Comparative study on reduced models of unsteady aerodynamics using proper orthogonal decomposition and deep neural network

• Published in: Journal of mechanical science and technology Vol. 36; no. 9; pp. 4491 - 4499
• Main Authors: Shin, Jung-Hun, Cho, Kum-Won
• Format: Journal Article
• Language: English
• Published: Seoul Korean Society of Mechanical Engineers 01.09.2022; Springer Nature B.V; 대한기계학회
• Subjects: Accuracy; Airfoils; Artificial neural networks; Comparative studies; Computational efficiency; Computational fluid dynamics; Computing costs; Control; Drag; Dynamical Systems; Engineering; Errors; Fluid flow; Industrial and Production Engineering; Inviscid flow; Laminar flow; Lift; Linearity; Machine learning; Mathematical models; Mechanical Engineering; Microprocessors; Neural networks; Optimization; Original Article; Proper Orthogonal Decomposition; Reduced order models; Regression analysis; Simulation; Structured grids (mathematics); Thermal expansion; Unsteady aerodynamics; Unstructured grids (mathematics); Vibration; 기계공학; Deep neural network; Unsteady flow; Computational fluid dynamics; Reduced order model; Non-intrusive proportional orthogonal decomposition; Machine learning
• ISSN: 1738-494X; 1976-3824
• DOI: 10.1007/s12206-022-0813-3

Data-driven researches based on various machine learning techniques, are being actively explored in science and technology areas. In the area of computational fluid dynamics, several studies have already been conducted in a reduced order modeling technique using principal orthogonal basis called proper orthogonal decomposition (POD). Recently the application of machine learning techniques represented by deep learning or deep neural network (DNN) to the existing reduced order model methods is increasingly drawing attention with the development of processor hardware technology such as GPU. This study, based on the data produced by a state-of-the-art flow solver, examined both POD and DNN techniques to three different methods: a) classical non-intrusive POD with local linear regression, b) fully-connected DNN, and c) mixed POD-DNN. Method a) and c) have difference in computing superposed time expansion coefficients. The target problem is unsteady aerodynamic simulation of a two dimensional airfoil with fixed angle-of-attack and three grid and flow condition sets: (structured grid, inviscid flow, Mach 0.2), (structured grid, turbulent flow, Mach 0.6, Reynolds 1×10 5 ), and (unstructured grid, laminar flow, Mach 0.4). The comparison items were flow fields of velocity/pressure for all cases and aerodynamic lift/drag performances only for the structured grid system respectively. In these computations the overall tendencies of aerodynamic lift and drag are similar, but the POD with existing local linear regression method in calculating time coefficients was found to show the highly robust and moderately accurate predictions. The direct DNN method was judged to be able to be used as a feasible reduced order model since it overcomes linearity error at both extracting POD basis and determining coefficients and has an advantage to be able to infer flow variables in arbitrary spatial locations. It showed better level of error than the classical POD method, but had model optimization cost to tune hyper-parameters and determine how many training data should be obtained to mitigate partial error. As an intermediate way, the mixed POD-DNN provided a robust reduced model of airfoil aerodynamic simulation due to the moderate computational cost and better accuracy comparing to the two other methods, but it had a shortcoming of fixed spatial coordinates like the classical POD method because the POD basis has fixed dimension of vector. In conclusion, fully-connected deep neural network method is helpful to predict flow field distribution as a universal field approximator in accordance with time and space such as fluid field simulation in this study, and, what is better, using POD basis will augment the accuracy and computational efficiency.