Bayesian Joint State-Parameter-Input Estimation of Flexible-Base Buildings from Sparse Measurements Using Timoshenko Beam Models

Abstract

This paper presents a computationally efficient framework for the Bayesian identification of sparsely instrumented building structures that is amenable to rapid postearthquake condition assessment. Flexible-base Timoshenko beam models are employed within a Bayesian framework, which uses the extended Kalman filter (EKF) as a joint state-parameter-input estimation tool. Highly sparse and noisy measurements are utilized to identify the properties of the superstructure, the soil–foundation substructure, and the foundation input motion simultaneously under strong nonstationary shaking. The proposed framework is verified and its robustness is examined through synthetic problems featuring wide-ranging random initial errors. A validation study is also carried out on an instrumented building, namely, Caltech’s Millikan Library. The results show that the proposed framework is capable of estimating the unknown parameters of the soil-foundation-structure system together with the input excitation using as few as three measurement channels. Representing the superstructure by a model that offers an analytical solution to system dynamics and determining the analytical derivatives for EKF using direct differentiation has led to a computationally efficient and accurate tool that robustly identifies the system from a minimal set of measurements.