Static reliability and resilience in dynamic systems

Two systems are modeled in this thesis. First, we consider a multi-component stochastic monotone binary system, or SMBS for short. The reliability of an SMBS is the probability of correct operation. A statistical approximation of the system reliability is provided for these systems, inspired in Monte Carlo Methods. Then, we are focused on the diameter constrained reliability model (DCR), which was originally developed for delay sensitive applications over the Internet infrastructure. The computational complexity of the DCR is analyzed. Networks with an efficient (i.e., polynomial time) DCR computation are offered, termed Weak graphs. Second, we model the effect of a dynamic epidemic propagation. Our first approach is to develop a SIR-based simulation, where unrealistic assumptions for SIR model (infinite, homogeneous, fully-mixed population) are discarded. Finally, we formalize a stochastic rocess that counts infected individuals, and further investigate node-immunization strategies, subject to a budget nstraint. A combinatorial optimization problem is here introduced, called Graph Fragmentation Problem. There, the impact of a highly virulent epidemic propagation is analyzed, and we mathematically prove that Greedy heuristic is suboptimal

A simulation Method for Network Performability Estimation using Heuristically-computed Pathsets and Cutsets

Consider a set of terminal nodes K that belong to a network whose nodes are connected by links that fail independently with known probabilities. We introduce a method for estimating any performability measure that depends on the hop distance between terminal nodes. It generalises previously introduced Monte Carlo methods for estimation of the K-reliability of networks with variance reduction compared to crude Monte Carlo. They are based on using sets of edges named d-pathsets and d-cutsets for reducing the variance of the estimator. These sets of edges, considered as a priori known in previous literature, heaviliy affect the attained performance; we hereby introduce and compare a family of heuristics for their selection. Numerical examples are presented, showing the significant efficiency improvements that can be obtained by chaining the edge set selection heuristics to the proposed Monte Carlo sampling plan

OPERATIONAL RELIABILITY AND RISK EVALUATION FRAMEWORKS FOR SUSTAINABLE ELECTRIC POWER SYSTEMS

Driven by a confluence of multiple environmental, social, technical, and economic factors, traditional electric power systems are undergoing a momentous transition toward sustainable electric power systems. One of the important facets of this transformation is the inclusion of high penetration of variable renewable energy sources, the chief among them being wind power. The new source of uncertainty that stems from imperfect wind power forecasts, coupled with the traditional uncertainties in electric power systems, such as unplanned component outages, introduces new challenges for power system operators. In particular, the short-term or operational reliability of sustainable electric power systems could be at increased risk as limited remedial resources are available to the operators to handle uncertainties and outages during system operation. Furthermore, as sustainable electric power systems and natural gas networks become increasingly coupled, the impacts of outages in one network can quickly propagate into the other, thereby reducing the operational reliability of integrated electric power-gas networks (IEPGNs). In light of the above discussion, a successful transition to sustainable electric power systems necessitates a new set of tools to assist the power system operators to make risk-informed decisions amid multiple sources of uncertainties. Such tools should be able to realistically evaluate the hour- and day-ahead operational reliability and risk indices of sustainable electric power systems in a computationally efficient manner while giving full attention to the uncertainties of wind power and IEGPNs. To this end, the research is conducted on five related topics. First, a simulation-based framework is proposed to evaluate the operational reliability indices of generating systems using the fixed-effort generalized splitting approach. Simulations show improvement in computational performance when compared to the traditional Monte-Carlo simulation (MCS). Second, a hybrid analytical-simulation framework is proposed for the short-term risk assessment of wind-integrated power systems. The area risk method – an analytical technique, is combined with the importance sampling (IS)-based MCS to integrate the proposed reliability models of wind speed and calculate the risk indices with a low computational burden. Case studies validate the efficacy of the proposed framework. Third, the importance sampling-based MCS framework is extended to include the proposed data-driven probabilistic models of wind power to avoid the drawbacks of wind speed models. Fourth, a comprehensive framework for the operational reliability evaluation of IEPGNs is developed. This framework includes new reliability models for natural gas pipelines and natural gas-fired generators with dual fuel capabilities. Simulations show the importance of considering the coupling between the two networks while evaluating operational reliability indices. Finally, a new chance-constrained optimization model to consider the operational reliability constraints while determining the optimal operational schedule for microgrids is proposed. Case studies show the tradeoff between the reliability and the operating costs when scheduling the microgrids

A Hostile model for network reliability analysis

In reliability analysis, the goal is to determine the probability of consistent operation of a system. We introduce the Hostile model, where the system under study is a network, and all the components may fail (both sites and links), except for a distinguished subset of sites, called terminals. The Hostile model includes the Classical Reliability model as a particular case. As a corollary, the exact reliability evaluation of a network in the Hostile model belongs to the list of N P-hard computational problems. Traditional methods for the classical reliability model such as Crude Monte Carlo, Importance Sampling and Recursive Variance Reduction are here adapted for the Hostile model. The performance of these methods is finally discussed using real-life networks

