CN-122021722-A - High-speed pneumatic derivative analytical modeling method and system based on symbolic regression

CN122021722ACN 122021722 ACN122021722 ACN 122021722ACN-122021722-A

Abstract

The invention discloses a high-speed pneumatic derivative analysis modeling method and a system based on symbolic regression, which belong to the technical field of pneumatic modeling and artificial intelligence intersection of aircrafts, and acquire and preprocess a pneumatic data set of the high-speed aircraft; defining grammar of generating candidate symbol expression and constructing expression tree, adopting hierarchical symbol regression frame to make modeling to obtain analysis model based on training set, verifying prediction accuracy of analysis model on test set and making physical consistency analysis, making uncertainty quantization on analysis model to obtain uncertainty estimation of its prediction, finally outputting analysis model and uncertainty estimation of mathematical expression form for describing relationship between aerodynamic derivative and flight state variable.

Inventors

Xiang Gaoxiang
CHEN YANGYANG
MA XINGPU
WU MENGJIA
Quan Enqian
GAO ZIYI
TU QIRONG

Assignees

西北工业大学

Dates

Publication Date: 20260512
Application Date: 20260413

Claims (9)

1. The high-speed pneumatic derivative analysis modeling method based on symbolic regression is characterized by comprising the following steps of: S1, acquiring a pneumatic data set of a high-speed aircraft under a specific configuration, wherein the pneumatic data set comprises a flight state variable and a corresponding pneumatic derivative, preprocessing the pneumatic data set, and dividing the preprocessed pneumatic data set into a training set and a testing set; s2, defining grammar for generating candidate symbol expressions, and constructing an expression tree based on the grammar for generating the candidate symbol expressions, wherein the expression tree comprises leaf nodes and internal nodes, the leaf nodes comprise state variables and trainable constants, and the internal nodes comprise a monobasic function and a dibasic function; s3, modeling by adopting a hierarchical symbol regression framework based on a training set, wherein the modeling comprises the following steps: The first stage, carrying out global structure search on the expression tree based on genetic programming to obtain a candidate symbol expression structure set; The second stage, converting the candidate symbol expression structure in the candidate symbol expression structure set into a differentiable symbol neural network, and optimizing parameters of the symbol neural network based on a training set to obtain an analysis model; S4, carrying out numerical verification on the analysis model on the test set to obtain prediction precision and carrying out comparison analysis; S5, carrying out uncertainty quantification on the analytical model to obtain uncertainty estimation of analytical model prediction, wherein the uncertainty estimation is used for indicating the prediction reliability of the analytical model in different input areas; s6, outputting an analysis model and uncertainty estimation of the analysis model, wherein the analysis model is a mathematical expression describing the relationship between the aerodynamic derivative and the flight state variable.
2. The method for high-speed pneumatic derivative analytical modeling based on symbolic regression according to claim 1, wherein the unitary function in S2 comprises a sine function, a cosine function, an exponential function, a logarithmic function, an absolute value function, a square function and a cubic function, and the binary function comprises addition, subtraction, multiplication and division.
3. The method for modeling high-speed pneumatic derivative analysis based on symbolic regression according to claim 1, wherein the specific steps of the genetic programming of the first stage in S3 are as follows: Generating an initial population comprising a plurality of expression tree individuals; evaluating the fitness of each individual through a fitness function, wherein the fitness function comprises the original fitness and a physical constraint penalty term; selecting operation is executed according to the fitness, and cross operation and mutation operation are executed on the selected individuals, so that a next generation population is generated; And iteratively evolving until the termination condition is met, and outputting the candidate symbol expression structure set.
4. A method of modeling high-speed pneumatic derivative analysis based on symbolic regression according to claim 3, wherein the fitness function is calculated as follows: Replacing constant leaf nodes in the expression tree with trainable parameters, and optimizing the trainable parameters on a training set through gradient descent to obtain a data fitting error as an original fitness; Constructing a physical constraint penalty term according to physical priori knowledge; And carrying out weighted summation on the original fitness and the physical constraint penalty term to obtain the comprehensive fitness.
5. The method of high-speed pneumatic derivative analytical modeling based on symbolic regression as claimed in claim 4, wherein the physical constraint penalty includes symmetry constraint, antisymmetry constraint, derivative symbolic constraint and asymptotic behavior constraint.
6. The method of claim 3, wherein in the second stage S3, the network structure of the symbolic neural network is defined by a candidate symbolic expression structure, and the weights of the symbolic neural network are constant terms in the candidate symbolic expression structure; Based on the training set, parameters of the symbolic neural network are optimized through a gradient descent method, and the loss function comprises data fitting loss, physical constraint loss and L 2 regularization terms.
7. The method for high-speed pneumatic derivative analysis modeling based on symbolic regression according to claim 1, wherein the uncertainty quantization in S5 is achieved by adopting a Bayesian method or a Bootstrap integration method to obtain the mean value and variance of analysis model prediction.
8. A symbolic regression-based high-speed aerodynamic derivative analytical modeling system for implementing a symbolic regression-based high-speed aerodynamic derivative analytical modeling method as claimed in any one of claims 1-7, comprising: the data acquisition and preprocessing module is used for acquiring and preprocessing a pneumatic data set of the high-speed aircraft; The grammar definition and expression tree construction module is used for defining grammar for generating candidate symbol expressions and constructing an expression tree; The hierarchical symbol regression module is used for modeling by adopting a hierarchical symbol regression frame based on the training set to obtain an analytical model; the uncertainty quantization module is used for carrying out uncertainty quantization on the analysis model to obtain uncertainty estimation of model prediction; And the output module is used for outputting the analysis model and the uncertainty estimation.
9. The high-speed pneumatic derivative analytical modeling system based on symbolic regression of claim 8, wherein the hierarchical symbolic regression module comprises: The global structure searching unit is used for carrying out global structure searching on the expression tree based on genetic programming to obtain a candidate symbol expression structure set; And the local parameter optimization unit is used for converting the candidate symbol expression structures in the candidate symbol expression structure set into a symbol neural network, and optimizing parameters of the symbol neural network based on the training set to obtain an analysis model.

