Abstract Summary
In updated model based structural health monitoring problems, updating of displacement-strain transformation matrix has not garnered much attention over the years, as most studies focus on updating mass and stiffness matrices. In this study, updating of the parametrized displacement-strain transformation matrix is carried out in a Bayesian probabilistic framework by combining the data from both acceleration and strain sensors. The Bayesian framework ensures that the uncertainties, especially modeling uncertainties, are explicitly considered and provides multiple possible estimates of the parameters, unlike a classical estimation framework where only one value is estimated. Samples from the posterior probability density function of the parameters are simulated using the transitional Markov Chain Monte Carlo method. Further, in the formulation part, the estimation of the parameters through classical estimation is also developed, and the relationship with Bayesian estimation is established. The updated displacement-strain transformation matrix can be used to obtain strains with higher fidelity in numerical simulations and to obtain robust response predictions incorporating modeling uncertainties. In addition, once a transformation matrix has been updated, only acceleration data are required for damage localization, i.e., strain measurements are not required post-updating, thereby reducing the overall health monitoring costs and storage burden. The Bayesian updating procedure is illustrated using experimental data from a four-story shear building laboratory model.
