points were merged, keeping only one set. Outlier data: When a set of data contains data types other than real numbers, the set of data is considered outlier data; The repeated data points: When two sets of data are completely identical and both are non-outlier data points, then these two sets of data are considered to be repeated data points.

3. The simulation agent model recommendation method based on multi-dimensional feature fusion as described in claim 1, characterized in that, The dim, N, and h in the fingerprint vector are obtained as follows: When the control variable of the dataset used as sample data has a dimension of d and a length of n, it is considered to have n data points, and each data point has a dimension of d. Then the control variable dimension dim of the sample data is d, and the number of data points N is n; With x ij Let x represent the j-th dimension control variable of the i-th data point, and transpose it to obtain x. i =[x i1 ,x i2 ,...x id ] T ; Generate a space D: D={x1,x2,...x n } And in space D, x i ∈R d i = 1, 2, ..., n; m points P1, P2, ... P are randomly selected from D in sequence. m And for each point P i Before extraction, 1≤i≤m<n, find P. i Remove itself from the nearest neighbor v in D, and let X i For P i The Euclidean distance between v and v is: In space D, m points Q1, Q2, ... Q are randomly generated again in a uniform manner. n And for each point Q i Given that 1 ≤ i ≤ m < n, find Q. i Find the nearest neighbor w point in D, and let Y i For Q i The Euclidean distance between w and w is: Then the Hopkins statistic h is: The range of h values ​​is [0,1]. The larger the h value, the worse the uniformity of the data distribution; the smaller the h value, the better the uniformity of the data distribution.

4. The simulation agent model recommendation method based on multi-dimensional feature fusion as described in claim 1, characterized in that, The curvature entropy S in the fingerprint vector is the globally normalized curvature entropy, which is obtained as follows: ① Construct a local quadratic surface based on data points in the sample data; For the current data point y i Select k y values ​​within its neighborhood. i Data points other than those mentioned above, and denoted as y. j Then, based on the weighted least squares method, a system of equations for the quadratic surface is constructed: Where c is a constant term, T denotes transpose; g is the gradient vector, and H is the Hessian matrix representing the curvature of the local surface. Both are derived from f at the current data point y. i The definition of partial derivatives at point A; ② Calculate the eigenvalues ​​of the Hessian matrix and perform eigenvalue decomposition on H to obtain curvature information in different directions: H=QΛQ T ,Λ=diag(λ1,λ2,…,λ d ) Where Q represents the matrix composed of unit eigenvectors obtained by eigenvalue decomposition of matrix H, T represents the transpose of a vector or matrix, λ represents the eigenvalues ​​of matrix H, and λ1~λ2 d Represents the eigenvalues ​​from 1 to d; ③ Take the absolute value of the eigenvalues ​​of the H matrix to characterize the magnitude of the curvature: Where λ k For the k-th eigenvalue obtained from the decomposition, p k For λ k Weights among all eigenvalues; ④ Calculate the normalized curvature entropy: Where Si is p k Information entropy; ⑤ Calculate the normalized curvature entropy of all valid points in the neighborhood for each of steps ① to ④. Average the normalized curvature entropy of all data points to obtain the global normalized curvature entropy.

5. The simulation agent model recommendation method based on multi-dimensional feature fusion as described in claim 1, characterized in that, The correspondence between the preset fingerprint vector and the calculation function is as follows: Apart from the cases listed above, in all other cases, f of all candidate proxy models dim f N f h f S All are: ×1.

6. The simulation agent model recommendation method based on multi-dimensional feature fusion as described in claim 1, characterized in that, The recommendation decision for a candidate agent model is based on the following: ①7 ≤ rating ≤ 10: Recommended for use; ②6 ≤ rating ≤ 7: The effect is average, but it can be used; ③ 0 ≤ rating ≤ 6: Not recommended; ④ If all algorithms score less than 6 points, it indicates that further sample data is needed for re-evaluation.

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