A Bayesian network methodology is developed for performing infrastructure seismic risk assessment and providing decision support with an emphasis on immediate post-earthquake applications. The methodology consists of four major components: (1) a seismic demand model of ground motion intensity as a spatially distributed Gaussian random field accounting for multiple seismic sources with uncertain characteristics and including finite fault rupture and directivity effects; (2) a model of the performance of point-site and distributed components under seismic loading; (3) models of system performance as a function of component states; and (4) the extension of the Bayesian network to include decision and utility nodes to aid post-earthquake decision-making.
A Bayesian network is a probabilistic graphical model that represents a set of random variables and their probabilistic dependencies. The variables may represent demand or capacity values, or the states of components and systems. Bayesian networks are graphical and intuitive, facilitate information updating, can be used for identification of critical components within a system, and can be extended by decision and utility nodes to solve decision problems. The facility for information updating renders the Bayesian network an ideal tool for infrastructure seismic risk assessment and decision support, particularly in near-real time applications immediately following a destructive earthquake. Evidence on one or more variables (e.g. observed component capacities, demands, or damage states) can be entered into the Bayesian network and this information propagates throughout the network to provide an up-to-date probabilistic characterization of the performance of the infrastructure system under the uncertain and evolving state of information that is characteristic of the post-event period. Like most computational methods, Bayesian networks have limitations. In particular, calculations in Bayesian networks can be highly demanding of computer memory. The present study develops methodologies to minimize computational demands by optimizing network topology and, when necessary, making trade-offs between accuracy and computational efficiency.
The study begins with a brief introduction to Bayesian networks. Next, each of the aforementioned components of the methodology is described. The seismic demand model provides distributions of ground motion intensity at discrete points in the geographic domain of a spatially distributed infrastructure system. This model can be used to perform and go beyond conventional probabilistic seismic hazard assessment. In particular, the model provides a full random field characterization of the ground motion intensity, thus allowing assessment of seismic risk for spatially distributed systems. Equally important, the model enables updating of the distribution of intensity at any selected site upon observation of the intensity at other sites. The modeling of random fields via Bayesian network results in a densely connected topology that renders probabilistic inference computationally demanding and possibly intractable. To address this problem, several approaches for approximating the correlation structure of variables drawn from a random field are developed, which amount to selectively removing links and nodes in the Bayesian network. It is found that a method based on numerical optimization achieves the best trade-off of accuracy versus efficiency.
Bayesian network formulations are presented for modeling component performance as a function of seismic demand using fragility functions. The framework accounts for potential sources of correlation in component response. Models for point-site and distributed components are presented. The latter is based on an assumption that damages along a component occur according to a non-homogenous Poisson process. Five Bayesian network formulations for modeling system performance as a function of component states are developed. One approach uses a naïve topology, two formulations are based on an intuitive interpretation of system performance, and two approaches utilize minimal link and cut sets. The last two formulations are then adapted and refined with the goal of minimizing computational demands by arranging nodes in chain-like structures that reduce the size of conditional probability tables and, consequently, required computation time and memory.
The Bayesian network is extended by decision and utility nodes to create a new graphical construct known as an influence diagram. This diagram aids decision-making by specifying decision alternatives that maximize expected utility given all available evidence. The extension of the framework to include decision and utility nodes is demonstrated by application to a post-earthquake decision scenario involving inspection and shutdown decisions. A limited memory influence diagram is constructed to model this decision problem. A heuristic based on a value of information criterion is described for prioritizing component inspections following an earthquake.
Two example applications demonstrate the Bayesian network methodology for infrastructure seismic risk assessment and decision support. The second example employs a preliminary and hypothetical model of the proposed California high speed rail system.