为快速进行模型的降阶,结合平衡截断(Balanced Truncation,BT)方法和特征正交分解(Proper Orthogonal Decomposition,POD)方法提出一种模型降阶方法.该方法采用频域POD快照矩阵低阶逼近系统的可控、可观Gram矩阵;通过奇异值分解(Singula...为快速进行模型的降阶,结合平衡截断(Balanced Truncation,BT)方法和特征正交分解(Proper Orthogonal Decomposition,POD)方法提出一种模型降阶方法.该方法采用频域POD快照矩阵低阶逼近系统的可控、可观Gram矩阵;通过奇异值分解(Singular Value Decomposition,SVD)提取BT+POD模态,对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶模型(Reduced Order Model,ROM);该模型就成为全阶模型(Full Order Model,FOM)的ROM.通过对阶数n=406的LTI SISO系统和阶数n=9的2区间电力系统进行的验证表明,在保留BT方法输入输出平衡特性的基础上,该方法效率高于BT方法.展开更多
The main goal of this paper is to construct an efficient reduced-order model (ROM) for unsteady aerodynamic force modeling. Balanced truncation (BT) is presented to address the problem. For conventional BT method, it ...The main goal of this paper is to construct an efficient reduced-order model (ROM) for unsteady aerodynamic force modeling. Balanced truncation (BT) is presented to address the problem. For conventional BT method, it is necessary to compute exact controllability and observability grammians. Although it is relatively straightforward to compute these matrices in a control setting where the system order is moderate, the technique does not extend easily to high order systems. In response to the challenge, snapshots-BT (S-BT) method is introduced for high order system ROM construction. The outline idea of the S-BT method is that snapshots of primary and dual system approximate the controllability and observability matrices in the frequency domain. The method has been demonstrated for 3 high order systems: (1) unsteady motion of a two-dimensional airfoil in response to gust, (2) AGARD 445.6 wing aeroelastic system, and (3) BACT (benchmark active control technology) standard aeroservoelastic system. All the results indicate that S-BT based ROM is efficient and accurate enough to provide a powerful tool for unsteady aerodynamic force modeling.展开更多
Vibration mode based model reduction methods like Component Mode Synthesis (CMS) will be compared to methods coming from control engineering, namely moment matching (MM) and balanced truncation (BT). Conclusions based...Vibration mode based model reduction methods like Component Mode Synthesis (CMS) will be compared to methods coming from control engineering, namely moment matching (MM) and balanced truncation (BT). Conclusions based on the theory together with a numerical demonstration will be presented. The key issues on which the paper is focused are the reduction of metallic structures, the sensitivity of the reduced model to varying boundary conditions, full system response, accurate statics and the possibility to determine “a priori” the number of needed modes (trial vectors). These are important topics for the use of reduction methods in general and in particular for the implementation of FE models in multi body system dynamics where model reduction is widely used. The intention of this paper is to give insight into the methods nature and to clarify the strengths and limitations of the three methods. It turns out, that in the considered framework CMS delivers the best results together with a clear strategy for an “a priori” selection of the modes (trial vectors).展开更多
文摘为快速进行模型的降阶,结合平衡截断(Balanced Truncation,BT)方法和特征正交分解(Proper Orthogonal Decomposition,POD)方法提出一种模型降阶方法.该方法采用频域POD快照矩阵低阶逼近系统的可控、可观Gram矩阵;通过奇异值分解(Singular Value Decomposition,SVD)提取BT+POD模态,对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶模型(Reduced Order Model,ROM);该模型就成为全阶模型(Full Order Model,FOM)的ROM.通过对阶数n=406的LTI SISO系统和阶数n=9的2区间电力系统进行的验证表明,在保留BT方法输入输出平衡特性的基础上,该方法效率高于BT方法.
基金Supported by the National Natural Science Foundation of China (Grant No. 90816008)Doctoral Fund of Ministry of Education of China (Grant No. 20070699054)
文摘The main goal of this paper is to construct an efficient reduced-order model (ROM) for unsteady aerodynamic force modeling. Balanced truncation (BT) is presented to address the problem. For conventional BT method, it is necessary to compute exact controllability and observability grammians. Although it is relatively straightforward to compute these matrices in a control setting where the system order is moderate, the technique does not extend easily to high order systems. In response to the challenge, snapshots-BT (S-BT) method is introduced for high order system ROM construction. The outline idea of the S-BT method is that snapshots of primary and dual system approximate the controllability and observability matrices in the frequency domain. The method has been demonstrated for 3 high order systems: (1) unsteady motion of a two-dimensional airfoil in response to gust, (2) AGARD 445.6 wing aeroelastic system, and (3) BACT (benchmark active control technology) standard aeroservoelastic system. All the results indicate that S-BT based ROM is efficient and accurate enough to provide a powerful tool for unsteady aerodynamic force modeling.
文摘Vibration mode based model reduction methods like Component Mode Synthesis (CMS) will be compared to methods coming from control engineering, namely moment matching (MM) and balanced truncation (BT). Conclusions based on the theory together with a numerical demonstration will be presented. The key issues on which the paper is focused are the reduction of metallic structures, the sensitivity of the reduced model to varying boundary conditions, full system response, accurate statics and the possibility to determine “a priori” the number of needed modes (trial vectors). These are important topics for the use of reduction methods in general and in particular for the implementation of FE models in multi body system dynamics where model reduction is widely used. The intention of this paper is to give insight into the methods nature and to clarify the strengths and limitations of the three methods. It turns out, that in the considered framework CMS delivers the best results together with a clear strategy for an “a priori” selection of the modes (trial vectors).
