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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Spectral risk measures: the risk quadrangle and optimal approximation

We develop a general risk quadrangle that gives rise to a large class of spectral risk measures. The statistic of this new risk quadrangle is the average value-at-risk at a specific confidence level. As such, this risk quadrangle generates a continuum of error measures that can be used for superquantile regression. For risk-averse optimization, we introduce an optimal approximation of spectral risk measures using quadrature. Lastly, we prove the consistency of this approximation and demonstrate our results through numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

MEASURING RISK IMPORTANCE IN A DYNAMIC PRA FRAMEWORK

Risk importance measures are indexes that are used to rank systems, structures and components (SSCs) using risk-informed methods. The most used/known measures are: Risk Reduction Worth (RRW), Risk Achievement Worth (RAW), Birnbaum (B) and Fussell-Vesely (FV). Once obtained from classical Probabilistic Risk Analysis (PRA) analyses, these risk measures can be effectively employed to optimize component testing and maintenance. In contrast to classical PRA methods, Dynamic PRA methods couple stochastic methods with safety analysis codes to determine risk associate to complex systems such as nuclear plants. Compared to classical PRA methods, they can evaluate with higher resolution the safety impact of timing and sequencing of events on the accident progression. The objective of this paper is to present a series of algorithms that can be used to determine classical risk importance measures (RRW, RAW, B and FV) along with newly developed ones from a Dynamic PRA analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Epi-Regularization of Risk Measures

Uncertainty pervades virtually every branch of science and engineering, and in many disciplines, the underlying phenomena can be modeled by partial differential equations (PDEs) with uncertain or random inputs. This work is motivated by risk-averse stochastic programming problems constrained by PDEs. These problems are posed in infinite dimensions, which leads to a significant increase in the scale of the (discretized) problem. In order to handle the inherent nonsmoothness of, for example, coherent risk measures and to exploit existing solution techniques for smooth, PDE-constrained optimization problems, we propose a variational smoothing technique called epigraphical (epi-)regularization. Here, we investigate the effects of epi-regularization on the axioms of coherency and prove differentiability of the smoothed risk measures. In addition, we demonstrate variational convergence of the epi-regularized risk measures and prove the consistency of minimizers and first-order stationary points for the approximate risk-averse optimization problem. We conclude with numerical experiments confirming our theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Application of Banking Scoring and Rating for Coherent Risk Measures in Electricity Systems ABSCORES

This project developed a framework for asset and system risk management that can be incorporated into current electricity system operations to improve economic efficiency and establish an Electric Assets Risk Bureau. We leveraged scoring and ratings from banking and financial institutions alongside current optimization methods in dispatching power systems to help system operators and electricity markets schedule resources. This approach is based on the observation that there are major discrepancies between the power scheduled by a system operator and the actual power generated/consumed. These discrepancies—exacerbated by unplanned contingencies (e.g., natural disasters)—are caused by multiple factors, including the different financial, environmental and risk preferences of power producers, consumers, and aggregators. We developed a framework that counteracts two failures in electricity system operations: imperfect information and missing markets for products. The technical approach included five tasks. Tasks 1 and 2 supported the development of risk scores at the asset level with historical data collected for this project. Tasks 3, 4, and 5 incorporated scoring into decision-making at the system level. The proposed effort achieved PERFORM's Program Objectives because the proposed outputs and algorithms do not exist in the electricity industry and are an innovative approach to managing risk. Since the acknowledged need to better assess and act upon risk profiles for grid assets has not been met by the industry, this project will also impact ARPA-E's Mission Areas, including improving energy efficiency and giving the U.S. a technological lead in advanced energy technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. Risk measures combine objective probabilities with the subjective values of a decision maker to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical approximations obtained from the training data. These surrogate models limit over-confidence in reliability and safety assessments and produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to a stakeholder’s risk preferences and then present an approach, based on stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. Our surrogate models include biases that permit them to conservatively estimate the target risk measures. We provide theoretical results that show that these biases decay at the same rate as the L 2 error in the surrogate model. Numerical demonstrations confirm that risk-adapted surrogate models do indeed overestimate the target risk measures while converging at the expected rate.

