General Conditions for Full-Field Response Monitoring in Structural Systems Driven by a Set of Identified Equivalent Forces

Abstract

Kalman-type filters are being increasingly used to estimate the full-field dynamic response of structures from a limited set of vibration measurements. Various coupled input-state and coupled input-state-parameter estimation algorithms have been developed in this context, ranging from an initial formulation for use with linear reduced-order structural systems to alternative filters for dealing with acceleration-only data and recently also nonlinear model descriptions. The use of these algorithms allows for response prediction to be performed in the absence of any knowledge of the excitation forces, where often a set of response-driving equivalent forces is identified from the measurements. Up to now, the success of response estimation based on the identification of equivalent forces has been related only to whether these forces satisfy the so-called controllability requirements. In this contribution, controllability is shown to be an insufficient criterion for guaranteeing the accuracy of response estimates based on equivalent loading. Instead, the need for a new criterion is advocated, which would allow for a proper assessment of the applicability of equivalent force based monitoring to various engineering problems. Concepts are illustrated using simple numerical examples where a comparison is made between the true and assumed noise statistics and the response prediction accuracy for a number of distinct cases. These include situations where (a) the applied and equivalent loads are concentrated and collocated, (b) the applied and equivalent loads are concentrated and non-collocated, and (c) modal equivalent forces are used. Results are applicable to any Kalman-type coupled input-state estimator derived using the principles of minimum-variance unbiased estimation.