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An unscented kalman filter with a decreased sigma points set size for dynamic nonlinear structural system identification

In this work we examine methods for decreasing the sigma points set size, used in an unscented Kalman filter (UKF), for efficient state estimation and identification of nonlinear structural systems. The computational cost of the filtering process is proportional to the number of sigma points used and minimizing the required number of points would therefore have important implications, especially for detailed, large-scale models. A minimum number of sigma points is necessary in each filtering application in order to provide mean and nonsingular covariance estimates. Incorporating more sigma points than this minimum set improves the accuracy of the estimates and can take advantage of a richer information content that can possibly exist in the structural data, but at the same time increases the computational cost. A comprehensive study is thus performed in this work, investigating reduced sigma points filters development and performance, comparing them to the standard UKF and other existing methods, and providing guidelines about their use in structural identification problems. Several nonlinear structural identification examples are provided, from a theoretical application with a 3-mass damped system, to an experimental performance of a cantilever steel beam, and larger-scale models based on simulated results of multi-story steel moment frames subjected to earthquake motions. Most of the nonlinear structural models in the provided examples are based on a hysteretic beam element model that supports the filtering procedure ideally in terms of computational implementation and performance. In the considered beam element formulation, hysteretic degrees of freedom are introduced and are set to evolve according to Bouc-Wen type evolution equations. The advantage of the formulation is that the stiffness matrix of the element is replaced by one elastic stiffness matrix and one plasticity matrix, which may only be needed to be evaluated once, given that inelasticity is treated through the hysteretic evolution equations.

Author(s):

Konstantinos Papakonstantinou    
Department of Civil Engineering & Engineering Mechanics, Columbia University
United States

Andrew Smyth    
Department of Civil Engineering & Engineering Mechanics, Columbia University
United States