Displacement Estimation of a Nonlinear SDOF System under Seismic Excitation Using an Adaptive Kalman Filter

A displacement estimation method for a nonlinear single-degree-of-freedom (SDOF) system under seismic excitation is proposed based on an extended Kalman filter (EKF). This method first identifies time intervals where a system experiences significant nonlinearity. For a time period when the system is in an elastic phase, available observations for EKF are acceleration, displacement from numerical integration, and residual displacement. During a time period with significant nonlinearity, acceleration and virtual displacement measurements are employed as observations. Two EKF schemes are applied in this part. In the first scheme, displacement is estimated along with time-varying stiffness using an augmented state vector. In the second scheme, a bilinear hysteresis model with optimized system parameters is employed. The results are further smoothed by extended Kalman smoother (EKS). The proposed displacement estimation method is numerically studied on a bilinear SDOF system and applied to various hysteresis models and earthquake excitations. Data obtained in shaking table experiments on a full-scale bridge pier and a 4-story building are analyzed to validate the method. The displacements are estimated with high accuracies. (C) 2021 American Society of Civil Engineers.

Automated summary

This paper proposes a displacement estimation method for a nonlinear SDOF system based on the extended Kalman filter. The method identifies time intervals of significant nonlinearity and uses acceleration, displacement, and residual displacement as observations for estimation. Numerical studies and experimental validations show that the proposed method can accurately estimate displacements.