Progress Report

Qiang Chen, Derek Dalle, Chad Griep, Jingwei Hu,

Jahmario Williams, Zhenqiu Xie

Multiobjective Modeling and Optimization in Design

Introduction• Optimal design of

subsonic aircraft– Study how changes in the shape

of aircraft affect aerodynamics.

• More importantly, figure out what to optimize.

• Apply this to quiet supersonic aircraft.– Investigate intricacies and

difficulties inherent in designing a cost-effective, efficient and quiet supersonic passenger aircraft.

Configuration Design

Variables for Conceptual Design

• Reference wing area

• Wing sweep angle

• Wing aspect ratio

• Wing taper ratio

• Wing-thickness chord ratio

• Gross weight

• Thrust

Objective

Functions

• Minimum gross weight

• Minimum fuel burned

• Maximum range

• Minimum cost

• Minimum NOx emissions

sweep angle

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MotivationTypical Engineer’s Method

• Establish requirements.

• Design an aircraft that successfully meets the requirements.

• Try to optimize by changing one (or several) design variable at a time.

• Ad hoc stopping criteria are used.

MotivationProblems with Old Methods

• This process is slow.

• Optimization occurs too late.

• Engineers have been successful, but design is based on experience.

• Some problems are too hard.

• Real problems are massively multiobjective.

Flight Optimization System FLOPS (A. McCullers)

• FLOPS analyzes a complete aircraft given a large set of design variables and options.

• FLOPS also does nonlinear optimization by minimizing Σωifi where each fi is a single objective function.

• We are looking for better decision-making tools.

Relationships between design variables and objective functions

Look at 5 main design variables:THRUST ---- Maximum rated thrust per engine

SWEEP ---- Quarter-chord sweep angle of the wing

AR ---- Wing aspect ratio

TCA ---- Wing thickness-chord ratio

SW ---- Reference wing area

Objective functions: Fuel Usage, Gross Weight and their (weighted) average.

Optimality forSingle Objective

Study sensitivity of single objective function to variations in design variables

• FLOPS aproach– Enter parametrically varied design variables into input file and

chose objective function to study– Run FLOPS to analyze the inputs– Read values of objective function from (contour plot data) output file

• FLOPS with Matlab approach– Use Matlab to generate mesh of two design variables– Rewrite the input file with updated variables– Call FLOPS to analyze the inputs– Read output for objective function– Write data file and plot results

Optimality for Multiple Objectives

• Analyze competing elements in supersonic aircraft shape optimization (i.e., low boom versus low drag).

• Discuss condition where one objective cannot be improved without hurting another.

Pareto optimality

• Pareto optimality (or efficiency) occurs when one cannot decrease one objective without increasing another.

• Decision making plays

an important role.• Choose proper weights

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Not perfect curve.• Objective functions have many local minima

(artifact of numerical procedures).• The graph implies that we need more work on

optimization.

Using other optimization codes• To investigate alternative formulations, we need to use

tools that are external to FLOPS.• NPSOL (Stanford Software, Gill et al.) is a set of Fortran

subroutines for minimizing a smooth function subject to bounds on variables, linear constraints and smooth nonlinear constraints.

• It uses a sequential quadratic programming (SQP) algorithm.

• Call previous Matlab codes to adjust input variables, perform analysis and read output results.

• Use NPSOL to minimize the result (weighted objective function)

• Used “out of the box”, NPSOL did not provide better results than FLOPS itself

– Price of running FLOPS is quite high– May not be efficient enough in handling this

special problem– May need fine tuning

• A bootstrapping strategy of the two codes can do quite well

Minimization Obtained

Minimum of Gross Weight

FLOPS 213554

NPSOL 221495

FLOPS + NPSOL 211920

2 * (FLOPS + NPSOL)

210046

Progress• Unconstrained optimal

design of subsonic aircraft.– Done using Mathematica’s

FindMinimum command and FLOPS

– “Optimal” designs are often unrealistic (because of the problem formulation).

• Once constraints are applied, more sophisticated objective functions can be used.

• More design variables can also be used.

Feasible designs

Impractical aircraft

“Optimal”

Future Work

• Investigate the effects of multiple objectives.

• Model sound and energy produced from sonic overpressure signal.

• Understand relationships between aircraft design and overpressure signal.

• The goal is an analysis method that could be used with an optimization algorithm.

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