Estimation of Stochastic Degradation Models Using Uncertain Inspection Data
Modelling and forecasting the progress of corrosion and other degradation phenomena in engineering systems is an important element of reliability management programs. Because of the random nature of the degradation process, probabilistic models are mostly employed. Parameters of the probabilistic models are estimated using degradation data from in-service inspections. The estimated model parameters are then used for predicting future degradation growth or failure time of the components. In the nuclear power plants, usually small samples of degradation data are collected using non-destructive examination (NDE) tools, which are not perfect in detecting degradation flaws and they also add random noise when measuring the size of the detected flaws. Ignoring these inspection uncertainties in the estimation of the degradation model would result in biased estimates and subsequently erroneous predictions of future degradation. The main objective of the thesis is to develop methods for the accurate estimation of stochastic degradation models using uncertain inspection data. Three typical stochastic models are considered, namely, the random degradation rate model, the gamma process model and the Poisson process model. The random rate model and the gamma process model are used to model the flaw growth, and the Poisson process model is used to model the flaw generation. Likelihood functions of the three stochastic models from noisy and incomplete inspection data are derived. The thesis also investigates Bayesian inference of the stochastic degradation models. The most notable advantage of Bayesian inference over classical point estimates is its ability to incorporate background information in the estimation process, which is especially useful when inspection data are scarce. It is shown in the thesis that likelihood evaluationof the stochasticmodels usinguncertain inspection data is a computationally challenging task as it often involves calculation of high dimensional integrals or large number of convolutions. The thesis develops efficient numerical methods to overcome this difficulty. For example, for the maximum likelihood estimation of the gamma process model, the Genz’s transform and quasi-Monte Carlo simulation are adopted. The Markov Chain Monte Carlo simulation with sizing errors