Optimal Aircraft Design Deicions under Uncertainty via Robust Signomial Programming

Öztürk, Berk; Saab, Ali

doi:10.2514/6.2019-3351

Cited by 8 publications

(7 citation statements)

References 16 publications

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“…Many design queries can be answered with optimization approaches. When including uncertainty, one can use either robust design optimization or reliability-based design optimization [1][2][3]. These approaches usually convert a probability distribution into scalar measures like mean and variance.…”

Section: Selecting Technologies In Aircraft Conceptualmentioning

confidence: 99%

Selecting Technologies in Aircraft Conceptual Design Using Probabilistic Inversion

Roelofs

Kurowicka

Vos

2021

Journal of Aircraft

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Section: Selecting Technologies In Aircraft Conceptualmentioning

confidence: 99%

Selecting Technologies in Aircraft Conceptual Design Using Probabilistic Inversion

Roelofs

Kurowicka

Vos

2021

Journal of Aircraft

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“…Nonconvex signomial programs have been used in chemical engineering since the 1970's [3,20,23]. More recently, there has been a surge of interest in nonconvex signomial programming for aerospace engineering and transportation systems; see [29,54,72] for academic work on this topic and [37] for an industrial example. The conceptual source of these signomial models in engineering is the simple practice of modeling systems with non-polynomial power laws [27,28].…”

Section: Why Study Signomials?mentioning

confidence: 99%

Algebraic perspectives on signomial optimization

Dressler¹,

Murray²

2021

Preprint

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Signomials are obtained by generalizing polynomials to allow for arbitrary real exponents. This generalization offers great expressive power, but has historically sacrificed the organizing principle of "degree" that is central to polynomial optimization theory. We reclaim that principle here through the concept of signomial rings, which we use to derive complete convex relaxation hierarchies of upper and lower bounds for signomial optimization via sums of arithmetic-geometric exponentials (SAGE) nonnegativity certificates. The Positivstellensatz underlying the lower bounds relies on the concept of conditional SAGE and removes regularity conditions required by earlier works, such as convexity and Archimedeanity of the feasible set. Through worked examples we illustrate the practicality of this hierarchy in areas such as chemical reaction network theory and chemical engineering. These examples include comparisons to direct global solvers (e.g., BARON and ANTIGONE) and the Lasserre hierarchy (where appropriate). The completeness of our hierarchy of upper bounds follows from a generic construction whereby a Positivstellensatz for signomial nonnegativity over a compact set provides for arbitrarily strong outer approximations of the corresponding cone of nonnegative signomials. While working toward that result, we prove basic facts on the existence and uniqueness of solutions to signomial moment problems.

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“…By asking users about how they used cost functions, we learned that their value was not in returning the "best result", but rather in getting a better understanding of the set of potentially desirable designs by collapsing it along a particular axis. We observed engineers optimizing for multiple performance parameters, each generating a "paragon" optimal by that metric [49]. Comparison of these paragons gave a sense of possibilities for their design [48].…”

Section: Feature D: Modularity and Convexitymentioning

confidence: 99%

“…It did so by embracing a participatory human-centered framework focused on validating workers' knowledge [26] and using connections between that knowledge and the mathematics of optimization to develop GPkit, a toolkit for convex Geometric Programs. GPkit was used by many engineers and researchers during its development [1,2,11,14,16,17,27,28,32,33,36,46,48,49,53,60,64,68], which resulted in features that are:…”

Section: Introductionmentioning

confidence: 99%

GPkit: A Human-Centered Approach to Convex Optimization in Engineering Design

Burnell

Damen

Hoburg

2020

Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems

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We present GPkit, a Python toolkit for Geometric and Signomial Programming that prioritizes explainability and incremental complexity. GPkit was designed through an ethnographic approach in the firms, classrooms, and research labs where it became part of the fabric of daily engineering work. Organizations have approached GPkit both in ways which centralize design work and in ways which distribute it, usecases which emerged from and inspired new toolkit features. This twoway flow between mathematical structure and practitioner knowledge resulted in several novel contributions to the formulation and interpretation of convex programs and to our understanding of early-stage engineering design. For example, dual solutions (often considered incidental) can be more valuable to a design process than the "optimal design" itself, and we present novel algorithms and design methods based on this insight.

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Optimal Aircraft Design Deicions under Uncertainty via Robust Signomial Programming

Cited by 8 publications

References 16 publications

Selecting Technologies in Aircraft Conceptual Design Using Probabilistic Inversion

Selecting Technologies in Aircraft Conceptual Design Using Probabilistic Inversion

Algebraic perspectives on signomial optimization

GPkit: A Human-Centered Approach to Convex Optimization in Engineering Design

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