Multiple Damage Identification Using the Reversible Jump Markov Chain Monte Carlo

This study investigates the application of an advanced probabilistic method Reversible Jump Markov Chain Monte Carlo (RJMCMC) - to the problem of locating, characterizing and assessing structural damage. A great deal of interest has been paid to treating the damage identification task as one of model updating with both deterministic and non-deterministic updating methods having been extensively investigated. Among these frameworks, Bayesian Inference has found particular success when applied in the fields of both System Identification and Structural Health Monitoring (SHM). The advantages of using Bayesian Inference in SHM applications include its reliance upon prior knowledge, enabling beliefs regarding the state of the structure, the bounds on its physical parameters and the likely damage scenarios encountered to be included in the estimation process. A further advantage of adopting a Bayesian approach is that outcomes are presented as the posterior probability distributions of the variables of interest. As the geometries of these posterior probability distributions are generally complex it is typical for Markov Chain Monte Carlo (MCMC) samplers to be employed in their estimation. However, while MCMC methods offer an effective tool for estimation of damage parameters, they do not directly lend themselves to the model selection problem. Having the ability to consider multiple explanatory models simultaneously would offer new opportunities for damage classification and identification of multi-site damage. Reversible Jump Markov Chain Monte Carlo (RJMCMC) offers a potentially powerful extension of standard MCMC methods. The first strength of the RJMCMC method is that it addresses both parameter estimation and model selection simultaneously. As such, RJMCMC returns not only the parameter estimates for each model but also provides a probabilistic indication of which model is most consistent with the data. The second strength of RJMCMC is that it is sufficiently general that the models being compared may contain different numbers of parameters. These characteristics open up a number of potential approaches to the SHM problem. The damage classification task may be approached by generating a set of alternative damage models, each of which is a function of its own set of damage parameters (e.g. depth of crack, location, orientation). In this case the method would provide the evidence for each class of damage alongside the parameter estimates. Alternatively, the set of models may comprise single and multiple damage scenarios. RJMCMC would return both the likely number of damage locations and estimates of their parameters simultaneously, addressing one of the more challenging tasks within model-based SHM. It should be noted that being Bayesian, the algorithm penalizes unjustified complexity. In this paper the RJMCMC algorithm is employed to assess a multiple damage scenario on a numerical case study. A framework for applying RJMCMC methods in this context is proposed and demonstrated for a numerical case study using simulated data. The RJMCMC algorithm is used to identify the likely number of damage locations as well as to assess the extent of damage.