Keywords: nonlinear dynamics, composites, delamination, interface models, Kalman filter, parallel processing.

The sigma-point Kalman filter (S-PKF) [1,2] has shown promising performances when parameter identification and state tracking are simultaneously pursued in damaged structures [3,4]. Unlike the extended Kalman filter, it does not require the computation of the gradient of the system evolution equations; instead, the S-PKF continuously improves the estimates by averaging the responses of a set of independent sigma-points, which evolve in time according to the actual system dynamics. Being N the number of unknown model parameters and tracked state variables gathered in a joint state vector, sigma-points to deal with amount to 2N+1: the S-PKF technique can thus become computationally demanding, but its formulation can be exploited in a parallel implementation. With the final goal of developing a health monitoring system for damaging composite structures, the speed-up factor (or parallel efficiency) of a parallelization scheme, optimized within a shared-memory (OPEN-MP) architecture, is here explored.

In this study, the S-PKF is adopted to calibrate an interface constitutive model for inter-laminar phases in a composite laminate subjected to impact loadings: allowing for pseudo-experimental data, the relevant mode I tensile strength and fracture energy are identified. In standard plane impact tests, observations consist in the free velocity at the rear surface of the laminate, and only a quite narrow time window of the observation signal can carry information concerning the properties of the inter-laminar phases. Even in this challenging test, the S-PKF demonstrates good performance concerning the tracking of the system dynamics in noisy environments. Concerning model calibration, converged estimates of the inter-laminar tensile strength well match the target data, whereas estimates of the fracture energy are often biased by the measurement noise.

1

S. Julier, J. Uhlmann, H. Durrant-Whyte, "A new approach for filtering nonlinear systems", In Proceedings of the American Control Conference, 1628-1632, Seattle, 1995. doi:10.1109/ACC.1995.529783

2

E. Wan, R. van der Merwe, "The unscented Kalman filter", In S. Haykin, (Editor), "Kalman filtering and neural networks", 221-280, John Wiley & Sons, Inc., 2001. doi:10.1002/0471221546.ch7

3

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

4

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

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