Research Overview. Chris Paredis

Transcription

1 Research Overview Chris Paredis Systems t Realization Laboratoryb t Product and Systems Lifecycle Management Center G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology

2 Presentation Overview Research Scope, Context, and Foundation Model-Based Systems Engineering 1. Reusable Analysis Models Defined in SysML 2. Predictive Trade-off Models 3. Variable Fidelity Analysis 4. Capturing Synthesis Knowledge as Graph Transformations 5. Risk Management in Systems Engineering Summary 2

3 Research Area Research Scope and Context Modeling and Simulation in Design Application Focus: Systems engineering Fluid power systems Mechatronic systems Research Focus Decision theory Modeling and Simulation Information technology 3

4 Product Development: A Decision-Based Perspective Decisions Portfolio Planning Concept Production Sales & Maintenance Design Development & Testing Distribution & Support Modeling and Simulation Provides Information in Support of Decisions Generic Decision Process Generate Alternatives Evaluate Alternatives Select Alternative Information Knowledge 4

5 A Generic Design Decision Decision A 1 A 2 A n O 11 UO 11 O 12 O 1k O 21 O 22 O 2k O n1 O n n2 2 O nk ( ) UO ( 12) UO ( 1 k ) UO ( 21) UO ( 22) UO ( 2 k ) UO ( n 1) UO ( n 2 ) ( ) UO nk Alternatives Outcomes Preferences (Attributes) Select A i where E [ U ] is maximum 5

6 Why are Design Decisions Difficult? Uncertainty Uncertainty Decision A 1 Infinite number A of 2 alternatives A n O 11 UO 11 O 12 O 1k O 21 O 22 O 2k O n1 O n n2 2 O nk ( ) UO ( 12) UO ( 1 k ) UO ( 21) UO ( 22) UO ( 2 k ) UO ( n 1) UO ( n 2 ) ( ) UO nk Select A i where E [ U ] is maximum Alternatives Outcomes Preferences (Attributes) Limited Resources

7 Integration of Design Product & Design Process Goal: maximize overall utility Must consider process in utility assessment Value trade-offs between product and process Decrease expected utility of product to reduce expected cost of process "Optimal" solution is guaranteed not to be optimal from a pure product perspective Information Economics Meta-level decision: How to frame your design problem? Value Cost 7

8 Systems Approach to Product Development The systems approach provides a balanced trade-off between product and process objectives Systematic decomposition Large, flexible, yet manageable design space Decoupling Limit the risk due to unexpected interactions Enable collaborative engineering Helps us deal with complexity 8

9 Model-based Systems Engineering (MBSE) MBSE: Model formally all aspects of a systems engineering problem Requirements & Objectives System Alternatives System Behavior Models Executable Simulations Design Optimization Model Libraries Effective and Efficient Analysis of Alternatives Model from different perspectives Model at different levels of abstraction Model reuse & modularity Optimization with grid-computing Effective Generation of Alternatives Graph transformations for generating plausible system architectures Automated generation of system models 9

10 Given: Find: MBSE: Example Problem Primary components Decision objectives / preferences Best system topology Best component parameters Excavator How to size and connect these? engine pump_vdisp accum Very large search and optimization problem Many competing objectives Many topologies Many component types/sizes Many control strategies cylinder v_3way 10 10

11 Research Questions Which decisions should be made at each point in the product development process? How should decisions be ordered in a decision sequence? How should the decisions be framed? Which decision alternatives should one consider? Which information should be used in support of these decisions? How accurate should the information be? How do we trade off accuracy versus cost? Which tools allow us to obtain this information most cost effectively? Which Information Technologies can be used to reduce the cost of information? Is it cost effective to use repositories i of reusable models? 11

12 Presentation Overview Research Scope, Context, and Foundation Model-Based Systems Engineering 1. Reusable Analysis Models Defined in SysML 2. Predictive Trade-off Models 3. Variable Fidelity Analysis 4. Capturing Synthesis Knowledge as Graph Transformations 5. Risk Management in Systems Engineering Summary 12

13 Reusable Analysis Models Systems t Realization Laboratoryb t Formal Representation of Engineering Analysis Models in SysML Student: Jonathan Jobe

14 Multi-Aspect Component Models Components are the reusable elements of design MAsCoMs: Group all models related to single fluid power component Multiple disciplines and levels of abstraction Modular Formal & unambiguous Systems Modeling Language (OMG SysML TM ) Formally model systems design information, from requirements through testing 14

