Gradients and subgradients of buffered failure probability

17 USC 105 interim-entered record; under review.The article of record as published may be found at http://dx.doi.org/10.1016/j.orl.2021.10.004Gradients and subgradients are central to optimization and sensitivity analysis of buffered failure probabilities. We furnish a characterization of subgradients based on subdifferential calculus in the case of finite probability distributions and, under additional assumptions, also a gradient expression for general distributions. Several examples illustrate the application of the results, especially in the context of optimality conditions.Office of Naval ResearchAir Force Office of Scientific Research18RT0599MIPR N0001421WX0149

S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method

Reliability-based optimization (RBO) is crucial for identifying optimal risk-informed decisions for designing and operating engineering systems. However, its computation remains challenging as it requires a concurrent task of optimization and reliability analysis. Moreover, computation becomes even more complicated when considering performance of a general system, whose failure event is represented as a link-set of cut-sets. This is because even when component events have smooth and convex limit-state functions, the system limit-state function has neither property, except in trivial cases. To address the challenge, this study develops an efficient algorithm to solve RBO problems of general system events. We employ the buffered optimization and reliability method (BORM), which utilizes, instead of the conventional failure probability definition, the buffered failure probability. The proposed algorithm solves a sequence of difference-of-convex RBO models iteratively by employing a proximal bundle method. For demonstration, we design three numerical examples with increasing complexity that includes up to 108 cut-sets, which are solved by the proposed algorithm within a minute with high accuracy. We also demonstrate its robustness by performing extensive parametric studies.Comment: Codes and data are available at https://github.com/jieunbyun/sbor

Linear Programming by Delayed Column Generation for Bounds on Reliability of Larger Systems

In various efforts to secure the resilience of community, accurate reliability analysis of civil systems is critical considering their pivotal functions. As such systems generally consist of multiple components, their reliability analysis requires complete information to construct joint probabilistic dis-tributions of component events, which is rarely available in practice. In order to obtain the best estimates on the system reliability based on the available information, the linear programming (LP) bounds method was proposed (Song and Der Kiureghian 2003).The method obtains bounds on system reliability by solv-ing LP problems constructed by decomposing the event space into mutually exclusive and collectively exhaustive (MECE) events. Despite the optimality and flexibility of the LP bounds method, there is a limitation in the size of systems as the number of MECE events increases exponentially in regards to that of component events. In order to address this issue, this paper develops an alternative LP bounds formu-lation by employing delayed column generation, in which the LP is solved as an iteration of smaller binary integer programming (BIP). The BIP can be formulated by Boolean algebra that represents the inclusion relationships between component events, system event, and constraint events. The proposed formulation requires polynomial memory in regards to the number of constraints, allowing the evaluation of the LP bounds for larger systems and changing the major bottleneck from the number of components to that of constraint events incorporated into the LP. Four numerical examples are provided to illustrate and demonstrate the proposed method.This research was supported by a grant (18SCIP-B146946-01) from Smart Civil Infrastructure Re-search Program funded by Ministry of Land, In-frastructure, and Transport of Korean government

Generalized matrix-based Bayesian network for multi-state systems

To achieve a resilient society, the reliability of core engineering systems should be evaluated accurately. However, this remains challenging due to the complexity and large scale of real-world systems. Such complexity can be efficiently modelled by Bayesian network (BN), which formulates the probability distribution through a graph-based representation. On the other hand, the scale issue can be addressed by the matrix-based Bayesian network (MBN), which allows for efficient quantification and flexible inference of discrete BN. However, the MBN applications have been limited to binary-state systems, despite the essential role of multi-state engineering systems. Therefore, this paper generalizes the MBN to multi-state systems by introducing the concept of composite state. The definitions and inference operations developed for MBN are modified to accommodate the composite state, while formulations for the parameter sensitivity are also developed for the MBN. To facilitate applications of the generalized MBN, three commonly used techniques for decomposing an event space are employed to quantify the MBN, i.e. utilizing event definition, branch and bound (BnB), and decision diagram (DD), each being accompanied by an example system. The numerical examples demonstrate the efficiency and applicability of the generalized MBN. The supporting source code and data can be download at https://github.com/jieunbyun/Generalized-MBN-multi-state

Urban seismic resilience mapping: a transportation network in Istanbul, Turkey

When a seismic event occurs, transportation networks play a critical role in undertaking emergency activities such as evacuation and relief supply. Accordingly, to secure their functionality, it is essential to accurately assess their resilience. In particular, this study performs a rigorous probabilistic analysis on the seismic resilience of a transportation network in Istanbul, Turkey. The analysis accuracy is enhanced by considering, along with the structural damage of roadways, the additional disruption mode of network performance caused by the debris falling from damaged objects in their vicinity. Moreover, we obtain the results as a map of resilience measure, which enables us to investigate the disruption inequality across the study area and identify critical factors that govern the system resilience. To enable such sophisticated probabilistic analysis, a Bayesian network (BN) model is developed that involves various types of information from the hazard process to the performance of structures and systems. Then, the BN is quantified by identifying and compiling a comprehensive list of datasets. Thereby, this study analyses large-scale systems involving thousands of structures, while providing general probabilistic models and data schema that can be employed for other transportation networks

Efficient Optimization for Multi-Objective Decision-Making on Civil Systems Using Discrete Influence Diagram

The breakdown of civil systems, e.g. bridge networks and water distribution networks, has a significant social and economic impact, highlighting the importance of optimal decision-making on such systems. Modeling and optimization of probabilistic decision-making problems for civil systems, can be facilitated by graphical methodologies such as influence diagram (ID). However, the converging structure in IDs representing civil systems, which relates the random variables standing for component events and that for system event, results in the exponential increase in the number of modeling parameters and variables to be optimized as that of component events increases. In order to address these challenges, in this paper, the recently proposed matrix-based Bayesian network (MBN) is employed to quantify the IDs. To facilitate the optimization process, a proxy objective function is also proposed. The proxy func-tion not only significantly reduces the number of variables to be optimized, but also allows an efficient framework for multi-objective optimization in which the weighted sum of the objectives is optimized to obtain a set of non-dominated solutions. Three numerical examples demonstrate the performance of the proposed methodology.This research was supported by a grant (18SCIP-B146946-01) from Smart Civil Infrastructure Re-search Program funded by Ministry of Land, In-frastructure, and Transport of Korean government

ResMapper: Matlab tool for seismic resilience mapping of large-scale road networks

A resilience analysis of large-scale road networks is challenging owing to the complexity of analysis and the need for large-scale data. Nonetheless, a development of a general-purpose software to this end is desired to enhance the accessibility to such an advanced analysis and to facilitate interdisciplinary research collaborations. To this end, a Matlab-based toolkit, ResMapper is developed to perform a seismic resilience analysis of road networks. ResMapper innovates on the previous works in two perspectives. First, it performs a probabilistic resilience analysis, being specialised for large-scale networks. Second, it considers various causes of road closures: structural damage of roadways and debris impacts by overpasses and adjacent buildings. The applicability of ResMapper is demonstrated by a benchmark example of the road network of Istanbul, Turkey. In addition, the detailed analyses available in the supplementary document demonstrate the utility of ResMapper for understanding the resilience of a road network and help understand the varying influences of analysis parameters