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On the applicability of the Ho-Kalman minimal realization theory

机译：Ho-Kalman最小实现理论的适用性

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摘要

The reduced-order model of a time-invariant linear dynamical system, excited by a force of an impulsive type, may be readily obtained using the Ho-Kalman minimal-realization algorithm. The method is based upon a particular factorization of the Hankel matrix in the Markovian representation of the discrete-time process. For stochastic systems, the applicability of the theory has been demonstrated by Akaike on the assumption that the excitation is a zero-mean white noise of a gaussian type. Some of the most widely known output-only identification methods, such as Eigensystem Realization Algorithm (ERA), Canonical Variate Analysis (CVA), and Balanced Realization (BR)) are based upon the above-mentioned work, with the aid of a robust factorization technique, such as Singular-Value Decomposition (SVD). Notwithstanding the growing popularity of the above methods, some aspects of their applicability are not yet understood. Two points are of particular interest: the first regards the applicability of the theory in highly damped systems; and the second regards its applicability to systems driven by excitations different from the one hypothesized. The aim of the present work is to define a reliable test on the hypotheses. Some numerical and experimental results are presented.
机译：可以使用Ho-Kalman最小实现算法轻松获得由脉冲型力激发的时不变线性动力学系统的降阶模型。该方法基于离散时间过程的马尔可夫表示中的汉克尔矩阵的特定因式分解。对于随机系统，Akaike已在假设激励是高斯型零均值白噪声的假设下证明了该理论的适用性。一些最广为人知的仅输出识别方法，例如本征系统实现算法（ERA），规范变量分析（CVA）和平衡实现（BR））是基于上述工作并借助鲁棒性的。分解技术，例如奇异值分解（SVD）。尽管上述方法越来越流行，但是其适用性的某些方面尚未被理解。有两点特别有趣：第一点是该理论在高阻尼系统中的适用性。第二个方面是它适用于由假设所激发的激励驱动的系统。本工作的目的是定义关于假设的可靠检验。给出了一些数值和实验结果。

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