Generalized Integral Transform and Hamiltonian Monte Carlo for Bayesian structural damage identification

Abstract

The present work addresses the inverse problem of damage identification within the Bayesian framework. The inverse problem is formulated as a parameter estimation one and it is built on the response of the continuous model of the structure provided by the Generalized Integral Transform technique. The Hamiltonian Monte Carlo (HMC) method is considered for sampling the posterior probability density function of the cohesion parameters, which are the ones considered for the description of the damage state of the structure. Numerical simulations considering an Euler-Bernoulli beam were carried out in order to assess the applicability of the proposed damage identification approach. The numerical results shown that the HMC method was able to identify the considered damage scenarios, yielding Markov chains with relatively high convergence rates and with uncorrelated states right at the beginning of the chains.