On the observability and identifiability of nonlinear structural and mechanical systems

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.