麻省理工学院：《Multidisciplinary System》Lecture 3: Modeling and Simulation

Mles 16888 ES077 Multidisciplinary System Design Optimization MSDO) Lecture 3: Modeling and Simulation 11 February 2004 Olivier de weck Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ 2OLYLHUGH:HFN 0XOWLGLVFLSOLQDU\6\VWHP 0XOWLGLVFLSOLQDU\6\VWHP 'HVLJQ2SWLPL]DWLRQ06'2 'HVLJQ2SWLPL]DWLRQ06'2 /HFWXUH /HFWXUH 0RGHOLQJDQG6LPXODWLRQ 0RGHOLQJDQG6LPXODWLRQ )HEUXDU\ )HEUXDU\

Today 's Topics 16888 ES077 Definitions of Modeling and simulation physics-based modeling empirical modeling Model/simulation Development process module identification module ordering DSM's and n2 diagrams module coding: fidelity and benchmarking model execution simulation Computational Issues runtime reduction strategies coupling disparate CAE/CAD tools Massachusetts Institute of Technology - Prof de Weck and Prof Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ 7RGD\¶V7RSLFV 7RGD\¶V7RSLFV &RPSXWDWLRQDO,VVXHV UXQWLPHUHGXFWLRQVWUDWHJLHV FRXSOLQJGLVSDUDWH&$(&$'WRROV 'HILQLWLRQVRI0RGHOLQJDQG6LPXODWLRQ SK\VLFVEDVHGPRGHOLQJ HPSLULFDOPRGHOLQJ 0RGHO6LPXODWLRQ'HYHORSPHQW3URFHVV PRGXOHLGHQWLILFDWLRQ PRGXOHRUGHULQJ'60¶VDQG1GLDJUDPV PRGXOHFRGLQJILGHOLW\DQGEHQFKPDUNLQJ PRGHOH[HFXWLRQ VLPXODWLRQ

MSDO Framework 16888 ES077 Design Vecto Simulation model Objective vector x Module a Module b Module c Coupling this Multiobjective Optimization lecture Approximation Optimization Algorithms Methods Numerical Techniques Sensitivity Tradespace (direct and penalty methods) Analysis Exploration Heui」 tic Techniques Coupling (DOE) SA, GA) sopertormance Output Evaluatie Massachusetts Institute of Technology- Prof de Weck and Prof Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ 6LPXODWLRQ0RGHO WKLV OHFWXUH 06'2)UDPHZRUN 06'2)UDPHZRUN 0RGXOH$ 0RGXOH% 0RGXOH& , Q S X W 2 X W S X W 7UDGHVSDFH ([SORUDWLRQ '2( 2SWLPL]DWLRQ$OJRULWKPV 0XOWLREMHFWLYH 2SWLPL]DWLRQ 1XPHULFDO7HFKQLTXHV GLUHFWDQGSHQDOW\PHWKRGV +HXULVWLF7HFKQLTXHV 6$*$   Q [ [ [ ª º « » « » « » « » « » ¬ ¼ # 'HVLJQ9HFWRU &RXSOLQJ   P - - - ª º « » « » « » « » « » ¬ ¼ # $SSUR[LPDWLRQ 0HWKRGV &RXSOLQJ 6HQVLWLYLW\ $QDO\VLV ,VRSHUIRUPDQFH 2EMHFWLYH9HFWRU 2XWSXW(YDOXDWLRQ

Definitions 16888 ES077 Definition: Model (as used in this class A model is a mathematical object that has the ability to predict the behavior of a real system under a set of defined operating conditions and simplifying assumptions Definition Simulation (as used in this class) Simulation is the process of exercising a model for a particular instantiation of the system and specific set of inputs in order to predict the system response Massachusetts Institute of Technology - Prof de Weck and Prof Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ 'HILQLWLRQV 'HILQLWLRQV 'HILQLWLRQ0RGHO 0RGHODVXVHGLQWKLVFODVV DVXVHGLQWKLVFODVV $PRGHOLVDPDWKHPDWLFDOREMHFWWKDWKDVWKHDELOLW\ WRSUHGLFWWKHEHKDYLRURIDUHDOV\VWHPXQGHUDVHWRI GHILQHGRSHUDWLQJFRQGLWLRQVDQGVLPSOLI\LQJDVVXPSWLRQV 'HILQLWLRQ6LPXODWLRQ 6LPXODWLRQDVXVHGLQWKLVFODVV DVXVHGLQWKLVFODVV 6LPXODWLRQLVWKHSURFHVVRIH[HUFLVLQJDPRGHOIRUD SDUWLFXODULQVWDQWLDWLRQRIWKHV\VWHPDQGVSHFLILFVHW RILQSXWVLQRUGHUWRSUHGLFWWKHV\VWHPUHVSRQVH

