MIest Constraint Scaling 16888 Scal A well scaled set of constraints has two properties o reasons to scale each constraint is well conditioned with respect to perturbations in the design variables 1. At the beginning of optimization, using X, improve algorithm performance(e.g. decrease the constraints are balanced with respect to number of iterations) each other, i.e. all constraints have an equal weighting in the optimization → dairy farm demo 2. At the end of optimization, using x*, to make sure that the "optimal solution is indeed the The scaling of constraints can have a major effect on the best we can achieve path chosen by the optimizer. For example, many → BWB example algorithms maintain a set of active constraints and from one iteration to the next they interchange one active and one inactive constraint Constraint scaling impacts the selection of which constraint to add or delete e Massachusetts Institute of Technology- Prof de Weck and Prof Willcox e Massachusetts Insttute of Technology. Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics Engineering Systems Division and Dept of Aeronautics and Astronautics MIest Scaling Example Scaling EXample Consider optimization of the BWB Consider a two-aircraft family with common wings Rather than optimizing just a single aircraft, we want to design a family of aircraft commor ■ different This family has commonality-the planes share cente common parts, planforms and systems Commonality can help to reduce costs e.g. manufacturing costs design costs spare parts BWB3-450 BWB 3-250 475 passengers, 8550 nm 272 passengers, 8550 nm Inner wng But will require a trade with performance We set up an MDo framework for each aircraft It is easier to achieve commonality with the BWb thai We link the variables that are common between the two a, with conventional tube wing aircraft ogy- Prof de Weck and Prof Willcox 32 aircraft etts Institute of Technology . Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics ystems Divsion and Dept of Aeronautics and Astronautics29 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Constraint Scaling Constraint Scaling A well scaled set of constraints has two properties: – each constraint is well conditioned with respect to perturbations in the design variables – the constraints are balanced with respect to each other, i.e. all constraints have an equal weighting in the optimization The scaling of constraints can have a major effect on the path chosen by the optimizer. For example, many algorithms maintain a set of active constraints and from one iteration to the next they interchange one active and one inactive constraint. Constraint scaling impacts the selection of which constraint to add or delete. 30 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Scaling Scaling Two reasons to scale: 1. At the beginning of optimization, using x0, to improve algorithm performance (e.g. decrease number of iterations). ⇒ dairy farm demo 2. At the end of optimization, using x*, to make sure that the “optimal” solution is indeed the best we can achieve. ⇒ BWB example 31 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Scaling Example Scaling Example • Consider optimization of the BWB • Rather than optimizing just a single aircraft, we want to design a family of aircraft • This family has commonality – the planes share common parts, planforms and systems • Commonality can help to reduce costs e.g. manufacturing costs design costs spare parts crew training • But will require a trade with performance • It is easier to achieve commonality with the BWB than with conventional tube & wing aircraft centerbody inner wing outer wing winglet 32 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Scaling Example Scaling Example • Consider a two-aircraft family with common wings: • We set up an MDO framework for each aircraft • We link the variables that are common between the two aircraft BWB 3-250 272 passengers, 8550 nm BWB 3-450 475 passengers, 8550 nm common different