Quantification and Management of Uncertainty in Model-Based Vehicle Design

Transcription

1 Quantification and Managmnt of Uncrtainty in ModlBasd Vhicl Dsign Zhn Jiang, Ph.D. Analytics Scintist, Product Dvlopmnt and Stratgy Analytics Ford Rsarch and Innovation Cntr, Palo Alto, CA Fbruary 23, 2016

2 Complxity of Vhicl Dsign Vhicl Prformanc V: Vhicl Lvl S: Systm Lvl C: Componnt Lvl Vhicl NVH Safty Body Structur (NVH & Durability) Chassis & Full Vhicl Durability Vhicl Dynamics TASE* & Climat Control Idl Tactil (V) Idl Acoustic (V) Drivlin Unbalanc Tactil (V) Drivlin Unbalanc Sound (V) Gln Eagl Tactil (V) Rough Road Tactil (V) Brak Roughnss Tactil Impact Harshnss Tactil R1H / CP2 Tactil (V) Gln Eagl Acoustic (V) Rough Road Acoustic (V) Impact Harshnss Acoustic (V) Brak Squal Exhaust NVH Wind Nois Shift Quality FRONT IMPACT (V) Nw FMVSS 208 NCAP OOP IIHS Offst SIDE IMPACT (V) 33.5 mph FMVSS214 LINCAP Rar Impact (V) 35 mph RMB 50 mph C/C Inlin 50 mph C/C Sid 50 mph C/C 50% Offst Roof Crash (S) Had Impact (S) Trimmd Body Principal Mods (V) Trimmd Body Static Stiffnss (V) BIP Principal Mods (S) PM at Body Attach. Loc.(S) LP6 for Body Attachmnts (S) Static Stiffnss for Body Attachmnt Locations (S) Body SDS/WCR/FMVSS (S/C) Hood (S) Dcklid (S) Doors (S) Trailr Tow (C) Dash/Cowl fatigu (C) Chassis NVH Fram Principal Mods Fram Static Stiffnss Static Stiff. at Fram Attach. PM at Fram Attachmnts Suspnsion Mods Chassis Durability Front Suspnsion Rar Suspnsion Fram and Mounting Systm Vhicl Dynamics (V) String Handling Rid Braking Chassis Systms (S) Gnral Vhicl Front Suspnsion Rar Suspnsion String Arodynamics CFD Analysis (V) Hat Managmnt (V) Coolant Flow Simulations (S) Vhicl Lvl Climat Control (V) Front End Air Flow Front End Opnings Systm Lvl Climat Control (S) A/C Prformanc Hatr Prformanc *TASE: Thrmal Arodynamics Systm Enginring

3 Simulation Procss Complxity ModlSystm Intgration Optimization Optimization Systm Dfin Virtual Tst Tst SubSystm Componnt Dsign Virtual Intgration Intgrat Modl Implmnt Tim

4 Sourcs of Uncrtainty SOURCES OF UNCERTAINTY THAT AFFECT MODEL PREDICTION Modl Bias Du to lack of knowldg, missing undrlying physics Paramtr Uncrtainty Du to naturally fixd but unknown modl paramtrs Intrpolation Uncrtainty Having to prdict th rspons whr no xisting data is availabl Exprimntal Variability Nois of th tst data DESIGN UNDER UNCERTAINTY To achiv a dsign that is insnsitiv to uncrtaintis Knndy & O Hagan, Baysian Calibration of Computr Modls, J. Roy. Stat. Soc. B, 63(3), 2001 Uncrtainty quantification provids critical information about how much w could b wrong in th modling procss

5 Procdur of Information Fusion Information Sourcs LowFidlity Modl Intrmdiat Fidlity Modl HighFidlity Modl / Physical Tsts Modl Rfinmnt LowFidlity Data Intrmdiat Fidlity Data Training Data HighFidlity Data Validation Data Construct a nw modl Additional Sampling Validat th modl No Satisfid? Ys Dsign

6 Typical Challnging Scnarios 1 2 Surrogat Modling (Mtamodling) Hav a sophisticatd and yt xpnsiv modl Rgrssion Analysis Hav tst data but no modl Build a surrogat modl to rplac th original modl Construct a modl basd on th tst data Rspons Surfac Modling (RSM) 3 Modl Bias Corrction Hav tst data and a not so accurat modl Updat th modl and corrct its bias 4 (Multi)Modl Fusion Hav tst data and svral diffrnt modls Intgrat th information from tsts and modls

7 Exampl: Vhicl Dsign of Frontal Impact Collaborators Ford Passiv Safty Dpartmnt Dsign Variabls HighFidlity FE Simulations LowFidlity RSM Training data 64 3 FE Simulations Validation data 15 3 Intrpolation FE Simulations 25 3 Extrapolation FE Simulations Z Y X 64 RSM Simulations Rsponss: Wight, Chst G & Crush Distanc Find X,, X, min E Wight, s.t. Pr Chst G T %,Pr Crush Distanc T % Jiang, Chn, Fu, Yang, RliabilityBasd Dsign Optimization with Modl Bias and Data Uncrtainty, SAE Int. J. Matr. Manf., 6(3), 2013

8 Gaussian Procss Modling for Modl Bias Corrction Formulation Physical Tst Bias Function m y ( x) y ( x) ( x) CAE Modl Tst Variation Basic Ida Trat both th original modl and th bias function as GPs Th tst rspons would also b a GP (by dfinition) Us MLE to stimat th paramtrs of th GPs.

