Probabilistic framework for assessing maximum structural response based on sensor measurements

• Probabilistic framework based on Bayesian inference and Kalman filter is proposed.
• The maximum structural response under stochastic load is investigated.
• An analytical solution for extreme values of structural response is presented.
• The framework is successfully demonstrated by numerical application.
• Robustness of the framework to parameter uncertainties is demonstrated.

A probabilistic framework for Bayesian inference combined with extreme values of Gaussian processes is proposed to assess the maximum of the response of an uncertain structure instrumented with sensors and subject to a stochastic load. The framework is applied to the analysis of the inter-story drift of a multi-story shear-type building under seismic hazard using measurements collected by accelerometers. A cascade of two dynamic systems is proposed to model the stochastic ground motion and the response of the structure. We present an approximate analytical solution to estimate the distribution of the maximum response, and verify the accuracy and limitations of this solution against simulation results. Finally, robustness of the proposed framework to system uncertainties, including uncertainties in the structural characteristics, ground characteristics, and input motion parameters, is investigated.