A Perspective on the Role of Engineering Decision-Based Design: Challenges and Opportunities

Transcription

1 A Perspective on the Role of Engineering Decision-Based Design: Challenges and Opportunities Zissimos P. Mourelatos Associate Professor Mechanical Engineering Department Oakland University Rochester, MI 1

2 Outline Some definitions / statements on decision analysis Normative decision analysis Decision making and optimization A multi-objective design example Preference aggregation Decision analysis cycle Uncertainty types DBD research topics DBD implementation hurdles 2

3 Workshop Theme Hurdles of Decision-Based Design approach in practice. Top research issues in DBD approach. 3

4 Some Definitions/Statements Decision is a present action to achieve a future outcome. A decision is an irrevocable allocation of resources, in the sense that it would take additional resources, perhaps prohibitive in amount, to change the allocation. * A Decision Maker is an authority with power to allocate an organization s resources. * Matheson, J.E. and Howard, R.A., An Introduction to Decision Analysis, Stanford Research Institute,

5 Some Definitions/Statements A Decision is made according to the preferences of the decision-maker ONLY. The preferences are applied to outcomes not to the alternatives. Since decisions are made at the present for a future outcome, there is inherent uncertainty in any decision. 5

6 Normative Decision Analysis is a logical process for ranking design alternatives based on : outcomes from each alternative with assigned probabilities value assessment decision maker s preferences 6

7 Normative Decision Analysis Outcome U(Out) Alternative A 1 M O 1 O 2 O 3 O k PDF Outcome Decision M A 2 A n Outcome Utility; D_M preference ( ) = U ( out) PDF ( out) d( out) E Utility out outcome 7

8 Utility Curve (von Neumann, Morgenstern) From: Cook, H.E., Product management, Chapman & Hall,

9 value assessment Decision Making and Optimization* Max x s.t. g x ( x) ( x) 0 The objective function f : f outcome x x min max is a scalar (multi-attribute problems??) feasibility design alternatives represents a design space to performance space translator; a model ( validated model??) represents decision maker s preferences *Hazelrigg, G.A., The Cheshire Cat on Engineering Design, draft to ASME J. of Mech. Design. 9

10 Normative Decision Analysis; Multi-Attribute Environment Alternative A 1 M O 1 O 2 O 3 O k 1 st Attribute Decision M O 1 O 2 O 3 O k 2 nd Attribute A 2 M A n Outcome 10

11 A Multi-Attribute Example; Wind-Noise vs Closing Effort Hinges: UHCC UHFA UHUD Seal: Latch: NOMGAP 1-8 STHICK FLBAR DELBAR LHCC 11

12 Pareto Frontier for Wind Noise vs Closing Effort Pf_Wind Noise Pf_Clos. Effort 12

13 Aggregation of Preference Functions h s s, w1h1 + w2h w1 w = + 2 [( h w ), ( h w )] 1, 1 s * individual preferences aggregate preference trade-off strategy Calculation of w and s is based on indifference points which describe the decision maker s preferences * Michael Scott, (Univ. of Illinois at Chicago), Erik Antonsson, (CalTech) 13

14 Desired Aggregation Properties Annihilation : h(, h ) = h( h,0) = h h, h = h 1 Idempotency : ( ) 1 1 Monotonicity : ( ) ( ' h, h h h h ) h if 1 2 1, 2 ' h2 h 2 Commutativity : h ( h, h ) = h( h h ) 1 2 2, Continuity : ( ) [ ( )] ' h h, h = h h h lim 1 2 1, ' h h

15 Example Preference Function for Target Compliance Rate R=0.99 Preference Function h Compliance Rate r 15

16 Prior Information Decision Analysis Cycle Deterministic Phase Probabilistic Phase Informational Phase Decision Act New Information Information Gathering Gather New Information From: Matheson, J.E. and Howard, R.A., An Introduction to Decision Analysis,

17 Decision Diagram in Product Development Design Attribute Set Market Performance Profit beliefs on decision uncertainty relationships value From: Matheson, J.E. and Howard, R.A., An Introduction to Decision Analysis,

18 Uncertainty Types Input Model (Transfer Function) Output Uncertainty Uncertainty Uncertainty 18

19 Uncertainty Types Aleatory Uncertainty (Irreducible, Stochastic) Probabilistic distributions Bayesian updating Epistemic Uncertainty (Reducible, Subjective, Ignorance, Lack of Information) Fuzzy Sets; Possibility methods (non-conflicting information) Evidence theory (conflicting information) 19

20 Uncertainty Types Evidence Theory Possibility Theory Probability Theory 20

21 Membership Function for a Fuzzy Variable µ X ( x ) 1.0 a 0.0 a x L x a R x α - cut provides confidence level At each confidence level, or α -cut, a set is defined as X a [ 0,1] { a a x : x x x, } = a L R convex normal set 21

22 Propagation of Uncertainty Using Fuzzy Sets (Cont.) Practical Approximations of Extension Principle Vertex method Discretization method 22

23 Simple Mathematical Example y 2 2 ( x x ) = x + x 4x 4 1, where x1, x 2 are fuzzy variables with ( x1 1) 2 1 x1 3 µ ( x ) = and ( x ) X 1 4 x x 1 4 µ X 2 x2 + 1 = 1 x2 1 x 0 2 x

24 Simple Mathematical Example Membership Function for X1 Membership Function for X2 24

25 µ Y ( y) Simple Mathematical Example Discretization Method α 10 - cuts 40 divisions per -cut α y = f ( x) 25

26 DBD: Research Topics Appropriate model(s)/transfer function(s) for specific decision. Concept of model validation Expression of decision maker s preferences (Utility, ) Multi-attribute environment (Preference aggregation) Ranking of alternatives; Value assessment (Expected Utility, ) Feasibility under uncertainty (RBDO, ) Quantification & propagation of uncertainty Probabilistic methods, non-probabilistic methods, combination of both Optimization under uncertainty 26

27 DBD Approach Hurdles Inadequate awareness of DBD Incorrect implementation of correct model for decision making preferences of decision maker identification of alternatives/outcomes value assessment treatment of uncertainty Paradigm shift from deterministic to non-deterministic thinking 27

28 Acknowledgments Robert V. Lust, General Motors Corporation John Cafeo, General Motors R&D Center Joe Donndelinger, General Motors R&D Center 28