A dual Kalman filter approach for state estimation via output-only acceleration measurements Saeed Eftekhar Azam a , Eleni Chatzi b , Costas Papadimitriou a,n a Department of Mechanical Engineering, University of Thessaly, Volos 38334, Greece b Institute of Structural Engineering, ETH Zürich, Zürich, Switzerland article info Article history: Received 28 June 2014 Received in revised form 24 January 2015 Accepted 5 February 2015 Available online 26 February 2015 Keywords: Kalman filter State estimation Input estimation Response prediction Unknown input abstract A dual implementation of the Kalman filter is proposed for estimating the unknown input and states of a linear state-space model by using sparse noisy acceleration measurements. The successive structure of the suggested filter prevents numerical issues attributed to un- observability and rank deficiency of the augmented formulation of the problem. Furthermore, it is shown that the proposed methodology furnishes a tool to avoid the so-called drift in the estimated input and displacements commonly encountered by existing joint input and state estimation filters. It is shown that, by fine-tuning the regulatory parameters of the proposed technique, reasonable estimates of displacements and velocities of structures can be accomplished. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction This paper contributes to the problem of state estimation in the entire body of the metallic structures that undergo vibrations due to unknown input forces during their operational life, aiming at prediction of fatigue damage identification. The idea of using the estimated response of the structures for fatigue damage identification was first suggested by Papadimitriou et al. [1]; where a technique was introduced that uses the Kalman filter for estimating power spectral densities of the strain in the body of the structure thereby predicting the remaining fatigue life. To estimate the fatigue damage, a time history of the strains in the hotspot points of the structure is required. To estimate the strain in a point of interest, the displacement field around that point is needed; therefore, a reliable state estimate could lead to a reliable fatigue damage identification. The subject of estimation of the states of a partially observed dynamic system in an stochastic frame has been studied by many scientists and there are well developed algorithms to manage both linear (e.g. the Kalman filter [2]) and nonlinear (e.g. the particle filter [3], the unscented Kalman filter [4]) state-space models. Dealing with structural systems, the states of the system are displacements and velocities of the response of the system at some points, namely degrees-of-freedom (DOF) on the structure. In practical cases, it is difficult or sometimes impossible to measure displacements and velocities of the system, hence when a knowledge of the displacements and velocities is required, a state estimation algorithm could be used to provide estimates of the whole state of the system. The Bayesian filters that exist in the literature, take advantage of the correlation between the observable part of the state of the system and the hidden part, and furnish an estimate of the whole Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing http://dx.doi.org/10.1016/j.ymssp.2015.02.001 0888-3270/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail address: costasp@uth.gr (C. Papadimitriou). Mechanical Systems and Signal Processing 60-61 (2015) 866–886