Mlesd Surrogate Variables("Tearing,") 6888 ES077 Information loop can be broken by introducing surrogate variables min(,,x2) minD(,x St St =8(x,8(02)20画8()20 2=82(x281(x1,2)≥0 g2(x2,l2)20 l2-g1(x1,1)=0 l1-82(x2,l2) u and u, are decision variables acting as the inputs to g1 SS1)and g2 (SS2 ). Introducing surrogate variables breaks information loop but increases the number of decision variables o Massachusetts Institute of Technology -Prof de Weck and Prof Willcox
Surrogate Variables (“Tearing”) Surrogate Variables (“Tearing”) Information loop can be broken by introducing surrogate variables. ( 1 min Jx x, 2 ) ( 1 min Jx x, 2 ) s.t. s.t. 1 = (, 2 ( 2 , w g x g x w1)) ≥ 0 g xu ( , ) ≥ 0 1 1 1 1 1 = ( , ( g xu ( , ) ≥ 0 1 w g x g x w, )) ≥ 0 2 2 2 1 2 2 2 2 u g x u ( , ) = 0 2 − 1 1 1 u g x u ( , 1 − 2 2 2 ) = 0 • u1 and u2 are decision variables acting as the inputs to g1(SS1) and g2 (SS2). Introducing surrogate variables breaks information loop but increases the number of decision variables. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox 11
M Numerical Example 6888 ESO.77 min],+2 +(x St.w,≥0 decoupled minxi+x2+(3 stw1=x-x2+2x3≥0 x+2x20 where,=x,+? J x-x2+2 +(x x32-x2+2x6-x5=0 W1=x-x2+212 =x3-x3+2m1 Solution coupled x=(0,0.4,3,12为,243 mix2+x2+(x2-3)2+(x4-4)2 MATLAB 5.3 s t. W,=g(r1,x2,x3,x4)20 coupled: 356, 423 FLOPS 4.844s uncoupled: 281, 379 FLOPS 0.453S 82(x1,x2x3,x)≥0 o Massachusetts Institute of Technology -Prof. de Weck and Prof WillcoX
Numerical Example Numerical Example 1 + 2 + min J J 2 2 decoupled min x x2 + ( x − 3)2 + ( x − 4)2 1 3 4 s.t. w1 ≥ 0 3 s.t. w x x 2 3 + 2 x = − 5 ≥ 0 1 1 w2 ≥ 0 3 = 2 + 2 w2 = x x4 + 2 x − 6 ≥ 0 3 where J x x 2 3 3 − 1 5 − J 2 1 = (x 1 − 3)2 + ( x − 4)2 x x 2 3 + 2x x6 = 0 3 4 3 = 3 − 3 2 x x 4 3 + 2x x 3 5 = 0 w x x2 + 2w − 6 − 1 1 3 − 3 w2 = x x 3 4 + 2 w1 Solution: coupled x = (0, 0, 4, 3,12 13 , 24 ) 2 3 2 + min x x 2 2 2 MATLAB 5.3 2 + ( x − 3) + ( x − 4) 1 3 4 s.t. w g x x x x = ( ) ≥ 0 coupled: 356,423 FLOPS 4.844s 1, 2 , 3 , 1 1 4 = ( 1, 2 , 3 , 4 ) ≥ 0 uncoupled: 281,379 FLOPS 0.453s w g x x x x 2 2 12 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Mlesd Distributed Design Methods 6888 ESO.77 Disciplinary models are provided with design tasks Optimization is performed at a subsystem level in addition to the system level Concurrent Subspace Optimization(CSsO) divide the design problem into several discipline related subspaces each subspace shares responsibility for satisfying constraints while trying to reduce a global objective Collaborative Optimization(CO) disciplinary teams satisfy local constraints while trying to match target values specified by a system coordinator preserves aIsciplinary-level design freedom o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox
Distributed Design Methods Distributed Design Methods • Disciplinary models are provided with design tasks • Optimization is performed at a subsystem level in addition to the system level Concurrent Subspace Optimization (CSSO) • divide the design problem into several disciplinerelated subspaces • each subspace shares responsibility for satisfying constraints while trying to reduce a global objective Collaborative Optimization (CO) • disciplinary teams satisfy local constraints while trying to match target values specified by a system coordinator • preserves disciplinary-level design freedom 13 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Mlesd Collaborative Optimization 6888 ESO.77 OPTIMIZER TARGET STATE Coupled Uncoupled o Massachusetts Institute of Technology -Prof de Weck and Prof Willcox
Collaborative Optimization Collaborative Optimization OPTIMIZER TARGET STATE Coupled Uncoupled 14 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox