Application of Signomial Programming to Aircraft Design

Kirschen, Philippe G.; York, Martin A.; Öztürk, Berk; Hoburg, Warren

doi:10.2514/1.c034378

Cited by 24 publications

(25 citation statements)

References 14 publications

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“…GPkit has a number of built-in heuristics for solving SPs via a series of GP approximations. This work employs the relaxed constants penalty function heuristic detailed in [5].…”

Section: Optimization Formulationmentioning

confidence: 99%

“…Other techniques to make constraints GP compatible include using variable transformations and Taylor approximations. Variable transformations are used in the tail cone model from [5] and the stagnation relations in Appendix B. Taylor approximations are used in the GP-compatible Breguet range equation presented in [2] and the structural model in Appendix A. Additionally, empirical relations can be used to formulate constraints using the methods described in [14]. An example of GP-compatible fits can be found in [5], where XFOIL [15] data is used to generate a posynomial inequality constraint for TASOPT C-series airfoil parasitic drag coefficient as a function of wing thickness, lift coefficient, Reynolds number, and Mach number.…”

Section: B Geometric Programmingmentioning

confidence: 99%

“…For example, the wing structural model depends on engine weight and the fuselage structural model depends on maximum tail aerodynamic loads. A full description of subsystem variable linking can be found in [5]. A qualitative description of all submodels is provided in the following subsections.…”

Section: Aircraft Model Overviewmentioning

confidence: 99%

“…The fuselage model is adapted from the model in [5], and borrows heavily from TASOPT [7]. Modifications, described in Appendix A, were made to support double-bubble fuselages in addition to traditional tube fuselages.…”

Section: A Fuselagementioning

confidence: 99%

“…The utility of this new architecture is demonstrated through the solution of a series of commercial aircraft MDO problems. Prior work has developed physics-based SP-compatible models for aircraft wings, fuselages, horizontal tails, vertical tails, landing gear, and turbofan engines [5,6]. These models, along with a mission profile, have been combined to form a full-system aircraft MDO tool of comparable fidelity to the widely used Transport Aircraft System Optimization (TASOPT) [7].…”

Section: Introductionmentioning

confidence: 99%

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Efficient Aircraft Multidisciplinary Design Optimization and Sensitivity Analysis via Signomial Programming

et al. 2018

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This paper proposes a new methodology for physics-based aircraft multidisciplinary design optimization (MDO) and sensitivity analysis. The proposed architecture uses signomial programming (SP), a type of difference-of-convex optimization that is solved iteratively as a series of log-convex problems. A requirement of SP is that all constraints and objective functions must have explicit signomial formulas. The SP MDO architecture facilitates the low-cost computation of optimal sensitivities through Lagrange duality. The specific example of commercial aircraft MDO is considered. Using SP, a small-, medium-, and large-scale benchmark problem is solved 16, 39, and 26 times faster, respectively, than Transport Aircraft System Optimization (TASOPT), a comparable and widely used aircraft MDO tool. The SP solution times include computation of all optimal parameter and constraint sensitivities, a feature unique to the presented architecture. The reliability of SP is demonstrated by converging a commercial aircraft MDO problem for a number of different objective functions and evaluating both traditional and nontraditional aircraft configurations. While the presented example is commercial aircraft MDO, the SP MDO architecture is applicable to a range of engineering optimization problems.

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“…GPkit has a number of built-in heuristics for solving SPs via a series of GP approximations. This work employs the relaxed constants penalty function heuristic detailed in [5].…”

Section: Optimization Formulationmentioning

confidence: 99%

Section: B Geometric Programmingmentioning

confidence: 99%

Section: Aircraft Model Overviewmentioning

confidence: 99%

Section: A Fuselagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Aircraft Multidisciplinary Design Optimization and Sensitivity Analysis via Signomial Programming

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Newton Polytopes and Relative Entropy Optimization

2021

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Newton polytopes play a prominent role in the study of sparse polynomial systems, where they help formalize the idea that the root structure underlying sparse polynomials of possibly high degree ought to still be "simple." In this paper we consider sparse polynomial optimization problems, and we seek a deeper understanding of the role played by Newton polytopes in this context. Our investigation proceeds by reparametrizing polynomials as signomialswhich are linear combinations of exponentials of linear functions in the decision variable -and studying the resulting signomial optimization problems. Signomial programs represent an interesting (and generally intractable) class of problems in their own right. We build on recent efforts that provide tractable relative entropy convex relaxations to obtain bounds on signomial programs. We describe several new structural results regarding these relaxations as well as a range of conditions under which they solve signomial programs exactly. The facial structure of the associated Newton polytopes plays a prominent role in our analysis. Our results have consequences in two directions, thus highlighting the utility of the signomial perspective. In one direction, signomials have no notion of "degree"; therefore, techniques developed for signomial programs depend only on the particular terms that appear in a signomial. When specialized to the context of polynomials, we obtain analysis and computational tools that only depend on the particular monomials that constitute a sparse polynomial. In the other direction, signomials represent a natural generalization of polynomials for which Newton polytopes continue to yield valuable insights. In particular, a number of invariance properties of Newton polytopes in the context of optimization are only revealed by adopting the viewpoint of signomials.

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Hyperloop system optimization

Kirschen

Burnell²

2022

Optim Eng

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Application of Signomial Programming to Aircraft Design

Cited by 24 publications

References 14 publications

Efficient Aircraft Multidisciplinary Design Optimization and Sensitivity Analysis via Signomial Programming

Efficient Aircraft Multidisciplinary Design Optimization and Sensitivity Analysis via Signomial Programming

Newton Polytopes and Relative Entropy Optimization

Hyperloop system optimization

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