9 Situations with Multipl Modls Highfidlity physicsbasd CAE modl Intrmdiatfidlity physicsbasd CAE modl Highfidlity physical tst Lowfidlity simplifid handbook quations Intrmdiatfidlity surrogat modl Chn, Jiang, Yang, Aply, Chn, Nonhirarchical Multimodl Fusion Using Spatial Random Procsss, Int. J. Numr. Mthods Eng., 2015

10 Multidisciplinary Dsign Collaboration Powrtrain. Safty Durability NVH Systm SubSystm Componnt Multidisciplinary Dsign Optimization (MDO) Collaboration Across Systms

11 A Multidisciplinary Systm Systm Quantitis of Intrst (QOIs): y sys Systm Analysis y 1 Disciplinary outputs y 2 Disciplin 1 Disciplin 2 u 12 u 21 x s x 1 x 2

12 Rsourc Allocation in MDO OBJECTIVE To improv th global modling capability of a multidisciplinary systm Such that th prdiction uncrtainty of systm QOIs is accptabl ovr th input spac. Rsourcs: Exprimnts and/or simulations SEQUENTIAL DECISION MAKING Whr in th input spac of a multidisciplinary systm shall w allocat mor rsourcs? To what disciplinary rspons(s) shall w allocat mor rsourcs? Which typ of rsourc shall w allocat, xprimnts or simulations? Simulation modls in th systm Rspons 1 Rspons 2 Rspons 3 Input spac Jiang t al., DETC , DAC Top 10 Bst Papr x 2 x 1 x 1, x 2 : Disciplinary inputs and/or shard inputs

13 Multidisciplinary Uncrtainty Analysis Systm Analysis y i u i Disciplin i u i DISCIPLINARY UNCERTAINTY QUANTIFICATION u ( x, x, u ) uˆ ( x, x, u ) Z ( x, x, u ) i i s i i i s i ui i s i y ( x, x, u ) yˆ ( x, x, u ) Z ( x, x, u ) i i s i i i s i yi i s i 1STORDER TAYLOR SERIES APPROXIMATION u ( x, x, u ) uˆ ( x, x, μ ) i i s i i i s ui uˆ u μ Z ( x, x, u ) ND i j1, ji u j j uj ui i s i x i A MATRIX FORM x s Au ( μ ) Z, y μ BA Z Z 1 u u y u y Analytical; can b drivd from th structur of GP μ uˆ ( x, x, μ ), Σ ui i i s ui u y ( x, x, u ) yˆ ( x, x, μ ) i i s i i i s ui 1 1 T ( A ) ΣZu ( A ). yˆ u μ Z ( x, x, u ) ND i j1, ji u j Jiang t al., DETC Jiang t al., ASME J. Mch. Ds., 2015 j uj yi i s i μ yˆ ( x, x, μ ), yi i i s ui 1 1 B Σ BA Σ A Σ y Zu Zy T.

14 Multidisciplinary Statistical Snsitivity Analysis QOI uncrtainty Y Z 1 Z 1 Z 2 intraction Z 2 VARIANCEBASED SENSITIVITY INDICES MSI Z l TSI Z 1 l Var Z Var l Z Z ~ l Var( y) yz y l ~ l Zl ~ Var( y) Z l RELATIVEENTROPYBASED SENSITIVITY INDICES f y Z Y Z ~ l Z E f y y fy y l Z ~ l Z Y Z~ l ~ l ~ l MSI log d TSI log f y Z YZl l d Zl EZ f y Z l YZl l y fy y Jiang t al., AIAA Jiang t al., AIAA J., 2015 (accptd)

15 Which (simulations vs. xprimnts): A Prpostrior Analysis AFTER SELECTING LOCATIONS AND RESPONSES Dcision mad in prvious stps: To allocat rsourcs to slctd N L locations for rspons L, and N L locations for rspons L, tc. Suggst an affordabl rsourc allocation plan.g., conducting xprimnts at N L locations and simulations at N L N L locations for rspons L; similarly for L, tc. Mont Carlo loop Gnrat hypothtical data Updat th mulators Evaluat th rducd uncrtainty of y sys Evaluat th xpctd rducd uncrtainty of y sys No Is th rducd uncrtainty of y sys accptabl? Ys Us this plan Suggst anothr rsourc allocation plan

16 Conclusions Procss Six Sigma Quality Dsign Dsign undr Uncrtainty Dsign Prformanc Uncrtainty Dsign Procss Dynamic Dsign Procss Uncrtainty Quantification Multidisciplinary Dsign Uncrtainty Propagation

17 Thank You! Zhn Jiang, Ph.D. Analytics Scintist Product Dvlopmnt and Stratgy Analytics Ford RIC, Palo Alto, CA 94304