15 How to use MAsCoMs? Log Splitter Design Example ISO 1219 Fluid Power Graphics Design Concept Schematics -Hydraulic System 15

16 Log Splitter Model Composition Power Subsystem 16

17 Automatic Translation from SysML to Modelica Formal Graph Transformations Modelica SysML 17

18 Presentation Overview Research Scope, Context, and Foundation Model-Based Systems Engineering 1. Reusable Analysis Models Defined in SysML 2. Predictive Trade-off Models 3. Variable Fidelity Analysis 4. Capturing Synthesis Knowledge as Graph Transformations 5. Risk Management in Systems Engineering Summary 18

19 Predictive Trade-off Models Systems t Realization Laboratoryb t Reusable Models for Predicting the Performance of Design Concepts Student: Rich Malak

20 Decision Chains: From Concept to Detail Design Decision Alternative 1 Alternative 2 Alternative ti 3. Alternative n Decision 1 Concept 2.1 Decision i Concept 3.1 Decision Concept 3.2 Concept 2.2 Decision Decision 3.2 Concept 3.3 Decision Concept 3.4 Decision 3.4 Alternative 1 Alternative 2 Alternative 3 Alternative 4 Alternative Alternative Alternative n-1 Alternative n One-Shot Decision A Chain of Decisions 20

21 Decision Chains: From Concept to Detail Design Decision Alternative 1 Alternative 2 Alternative ti 3. Alternative n Decision 1 Concept 2.1 Decision i 2.1 Concept 3.1 Decision Concept 3.2 Concept 2.2 Decision Decision 3.2 Concept 3.3 Decision Concept 3.4 Decision 3.4 Alternative 1 Alternative 2 Alternative 3 Alternative 4 Alternative Alternative Alternative n-1 Alternative n One-Shot Decision A Chain of Decisions Each Concept = Set of Design Alternatives 21

22 Modeling Set-Based Design Concepts What is the appropriate gear ratio for the differential? it depends On the other drivetrain components On manufacturing and cost considerations On the details of differential itself How do we best model a subsystem concept to support decision making at the systems level? 22

23 Functional and Preference Attributes What is important about the differential? Gear ratio Maximum torque Functional Attributes Maximum speed Size, mass Cost Preference Attributes What is NOT important t about the differential? Working principle Detailed dimensions Only important to the extent that they Manufacturing processes influence the preference attributes Model Preference Attributes as Function of Key Functional Attributes 23

24 Predictive Tradeoff Model: Hydraulic Cylinder Key functional attributes Bore diameter Stroke length Predicted preference attributes Mass Cost Raw Cylinder Data mass Predictive Cylinder Model mass bore stroke cost bore stroke cost

25 Taking Designer Preferences into Account Not all feasible designs are preferred: Pareto optimality Cost ($) Valid Designs: Planetary Gear Train Feasible Designs: Planetary Gear Train Feasible, but dominated. No engineer will choose these Non-dominated set (efficient frontier). Every point is optimal under some tradeoff Reliability Care only about non-dominated set 25

26 Parameterized Efficient Sets Cost ($) Reliability Torque Gear Ratio Ratio No problem-independent preference for gear ratio. Solution: find efficient set as function of gear ratio. 26

27 Combining Multiple Concepts with the same Functionality Cos st ($) Reliability Torque Gear Ratio 3 Blue reverted gear train dominates at gear ratios < 5 Red planetary gear train dominates at gear ratios > 5 Best concept can be identified after considering systems-level tradeoff for gear ratio and other attributes. 27

28 Another Example: Small 4-stroke Engines Some engines are dominated E.g. same torque, mass, power, but lower price 3D Projection of Small Engine Data (6D) (Clustering and Domination) dominated tradeoffs Not all combinations of the functional attributes are feasible Clustering algorithms are used to define the feasible set (Support Vector Machines) non-dominated tradeoffs Cluster ID max power max torque mass 28

29 Predictive Tradeoff Modeling: Making System-Level Decisions Typical Iterative ti Loop (optimization / search) Utility Model System Model Often more than technical performance E.g., price/cost, mass, -ilities (reliability, usability, ) Pump Attributes: Cylinder Attributes: Engine Attributes: Other max displacement bore diam. max power Components max speed stroke length max speed efficiency mass max torque mass price price efficiency mass price Attribute values for a given component are not independent How to formalize the dependencies efficiently and effectively? Project 2E Webcast - 23 July

