On the observability and identifiability of nonlinear structural and mechanical systems
On the observability and identifiability of nonlinear structural and mechanical systems
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DOI：
10.1002/stc.1690
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发表时间：
2015-03-01
影响因子：
5.4
通讯作者：
Smyth, Andrew W.
中科院分区：
文献类型：
--
作者：
Chatzis, Manolis N.;Chatzi, Eleni N.;Smyth, Andrew W.
动态系统的先验可观测性问题，即在给定一组特定测量量的情况下，系统的状态是否可以被识别的问题，在包括生物学、经济学和工程学在内的多个学科中具有极其重要的意义。通常，需要确定系统的一些参数，因此，可辨识性问题，即测量是否导致参数值的唯一解或有限解，是令人感兴趣的。可辨识性与可观测性问题一起出现，当状态的概念可以扩展到包括动态系统的实际状态变量及其参数时。这导致了非线性增广系统的公式，即使原始系统的动态运动方程可能是线性的。在这项工作中，考虑了三种方法来判定非线性动态系统的可观性和可辨识性。更具体地说，对于状态方程和测量方程都是解析的系统，可以使用基于Lie导数的几何可观测性秩条件。如果方程是有理的，代数方法也是可用的。这些方法包括确定参数解的有限性或唯一性的代数可观测性方法和代数可辨识性算法。用上述方法研究了土木工程中适用问题的可观测性和可识别性，并突出了它们与相应概念之间的联系。版权所有(C)2014 John Wiley&Sons，Ltd.
The question of a priori observability of a dynamic system, that is, whether the states of a system can be identified given a particular set of measured quantities is of utmost importance in multiple disciplines including biology, economics, and engineering. More often than not, some of the parameters of the system need to be identified, and thus the issue of identifiability, that is, whether the measurements result in unique or finite solutions for the values of the parameters, is of interest. Identifiability arises in conjunction with the question of observability, when the notion of states may be augmented to include both the actual state variables of the dynamic system and its parameters. This results in the formulation of a nonlinear augmented system even though the dynamic equations of motion of the original system might be linear. In this work, three methods for the observability and identifiability of nonlinear dynamic systems are considered. More specifically, for a system whose state and measurement equations are analytic, the geometric Observability Rank Condition, which is based on Lie derivatives may be used. If the equations are rational, algebraic methods are also available. These include the algebraic observability methods and the algebraic identifiability algorithms which determine the finiteness or uniqueness of the solutions for the parameters. The aforementioned methods are used to study the observability and identifiability of suitable problems in civil engineering and highlight the connections between them and the corresponding concepts. Copyright (c) 2014 John Wiley & Sons, Ltd.