几种模型降阶方法的仿真对比研究  

Comparison Research of Several Model Reduction Methods Based on Simulation

作　　者：代冀阳[1,1] 冉桥[1] 蒋沅[1] 黄盈[1] 

机构地区：[1]南昌航空大学无损检测技术教育部重点实验室,江西南昌330063

出　　处：《计算机仿真》2013年第2期257-260,共4页Computer Simulation

基　　金：国家自然科学基金资助项目(61164015);航空科学基金(2011ZA56021);江西省研究生创新专项资金(YC10A114)

摘　　要：算法比较研究,比较几种主要模型降阶方法的优缺点,为给工程应用提供方法参考。利用奇异值分解的模型降阶方法具有较好的理论性质,能够保持降阶系统结构特性,但计算成本较高故不适合大规模动态系统的降阶;采用矩匹配的模型降阶方法计算简便,适合大规模系统降阶,但无法保证降阶系统稳定性,也很难求得降阶误差界。最小二乘降阶法同时利用了系统的Gramian矩阵和Krylov子空间理论,结合了二者的优点,使得降阶过程计算简化,保持了降阶系统的结构特性,而且降阶误差进一步减小。仿真算例证明了最小二乘法较前两者具有优越性。To provide a suitable method for engineering application, we proposed a comparison of several reduction methods. Model reduction based on Singular Value Decomposition holds good theoretical features, which preserves the structure of the reduced model, however it can not be used in large - scale dynamical systems because high computation prices. Method based on moment matching is suitable for large - scale systems, but its stability is not preserved, and the error bound is not available either. The Least Squares method uses the system＇s Gramian matrix and the Krylov subspace theory, which combines the advantages of the two so that the reducing process becomes simple, the structure of reduced system is preserved and the error bound becomes smaller. The simulation proves its advantages.

关 键 词：奇异值分解 矩匹配 模型降阶 最小二乘法 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]