Exchangeable condition states and Bayesian reliability updating

摘要

Inspection of deteriorating infrastructure often raises the issue of spatial differences and variations within similar structural elements or zones. A possible approach consists of modelling these "zones" using an unobservable condition state which can be either discrete (as in the case where indicators or state variables are used) or continuous (as in the case of a global degree of damage or exposure). Subsequently, inspection data or process outputs may be used to "update" these uncertain condition states. The challenge is to assimilate such data from different zones and sources so that the "shared" information as well as the "zone-specific" information can be used to update each individual condition state in an optimal way. In this paper Bayesian models based on exchangeable condition states are used to model the proper "mixing" of such observations and to allow flexible decision making. We investigate the merit and the effect of different mixing assumptions, including the effect of correlation between condition states. This type of modeling is linked to a key concept in Bayesian inference, namely that of exchangeability. The paper discusses some of the implications and challenges of working with exchangeable mixtures. Multi-stage Bayesian models have been used in structural inspection and maintenance planning, in the context of deteriorating R/C structures, pipelines, large industrial plants, and failure rate modeling in complex systems. The present paper shows how a multi-stage Bayesian approach with continuous condition states and both discrete and continuous hyper-parameters can be used to update time-dependent reliabilities for a system consisting of n exchangeable zones subject to deterioration, both in the case of section-specific limit states or limit states involving spatial extremes. An example application is given of an offshore gas pipeline subject to internal corrosion due to spatially variable CO_2 condensation. The pipeline is subject to planned inspections at certain points in time and this information can be used to update the condition states throughout the system as well as its long-term reliability.