JOURNAL OF SOUND AND VIBRATION Journal of Sound and Vibration 306 (2007) 524–563 Nonlinear structural dynamical system identification using adaptive particle filters Vikas Namdeo, C.S. Manohar à Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India Received 30 January 2007; received in revised form 18 May 2007; accepted 27 May 2007 Abstract The problem of identifying parameters of nonlinear vibrating systems using spatially incomplete, noisy, time-domain measurements is considered. The problem is formulated within the framework of dynamic state estimation formalisms that employ particle filters. The parameters of the system, which are to be identified, are treated as a set of random variables with finite number of discrete states. The study develops a procedure that combines a bank of self-learning particle filters with a global iteration strategy to estimate the probability distribution of the system parameters to be identified. Individual particle filters are based on the sequential importance sampling filter algorithm that is readily available in the existing literature. The paper develops the requisite recursive formulary for evaluating the evolution of weights associated with system parameter states. The correctness of the formulations developed is demonstrated first by applying the proposed procedure to a few linear vibrating systems for which an alternative solution using adaptive Kalman filter method is possible. Subsequently, illustrative examples on three nonlinear vibrating systems, using synthetic vibration data, are presented to reveal the correct functioning of the method. r 2007 Elsevier Ltd. All rights reserved. 1. Introduction Engineering structures are generally designed to behave linearly and, consequently, linear models for strain–displacement relations, stress–strain laws, and energy dissipation mechanisms could be considered adequate for the purpose of structural analysis, design, and optimization. Concomitant with the development of methods for mathematical modeling and solution of resulting equations of these problems, extensive efforts have been made in the exiting literature to develop methods for identification of structural model parameters, and to reconcile predictions of mathematical and experimental models [1–6]. Within the framework of linear system modeling, issues related to characterizing damping mechanisms at the structure level, joint flexibility, boundary conditions, and material constitutive laws, are intimately connected with experimental investiga- tions. Also, several algorithmic issues related to non-uniqueness of solutions, spatio-temporal incompleteness of response measurement, presence of measurement noise, modeling uncertainties, and difficulties arising out ARTICLE IN PRESS www.elsevier.com/locate/jsvi 0022-460X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2007.05.040 à Corresponding author. Tel.: +91 80 2293 3121; fax: +91 80 2360 0404. E-mail addresses: vnamdeo@civil.iisc.ernet.in (V. Namdeo), manohar@civil.iisc.ernet.in (C.S. Manohar).