Probability-Based Structural Health Monitoring Through Markov Chain Monte Carlo Sampling

Abstract

The classical nonuniqueness problem exists due to uncertainty in the finite element (FE) calibration field. Namely, multiple models with different intrinsic parameters may all fit the observed data well, thus the selected single “best” model probably is not the truly best model to reflect the structural intrinsic property. A probability-based method using a population of FE models, not the single “best” method, is proposed to deal with the nonuniqueness problem. In this method, the Markov Chain Monte Carlo (MCMC) technique is first performed to sample the key structural parameters representing the main sources of uncertainty. Then a FE model population is generated using the samples, and the posterior probability of each model is evaluated by calculating the correlation between the simulation results and measurements through the Bayesian theorem. Finally, all the FE models from the stochastic sampling with their posterior probabilities are used for structural identification (St-Id) and performance evaluation. The advantage of the proposed method is that it not only identifies the magnitudes of structural parameters, but also generates their probability distributions for subsequent probability-based reliability analysis and risk evaluation. The feature provided by the stochastic sampling and statistical techniques makes the proposed method suitable for dealing with uncertainty. The example of the Phase I IASC-ASCE benchmark structure investigated demonstrates the effectiveness of the proposed method for probability-based structural health monitoring.