Abstract
The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.
Highlights
Academic Editor: Zeqi Lu e large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters
Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. is paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. e POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades
A series of model order reduction methods were proposed to reduce the number of DOFs of the system to improve the efficiency of calculation in the field of science and engineering, for example, center manifold method, Lyapunov–Schmidt (L-S) method, Galerkin method, nonlinear Galerkin method, mode synthesize method, Krylov approximation method, balanced truncation method, and POD method [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. us, the area of model reduction contains a broad set of mathematical methods to yield and evaluate the reduced models. ese model order reduction methods have been applied in various engineering fields and become more mature, but each method has its adaptability and limitations
Summary
E POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. A series of model order reduction methods were proposed to reduce the number of DOFs of the system to improve the efficiency of calculation in the field of science and engineering, for example, center manifold method, Lyapunov–Schmidt (L-S) method, Galerkin method, nonlinear Galerkin method, mode synthesize method, Krylov approximation method, balanced truncation method, and POD method [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. Nonlinear function is at least second-order differentiable, so according to center manifold theory [13, 23,24,25], there is a differential homeomorphism mapping in partial neighborhood of (u, v) (0, 0) so that formulas (3) and (4) can be expressed as follows: Model order reduction
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