Hierarchical Bayes models in engineering: theory and applications
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2011
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Abstract
Complex engineering systems often allow decomposition into hierarchically organized sub-systems. The objective of this work is to introduce a new method of probabilistic modeling based on so-called Hierarchical Bayes Models (HBMs ), for the stochastic representation and analysis of such engineering systems and their as ociated uncertainties. After defining the theory behind HBMs, their advantages are investigated and demonstrated in practical applications. Two applied engineering field are subsequently focused on: stochastic structural deterioration modeling and the mod ling of discrete spatial hazards and their consequences. It is concluded that the use of HBMs in engineering results in improved statistical analysis and uncertainty estimation for comprehensive risk and reliability assessment and informed decision making under uncertainty. HBMs consist of hierarchically organized random variables or random process where the lower level variables depend probabilitically on the upper level variable Local, simple stochastic relationships are the backbone of complex hierarchical model structures. HBMs also allow graphical representation of systems using directed acyclic graphs. Bayes Theorem determines the posterior probability density function of all unknown random variables conditional on known and observed quantities. Markov chain Monte Carlo (MCMC) sampling techniques provide numerical solutions. A HBM for stochastic deterioration processes of structures and infrastructure systems is presented. The approach takes temporal, spatial, model, and measurement uncertainties into account. Additionally, a simplified likelihood-based approach is developed for the pre-analysis of very large inspection data sets to identify critical locations that are then further examined using HBM. This is applied to pipeline corrosion defects in order to estimate the future progress of corrosion for optimal decision making regarding pipeline integrity. A second application focuses on the hierarchical analysis of natural and technological hazards (e.g. earthquakes, discrete accidents, explosions) and their consequences. A HBM is developed to estimate the spatially and temporally varying risk of hazard induced events. It serves as a real-time decision making tool for risk mitigation actions and accurate assessment of consequences based on different sources of hazard-related information.
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Bibliography: p. 229-275
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Dann, M. R. (2011). Hierarchical Bayes models in engineering: theory and applications (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/4553