Gradient prediction method based on POD technology in aerodynamic configuration optimization design

Abstract

The invention relates to application based on the POD technology, in particular to a gradient prediction method based on the POD technology in aerodynamic configuration optimization design, and aims at solving the problem that the gradient calculation amount is too large in the gradient-based aerodynamic configuration optimization design process. The method specifically comprises the following steps: (a) randomly extracting a plurality of airfoil profile samples near an initial profile parameter vector; (b) solving gradient distribution vectors corresponding to different airfoil profile samples; (c) forming a covariance matrix C, and obtaining a POD modal coefficient sample corresponding to the airfoil profile sample through POD analysis; (d) constructing an RBF proxy model of the POD modal coefficient with respect to the airfoil parameters; (e) predicting a POD modal coefficient corresponding to any airfoil profile through the constructed model; and (f) according to a chain derivation rule, calculating a gradient vector of the objective function about the shape parameters, and applying the gradient vector to aerodynamic shape optimization design.

Description

technical field [0001] The invention relates to an application based on POD technology, in particular to a gradient prediction method based on POD technology in aerodynamic shape optimization design. Background technique [0002] In the optimization design of aerodynamic shape, the gradient method is the most common type of algorithm in engineering. It uses the gradient of the objective function with respect to the shape parameters to construct the search direction to find the final shape that meets the optimal aerodynamic performance. A key problem of the gradient method is how to quickly and accurately obtain the gradient of the objective function with respect to the shape parameters. The calculation efficiency of the gradient significantly affects the efficiency of the optimization design. [0003] The finite difference method is a relatively simple traditional method for solving the gradient. It obtains the change value of the objective function by slightly perturbing t...

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Problems solved by technology

[0004] In order to solve this problem, the present invention proposes a gradient prediction method based on POD technology in the optimization design of aerodynamic shape, which can quickly predict the objective function based on the problem of excessive gradient calculation in the process of gradient-based aerodynamic shape optimization design. The variable gradient method significantly improves the optimization design efficiency through the rapid prediction of the gradient. This method has nothing to do with the dimension of the design variable and the shape parameterization method, and has wide applicability in engineering

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