30 Making System-Level Decisions with Predictive Models Log Loading & Splitting Area Directional Control Valve Hydraulic Cylinder & Ram Engine & Pump Engine Load Predictive Cylinder Model mass bore System Tradeoffs pump disp bore stroke cost stroke utility

31 Efficient Design Optimization under Uncertainty Systems t Realization Laboratoryb t Adaptive Kriging Models Students: Alek Kerzhner, Roxanne Moore

32 Motivating Study: Backhoe Dig-Cycle optimizer Latin Hypercube + Kriging response surface Optimization under uncertainty LatinHyperCube sampler used to predict expected value Kriging model used in conjunction with sampler to generate response surface to reduce computational cost Objectives: Maximize Efficiency Minimize Cost Design variables: bore diameters pump max disp 32

33 Adaptive Kriging Models Why Surrogate Models? Without Kriging: 50 optimizer iterations* 7 evaluations per iteration*1000 LHS samples = 350,000 runs With Kriging: 2000 seeding runs extra runs = 2,100 runs! Adaptive Kriging model Kriging: computational complexity is O(n4) Adaptive approach: keep n small Many localized (small) response surfaces Automatically requests additional simulations Automatically ti regenerates response surface 33

34 The Information Economic Challenge Level of Fidelity Level of Effort Required Level of Exploration / Optimization

35 The Information Economic Challenge Level of Fidelity Level of Effort Required Level of Exploration / Optimization

36 Variable Fidelity Modeling Low fidelity for broad exploration identify ypromising regions of design space High fidelity for detailed optimization x2 Feasible solutions Obj C A B x1 x1

37 Presentation Overview Research Scope, Context, and Foundation Model-Based Systems Engineering 1. Reusable Analysis Models Defined in SysML 2. Predictive Trade-off Models 3. Variable Fidelity Analysis 4. Capturing Synthesis Knowledge as Graph Transformations 5. Risk Management in Systems Engineering Summary 37

38 Capturing Synthesis Knowledge as Graph Transformations Systems t Realization Laboratoryb t Formal Representation of Domain- Specific Knowledge Student: Alek Kerzhner

39 Most Knowledge Can Be Represented as Graphs or Graph Transformations Requirements & Objectives SysML Topology Generation using Graph Transf System Alternatives MAsCoMs Model Composition using Graph Transf System Behavior Models SysML Model Translation using Graph Transf Executable Simulations Dymola SysML Dig Cycle Traj Sw ing Boom Arm Bucket system alternative hydraulics behavior model y world x ibd [Block] Hydraulic_Subsystem[ Schematic ] pump : FDpump discharge : FlowPort inputshaft : FlowPort housing : FlowPort suction : FlowPort tank-to-pump : Line b : FlowPort a : FlowPort tank : Tank sump : FlowPort return : FlowPort filter-to-tank : Line b : FlowPort a : FlowPort filter : Filter in : FlowPort out : FlowPort pump-to-valve : Line a : FlowPort b : FlowPort valve-to-filter : Line a : FlowPort b : FlowPort valve : 4port3wayServoValve portp : FlowPort portt : FlowPort cylb : FlowPort cyla : FlowPort actuator : Double-ActingCylinder housing : FlowPort rod : FlowPort b : FlowPort a : FlowPort valve-to-cylp1 : Line a : FlowPort b : FlowPort valve-to-cylp2 : Line a : FlowPort b : FlowPort simulation configuration Simulation Configuration using Graph Transf Design Optimization ModelCenter

40 MOFLON: Meta-Modeling & Graph Xform Tool Define graph transformations in Storyboards: activity diagrams + graphs Easily integrated with SysML tools (through standardized JMI interface) Capture domain-specific knowledge 40

41 Generative Grammar for Design Synthesis Graph Transformation rules to generate systems Generate random system alternatives by applying rules in randomized order Improve system alternatives through evolutionary search algorithms ago 41

42 Composition of Multi-Aspect Models MACM Repository Automated Composition System Models Perspective C Perspective B Perspective A Architecture t Optimization 42

