Geometric Programming for Aircraft Design Optimization

Hoburg, Warren; Abbeel, Pieter

doi:10.2514/6.2012-1680

Cited by 24 publications

(47 citation statements)

References 12 publications

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“…The corresponding bypass ratio is therefore relatively low. If we raise the turbine inlet temperature, the core airflow can be smaller, thus increasing bypass ratio [2].…”

Section: The Matmentioning

confidence: 99%

Sustainable Design of Turbofan Engine: A Computer-Aided Design and Finite Element Analysis

Jha¹

2018

JMEA

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A compressive design and analysis of a turbofan engine is presented in this paper. The components of jet engine have been analyzed based on mechanical design concept. An attempt has been to select materials based on sustainability and green design considerations. The energy content (e) of the materials has been one of the parameters for material selection. The choice of material has a substantial impact on cost, manufacturing process, and the life cycle efficiency. All components nose cone, fan blade, inlet shaft, including compressor has been solid modeled using Siemens NX 11.0 CAD software. The finite element analysis of every component was performed and found safe. A tolerance analysis was performed before assembly of the turbofan engine. A numerical analysis was completed on blade and inlet geometries to determine a more efficient turbofan engine. Thermal analysis was executed on the cone and suitable corrections were made. Finally, the cost and the total energy were estimated to show how much energy is needed to manufacture a turbofan jet engine.

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“…The corresponding bypass ratio is therefore relatively low. If we raise the turbine inlet temperature, the core airflow can be smaller, thus increasing bypass ratio [2].…”

Section: The Matmentioning

confidence: 99%

Sustainable Design of Turbofan Engine: A Computer-Aided Design and Finite Element Analysis

Jha¹

2018

JMEA

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“…In this example, we identified a posynomial model for the drag force of the airfoil, from data obtained from the CFD simulations. The posynomial form is important since it allows the application of geometric programming algorithms, which in turn allow for efficient optimization of the airfoil characteristics, see, e.g., [14].…”

Section: Example 2: Identification Of Airfoil Drag Forcementioning

confidence: 99%

“…Note that, while in polynomial models the exponents α ij are nonnegative integers, in posynomial models these exponents may also be negative and/or noninteger. Posynomial models are of great importance in many fields of technology, ranging from structural design, network flow, optimal control (see [2,33]), to aerospace system design [14], circuit design [5,8,26], antennas [1] and communication systems [7]. The interest in posynomials is motivated by the fact that they lead to computationally efficient geometric programming models for optimal system design, see, e.g., [10,2,33].…”

Section: Introductionmentioning

confidence: 99%

Sparse identification of posynomial models

2015

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Posynomials are nonnegative combinations of monomials with possibly fractional and both positive and negative exponents. Posynomial models are widely used in various engineering design endeavors, such as circuits, aerospace and structural design, mainly due to the fact that design problems cast in terms of posynomial objectives and constraints can be solved efficiently by means of a convex optimization technique known as geometric programming (GP). However, while quite a vast literature exists on GP-based design, very few contributions can yet be found on the problem of identifying posynomial models from experimental data. Posynomial identification amounts to determining not only the coefficients of the combination, but also the exponents in the monomials, which renders the identification problem numerically hard. In this draft, we propose an approach to the identification of multivariate posynomial models, based on the expansion on a given large-scale basis of monomials. The model is then identified by seeking coefficients of the combination that minimize a mixed objective, composed by a term representing the fitting error and a term inducing sparsity in the representation, which results in a problem formulation of the "squareroot LASSO" type, with nonnegativity constraints on the variables. We propose to solve the problem via a sequential coordinate-descent scheme, which is suitable for large-scale implementations.

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“…For problems that can be formulated as Geometric Programs (GPs), modern solvers guarantee globally optimal solutions, are extremely fast, and return local sensitivities at no extra cost, thanks to the principle of lagrange duality. In previous work, Hoburg [1] shows, firstly, that many models common to aircraft design can be represented directly in GP-compatible form, and, secondly, that there are a number of innovative ways of dealing with models that cannot, including, but not limited to, changes of variables and GP-compatible fitting methods. Finally, it is also shown that such problems can be solved efficiently using a standard laptop computer.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, it is also shown that such problems can be solved efficiently using a standard laptop computer. The aircraft design problem solved in [1] includes models for steady level flight, range, takeoff distance, landing speed, sprint flight condition, actuator disk propulsive efficiency, simple drag and weight buildups, and beam wing box structure.…”

Section: Introductionmentioning

confidence: 99%

Signomial Programming Models for Aircraft Design

Kirschen

Burnell

Hoburg

2016

54th AIAA Aerospace Sciences Meeting

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Due to the coupled nature of aircraft system design, it is important to consider all of the major subsystems when trying to optimize a configuration. This, however, is easier said than done, particularly because each individual subsystem model can be arbitrarily complex, thus making optimization difficult. By restricting an optimization problem to have a certain mathematical structure, significantly more effective and tractable solution techniques can be used. Geometric programming, an example of one such technique, guarantees finding a globally optimal solution. Although it has been shown that geometric programming can be used to solve some conceptual aircraft design problems, the required formulation can prove too restrictive for certain relationships. Signomial programming is a closely related relaxation of geometric programming that offers enhanced expressiveness, but without the guarantee of global optimality. Despite this, solution methods for signomial programs are disciplined and effective. In the present work, signomial programming models are proposed for optimal preliminary sizing of the vertical tail, fuselage, and landing gear of a commercial aircraft with a tubeand-wing configuration. Signomial programming's relaxed formulation allows it to handle some of the key constraints in tail, fuselage, and landing gear design and therefore a significant improvement in fidelity over geometric programming models is achieved. The models are readily extensible and easily combined with other models, making them effective building blocks for a full aircraft model. A primary contribution of this work is to demonstrate signomial programming as a viable tool for multidisciplinary aircraft design optimization.

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Geometric Programming for Aircraft Design Optimization

Cited by 24 publications

References 12 publications

Sustainable Design of Turbofan Engine: A Computer-Aided Design and Finite Element Analysis

Sustainable Design of Turbofan Engine: A Computer-Aided Design and Finite Element Analysis

Sparse identification of posynomial models

Signomial Programming Models for Aircraft Design

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