Taher, S., Li, J., and Fang, H. (2023).  Simultaneous seismic input and state estimation with optimal sensor placement for building structures using incomplete acceleration measurements.  Mechanical Systems and Signal Processing, 188, 110047.

Abstract

Simultaneous real-time input and state estimation and optimal sensor placements are investigated in this paper, focusing on systems without direct feedthrough, such as earthquake-excited building structures with absolute floor acceleration measurements. Current studies showed that system properties such as strong observability, strong* detectability (the asterisk distinguishes strong* detectability from strong detectability), and invertibility conditions are crucial to the stability and convergence of unknown input and state estimation, but they can often be violated in practice. Consequently, uncertainties such as modeling errors and measurement noise can greatly degrade the accuracy and stability of the estimations. Estimation in this case has remained challenging due to the above reasons. To fill this gap, this paper develops an optimal sensor placement algorithm (OSPA) for real-time unknown input and state estimation, which ensures the required system conditions are met. The developed OSPA is integrated with two optimal real-time Kalman-based filters, a minimum-variance unbiased input and state estimation filter (MVUIS) and an Augmented State Kalman Filter (ASKF), for simultaneous input and state estimation. In particular, the MVUIS is presented in a recursive three-step structure without using the arbitrary matrix in the gain, which makes no assumptions on the input but requires strong* detectability. To avoid the requirement, ASKF is derived from the MVUIS by incorporating prior knowledge of the input. The developed OSPA along with the MVUIS and ASKF provide the optimal input and state estimation in real-time without incurring low-frequency drift or unstable estimations. Notably, the OSPA improves the performance of MVUIS by reducing amplitude errors and enhances the accuracy of ASKF by reducing phase errors. The developed OSPA integrated with the MVUIS and ASKF are validated through numerical and experimental studies as well as a real-world instrumented building structure under earthquakes using incomplete absolute acceleration measurements.