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At least 19 records

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↗

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↗

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↗

A Case Study of Measuring Process Risk for Early Insights into Software Safety

In this case study, we examine software safety risk in three flight hardware systems in NASA's Constellation spaceflight program. We applied our Technical and Process Risk Measurement (TPRM) methodology to the Constellation hazard analysis process to quantify the technical and process risks involving software safety in the early design phase of these projects. We analyzed 154 hazard reports and collected metrics to measure the prevalence of software in hazards and the specificity of descriptions of software causes of hazardous conditions. We found that 49-70% of 154 hazardous conditions could be caused by software or software was involved in the prevention of the hazardous condition. We also found that 12-17% of the 2013 hazard causes involved software, and that 23-29% of all causes had a software control. The application of the TPRM methodology identified process risks in the application of the hazard analysis process itself that may lead to software safety risk.

Layman, Lucas↗

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↗

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↗

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↗

Measurement Decision Risk - The Importance of Definitions

One of the more misunderstood areas of metrology is the Test Uncertainty Ratio (TUR) and the Test Accuracy Ratio (TAR). There have been many definitions over the years, but why are these definitions important to a discussion on measurement decision risk? The importance lies in the clarity of communication. Problems can immediately arise in the application (or misapplication) of the definition of these terms. In other words, while it is important to understand the definitions, it is more important to understand concepts behind the definitions and to be precise in how they are applied. The objective of any measurement is a decision. Measurement Decision Risk is a way to look at the quality of a measurement, and although it is not a new concept, it has generated a lot of attention since its addition as a requirement in the new U.S. National Standard, ANSIINCSL Z540.3-2006. In addition to Measurement Decision Risk as the prime method of managing measurement risk, Z540.3 has added, as a fall-back, an explicit definition for TUR. The impact these new requirements may have on calibration service providers has become the topic of much discussion and in some cases concern. This paper will look at the concepts behind the definitions and how they relate to Measurement Decision Risk. Using common examples, this paper will also provide a comparison of various elements of risk related to measurement science using the concepts of TAR, TUR, accuracy ratios, and Consumer Risk (False Accept Risk). The goal of this paper is to provide a better understanding of their relevance to the measurement decision process.

Mimbs, Scott M.↗

Measurement Decision Risk - The Importance of Definitions

One of the more misunderstood areas of metrology is the Test Uncertainty Ratio (TUR) and its cousin, the Test Accuracy Ratio (TAR). There have been many definitions over the years, but why are these definitions important to a discussion on measurement decision risk? The importance lies in the clarity of communication. Problems can immediately arise in the application (or misapplication) of the definition of these terms. In other words, while it is important to understand the definitions, it is more important to understand concepts behind the definitions and to be precise in how they are applied. The objective of any measurement is a decision. Measurement Decision Risk is a way to look at the quality of a measurement and although it is not a new concept, it has generated a lot of attention since its addition as a requirement in the new U.S. National Standard, ANSI/NCSL Z540.3-2006. In addition to Measurement Decision Risk as the prime method of managing measurement risk, Z540.3 has also added, as a fall-back, an explicit definition for TUR. The impact these changes might have on calibration service providers if these requirements are levied on them has become the topic of much discussion and in some cases concern. This paper looks at the concepts behind the definitions and how they relate to Measurement Decision Risk. Using common examples, this paper will also provide a comparison of various elements of risk related to measurement science using the concepts of TAR, TUR, accuracy ratios, and Consumer Risk (False Accept Risk). The goal is to provide a better understanding of their relevance to the measurement decision process.

Mimbs, Scott M.↗

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↗

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↗

Measurement Decision Risk - The Importance of Definitions

The idea behind this presentation is how the difference in definitions can change the application. 1. Look at history, concepts, and definitions. 2. Link the test uncertainty ratio (TUR) to measurement decision risk.

Mimbs, Scott↗

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↗

Hawai‘i Island Disasters: Using NASA Earth Observations to Assess Coastal Flood Risk with Measures of Land Cover Change, Flood Extent, and Vulnerability for Adaptation and Mitigation Planning on Hawai‘i Island

As the County of Hawai‘i faces an increased risk of extreme flooding events, sea-level rise, and other hazards associated with climate change, the need for building geospatial capacity to make better-informed decisions is critical. The County of Hawai‘i and Arizona State University partnered with NASA DEVELOP to complete a macro-scale risk analysis for the island of Hawai‘i analyzing flooding, land cover, vulnerability, and exposure factors using Earth observations and socio-economic data. The team assessed the variation in urban coastal vulnerability around the entire island of Hawai‘i, using satellite imagery of coastal land cover typology from satellite products such as Landsat 8 Operational Land Imager (OLI), Landsat 7 Enhanced Thematic Mapper Plus (ETM+), and Sentinel-1 Synthetic Aperture Radar (SAR). The team made a sharable geodatabase containing datasets modeling vulnerability to coastal flooding as well as the Hawai‘i Flood Risk Toolbox (HiFloRT) which contains multiple tools for the County to map land cover, extreme rainfall and flood extent across the Island. The end products will allow the County of Hawai‘i to establish a protocol and standard framework for the utilization of Earth observations in future planning.

