Nonlinear structural dynamical system identification using adaptive particle filters

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

Nonlinear filters for chaotic oscillatory systems

“…For a comparative study between Monte Carlo assimilation algorithms and variational techniques, the reader may refer to [1,29]. The most widely used Monte Carlo based filtering algorithms are (i) ensemble Kalman filter (EnKF) [30][31][32]; and (ii) particle filter (PF) [33][34][35][36][37][38][39][40][41].…”

Joint maximum a posteriori state path and parameter estimation in stochastic differential equations

“…To illustrate the proposed estimator, we apply it on simulated data of the Duffing oscillator, a benchmark model for modeling nonlinear dynamics and chaos [Aguirre and Letellier, 2009] and state estimation in SDEs [Ghosh et al, 2008, Khalil et al, 2009, Namdeo and Manohar, 2007. We note that the standard Duffing oscillator does not satisfy Assum.…”

Damped One-Mode Vibration Model State and Parameter Estimation via Pre-Filtered Moving Horizon Observer

“…Moreover, the method is sensitive to initial condition of the estimate. In this case the approaches based on probabilistic Bayesian Particle Filter (PF) methods with the application of stochastic Monte Carlo simulations lead to more accurate estimates of state and parameters of the nonlinear vibration dynamics (Ching et al, 2006;Namdeo and Manohar, 2007;Sajeeb et al, 2009). …”

“…The lumped parameter model often describes the vibration dynamics sufficiently where this model was experimentally applied in relation to EKF and PF in Jones et al (1995) and Namdeo and Manohar (2007); Uchino and Ohta (1986) respectively.…”