42 ENGINEERING↗
DOE OSTI2021

Surrogate Modeling For Efficiently Accurately and Conservatively Estimating Measures of Risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. We adopt a probabilistic description of risk that assigns probabilities to consequences associated with an event and use risk measures, which combine objective evidence with the subjective values of decision makers, to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical estimates obtained from the training data. These surrogate models not only limit over-confidence in reliability and safety assessments, but produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to the specific risk preferences of the stakeholder and then present an approach, based upon stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. The surrogate models introduce a bias that allows them to conservatively estimate the target risk measures. We provide theoretical results that show that this bias decays at the same rate as the L 2 error in the surrogate model. Our numerical examples confirm that risk-aware surrogate models do indeed over-estimate the target risk measures while converging at the expected rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Improved Risk Priority Measure for the Management of Project Risk

Monte Carlo-based project risk models are essential tools in project risk management, particularly for large, complex projects in which it is difficult to glean intuitively the importance of individual risks to the overall project. Conventional correlation-based methods for measuring the importance of contributing risks in such models are argued here to be both statistically flawed and unintuitive in the importance metrics they produce. Drawing on and adapting methods more traditionally associated with engineering risk models, Risk Reduction Worth (RRW) is introduced as an importance measure. RRW is shown to be statistically robust and provide an easily interpretable, quantitative measure of the importance of a risk to the overall performance of a project; specifically, measuring the extent to which removal of a risk would improve confidence in project outcomes. To ensure practicality of the method, an approach is described in which RRWs can be produced for all contributing risks based on a single Monte Carlo sample. This is demonstrated through application to a large, complex project risk model from which intuitive risk importance insights provide a robust, transparent basis for the allocation of risk management resources.

Risk↗
DOE OSTI2017

Risk Importance Measures in the Designand Operation of Nuclear Power Plants

This monograph presents and discusses risk importance measures as quantified by the probabilistic risk assessment (PRA) models of nuclear power plants (NPPs) developed according to the current standards and practices. Usually, PRA tools calculate risk importance measures related to a single ?basic event? representing particular failure mode. This is, then, reflected in many current PRA applications. The monograph focuses on the concept of ?component-level? importance measures that take into account different failure modes of the component including common-cause failures (CCFs). In opening sections the roleof risk assessment in safety analysis of an NPP is introduced and discussion given of ?traditional?, mainly deterministic, design principles which have been established to assign a level of importance to a particular system, structure or component. This is followed by an overview of main risk importance measures for risk increase and risk decrease from current PRAs. Basic relations which exist among the measures are shown. Some of the current practical applications of risk importancemeasures from the field of NPP design, operation and regulation are discussed. The core of the monograph provides a discussion on theoreticalbackground and practical aspects of main risk importance measures at the level of ?component? as modeled in a PRA, starting from the simplest case, single basic event, and going toward more complexcases with multiple basic events and involvements in CCF groups. The intent is to express the component-level importance measures via theimportance measures and probabilities of the underlying single basic events, which are the inputs readily available from a PRA model andits results. Formulas are derived and discussed for some typical cases. The formulas and their results are demonstrated through some practicalexamples, done by means of a simplified PRA model developed in and run by RiskSpectrum? tool, which are presented in the appendices. The monograph concludes with discussion of limitations of the use of risk importance measures and a summary of component-level importance cases evaluated.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization

Uncertainty is ubiquitous in virtually all engineering applications, and, for such problems, it is inadequate to simulate the underlying physics without quantifying the uncertainty in unknown or random inputs, boundary and initial conditions, and modeling assumptions. Here in this paper, we introduce a general framework for analyzing risk-averse optimization problems constrained by partial differential equations (PDEs). In particular, we postulate conditions on the random variable objective function as well as the PDE solution that guarantee existence of minimizers. Furthermore, we derive optimality conditions and apply our results to the control of an environmental contaminant. Lastly, we introduce a new risk measure, called the conditional entropic risk, that fuses desirable properties from both the conditional value-at-risk and the entropic risk measures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

RECOVERY ACT - Robust Optimization for Connectivity and Flows in Dynamic Complex Networks

