Combined impulse-response/Kalman filtering (CIRKF) for input/state estimation

Abstract

A combined approach is proposed for estimating forces and states based on a sequential implementation of an impulse response matrix deconvolution and a Kalman filter. The deconvolution is formulated from an experimental identification to compute the system inputs while the Kalman filter employs an updated model to estimate the states. The split implementation allows for improved input estimates that current joint estimation techniques struggle to determine when model mismatches are introduced. The enhanced forces are later on incorporated into the Kalman filter to generate estimates of the states at any particular location of the geometric domain, covering the deficiency of the impulse response filter to estimate unmeasured states. This methodology is reliant on measurements of commonly used sensors for experimental modal analysis and thus they can be complementarily acquired during the process of model updating. The approach alleviates the adverse effects induced by model inaccuracies, typical of structures with complex boundary conditions, large frequency bands of interest and high modal density. Additionally, this paper proposes an optimization procedure of the covariance matrix entries in order to minimize the error between observations and the Kalman filter estimates. The optimization circumvents the problem of accuracy loss in the Kalman filtering estimates in absence of prior knowledge of the system uncertainties. An industrial example of a complex mechanical component is analyzed in order to demonstrate the effectiveness of the current approach.