Reliability Engineering and System Safety 94 (2009) 1838–1847
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Reliability Engineering and System Safety
journal homepage: www.elsevier.com/locate/ress
A Bayesian approach to modeling and predicting pitting ﬂaws in steam generator tubes
X.-X. Yuan a,Ã, D. Mao b, M.D. Pandey b
Department of Civil Engineering, RyersonUniversity, 350 Victoria Street, Toronto, Ont., Canada M5B 2K3 Department of Civil and Environmental Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ont., Canada N2L 3G1
a r t i c l e in f o
Article history: Received 7 February 2009 Received in revised form 22 May 2009 Accepted 14 June 2009 Available online 21 June 2009 Keywords: Stochastic deterioration modelingPitting corrosion Bayesian modeling Markov chain Monte Carlo simulation Risk-based life-cycle management
a b s t r a c t
Steam generators in nuclear power plants have experienced varying degrees of under-deposit pitting corrosion. A probabilistic model to accurately predict pitting damage is necessary for effective life-cycle management of steam generators. This paper presents an advancedprobabilistic model of pitting corrosion characterizing the inherent randomness of the pitting process and measurement uncertainties of the in-service inspection (ISI) data obtained from eddy current (EC) inspections. A Markov chain Monte Carlo simulation-based Bayesian method, enhanced by a data augmentation technique, is developed for estimating the model parameters. The proposed model is able to predictthe actual pit number, the actual pit depth as well as the maximum pit depth, which is the main interest of the pitting corrosion model. The study also reveals the signiﬁcance of inspection uncertainties in the modeling of pitting ﬂaws using the ISI data: Without considering the probability-of-detection issues and measurement errors, the leakage risk resulted from the pitting corrosion would beunder-estimated, despite the fact that the actual pit depth would usually be over-estimated. & 2009 Elsevier Ltd. All rights reserved.
1. Introduction Steam generators (SGs) are a major pressure retaining component of great safety signiﬁcance in nuclear power plants. A typical CANDU nuclear steam generator usually consists of thousands of small-diameter SG tubes through which ﬂows heavy water ofhigh temperature and high pressure. The SG tubes are designed with nominal tube wall thickness ranging from 1.13 to 1.2 mm, depending on the type of tube alloy used. Due to various manufacturing, operation and maintenance activities, as well as material interaction with the surrounding chemical environment, the SG tubes have been subject to a number of degradation modes . Among them, theunder-deposit pitting corrosion at outside surfaces of the SG tubes just on top of the tubesheet support plates has had a serious impact on the integrity of the SG tubes . If left unchecked, the pits would develop to the extent of a leakage, which might further trigger a loss of coolant accident (LOCA) event. Therefore, an effective life-cycle management of steam generators, including both effectiveintervention methods and accurate prediction of pitting damages, is in great need for nuclear power utilities to manage the pitting corrosion problems. Current intervention methods include water lancing (WL) and chemical cleaning (CC), i.e., removal of the deposits in the steam
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E-mail address: Arnold.firstname.lastname@example.org(X.-X. Yuan). 0951-8320/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ress.2009.06.001
generators, which have been proved effective and efﬁcient . On the other hand, an efﬁcient method is still lacking for estimating the number of tubes that require plugging and the probability of tube leakage in the next operating period. The objective of the paper is to...