A compact self-adaptive recursive least square approach for real-time structural identification with unknown inputs

A new online tracking technique, based on recursive least square with adaptive multiple forgetting factors, is presented in this article which can estimate abrupt changes in structural parameters during excitation and also identify the unknown inputs to the structure, for example, earthquake signal. The method considers an adaptive rule for each of the forgetting factors assigned to each of the unknown parameters and thus enables simultaneous identification of different time-varying parameters of the system. The method is validated through both linear and nonlinear case studies, with different excitations and damage scenarios. The results show that the proposed algorithm can effectively identify the time-varying parameters such as damping, stiffness as well as unknown excitations with high computational efficiency, even when the measured data are contaminated with different levels of noise. However, when damage occurs while the excitation is small, the identification error remains at a small range, and therefore, covariance cannot be amplified to effectively track the changes in unknown parameters.