System reliability analysis methods for rapid multi-scale network risk assessment and decision making

For effective hazard mitigation planning and prompt-but-prudent responses, it is essential to evaluate the reliability of infrastructure networks accurately and efficiently and if needed, to make a reasonable decision under a budgetary constraint on retrofitting prioritization of vulnerable components. In general, however, network analysis is highly intricate in nature because of a large number of network components, complex network topology, statistical dependence between component failures, and network interdependency. Thus, network analysis is often performed by repeating computational simulations of network performance for random samples of hazard intensity measures and corresponding component status. This simulation-based approach allows for straightforward applications of deterministic network analysis algorithms, yet hampers rapid risk assessment and effective decision-making. Even though a non-simulation based algorithm, termed as a recursive decomposition algorithm (RDA), was recently proposed to identify disjoint cut sets and link sets and to compute the network reliability based on the identified sets, it is not feasible for a large-sized network because of the exponential program nature. Besides these challenges, it is a more daunting task to conduct a decision-making analysis on the network-retrofitting problem because of multiple conflicting decision-making criteria, re-retrofitting effects, integer optimization for a large-size problem and others.;This thesis proposes noble network analysis methods to efficiently compute the system reliability and make a reasonable decision on retrofitting prioritization of vulnerable components in the large-sized network. First of all, an efficient risk assessment framework for large-size networks is introduced with consideration of both inter-event and intra-event uncertainties in spatially correlated ground motions. Subsequently, two advanced analytical network reliability approaches are developed for the framework -- the "selective" Recursive Decomposition Algorithm (RDA) and the clustering-based multi-scale network reliability analysis. In calculating the probabilities of network disconnection events, the selective RDA achieves faster convergence of the bounds on the probabilities with a significantly reduced number of identified sets by identifying critical disjoint cut set and link sets preferentially by use of the most reliable path algorithm and a selective graph decomposition scheme. Besides, the clustering-based multi-scale network reliability approach overcomes the intrinsic limitation of the selective RDA that the computational cost may increase exponentially with the network size. The approach identifies an adequate number of clusters by use of spectral clustering algorithms and represents the clusters with representative super-links connecting inter-cluster nodes. If the simplified network is still exceedingly large to handle, additional levels of hierarchical clustering are introduced. By use of the proposed approach, any sizable problem can be solved without significant accuracy compromise. Lastly, a multi-scale multi-criteria decision making analysis approach is developed by incorporating the component-level multi-criteria utility theory and the network component importance measure to the aforementioned advanced analytical network reliability analysis approaches. Given an integer-based budgetary constraint and interaction of network components, the approach consists of a constraint binary integer optimization program and an iteration process to select a component to retrofit with preference while updating the CPIM component utilities based on the retrofit decisions. All of the proposed methods are applied to the hypothetical and/or real-world examples to demonstrate their accuracy and efficiency.