Risk-cost optimization of buried pipelines using subset simulation

On the basis of time-dependent reliability analysis, a computational framework called subset simulation (SS) has been applied for risk-cost optimization of flexible underground pipeline networks. SS can provide better resolution for rare failure events that are commonly encountered in pipeline engineering applications. Attention in this work is devoted to scrutinize the robustness of SS in risk-cost optimization of pipelines. SS is first employed to estimate the reliability of flexible underground pipes subjected to externally applied loading and material corrosion. Then SS is extended to determine the intervention year for maintenance and to identify the most appropriate renewal solution and renewal priority by minimizing the risk of failure and whole life-cycle cost. The efficiency of SS compared to genetic algorithm has been demonstrated by numerical studies with a view to prevent unexpected failure of flexible pipes at minimal cost by prioritizing maintenance based on failure severity and system reliability. This paper shows that SS is a more robust method in the decision-making process of reliability-based management for underground pipeline networks

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure

Simulation methods for reliability-based design optimization and model updating of civil engineering structures and systems

This thesis presents a collection of original contributions pertaining to the subjects of reliability-based design optimization (RBDO) and model updating of civil engineering structures and systems. In this regard, probability theory concepts and tools are instrumental in the formulation of the herein reported developments. Firstly, two approaches are devised for the RBDO of structural dynamical systems under stochastic excitation. Namely, a stochastic search technique is proposed for constrained and unconstrained RBDO problems involving continuous, discrete and mixed discrete-continuous design spaces, whereas an efficient sensitivity assessment framework for linear stochastic structures is implemented to identify optimal designs and evaluate their sensitivities. Moreover, two classes of model updating problems are considered. In this context, the Bayesian interpretation of probability theory plays a key role in the proposed solution schemes. Specifically, contaminant source detection in water distribution networks is addressed by resorting to a sampling-based Bayesian model class selection framework. Furthermore, an effective strategy for Bayesian model updating with structural reliability methods is presented to treat identification problems involving structural dynamical systems, measured response data, and high-dimensional parameter spaces. The approaches proposed in this thesis integrate stochastic simulation techniques as an essential part of their formulation, which allows obtaining non-trivial information about the systems of interest as a byproduct of the solution processes. Overall, the findings presented in this thesis suggest that the reported methods can be potentially adopted as supportive tools for a number of practical decision-making processes in civil engineering.Diese Arbeit stellt eine Sammlung von Beiträgen vor, die sich mit der Reliability-based-Design-Optimization (RBDO) und dem Model updating von Strukturen und Systemen im Bauwesen befassen. In diesem Zusammenhang sind wahrscheinlichkeitstheoretische Konzepte für die Formulierung der hier vorgestellten Entwicklungen von entscheidender Bedeutung. Zunächst werden zwei Ansätze für eine RBDO von strukturdynamischen Systemen unter stochastischer Anregung entwickelt. Es wird eine stochastische Suchtechnik für beschränkte und unbeschränkte RBDO-Probleme vorgeschlagen. Diese beziehen kontinuierliche, diskrete und gemischt diskret-kontinuierliche Designräume ein. Gleichzeitig wird ein effizientes Framework zur Bewertung der Sensitivität lineare stochastische Strukturen implementiert, um optimale Designs zu identifizieren und ihre Sensitivitäten zu bewerten. Darüber hinaus werden zwei Klassen von Problem aus dem Model updating betrachtet. Der Fokus wird hierbei auf die Erkennung von Kontaminationsquellen in Wasserverteilungsnetzen mithilfe eines auf Stichproben basierenden Bayesian-Model-Class-selection-Framework gelegt. Ferner wird eine effektive Strategie zur Bearbeitung von Problemen des Bayesian-Model-updating, die strukturdynamischen Systeme, gemessene Systemantwortdaten und hochdimensionale Parameterräume umfassen, vorgestellt. Die beschriebenen Ansätze verwenden stochastische Simulationstechniken als wesentlicher Bestandteil ihrer Formulierung, wodurch nicht-triviale Informationen über betrachtete Systeme als Nebenprodukt der Lösungsprozesse gewonnen werden können. Insgesamt deuten die vorgestellten Ergebnisse dieser Arbeit darauf hin, dass die beschriebenen Methoden potenziell als unterstützende Elemente in praktischen Entscheidungsproblemen im Zusammenhang mit Strukturen und Systemen im Bauwesen eingesetzt werden können

An Assessment of PIER Electric Grid Research 2003-2014 White Paper

This white paper describes the circumstances in California around the turn of the 21st century that led the California Energy Commission (CEC) to direct additional Public Interest Energy Research funds to address critical electric grid issues, especially those arising from integrating high penetrations of variable renewable generation with the electric grid. It contains an assessment of the beneficial science and technology advances of the resultant portfolio of electric grid research projects administered under the direction of the CEC by a competitively selected contractor, the University of California’s California Institute for Energy and the Environment, from 2003-2014