Horsetail Matching for Optimization Under Probabilistic, Interval and Mixed Uncertainties

Cook, Laurence W.; Jarrett, Jerome P.; Willcox, Karen

doi:10.2514/6.2017-0590

Cited by 12 publications

(4 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An alternative is horsetail matching, which has been shown to be superior to density matching in terms of computational efficiency while producing satisfactory designs. 164 Horsetail matching allows to optimize for different targets. However, when many uncertainties are involved, the employed surrogate model effectiveness deteriorates and it has to be investigated how to deal with higher dimensionality.…”

Section: Uncertainty-based Multidisciplinary Design and Optimizationmentioning

confidence: 99%

Uncertainty-Based Design Optimization and Technology Evaluation: A Review

Roelofs

Vos

2018

2018 AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

Evaluation and assessment of novel technologies for aerospace applications is essential for business strategy and decision making regarding development efforts. Since technology is evaluated in the conceptual design phase and little is known about the technology, large uncertainty is present. This uncertainty needs to be accurately assessed and managed. To investigate the research efforts that have been performed to perform technology evaluation under uncertainty, a literature review was conducted, focusing on methods and modeling approaches to assign and quantify these uncertainties. It is found that probability theory is still the most popular theory for representing uncertainty. Polynomial Chaos Expansions and Stochastic Collocation methods are gaining popularity for propagating uncertainty through a modeling environment, but Monte Carlo Simulations are still widely used. Commonly, surrogate models are used to reduce computational effort. Other efforts focus on the use of multifidelity approaches to reduce computational effort when high-fidelity methods are required. Four issues that may need to be addressed in future research were identified.

show abstract

Section: Uncertainty-based Multidisciplinary Design and Optimizationmentioning

confidence: 99%

Uncertainty-Based Design Optimization and Technology Evaluation: A Review

Roelofs

Vos

2018

2018 AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

show abstract

“…For this reason, PARFUM will also not achieve the specified margins exactly but will get as close as possible. The distance between the initial, obtained, and specified CDFs can be computed using the metric presented by Cook and Jarrett [45]. This shows for PRE −1 that the initial distance to the specified constraint is 6.1 ⋅ 10 −5 , and after PI it is 5.1 ⋅ 10 −5 .…”

Section: B Technology Prioritization Using Grouped Sample Reweightingmentioning

confidence: 99%

Selecting Technologies in Aircraft Conceptual Design Using Probabilistic Inversion

Roelofs

Kurowicka

Vos

2021

Journal of Aircraft

View full text Add to dashboard Cite

show abstract

“…This indicates a need for a means to determine stochastic dominance between design alternatives. To address this issue, Horsetail matching has been developed recently, which seeks to minimize the distance between the outcome CDF with a target [28]. As stochastic dominance is defined by the CDF, this method prevents the selection of a stochastically dominated design by basing the evaluation criterion directly off the CDF.…”

Section: Introductionmentioning

confidence: 99%

Beyond Mean–Variance: The Mean–Gini Approach to Optimization Under Uncertainty

Wang

Kannan

Bloebaum

2017

Journal of Mechanical Design

View full text Add to dashboard Cite

In probabilistic approaches to engineering design, including robust design, mean and variance are commonly used as the optimization objectives. This method, however, has significant limitations. For one, some mean–variance Pareto efficient designs may be stochastically dominated and should not be considered. Stochastic dominance is a mathematically rigorous concept commonly used in risk and decision analysis, based on the cumulative distribution function (CDFs), which establishes that one uncertain prospect is superior to another, while requiring minimal assumptions about the utility function of the outcome. This property makes it applicable to a wide range of engineering problems that ordinarily do not utilize techniques from normative decision analysis. In this work, we present a method to perform optimizations consistent with stochastic dominance: the Mean–Gini method. In macroeconomics, the Gini Index is the de facto metric for economic inequality, but statisticians have also proven a variant of it can be used to establish two conditions that are necessary and sufficient for both first and second-order stochastic dominance . These conditions can be used to reduce the Pareto frontier, eliminating stochastically dominated options. Remarkably, one of the conditions combines both mean and Gini, allowing for both expected outcome and uncertainty to be expressed in a single objective which, when maximized, produces a result that is not stochastically dominated given the Pareto front meets a convexity condition. We also find that, in a multi-objective optimization, the Mean–Gini optimization converges slightly faster than the mean–variance optimization.

show abstract

Horsetail Matching for Optimization Under Probabilistic, Interval and Mixed Uncertainties

Cited by 12 publications

References 35 publications

Uncertainty-Based Design Optimization and Technology Evaluation: A Review

Uncertainty-Based Design Optimization and Technology Evaluation: A Review

Selecting Technologies in Aircraft Conceptual Design Using Probabilistic Inversion

Beyond Mean–Variance: The Mean–Gini Approach to Optimization Under Uncertainty

Contact Info

Product

Resources

About