A COMPARISON OF PROBABILISTIC MODELS OF DETERIORATION FOR LIFE CYCLE MANAGEMENT OF STRUCTURES
Department of Civil Engineering, University of Waterloo, Waterloo, Ontario, Canada
The probabilistic modelling of deterioration in the time-dependent reliability analysis is a necessary step for developing a risk-based approach to the life cycle management of infrastructure systems. The decisions regarding the time and frequency of inspection, maintenance and replacement are confounded by sampling and temporal uncertainties associated with the deterioration of structural resistance. To account for these uncertainties, probabilistic models of deterioration have been developed under two broad categories, namely the random variable model and stochastic process model. The paper presents a conceptual exposition of these two models and highlights their profound implications to the age-based and condition-based preventive maintenances policies. The proposed stochastic gamma process model of deterioration is more versatile than the random rate model commonly used in the structural reliability literature.
Keywords: life cycle management, structural reliability, age-based replacement, condition-based maintenance, gamma process
Time-dependent reliability analysis is necessary to develop optimum strategies for the life-cycle management of infrastructure systems that include roads, bridges, nuclear plants and transmission lines. The decisions regarding the time and frequency of inspection, maintenance and replacement are confounded by uncertainties associated with the deterioration of structural resistance. In general, the modelling of deterioration is influenced by sampling and temporal uncertainties. The sampling uncertainty refers to the variability of deterioration from sample to sample. The uncertainty inherent with the progression of deterioration over time is referred to as temporal uncertainty. The sampling uncertainty, an epistemic uncertainty, can be reduced by additional inspections. The temporal uncertainty on the other hand is aleatory in nature so that it cannot be eliminated completely by increasing inspections. An adequate consideration of temporal uncertainty is necessary for a credible and effective life cycle management of critical infrastructures.
The probabilistic models of deterioration can be classified in two broad categories, namely, random variable (RV) model and stochastic process model. In the RV model, parameters associated with an empirical deterioration law are randomized to reflect the sampling variability observed in a sample of deterioration data, such as the rate of deterioration (Hong 2000, Pandey 1998). The stochastic process model, such as the Markov chain or Gamma process, incorporates the temporal uncertainty associated with evolution of deterioration (Bogdanoff and Kozin 1985, Nicolai et al. 2004, van Noortwijk and Frangopol 2004). A key distinction between these two models is that a specific sample path is deterministic in RV model, but it remains uncertain in the stochastic process model.
The application of the random variable and stochastic process deterioration models have been hitherto reported, but a clear interpretation of conceptual distinctions between these two models and their impact on maintenance optimization problem have been lacking in the engineering literature. To address this issue, the paper evaluates the random variable and stochastic Gamma process models in a simplified setting of time-dependent structural reliability analysis. The two equivalent versions of the deterioration models are compared in terms of distributions of lifetime, deterioration magnitude and the life cycle cost. The paper presents an original exposition of the implications of deterioration models to the age-based and condition-based preventive maintenances policies.
M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 735-746. © 2006 Springer. Printed in the Netherlands.