{"title":"基于平衡截断和迭代有理Krylov算法的双线性系统降阶逼近新方法","authors":"H. Nasiri Soloklo, N. Bigdeli","doi":"10.24200/sci.2023.61596.7394","DOIUrl":null,"url":null,"abstract":"This paper proposes a hybrid method for order reduction of the bilinear system model using Balanced Truncation (BT) and Bilinear Iterative Rational Krylov Algorithm (BIRKA). Bilinear BT (BBT) has low accuracy but guarantees stability, while BIRKA convergence suffers from sensitivity to initial choice of reduced-order system. The proposed method first determines the order of the reduced bilinear model by minimizing the index of Integral Square Error (ISE). Then, the initial guess of reduced-order system is provided via two approaches, BBT and Linear BT (LBT), to guarantee the convergence of BIRKA. The result of BBT is a good stable initial guess for BIRKA, but it is very computationally expensive to solve the generalized Lyapunov equations to find the solution. LBT decreases the computational complexity by providing the initial guess via solving the Lyapunov equations. To further decrease the complexity, the condition number is substituted in place of the eigenvalues in BIRKA. Three bilinear test systems are considered to show the efficiency of proposed method. Finally, the performance of the proposed method is compared with some classical methods. The results show that the convergence probability of BIRKA increases. Also, the time for the determining the model order reduction decreases.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms\",\"authors\":\"H. Nasiri Soloklo, N. Bigdeli\",\"doi\":\"10.24200/sci.2023.61596.7394\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes a hybrid method for order reduction of the bilinear system model using Balanced Truncation (BT) and Bilinear Iterative Rational Krylov Algorithm (BIRKA). Bilinear BT (BBT) has low accuracy but guarantees stability, while BIRKA convergence suffers from sensitivity to initial choice of reduced-order system. The proposed method first determines the order of the reduced bilinear model by minimizing the index of Integral Square Error (ISE). Then, the initial guess of reduced-order system is provided via two approaches, BBT and Linear BT (LBT), to guarantee the convergence of BIRKA. The result of BBT is a good stable initial guess for BIRKA, but it is very computationally expensive to solve the generalized Lyapunov equations to find the solution. LBT decreases the computational complexity by providing the initial guess via solving the Lyapunov equations. To further decrease the complexity, the condition number is substituted in place of the eigenvalues in BIRKA. Three bilinear test systems are considered to show the efficiency of proposed method. Finally, the performance of the proposed method is compared with some classical methods. The results show that the convergence probability of BIRKA increases. Also, the time for the determining the model order reduction decreases.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24200/sci.2023.61596.7394\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24200/sci.2023.61596.7394","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms
This paper proposes a hybrid method for order reduction of the bilinear system model using Balanced Truncation (BT) and Bilinear Iterative Rational Krylov Algorithm (BIRKA). Bilinear BT (BBT) has low accuracy but guarantees stability, while BIRKA convergence suffers from sensitivity to initial choice of reduced-order system. The proposed method first determines the order of the reduced bilinear model by minimizing the index of Integral Square Error (ISE). Then, the initial guess of reduced-order system is provided via two approaches, BBT and Linear BT (LBT), to guarantee the convergence of BIRKA. The result of BBT is a good stable initial guess for BIRKA, but it is very computationally expensive to solve the generalized Lyapunov equations to find the solution. LBT decreases the computational complexity by providing the initial guess via solving the Lyapunov equations. To further decrease the complexity, the condition number is substituted in place of the eigenvalues in BIRKA. Three bilinear test systems are considered to show the efficiency of proposed method. Finally, the performance of the proposed method is compared with some classical methods. The results show that the convergence probability of BIRKA increases. Also, the time for the determining the model order reduction decreases.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.