Description

High-speed pneumatic derivative analytical modeling method and system based on symbolic regression Technical Field The invention relates to the technical field of aircraft pneumatic modeling and artificial intelligence intersection, in particular to a high-speed pneumatic derivative analytical modeling method and system based on symbolic regression. Background Aerodynamic characteristics of high speed aircraft exhibit strong nonlinear, multivariable coupling and shock/viscous disturbance effects, the aerodynamic derivatives of which such as lift coefficientsCoefficient of resistanceCoefficient of pitch momentAnd the like are key preconditions for the design of flight control systems. Currently, high-speed pneumatic modeling relies mainly on the following three methods: 1. Physical-based engineering estimation/empirical formulation methods: simplified formulas derived using Newton flow theory, shock wave expansion theory, etc., such as . The method has definite physical meaning but lower precision, particularly has obvious error in complex flow state and wide parameter range, and can not meet the requirement of high-precision control. 2. Polynomial fitting and table look-up based on data, which are the dominant methods in current engineering practice. Data points are obtained by CFD calculations or experiments on discrete state points, and then polynomial surface fitting or direct multidimensional interpolation is employed. The method has the main defects of poor generalization capability of ①, unreliable prediction in a sparse or extrapolated area of data points, ② lack of physical hole finding, no clear physical meaning of polynomial coefficients, complex model and difficulty in mechanism analysis, ③ dimension disasters, exponential increase of required data quantity when state variables are increased, and heavy table look-up storage and query burden. 3. And a black box agent model based on deep learning, wherein a mapping from a state variable to a pneumatic coefficient is established by utilizing strong nonlinear fitting capacity of a deep neural network. Although DNN can reach very high precision, the DNN is essentially a 'black box' model, and tens of millions and hundreds of millions of parameters and complex nonlinear combinations thereof cannot provide an analytical expression which can be understood by human beings, are difficult to combine with a flight mechanics theory, and are not beneficial to frequency domain analysis, stability demonstration and online fault diagnosis of a control system. Therefore, the prior art faces a 'three-way paradox' in the field of high-speed pneumatic modeling, wherein the three core requirements of high precision, generalization and interpretability are difficult to meet simultaneously. Disclosure of Invention The invention aims to provide a high-speed pneumatic derivative analysis modeling method and system based on symbolic regression, which are used for solving the problems in the background technology. In order to achieve the above purpose, the invention provides a high-speed pneumatic derivative analysis modeling method and system based on symbolic regression, comprising the following steps: S1, acquiring a pneumatic data set of a high-speed aircraft under a specific configuration, wherein the pneumatic data set comprises a flight state variable and a corresponding pneumatic derivative, preprocessing the pneumatic data set, and dividing the preprocessed pneumatic data set into a training set and a testing set; s2, defining grammar for generating candidate symbol expressions, and constructing an expression tree based on the grammar for generating the candidate symbol expressions, wherein the expression tree comprises leaf nodes and internal nodes, the leaf nodes comprise state variables and trainable constants, and the internal nodes comprise a monobasic function and a dibasic function; s3, modeling by adopting a hierarchical symbol regression framework based on a training set, wherein the modeling comprises the following steps: The first stage, carrying out global structure search on the expression tree based on genetic programming to obtain a candidate symbol expression structure set; The second stage, converting the candidate symbol expression structure in the candidate symbol expression structure set into a differentiable symbol neural network, and optimizing parameters of the symbol neural network based on a training set to obtain an analysis model; S4, carrying out numerical verification on the analysis model on the test set to obtain prediction precision and carrying out comparison analysis; S5, carrying out uncertainty quantification on the analytical model to obtain uncertainty estimation of analytical model prediction, wherein the uncertainty estimation is used for indicating the prediction reliability of the analytical model in different input areas; s6, outputting an analysis model and uncertainty estimation of the analysis model, wherein the analysi