Garren Kalter↗

Cost and Benefit Analysis of Mitigating, Tracking, and Remediating Orbital Debris

Orbital debris may collide with crewed and robotic spacecraft, placing them at risk. The wide range of debris, from 9,000-kilogram rocket bodies to millions of millimeter-size debris, has led to a similarly wide range of proposed actions for addressing the risks posed by debris. However, the costs and benefits of these actions have historically been unknown. This is a challenge for decision makers who are choosing which actions to support through technology development or policy changes. NASA’s Office of Technology, Policy, and Strategy is addressing these technical and economic uncertainties by building a capability to (1) complete rigorous calculations of the net present value of each action, (2) identify an optimal portfolio of actions to reduce risk, and (3) quantitatively analyze policies related to space sustainability. This report describes our progress toward that capability and to solicit feedback from the space and economic communities. Our previous work, referred to here as Phase 1, assessed the costs and benefits of performing debris remediation on operationally relevant timescales. The current analysis contains major updates to the risk model used in Phase 1 and expands the breadth of actions considered to include mitigating the creation of debris, improving the ability to track debris, and more methods for cleaning up existing debris. We demonstrate that our approach of measuring risks in dollars allows for the effectiveness of seemingly incommensurate actions to be compared and generates insights that other approaches to measuring risk have missed.

Jericho Locke↗

Cost and Benefit Analysis of Mitigating, Tracking, and Remediating Orbital Debris

Presentation accompanying the technical report with the same name. The abstract for the report and the full study is repeated below. Orbital debris may collide with crewed and robotic spacecraft, placing them at risk. The wide range of debris, from 9,000-kilogram rocket bodies to millions of millimeter-size debris, has led to a similarly wide range of proposed actions for addressing the risks posed by debris. However, the costs and benefits of these actions have historically been unknown. This is a challenge for decision makers who are choosing which actions to support through technology development or policy changes. NASA’s Office of Technology, Policy, and Strategy is addressing these technical and economic uncertainties by building a capability to (1) complete rigorous calculations of the net present value of each action, (2) identify an optimal portfolio of actions to reduce risk, and (3) quantitatively analyze policies related to space sustainability. This report describes our progress toward that capability and to solicit feedback from the space and economic communities. Our previous work, referred to here as Phase 1, assessed the costs and benefits of performing debris remediation on operationally relevant timescales. The current analysis contains major updates to the risk model used in Phase 1 and expands the breadth of actions considered to include mitigating the creation of debris, improving the ability to track debris, and more methods for cleaning up existing debris. We demonstrate that our approach of measuring risks in dollars allows for the effectiveness of seemingly incommensurate actions to be compared and generates insights that other approaches to measuring risk have missed.

Jericho Locke↗

A Cost and Benefit Analysis of Orbital Debris Remediation, Mitigation,Tracking, and Characterization

Orbital debris may collide with crewed and robotic spacecraft, placing them at risk. The wide range of debris, from 9,000-kilogram rocket bodies to millions of millimeter-size debris, has led to a similarly wide range of proposed actions for addressing the risks posed by debris. However, the costs and benefits of these actions have historically been unknown. This is a challenge for decision makers who are choosing which actions to support through technology development or policy changes. NASA’s Office of Technology, Policy, and Strategy is addressing these technical and economic uncertainties by building a capability to (1) complete rigorous calculations of the net present value of each action, (2) identify an optimal portfolio of actions to reduce risk, and (3) quantitatively analyze policies related to space sustainability. This report describes our progress toward that capability and to solicit feedback from the space and economic communities. Our previous work(Colvin, Karcz, and Wusk. 2023), referred to here as Phase 1, assessed the costs and benefits of performing debris remediation on operationally relevant timescales. The current paper summarizes the work of Locke and Colvin (2024), which contains major updates to the risk model used in Phase 1 and expands the breadth of actions considered to include mitigating the creation of debris, improving the ability to track debris, and more methods for cleaning up existing debris. We demonstrate that our approach of measuring risks in dollars allows for the effectiveness of seemingly incommensurate actions to be compared and generates insights that other approaches to measuring risk have missed.

Orbital Debris↗