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It is necessary to investigate the identification of structural systems and unknown inputs under non-Gaussian measurement noises. In recent years, a few scholars have proposed methods of particle filter (PF) with unknown input for such task. However, these PF with unknown input require that unknown inputs appear in structural measurement equations. Such requirement may not always met, which restrict their practical application. To overcome this limitation, a generalized extended Kalman particle filter with unknown input (GEKPF-UI) is proposed for the simultaneous identification of structural systems and unknown inputs under non-Gaussian measurement noises. The proposed method is more general than the existing methods of PF with unknown input as it is applicable whether measurement equations contain or do not contain unknown inputs. It is proposed to establish the importance density function of PF by the generalized extended Kalman filter with unknown input (GEKF-UI) recently developed by the authors, in which GEKF-UI is utilized to generate particles and allow particles to carry the latest observational information. The effectiveness of the proposed method is verified through two numerical identification examples of a nonlinear hysteretic structure under two types of unknown inputs, including unknown external excitation and unknown seismic inputs, respectively.

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It is of great significance to identify structural state-parameters and the unknown seismic inputs using partial measurements of structural acceleration responses for the rapid evaluation of structures after unknown seismic excitations. However, unknown seismic inputs do not directly appear in the observation equations of measured absolute floor accelerations of building structures, i.e., there is no direct feedthrough of unknown seismic inputs in the observation equations. Current methods for the identification of joint structural systems and unknown inputs are either inapplicable or greatly influenced by measurement noises. In this paper, a method so-called smoothing extended Kalman filter with unknown input without direct feedthrough (smoothing EKF-UI-WDF) is proposed. The identification algorithm is derived in the framework of minimum-variance unbiased estimation (MVUE), and the smoothing technique is adopted to introduce subsequent observation steps in the current identification step. Then, structural states, parameters, and unknown seismic excitations without direct feedthrough are simultaneously identified recursively with only a few steps delay, and the identification results are tolerant to measurement noises. The proposed method is verified by a numerical simulation model and a practical engineering case study. Both identification results validate the effectiveness of the proposed method for the simultaneous identification of structural systems and seismic inputs without direct feedthrough.