The goal of this project was to study robust connectivity and flow patterns of complex multi-scale systems modeled as networks. Networks provide effective ways to study global, system level properties, as well as local, multi-scale interactions at a component level. Numerous applications from power systems, telecommunication, transportation, biology, social science, and other areas have benefited from novel network-based models and their analysis. Modeling and optimization techniques that employ appropriate measures of risk for identifying robust clusters and resilient network designs in networks subject to uncertain failures were investigated in this collaborative multi-university project. In many practical situations one has to deal with uncertainties associated with possible failures of network components, thereby affecting the overall efficiency and performance of the system (e.g., every node/connection has a probability of partial or complete failure). Some extreme examples include power grid component failures, airline hub failures due to weather, or freeway closures due to emergencies. These are also situations in which people, materials, or other resources need to be managed efficiently. Important practical examples include rerouting flow through power grids, adjusting flight plans, and identifying routes for emergency services and supplies, in the event network elements fail unexpectedly. Solutions that are robust under uncertainty, in addition to being economically efficient, are needed. This project has led to the development of novel models and methodologies that can tackle the optimization problems arising in such situations. A number of new concepts, which have not been previously applied in this setting, were investigated in the framework of the project. The results can potentially help decision-makers to better control and identify robust or risk-averse decisions in such situations. Formulations and optimal solutions of the considered problems need to capture uncertainty and risk using appropriate probabilistic, statistical and optimization concepts. The main difficulty arising in addressing these issues is the dramatic increase in the computational complexity of the resulting optimization problems. This project studied novel models and methodologies for risk-averse network optimization- specifically, network design, network flows and cluster detection problems under uncertainty. The approach taken was to incorporate a quantitative risk measure known as conditional value-at-risk that is widely used in financial applications. This approach presents a viable alternate modeling and optimization framework to chance-constrained optimization and mean-variance optimization, one that also facilitates the detection of risk-averse solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Risk-Aware Measurement Synchronization and Recovery for DSSE With Heterogeneous Data Sources

Power distribution systems are increasingly integrating heterogeneous sensors with varying data reporting rates and types, which pose challenges to achieving observability at the desired temporal resolution of distribution system state estimation (DSSE). Multisensor failures caused by extreme events exacerbate these issues, introducing substantial uncertainties into DSSE. This article proposes a novel solution to these challenges by ensuring high-resolution system observability despite heterogeneous data sources and multisensor failures. First, a deep learning architecture combining long short-term memory (LSTM) and graph convolutional network (GCN) is employed to synchronize meters with different reporting rates, aiming to achieve system observability. A random-walk-model-based approach is introduced to generate pseudo-measurements while properly characterizing their uncertainties under multisensor failures. Finally, a disaster-risk-informed observability metric (RiOM) is defined to quantify the uncertainty associated with state estimation results. The proposed framework offers deeper insights into the system observability on the fly compared with conventional analysis. The effectiveness of the framework is demonstrated on an IEEE standard test case and a large-scale real-world distribution feeder in mid-Minnesota in the U.S.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Risk Assessment in Event Evaluation P-302

Incidents at locations such as nuclear power plants, waste repositories, and medical treatment facilities occur at many different times and under a variety of situations. Even the most modern, well run organizations may experience events that are precursors to more serious situations. Currently, the U.S. Nuclear Regulatory Commission evaluates a variety of such events at commercial nuclear plants via the Significance Determination Process (SDP), Management Directive 8.3, and the Accident Sequence Precursor (ASP) program. In these programs, the analyst calculates a conditional risk measure (e.g., conditional core damage probability) for an initiating event situation or an unplanned equipment outage. This calculation is called an “event evaluation.” An “event evaluation” uses a probabilistic risk assessment model to obtain a risk measure that is conditional on the situation which existed during an incident. The Risk Assessment in Event Evaluation material is intended to address how this evaluation is performed using modern risk analysis tools.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2021

Integration of Risk Survival Measures Estimated From Pre- and Posttreatment Computed Tomography Scans Improves Stratification of Patients With Early-Stage Non-small Cell Lung Cancer Treated With Stereotactic Body Radiation Therapy

To predict overall survival of patients receiving stereotactic body radiation therapy (SBRT) for early-stage non-small cell lung cancer (ES-NSCLC), we developed a radiomic model that integrates risk of death estimates and changes based on pre- and posttreatment computed tomography (CT) scans. We hypothesize this innovation will improve our ability to stratify patients into various oncologic outcomes with greater accuracy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