Bayesian networks and infrastructure systems. Computational and methodological challenges

This chapter investigates the applicability of Bayesian Network methods to the seismic assessment of large and complex infrastructure systems. While very prom-ising in theory, Bayesian Networks tend to quickly show limitations as soon as the studied systems exceed several dozens of components. Therefore a benchmark study is conducted on small-size virtual systems in order to compare the computa-tional performance of the exact inference of various Bayesian Network formula-tions, such as the ones based on Minimum Link Sets. It appears that all formula-tions present some computational bottlenecks, which are either due to the size of Conditional Probability Tables, to the size of clique potentials in the junction-tree algorithm or to the recursive algorithm for the identification of Minimum Link Sets. Moreover, these formulations are limited to connectivity problems, whereas the accurate assessment of infrastructure systems usually requires the use of flow-based performance indicators. To this end, the second part of the chapter introduc-es a hybrid approach that presents the merit of accessing any type of system per-formance indicator: it uses simulation-based results and generates the correspond-ing Bayesian Network by counting the outcomes given the various combinations of events that have been sampled in the simulation. The issue of the system size is also addressed by a thrifty-naïve formulation, which limits the number of the components that are involved in the system performance prediction, by applying a cut-off threshold to the correlation coefficients between the components and sys-tem states. A higher resolution of this thrifty-naïve formulation is also obtained by considering local performance indicators, such as the flow at each sink. This ap-proach is successfully applied to a realistic water-supply network of 49 nodes and 71 pipes. Finally the potential of this coupled simulation-Bayesian approach as a decision support system is demonstrated, through probability updating given the observation of local evidences after an event has occurred.