Mes Distributed Analysis 16888 ESO.77 Optimizer objective design variables constraints X//9( g(x X h(x) h(x) aerodynamic performance structural analysis analysis analysis During the optimization the overseeing code keeps track of the values of the design variables and objective The values of the design variables are changed according to the optimization algorithm Disciplinary models are asked to evaluate constraints/objective o Massachusetts Institute of Technology -Prof de Weck and Prof Willcox
Distributed Analysis Distributed Analysis Optimizer objective design variables constraints x J(x) performance analysis aerodynamic analysis structural analysis x g(x) h(x) x g(x) h(x) • During the optimization, the overseeing code keeps track of the values of the design variables and objective • The values of the design variables are changed according to the optimization algorithm • Disciplinary models are asked to evaluate constraints/objective © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox 6
Mes Distributed Design 6888 ES077 System level optimizer command/result command/result command/result SS1 SS2 SSN optimizer optimize optimizer SS1 SS2 SSN analyzer analyzer analyzer Subsystem black boX (BB C Massachusetts Institute of Technology -Prof. de Weck and Prof WillcoX
Distributed Design Distributed Design System level optimizer SS1 optimizer SS2 optimizer SSN optimizer SS1 analyzer SS2 analyzer SSN analyzer …… command/result command/result command/result Subsystem black box (BB) 7 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Mes Advantages of Decoupling 6888 ES077 Computation of g(x)can be very time consuming, want to divide the work and compute in parallel For example, if x=(x,-x), where, xER and g(x)=(g(),g,(x Then g, and g2 can be computed in parallel. Graphically, Optimizer Optim g SS1 SS1 SS2 SS1 o Massachusetts Institute of Technology -Prof de Weck and Prof Willcox
Advantages of Decoupling Advantages of Decoupling Computation of g(x) can be very time consuming, want to divide the work and compute in parallel. n 2 For example, if x = ( , x x 2 ), where x ∈ ! n1 1 1 , x2 ∈ ! and g( x) = (g x g x ( ), ( )) 1 1 2 2 Then g1 and g2 can be computed in parallel. Graphically, Optimizer SS1 SS2 1 x 1 g 2 g x 2 g g 2 SS1 SS1 Optim 1 x 2 x 1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox 8
M Coupled Situation 16888 ESO.77 The decoupled constraints assumption is not general Subsystems can be coupled and loops can arise. For example Optimizer Optim x11 w SSI SS2 p 001 X. decision variables vline: SS input w: SS outputs(constraint, cost u:SS input( dependent) hline: SS output Computation of w, and w, requires an iterative method o Massachusetts Institute of Technology -Prof de Weck and Prof Willcox
Coupled Situation Coupled Situation The decoupled constraints assumption is not general. Subsystems can be coupled and loops can arise. For example, Optimizer SS1 SS2 1 x 2 x u 1 u 2 w 1 w2 SS1 SS2 Optim w 1 w 2 u 1 1 x u 2 2 x w 1 w 2 Loop x: decision variables vline: SS input w: SS outputs (constraint, cost) hline: SS output u: SS input (dependent) Computation of w1 and w2 requires an iterative method. 9 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Mlesd Information Flow Loop(2) 16888 ESO.77 An example where such a loop happens is as follows minD(x,x2) W=81(x,g2(x2,w1)20 6y2=8M1(x,m12)≥0 where x∈R,x2∈R,g1:x×;b,i=1,2 W,and w2 satisfy coupled relations at each optimization iteration At each constraint evaluation, nonlinear equations must be solved (e.g. by Newtons method)in order to obtain w and w2, which can be time consuming Want a way to return to the situation of decoupled constraints o Massachusetts Institute of Technology -Prof de Weck and Prof Willcox
Information Flow Loop (2) Information Flow Loop (2) • An example where such a loop happens is as follows: ( 1 min Jx x, 2 ) s.t. 1 = (, 2 ( 2 , w g x g x w1)) ≥ 0 1 1 ( , ( 1 w , 2 = g x g x w )) ≥ 0 2 2 1 2 n 2 × i where x , 1 ∈ ! n1 , x ∈ ! , g : x i " w i = 1, 2 2 i i • w 1 and w 2 satisfy coupled relations at each optimization iteration. At each constraint evaluation, nonlinear equations must be solved (e.g. by Newton’s method) in order to obtain w 1 and w 2, which can be time consuming. Want a way to return to the situation of decoupled constraints. © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox 10