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

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-08-16 DOI:10.24200/sci.2023.61596.7394
H. Nasiri Soloklo, N. Bigdeli
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引用次数: 0

摘要

本文提出了一种利用平衡截断(BT)和双线性迭代有理克雷洛夫算法(BIRKA)对双线性系统模型进行降阶的混合方法。双线性BT (BBT)精度较低,但能保证稳定性,而BIRKA收敛对降阶系统的初始选择敏感。该方法首先通过最小化积分平方误差(ISE)指标来确定降阶双线性模型的阶数。然后,通过BBT和线性BT (LBT)两种方法给出了降阶系统的初始猜测,以保证BIRKA的收敛性。对于BIRKA来说,BBT的结果是一个很好的稳定的初始猜测,但要求解广义Lyapunov方程来找到解,计算成本非常高。LBT通过求解李雅普诺夫方程来提供初始猜测,从而降低了计算复杂度。为了进一步降低复杂度,用条件数代替BIRKA中的特征值。以三个双线性测试系统为例,验证了该方法的有效性。最后,将该方法的性能与一些经典方法进行了比较。结果表明,BIRKA的收敛概率增大。此外,确定模型订单减少的时间也减少了。
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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.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
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.
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