43 Presentation Overview Research Scope, Context, and Foundation Model-Based Systems Engineering 1. Reusable Analysis Models Defined in SysML 2. Predictive Trade-off Models 3. Variable Fidelity Analysis 4. Capturing Synthesis Knowledge as Graph Transformations 5. Risk Management in Systems Engineering Summary 43

44 Risk Management in Systems Engineering Systems t Realization Laboratoryb t Trading off Product Quality and Risk versus Design Process Costs Student: Stephanie Thompson

45 Frame of Reference Maximize expected utility! Of what? Product (artifact) utility Product + Design Process utility Instead of What configuration of the product gives us the best product utility? we should ask What can we do now to give us the best balance of product and process utility later? 45

46 Questions To Answer When is it valuable to perform additional analyses to reduce risk? When is it valuable to perform detailed uncertainty analysis? In which order should the analyses be performed? How many design concepts should one carry forward in parallel? Approach: Investigate simplified design scenario for which a theoretically optimal design process can be determined Generalize these theoretical insights toward practical guidelines 46

47 Simple Illustration Problem Problem Definition Two Concepts Designer must choose concept A or B The utilities of concepts A and B are uncertain ( 2 ) i u ~ N μ, σ u Two Analyses Low quality (LQ) and high u = u+ ε quality (HQ) analyses to refine the utility estimates LQ is cheaper, but the HQ is more precise. Cost of analyses reduces expected utility. L H = + ( 2 ε ~ N 0, σ ) ε u = u+ δ 2 + δ ~ N ( 0, σ ) δ 47

48 Normal distributions: Simplifying Assumptions The utilities of A and B, and uncertainties of analyses are all distributed normally. All derived conditional distributions are also Normal Limited scope of decision tree The low quality analyses have already been performed for both concepts, reducing the size of the decision i tree. In further work, the decision tree will include branches to perform the low quality analyses. 48

49 Decision Tree of Design Process HQ A Select A p ( u A L ) Sl Select tb B p( u L ) ( B ) B B L HQ B Select A HQ B Select B p A A A H L u u, u A ( u ) p A A A ( u H ) ( B p ) B B uh u H u L u A p u p ( u B ) A u B u B L A A L u u ( ) u B Select A p u u u p ( u A u ) A u A L HQ A p B B B ( u u u H ) ( A p ) A A uh H L Select B p u u H H u u L L B B B H L u u, u B ( u ) u A -c HQA u B -c HQA u A -c HQB Select A Select B u B -c HQB Select A p u u H, u Select B p p p A A A L B B B H L u u, u A A A H L u u, u B B B H L u u, u A ( u ) B ( u ) A ( u ) B ( u ) u A -c HQA -c HQB u B -c HQA -c HQB u A -c HQA -c HQB u B -c HQA -c HQB 49

50 Probability Distributions for Chance Events Apply Bayes Theorem to derive conditional probabilities p ( x) xy = y = (, ) ( y ) p xy p Y All distributions end up being Normal: p u σ u N + σεμ σ σε u L u uu ( ) ~, L σ u + σε σu + σε σ uul + σμ ε σσ u ε + σσ u δ + σσ ε δ pu ( ) ~, H u u L H N σu + σε σu + σε p u σ u N + σδμ σ σδ u H u uu ( ) ~, H σ u + σδ σu + σδ p u σ u N + σμ δ σσ ε + σσδ + σσ ε u H u u d u ( ) ~, L uh L σu + σδ σu + σδ p u σσδu N + σσεu + σσμ ε δ σσσ ε δ u L u H u uu, ( ) ~, L uh σ uσε + σuσδ + σδσε σuσε + σuσδ + σεσδ 50

51 Decision Map Nominal Parameters: μ A = μ B = 100 σ 2 A = σ 2 B = 50 2 HQ costs = 10 σ 2 L = 45 2 σ 2 H =

52 Presentation Overview Research Scope, Context, and Foundation Model-Based Systems Engineering 1. Reusable Analysis Models Defined in SysML 2. Predictive Trade-off Models 3. Variable Fidelity Analysis 4. Capturing Synthesis Knowledge as Graph Transformations 5. Risk Management in Systems Engineering Summary 52

53 Summary Overall Research Theme How can one design systems better at a lower cost? Guiding Principle Maximize utility of both product and process Increase the value Decrease the cost Solution Principles Utility theory Modularity in components and models Formal knowledge capture and reuse Graph manipulation & transformation 53