Papers
Vikas Namdeo and C S Manohar, 2007, Nonlinear structural dynamical system identification using adaptive particle filters, Journal of Sound and Vibration, 306(3-5), 524-563. (among the top 25 most downloadable paper in July – September, 2007)
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.
LikeVikas Namdeo and C S Manohar, 2008, Force state maps using reproducing kernel particle method and kriging based functional representations, Computer Modeling in Engineering and Sciences, vol.32 (no. 3), 123-160.
The problem of identification of nonlinear system parameters from measured time histories of response under known excitations is considered. Solutions to this problem are obtained by using the force state mapping technique with two alternative functional representation schemes. These schemes are based on the application of reproducing kernel particle method (RKPM) and kriging techniques to fit the force state map. The RKPM has the capability to reproduce exactly polynomials of specified order at any point in a given domain. The kriging based methods represent the function under study as a random field and the parameters describing this field are optimally determined based on available observations. The present study investigates the performance of RKPM and kriging based fits to the force state maps for a variety of nonlinear dynamical systems. The study also examines the application of force state maps in (a) determining the fixed points limit cycles of the system and their stability, (b) determining the properties of the linear system which would result if nonlinearity were to be absent, and (c) dealing with nonlinearities that are continuous but not differentiable and nonlinearities that are discontinuous at a set of points within the domain of interest. Illustrative examples on single and multi-degrees of freedom nonlinear systems are presented to demonstrate the scope of the proposed procedures.
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