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The use of polynomial chaos for parameter identification from measurements in nonlinear dynamical systems
Author(s) -
Pandurangan Rangaraj,
Chaudhuri Abhijit,
Gupta Sayan
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300232
Subject(s) - polynomial chaos , nonlinear system , dynamical systems theory , mathematics , polynomial , subspace topology , system identification , duffing equation , filter (signal processing) , dynamical system (definition) , nonlinear system identification , algorithm , computer science , mathematical analysis , monte carlo method , statistics , physics , quantum mechanics , database , computer vision , measure (data warehouse)
This study focuses on the development of a computationally efficient algorithm for the offline identification of system parameters in nonlinear dynamical systems from noisy response measurements. The proposed methodology is built on the bootstrap particle filter available in the literature for dynamic state estimation. The model and the measurement equations are formulated in terms of the system parameters to be identified ‐ treated as random variables, with all other parameters being considered as internal variables. Subsequently, the problem is transformed into a mathematical subspace spanned by a set of orthogonal basis functions obtained from polynomial chaos expansions of the unknown system parameters. The bootstrap filtering carried out in the transformed space enables identification of system parameters in a computationally efficient manner. The efficiency of the proposed algorithm is demonstrated through two numerical examples ‐ a Duffing oscillator and a fluid structure interaction problem involving an oscillating airfoil in an unsteady flow.