Framework for Probabilistic Assessment of Maximum Nonlinear Structural Response Based on Sensor Measurements: Discretization and Estimation

Abstract

A probabilistic framework to draw real-time inferences on the maximum response of an uncertain nonlinear structural system under stochastic excitation based on sensor measurements is proposed. The primary contributions are twofold: first, an exact discretization solution is derived for the system evolution equation for the nonlinear case. This is validated against a Taylor expansion discretization solution. Second, a methodology for robust Bayesian estimation of the time-evolving system state is proposed. The system is instrumented by sensors placed on the structure with inferences drawn using Kalman-based approaches. The sensor observations are used in real time to estimate system state without any knowledge of the time history of the input motion. The distribution of the maximum response is assessed. The proposed methodology is applied to a 10-story shear-type sample structure under earthquake loading. The interstory drift is analyzed with measured data collected through accelerometers placed on the building. A simulation approach is used to demonstrate the ability of the proposed methodology to accurately estimate nonlinear structural response based on sensor measurements. In addition, the method is shown to be robust to varying system characteristics. This includes uncertainties in the structural, ground, and input motion parameters, as well as varying measurement characteristics.