1. Progress Report Qiang Chen, Derek Dalle, Chad Griep, Jingwei Hu, Jahmario Williams, Zhenqiu Xie Multiobjective Modeling and Optimization in Design

2. 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.

3. 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 c t

4. Motivation Typical 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.

5. Motivation Problems 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.

6. 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 Σω i f i where each f i is a single objective function. We are looking for better decision-making tools.

7. 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.

8. Optimality for Single 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

9. 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

10. 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.

11. 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 F1F1 F2F2

12. Not perfect curve. Objective functions have many local minima (artifact of numerical procedures). The graph implies that we need more work on optimization.

13. 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)

14. 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

15. Minimization Obtained Minimum of Gross Weight FLOPS213554 NPSOL221495 FLOPS + NPSOL211920 2 * (FLOPS + NPSOL) 210046

16. 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”

17. 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.