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Self‐regularized pseudo time‐marching schemes for structural system identification with static measurements
Author(s) -
Banerjee B.,
Roy D.,
Vasu R. M.
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2797
Subject(s) - inverse problem , kalman filter , ensemble kalman filter , system identification , dynamic mode decomposition , mathematics , noise (video) , sensitivity (control systems) , algorithm , regularization (linguistics) , covariance , mathematical optimization , computer science , extended kalman filter , mathematical analysis , statistics , database , machine learning , artificial intelligence , electronic engineering , engineering , image (mathematics) , measure (data warehouse)
We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non‐linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least‐square solution is through a regularized Gauss–Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo‐dynamical GNM (PD‐GNM) update equation addresses the major numerical difficulty associated with the near‐zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo‐dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo‐dynamic ensemble Kalman filter (PD‐EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of the PD‐EnKF by proposing an inner iteration within every time step. Results using the pseudo‐dynamic strategy obtained through PD‐EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD‐EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright © 2009 John Wiley & Sons, Ltd.