A Portfolio Approach to System-of-Systems Acquisition and Architecture. NDIA Conference 26-OCTOBER-2012

Transcription

1 A Portfolio Approach to System-of-Systems Acquisition and Architecture NDIA Conference 26-OCTOBER-2012 Dr. Daniel DeLaurentis Dr. Navindran Davendralingam School of Aeronautics & Astronautics Center for Integrated Systems in Aerospace Purdue University This material is based upon work supported, in whole or in part, by the U.S. Department of Defense through the Systems Engineering Research Center (SERC) under Contract H D SERC is a federally funded University Affiliated Research Center managed by Stevens Institute of Technology. 11/13/2012 1

2 Presentation Outline Motivation: Defense Acquisitions and Systems Engineering SoS Architecting and Acquisition: Wave Model context An Investment Portfolio Approach Mean Variance Approach Mean-Variance: A Robust Version Concept Problem: Simple Littoral Combat Ship (LCS) Robust Portfolio application Multiple risk measures Operational Robustness using Bertsimas-Sim method Future Work 11/13/2012 2

3 Motivation: Acquisitions and Systems Engineering Image from: Presentation slides by RDML Vic Guillory of OPNAV at Mine Warfare Association Conference (titled Littoral Combat Ship, 08-May-07) 11/13/2012 3

4 The Big Picture Stand-In Redundancy Petri-Nets Bayesian & FDNA Approach 11/13/2012 4

5 SoS Architecture Development How do we support these actions for SoS acquisitions? *adapted from Dahmann et. al, Integrating Systems Engineering and Test & Evaluation in System of Systems Development IEEE Vancouver, /13/2012 5

6 SoS Acquisition and Architecture How to leverage acquiring capabilities against associated risk? What about system interdependencies? What about performance/development uncertainty considerations? Can I exploit architectural connectivity for robustness? 11/13/2012 6

7 A Portfolio Approach: Background Classical Mean-Variance optimization among techniques adopted by financial engineering and operations research. Balance expected profit (performance) against risk (variance) in investments Generates efficiency frontier of optimal portfolios given investor risk averseness Systems (nodes) can be modeled as potential investment assets how do we invest? Nodes = systems 11/13/2012 7

8 Model individual system as nodes Functional & Physical representation Portfolio Approach: SoS Modelling Additions Rules for node connectivity Compatibility between nodes Bandwidth of linkages Supply (Capability) Demand (Requirements) Relay capability Inputs Outputs Capability Compatibility. Requirement Relay Bandwidth 11/13/2012 8

9 Constraints [Replace With Your Logo Here] Mean-Variance Portfolio Approach Objective Maximize Performance Index Capability Risk Cost Portfolio Fraction Portfolio Total Budget Requirements Satisfaction Selection Rules (Compatibility) Uncertainty in Covariance (Interdependencies) 11/13/2012 9

10 Extension to SoS Interconnectivities Maximize Capability Performance Index Sufficient Capabilities Supplied Individual System Requirements met Connectivity Rules Obeyed (Big-M formulation) Risk Tolerance (per measure of risk) max s.t. B ic i c 11/13/ i X X i S w X R X S R B cij j rj X S B cij j rj i 1 Xn 0 X c i X c cij ij c X M 0 M X X X X ij cij cij cij ij 0 B X X X S 0 X cij cij j rj j B i T Limit X B ij i critical cij 0 c capability L U ij X cij ij B, X binary {0,1} j

11 Portfolio Uncertainty Sources of uncertainty System Capability: Actual performance of system individually and as a whole SoS entity System Interdependence: Interdependency variances/covariances? System 1 System 2 Addressing uncertainty Operations Research/Financial Engineering Methods to address uncertainty measures Introduce uncertainty in interdependencies and individual asset performances Introduce SoS connectivity in portfolio space 11/13/

12 Mean-Variance Portfolio: A Robust Approach 11/13/

13 Robust Portfolio Case Study: Simple LCS Portfolio Diagonal : System Variance Off Diagonal : System Interdependency 11/13/

14 Robust Portfolio Case Study: Simple LCS Portfolio 11/13/

15 Performance Index [non-dim] [Replace With Your Logo Here] Portfolio Approach: LCS Multiple Risk Measures Layered measure of risk (e.g. weapons vs. communications layer) x Separate covariance for each measure of risk Variance Risk Measure (Comm) Variance Risk Measure (Weapons) Comm. Variance (Risk) Constraint Weapon Variance (Risk) Constraint 11/13/

16 Portfolio Robust Operational Constraints Constraint Rules for Connectivity & Operations Bertsimas-Sim Method: Adjust conservatism Γ i term to control probability of constraint violation Conservatism Added (This can be converted to an LP == easy to solve even for large problems) 11/13/

17 Probability of Violation [Replace With Your Logo Here] Portfolio Robust Operational Constraint Important Operational Constraint (e.g.) Level of Conservatism Package Bandwith Req ASW Variable Depth 3.54 Multi Fcn Tow 60 Lightweight tow MCN RAMCS II ALMDS (MH-60) 76.8 SUW N-LOS Missiles Griffin Missiles Seaframe Package System & Combat Package System Management Package System Subject to some uncertainty (+/-) 11/13/

18 Future Work: Portfolio Approach Semi Definite Programming (SDP) can be hard to solve/implement Conic and Linear Programming versions well developed open solvers Extend to multi-period portfolio dynamic programming Agent-Based Simulation (e.g. for covariance estimation, CVaR) 11/13/

19 Summary/Conclusion RMVO promising framework to leverage SoS performance against risk Considers uncertainty and system interdependencies explicitly in portfolio construction Develop further towards analytic workbench objectives 11/13/