On-line identification and damage detection in non-linear structural systems using a variable forgetting factor approach

This paper presents an adaptive on-line identification algorithm based on a newly defined variable forgetting factor approach. At each time step, the proposed methodology, a recursive least-square (Kalman filter) based algorithm, upgrades the adaptation gain matrix using an adaptive forgetting factor that is expressed as the ratio between the minimum value of the diagonal elements of the adaptation gain matrix and a set of pre-defined threshold values. This approach requires only acceleration measurements and is particularly robust to the integration errors introduced in determining velocities and displacements. Such an algorithm has been implemented for both parametric and non-parametric identification studies. For the case of no a priori information on the type of the structural model, an analytical method based on a power series of multivariable polynomial expansions has been introduced. The effectiveness and robustness of the proposed approach has been shown in various numerical simulations, considering the effects of excitation amplitude, of measurement noise, of a priori mass estimation error, and of exact-, under-, and over-parameterization of the structural model. General polynomial-type non-linear models such as Duffing and Van der Pole oscillators and Bouc-Wen hysteretic model have been analyzed using the proposed modeling process. The methodology presented in this paper leads to a more accurate and controllable on-line identification either for the estimation of time-invariant or time-varying structural parameters (for damage detection purposes) or for the prediction of the future structural response to dynamic loading. Copyright (C) 2003 John Wiley Sons, Ltd.