Mled Model Development Process 16888 ES077 Start Proces Define Master table DSM N2 Diagram Objectives Define Constraints Governing Equations Modules Design Variables Iterate to Improve Fidelity Code modules Integrate Benchmark Modules Sanity Check iTest Code Ready For U Massachusetts Institute of Technology - Prof de Weck and Prof Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ 0RGHO'HYHORSPHQW3URFHVV 0RGHO'HYHORSPHQW3URFHVV 2EMHFWLYHV &RQVWUDLQWV 'HVLJQ9DULDEOHV *RYHUQLQJ (TXDWLRQV ,QWHJUDWH 0RGXOHV 'HILQH 0DVWHU7DEOH &RGH0RGXOHV 'HILQH 0RGXOHV 7HVW&RGH %HQFKPDUN 6DQLW\&KHFN ,WHUDWHWR,PSURYH)LGHOLW\ '60 1'LDJUDP 6WDUW3URFHVV 5HDG\)RU8VH

Objectives, Constraints, Design 16888 ES077 Variables Define objectives J Define Design variables x Define Constraints and Bounds g, h Determine important fixed parameters p Influence matrix influence o no 9 influence model relationships Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ 2EMHFWLYHV&RQVWUDLQWV'HVLJQ 2EMHFWLYHV&RQVWUDLQWV'HVLJQ 9DULDEOHV 9DULDEOHV ‡ 'HILQH2EMHFWLYHV- ‡ 'HILQH'HVLJQ9DULDEOHV[ ‡ 'HILQH&RQVWUDLQWVDQG%RXQGVJK ‡ 'HWHUPLQHLPSRUWDQWIL[HGSDUDPHWHUVS ,QIOXHQFH0DWUL[ JM  R  -L   R [ « [Q LQIOXHQFH RQR LQIOXHQFH PRGHOUHODWLRQVKLSV

Mlesd Physics Based Modeling 50. 9 Start with governing equations Continuum Mechanics for physical systems Introduce Boundary conditions Introduce Initial conditions EXternal forcing functions Discretize system Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ 3K\VLFV%DVHG0RGHOLQJ 3K\VLFV%DVHG0RGHOLQJ ‡ 6WDUWZLWKJRYHUQLQJHTXDWLRQV ‡ &RQWLQXXP0HFKDQLFVIRUSK\VLFDOV\VWHPV ‡ ,QWURGXFH%RXQGDU\&RQGLWLRQV ‡ ,QWURGXFH,QLWLDO&RQGLWLRQV ‡ ([WHUQDOIRUFLQJIXQFWLRQV ‡ 'LVFUHWL]HV\VWHP

Mles Governing equations 16888 ES077 Continuum (Structural) Mechanics o, T MIstress s=It o. t tensor F2 F strain -equilibrium Equations 2F =0 -Constitutive equations o, Ee d x-dx compatibility equations e, dr Massachusetts Institute of Technology - Prof de Weck and Prof Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ *RYHUQLQJ(TXDWLRQV *RYHUQLQJ(TXDWLRQV &RQWLQXXP6WUXFWXUDO0HFKDQLFV [ [\ [] \[ \ \] ][ ]\ \ 6 στ τ τ στ ττσ ª º « » = « » « » ¬ ¼ VWUHVV WHQVRU (TXLOLEULXP(TXDWLRQV &RQVWLWXWLYHHTXDWLRQV &RPSDWLELOLW\HTXDWLRQV [ X [ ε ∂ = ∂ VWUDLQ ) ) )  Σ = )L σ ε [ [ = ( [ G[ G[ G[ ε − =

Mlesd Example: Finite Element Model E5. Mx+cxtkx=F Geometry Mass and Connectivity Inertia Matrix Material Properties Deflections Boundary Stress. Strain Conditions Natural Loads Frequencies Mode shapes Assumptions Discretization Time as variable Static Steady state Transient Massachusetts Institute of Technology- Prof de Weck and Prof Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ ([DPSOH)LQLWH(OHPHQW0RGHO ([DPSOH)LQLWH(OHPHQW0RGHO *HRPHWU\ 0DWHULDO 3URSHUWLHV %RXQGDU\ &RQGLWLRQV $VVXPSWLRQV 'LVFUHWL]DWLRQ /RDGV 0DVVDQG ,QHUWLD0DWUL[ 'HIOHFWLRQV 6WUHVV6WUDLQ 1DWXUDO )UHTXHQFLHV 0RGH6KDSHV 0&.   [ [ [) ++ =    &RQQHFWLYLW\ 7LPHDV9DULDEOH 6WDWLF 6WHDG\6WDWH 7UDQVLHQW

Mles Empirical Modeling 16888 ES077 Derive a model, not from physics and first principles, but from observation, i.e. data Usually leads to low order models Only valid under similar operating conditions Many cost models are of this nature Massachusetts Institute of Technology - Prof de Weck and Prof Willcox

 0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3URIGH:HFNDQG3URI:LOOFR[ (PSLULFDO0RGHOLQJ (PSLULFDO0RGHOLQJ ‡ 'HULYHDPRGHOQRWIURPSK\VLFVDQGILUVW SULQFLSOHVEXWIURPREVHUYDWLRQLHGDWD ‡ 8VXDOO\OHDGVWRORZRUGHUPRGHOV ‡ 2QO\YDOLGXQGHUVLPLODURSHUDWLQJFRQGLWLRQV ‡ 0DQ\FRVWPRGHOVDUHRIWKLVQDWXUH