Optimal model‐based state estimation in mechanical and structural systems. Issue 4 (30th December 2011) - Hernandez, Eric M.
SUMMARY In many applications, such as control, monitoring, assessment, and failure detection in mechanical and structural systems, the state of the system is sought. However, in almost all cases, the full state vector is not directly measured, and it must be reconstructed from sparse measurements contaminated by noise. If in addition, the excitations are not (or cannot be) measured, such as the case with wind loads, wave loading, and others, the problem becomes more challenging and standard deterministic methods are not applicable. This paper presents a model‐based state estimation algorithm for online reconstruction of the complete dynamic response of a partially instrumented structure subject to realizations of random loads. The proposed algorithm operates on noise‐contaminated measurements of dynamic response, a finite element model of the system, and a spectral density description of the random excitation and noise. The main contribution of the paper is the development of a second‐order estimator that can be directly implemented as a modified version of the finite element model of the system while minimizing the state error estimate covariance. The proposed observer results in a suboptimal Kalman filter that can be implemented as a modified version of the original finite element model of the system with added dampers and collocated forces that are linear combinations of the measurements. The proposed method is successfully illustrated and compared with the standard Kalman filter in a mass–spring–damper system under various ideal and nonideal conditions. Copyright © 2011 John Wiley & Sons, Ltd.