Keywords: Kalman filter, nonlinear structural dynamics, state tracking, parameter identification.

Simultaneous state tracking and model calibration for stochastic dynamic systems is usually pursued using the extended Kalman filter. However, in the presence of severe nonlinearities due to damage inception and growth, Kalman filtering may become unstable [1,2,3]. To improve the outcomes, a statistical linearization of the system evolution equations has been recently adopted within the sigma-point Kalman filtering approach [4,5,6,7]. Aiming to develop a real-time health monitoring procedure for composite structures experiencing delamination under dynamic loadings, in this study we focus on a single degree-of-freedom structural system suffering elasticity and strength degradation, and we comparatively present a possible implementation of the extended and sigma-point Kalman filters.

We show that the sigma-point Kalman filter behaves optimally for state tracking; even when the observed variable is diverging, the whole state of the system can be accurately tracked. As for calibration of softening material laws, outcomes can be instead biased by measurement errors. It is important to note that independent of the loading type and of the noise level, the sigma-point Kalman filter always outperforms (in terms of matching between available data and converged estimates of model parameters) the extended filter.

1

A. Corigliano, S. Mariani, "Parameter identification of a time-dependent elastic-damage interface model for the simulation of debonding in composites", Composites Science & Technology, 61, 191-203, 2001. doi:10.1016/S0266-3538(00)00171-8

2

A. Corigliano, S. Mariani, "Simulation of damage in composites by means of interface models: parameter identification", Composites Science & Technology, 61, 2299-2315, 2001. doi:10.1016/S0266-3538(01)00123-3

3

A. Corigliano, S. Mariani, "Parameter identification in explicit structural dynamics: performance of the extended Kalman filter", Computer Methods in Applied Mechanics and Engineering, 193, 3807-3835, 2004. doi:10.1016/j.cma.2004.02.003

4

S. Julier, J. Uhlmann, H. Durrant-Whyte, "A new method for the nonlinear transformation of means and covariances in filters and estimators", IEEE Transactions on Automatic Control, 45, 477-482, 2000. doi:10.1109/9.847726

5

S. Mariani, A. Ghisi, "Unscented Kalman filtering for nonlinear structural dynamics", Nonlinear Dynamics, 49, 131-150, 2007. doi:10.1007/s11071-006-9118-9

6

S. Mariani, "Failure of layered composites subject to impacts: constitutive modeling and parameter identification issues", In G. Mendes, B. Lago, (Editors), "Strength of Materials", Nova Science Publishers, NY (USA), 97-131, 2009.

7

S. Mariani, "Failure assessment of layered composites subject to impact loadings: a finite element, sigma-point Kalman filter approach", Algorithms, 2, 808-827, 2009. doi:10.3390/a2020808

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)