Value-Driven Design An Initiative to Move Systems Design from Requirements to Optimization

1. Value-Driven DesignAn Initiative to Move Systems Design from Requirements to Optimization 1 February 2007

2. Outline • Value-Driven Design (VDD) • Who? • What? • Why? • How? • What’s up?

3. Who? The World’s Forum for Aerospace Leadership

4. Gradient What? VDD Vision: Pervasive use of Optimizationin Engineering Design Engine Inlet Status Value Efficiency 90% 150,000 135,000 Weight 700 -130 -91,000 Reliability 1500 2.3 3,450 Maintainability -340 -2,652 7.8 Maintenance Cost 500 -0.5 -250 Support Equipment 12 -15 -180 -1200 Radar Cross-Section 0.1 -120 InfraRed Signature 1.4 -50 -70 Manufacturing Cost 700 -1 -700 Design Value $ 43,478 Technical detail on distributed optimization can be found at http://www.dfmconsulting.com/opt.pdf

5. Value-Driven Design = Optimization Value Improve Evaluate Optimizer Objective Function Design Optimization Attributes(Weight, Eff., Cost) Design Variables(Length, Displacement) Definition Analysis CAD System Physical Models Configuration

6. Staus Quo: Requirements Flowdown If each module meets its requirements, the overall system will meet its requirements Requirements Method promises Functionality Aircraft Systems Wing Design Cockpit Design Propulsion Systems Landing Gear Systems Avionics Systems Turbine Design Propulsion Control System Turbine Blade Heads-Up Servovalve Temperature FADEC Radar Design Design Design Design Sensor Design Display Design

7. VDD Vision: Distributed Optimal Design If you design the best components, you will realize the best system If each component is optimized, the overall system will be optimized Aircraft Systems Wing Design Cockpit Design Propulsion Systems Landing Gear Systems Avionics Systems Turbine Design Propulsion Control System Turbine Blade Heads-Up Servovalve Temperature FADEC Radar Design Design Design Design Sensor Design Display Design

8. Why? Three Reasons for VDD 1 - Optimization finds a better design 2 - Preference conflicts lead to clear loss of value 3 - Requirements cause performance erosion on cost growth

9. 1 - Optimization Finds a Better Design Requirements Increasing Score < $30 M unit mfg cost Limit of Feasibility Cost Cost < 30,000 lbs. weight Best (0,0) (0,0) Weight Weight Traditional Spec Method Optimal Design

10. 2 - Preference Conflicts Lead to Loss of Value Brake Material+ $11,000- 90 lbs. Rudder- $10,000+ 190 lbs. Net Impact + $ 1,000 + 100 lbs. Differences in revealed values within a design team lead to choices that, taken together, are clearly lose-lose

11. Conflicts: Folding in Attribute Space Design Potential Value A Requirements Method Distributed Optimal Design Value B

12. 3 - Requirements Cause Performance Erosion Requirements Allocation Preliminary Design Detailed Design Requirement Requirement Expectation Avoid Risk Prefer Risk Rudder Weight Rudder Weight Rudder Weight Targets cause performance erosion and cost growth

13. Requirements Lost Value initial performance limited by risk management Typical Cost Growth and Performance Erosion design testing production -5% net value +44% Cost Performance Time Mean cost growth estimated at 43% by Augustine based on 1970’s and 1980’s DoD projects; estimated at 45% by CBO in 2004 based on NASA projects

14. Lost Value on Large Air Platform Programs Lower Bound Lost Value (2006 $ billions) Constant Value Diminishing Returns (minimum) F-22 160 30 JSF 30 60 All estimates assume current performance = original promise F-22 JSF 1992 today 1985 today # aircraft 3,000 2,400 # aircraft 750 178 Unit cost $ 44 60 2006 $ million Unit cost $ 95 200 2006 $ million delay 2 years delay 10 years

15. How? Distributed Optimal Design • Extensive Variables • Design Attribute Spaces • Composition Function • Objective Function • Linearization and Decomposition

16. Extensive Variables Performance, Cost, and -ilities Composition Function

17.  z r z r r x z Design Attribute Spaces Unit Profit • Coordinate Axes are Design Attributes • Different Space for • Whole Product: x1, x2, ... xm • Each Component: yk1, yk2, ... ykn (describes component k) • Super attribute space composed of all attributes of all components: = [y11, y12, ... y21, ... ypn] • describes whole product; describes all components Reliability Horsepower Intake Manifold Weight 6.0 Cost 12.0 Life 20000.0 Intake Valve Weight 0.1 Cost 2.0 Efficiency 0.9 Cylinder Head Weight 0.5 Cost 42.0 Efficiency 0.9 Life 10000.0

