Systems and InteractionsDefinitionsInteraction ExamplesSystem Consistency and OptimalitySystem Optimization MethodsAiOIDFATCSystems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsIntroduction to System Optimization:Part 1James AllisonME 555March 7, 2007James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsSystem OptimizationSubsystem optimization results ⇒ optimal system?Objective: provide tools for developing system optimizationstrategyJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsSystem OptimizationSubsystem optimization results ⇒ optimal system?Objective: provide tools for developing system optimizationstrategyJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsOverview1Systems and InteractionsDefinitionsInteraction Examples2System Consistency and Optimality3System Optimization MethodsAiOIDFATCJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesSystem DefinitionWhat makes something a system?Comprised of several components (or subsystems)Interactions exist between the componentsSome aspect of one component influences the effect ofchanges in another componentJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesSystem DefinitionWhat makes something a system?Comprised of several components (or subsystems)Interactions exist between the componentsSome aspect of one component influences the effect ofchanges in another componentJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesSystem DefinitionWhat makes something a system?Comprised of several components (or subsystems)Interactions exist between the componentsSome aspect of one component influences the effect ofchanges in another componentJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesSystem DefinitionWhat makes something a system?Comprised of several components (or subsystems)Interactions exist between the componentsSome aspect of one component influences the effect ofchanges in another componentJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesExplicit Analysis InteractionsAnalysis: evaluate f , g, and h in design problem for a given xyij: analysis output passed from subsystem j to i(coupling variable)Example: deflection and pressures in aeroelastic analysisJames Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesInteraction Example (First Type)System objective function:f (y12, y13) = c1(y12− c2)2+ c3(y13− c4)2+ c5y12y13Inputs to subsystem 1:y12: output (response) of subsystem 2y13: output (response) of subsystem 3Three objective function terms:1Depends only on SS2 response2Depends only on SS3 response3Depends on a combination of the responses (interaction)James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesInteraction Example (First Type)Case I: No Interaction c = (1, 1, 1, 1, 0)T0 1 2 3 4 5 60123456x1x2(x1-1)2+(x2-1)2James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesInteraction Example (First Type)Case II: Interaction Present c = (1, 1, 1, 1, −1)T0 1 2 3 4 5 60123456x1x2(x1-1)2+(x2-1)2-x1 x2optimumOFAT solution James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesInteraction Example (Second Type)Governing Equations of Motion:m100 m2¨z1¨z2+k1+ k2−k2−k2k2z1z2=00Coupled in stiffness: Motion ofm1(i.e. x1(t)) is dependent ofthe value of k2(∴ z1(t) dependson the state of z2), andvisa-versa.m1k1m2k2z1z2James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesInteraction RepresentationExample system:a1(x1, x2, x4)a2(x6, y21)a3(x2, x3, x4, y31, y34)a4(x4, x5, y41)James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesInteraction IdentificationExample: Interaction between automotive subsystemsstructurepowertrainsuspensionsteeringbrakingcabin (interior geometry, HVAC, etc.)James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesAnalysis InteractionsWhat might result if interactions are ignored in systemdesign?Missed opportunity to improve performance (not systemoptimal)Incompatibility between subsystems (inconsistent system)James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesAnalysis InteractionsWhat might result if interactions are ignored in systemdesign?Missed opportunity to improve performance (not systemoptimal)Incompatibility between subsystems (inconsistent system)James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsDefinitionsInteraction ExamplesAnalysis InteractionsWhat are some interactions between your subsystems?Specific effects of ignoring interactions?James Allison Introduction to System Optimization: Part 1Systems and InteractionsSystem Consistency and OptimalitySystem Optimization MethodsSystem ConsistencyA system has coupling variable consistency if for every