Probabilistic framework for assessing maximum structural response based on sensor measurements

Abstract

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.

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

“…The RMS error is the highest when only one sensor is placed at the bottom floor because this captures the smallest response, thereby providing the least amount of information. Consistent with previous results in Tien et al (2013Tien et al ( , 2016 when only one sensor is placed on the structure, it is advantageous to mount it on the top floor compared to the bottom floor. As expected, looking at sensor noise, the error in the estimates increases with increasing uncertainty in the sensor measurements.…”

“…2. 10-story shear-type structure to be consistent with Tien et al (2016) and facilitate comparison of the results with the linear case. For application to real-world problems, a condensed structural parameter matrix can be used based on predicted eigenvalues of degrees of freedom with uncertainties added to reflect modeling errors.…”

“…In addition to real-time estimation of the structural response, this study is also interested in a probabilistic distribution of the maximum response. To obtain this, the probability of up-crossings of a nonstationary process as initially formulated by Rice (1944) and subsequently derived for non-zero-mean processes in Tien et al (2016) is used. This employs an approximation of the crossings of the maximum structural response over a safe threshold as Poisson events.…”

“…For reliability problems, the maximum response is of particular interest. To obtain the distribution of the maximum response, the authors use the analytical solution for extreme values of the inferred structural response derived in Tien et al (2016). This is based on an assumption of exceedances of extreme values over safe thresholds as Poisson events, which holds for high thresholds and lowprobability events.…”

“…Previously, Tien et al (2016) proposed a probabilistic framework to infer structural response in the linear range based on accelerometer data. However, the methodology changes considerably for nonlinear behavior.…”