18. For distributed optimization, h is the composition function Extensive attributes in affect collectively no other attributes matter for global optimization Example elements:   Weightchassis component system + Weightengine = Weighttractor + Weighttransmission . . . The Composition Function r r ( ) = x h z r r x z model 1 1   MTBF MTBF tractor component

19. Objective Function (Value Model) r ( ) p The objective function is for the whole system x ( ) r r r r ( ) * An optimum point is where for all p ³ p * x x x x We want local objective functions, vj for components j = 1 to n such that when ( ) ( ) r r r r r r ( ) ( ) * * ³ " " Þ p ³ p " v y v y y j x x x j j That is, when the components are optimized, the product is optimized

20.       h z Objective Function with Local Attributes r r r ( ) ( ) p = • Since value = and , then value , a function of local attributes • This gives us global value in terms of local attributes, but does not give an independent objective function for each component • For independence, we must linearize • Thus each component has its own goal x x h z ( ) r ( ) = p h z

21.  Given smoothness of and h, the linear approximation is reasonable for small changes (< 10% of whole system value) near the preliminary design Validity of Linearization

22.       h z Linearizing the Objective Function • Start with a reference design (preliminary design) with attributes x* and z* • Generate the Taylor expansion of around z* : • O2 represents second order and higher terms that we can ignore in the vicinity of z* • Without O2, the Taylor series is linear                 *   * 2    h z  h z    x  J  z  z  O   h * * z x 

23. Solving the Taylor Expansion         , , , ,     x  x  x  x   • is the gradient of • Jh is the Jacobian Matrix of h: 1 2 3 4  x  x  x  x   1 1 1 1     z  z  z  z   1 2 3 p   x  x  x  x  2 2 2 2     z  z  z  z  1 2 3 p   x  x  x  x   3 3 3 3     z  z  z  z 1 2 3 1 p           x  x  x  x   m m m m     z  z  z  z   1 2 3 p

24. Solving the Taylor Expansion p m        x          * i *      h z   h z    z  z j j    x  z   i j j  1 i  1 Objective functions are used for ranking—they are not changed by the addition or subtraction of a constant. Thus, the expression above can be simplified by dropping all terms that use the constant z*: p m    x         i    h z   z j    x  z   i j j  1 i  1  Linear objective functions have the property that can be maximized by maximizing each zj term or any group of zj terms independently

25. Component Optimization For a group of zj’s that correspond to a single component, we can relable them y1 though yn and determine the component objective function (in the vicinity of the preliminary design): n m    x    i      y component k    x  y    i k * k  1 i  1 x

26. “But you can’t DO that!” Value Evaluate Search $ Optimizer Objective Function Properties (Weight, Eff., Cost) Parameters (Length, Displ.) Definition Analysis Design Drawing Physical Models Configuration Value landscape in parameter space Value landscape in property space

27. Gradient Implementing Distributed Optimal Design Partial Derivatives of the Objective Function Engine Inlet Status Value Efficiency 90% 150,000 135,000 Component Design Value is Commensurate with System Design Value Weight 700 -130 -91,000 Reliability 1500 2.3 3,450 Maintainability -340 -2,652 7.8 Maintenance Cost 500 -0.5 -250 Support Equipment 12 -15 -180 -1200 Radar Cross-Section 0.1 -120 InfraRed Signature 1.4 -50 -70 Manufacturing Cost 700 -1 -700 Design Value $ 43,478

28. What’s up? Near Term VDD Activity • Building a Research Community • Workshop at MIT 26 Apr 2007 • VDD advocacy at Lockheed Martin and Boeing • VDD advocacy at NASA, OSD, and NSF • Connected with AFIT, Georgia Tech, Illinois, MIT, Purdue, Stanford • Dissemination • One session at ATIO 2006, two sessions at ATIO 2007 • Professional short course • Publish book (collection of papers) • Department of Defense VDD Guidebook • The Systems Engineering office in the Office of the Secretary of Defense has requested prototype work, perhaps led by universities

29. Value-Driven Design - Conclusion By relying on optimization and abandoning quantitative requirements, we will design large systems with tens of $billions greater value