Online jointly estimation of hysteretic structures using the combination of central difference Kalman filter and Robbins–Monro technique

Abstract

Rapid assessment of structural safety and performance right after the occurrence of significant earthquake shaking is crucial for building owners and decision-makers to make informed risk management decisions. Hence, it is vital to develop online and pseudo-online health monitoring methods to quantify the health of the building right after significant earthquake shaking. Many Bayesian inference–based methods have been developed in the past which allow the users to estimate the unknown states and parameters. However, one of the most challenging part of the Bayesian inference–based methods is the determination of the parameter noise covariance matrix. It is especially difficult when the number of unknown states and parameters is large. In this study, an effective online joint estimation method for nonlinear hysteretic structures, with consideration of degradation and pinching phenomena, is proposed. Simultaneous estimation of states and parameters is conducted using the combination of a central difference Kalman filter as an effective estimator and the Robbins–Monro stochastic approximation technique as the parameters noise covariance matrix regulator. The proposed algorithm is implemented on three shear buildings with 36, 54, and 90 unknown states and parameters. To verify the performance of the system identification method, robust simulations with synthetic measurement noises and modeling errors were generated using the Monte Carlo random simulation method. The result shows the proposed method can be used to estimate the unknown parameters and states of highly nonlinear systems efficiently and effectively.