On the use of equivalent forces for structural health monitoring based on joint input-state estimation algorithms

For the monitoring of large structures where the loading is typically characterized by large uncertainties in temporal and/or spatial evolution, algorithms capable of estimating a set of response driving equivalent forces are strongly desired. In this context, several Kalman-type coupled input-state and coupled input-state-parameter filters have recently been developed, allowing for an estimation of the full-field dynamic response of a structure from only a limited number of vibration 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 to assess the applicability of equivalent force based monitoring to various engineering problems. Concepts are illustrated by comparing true and assumed noise statistics as well as the response prediction accuracy for different numerical examples, 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.