On the application of the reversible jump Markov chain Monte Carlo method within structural dynamics

• Main Author: Tiboaca, Oana D.
• Other Authors: Barthorpe, Robert J. ; Antoniadou, Ifigeneia
• Published: University of Sheffield 2016
• Subjects: 629.8
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.713278

System Identification (SID) is an important area of structural dynamics and is concerned with constructing a functional relationship between the inputs and the outputs of a system. Furthermore, it estimates the parameters that the studied system depends upon. This aspect of structural dynamics has been studied for many years and computational methods have been developed in order to deal with the system identification of real structures, with the aim of getting a better understanding of their dynamic behaviour. The most straightforward classification of structures is into structures that behave linearly and structures that behave nonlinearly. Even so, one needs to keep in mind that no structure is indefinitely linear. During its service, a structure can behave nonlinearly at any given point, under the right working and environmental conditions. A key challenge in applying SID to real systems is in handling the uncertainty inherent in the process. Uncertainty arises from various sources such as modelling error and measurement error (noisy data), resulting in uncertainty in the parameter estimates. One of the ways in which one can deal with uncertainty is by adopting a probabilistic framework. In this way one admits the limitations in the process of SID through providing probability distributions over the models and parameters of interest, rather than a simple 'best estimate'. Throughout this work a Bayesian probabilistic framework is adopted as it covers the uncertainty issue without over-fitting (it provides the simplest, least complex solutions to the issue at hand). Of great interest when working within a Bayesian framework are Markov Chain Monte Carlo(MCMC) sampling methods. Of relevance to this research are the Metropolis-Hastings(MH) algorithm and the Reversible Jump Markov Chain Monte Carlo(RJMCMC) algorithm. Markov Chain Monte Carlo(MCMC) methods and algorithms have been extensively investigated for linear dynamical systems. One of the advantages of these methods being used in a Bayesian framework is that they handle uncertainty in a principled way. In recent years, increasing attention has been paid to the role nonlinearity plays in engineering problems. As a result, there is an increasing focus on developing computational tools that may be applied to nonlinear systems as well as linear systems, with the objective that they should provide reliable results at reasonable computational costs. The application of MCMC methods in nonlinear system identi cation(NLSID) has focused on parameter estimation. However, often enough, the model form of systems is assumed known which is not the case in many contexts(such as NLSID when the nonlinearity is hard to identify and model, or Structural Health Monitoring when the damage extent or number of damage sites is unknown). The current thesis is concerned with the development of computational tools for performing System Identification in the context of structural dynamics, for both linear and nonlinear systems. The research presented within this work will demonstrate how the Reversible Jump Markov Chain Monte Carlo algorithm, within a Bayesian framework, can be used in the area of SID in a structural dynamics context for doing both parameter estimation and model selection. The performance of the RJMCMC algorithm will be benchmarked throughout against the MH algorithm. Several numerical case studies will be introduced to demonstrate how the RJMCMC algorithm may be applied in linear and nonlinear SID; and one numerical case study to demonstrate application to a SHM problem. These will be followed by experimental case studies to evaluate linear and nonlinear SID performance for a real structure.