Current design decisions must be made while considering uncertainty in both models of the design and inputs to the design. In most cases, high fidelity models are used with the assumption that the resulting model uncertainties are insignificant to the decision making process. This paper presents a methodology for managing uncertainty during system-level conceptual design of complex multidisciplinary systems. This methodology is based upon quantifying the information available in a set of observations of computationally expensive subsystem models with more computationally efficient kriging models. By using kriging models, the computational expense of a Monte Carlo simulation to assess the impact of the sources of uncertainty on system-level performance parameters becomes tractable. The use of a kriging model as an approximation to an original computer model introduces model uncertainty, which is included as part of the methodology. The methodology is demonstrated as a decision-making tool for the design of a satellite system.
Issue Section:
Research Papers
1.
Hazelrigg
, G. A.
, 1996, Systems Engineering: An Approach to Information-Based Design
, Prentice Hall International Series in Industrial and Systems Engineering
, Prentice Hall
, Upper Saddle River, NJ
.2.
Maddulapalli
, K.
, Azarm
, S.
, and Boyars
, A.
, 2005, “Interactive Product Design Selection With an Implicit Value Function
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 367
–377
.3.
Lewis
, K.
, and Mistree
, F.
, 1998, “The Other Side of Multidisciplinary Design Optimization: Accomodating a Multiobjective, Uncertain and Non-Deterministic World
,” Eng. Optimiz.
0305-215X, 31
, pp. 161
–189
.4.
Chen
, V. C. P.
, Tsui
, K.-L.
, Barton
, R. R.
, and Allen
, J. K.
, 2003, “A Review of Design and Modeling in Computer Experiments
,” Handbook of Statistics
; R.
Khattree
and C.
Rao
, eds., Elsevier Science
, Amsterdam
, Vol. 22
, pp. 231
–261
.5.
Simpson
, T. W.
, Booker
, A. J.
, Ghosh
, S.
, Giunta
, A.
, Koch
, P. N.
, and Yang
, R. J.
, 2004, “Approximation Methods in Multidisciplinary Analysis and Optimization: A Panel Discussion
,” Struct. Multidiscip. Optim.
1615-147X, 27
(5
), pp. 302
–313
.6.
Cox
, D. D.
, and John
, S.
, 1997, “SDO: A Statistical Method for Global Optimization
,” Multidisciplinary Design Optimization: State of the Art
, N. M.
Alexandrov
and M. Y.
Hussaini
, eds., SIAM
, Philadelphia
, pp. 315
–329
.7.
Trosset
, M. W.
, and Torczon
, V.
, 1997, “Numerical Optimization Using Computer Experiments
,” ICASE Report No. 97-38, NASA Langley Research Center
, Hampton, VA.8.
Booker
, A. J.
, Conn
, A. R.
, Dennis
, Jr., J. E.
Frank
, P. D.
, Trosset
, M.
, and Torczon
, V.
, 1995, “Global Modeling for Optimization: Boeing/IBM/Rice Collaborative Project 1995 Final Report
,” ISSTECH-95–032, The Boeing Company
, Bellevue, WA.9.
Sasena
, M. J.
, Papalambros
, P.
, and Goovaerts
, P.
, 2002, “Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization
,” Eng. Optimiz.
0305-215X, 34
(3
), pp. 263
–278
.10.
Osio
, I. G.
, and Amon
, C. H.
, 1996, “An Engineering Design Methodology With Multistage Bayesian Surrogate and Optimal Sampling
,” Res. Eng. Des.
0934-9839, 8
(4
), pp. 189
–206
.11.
Simpson
, T. W.
, Maurey
, T. M.
, Korte
, J. J.
, and Mistree
, F.
, 2001, “Kriging Metamodels for Global Approximation in Simulation-Based Multidisciplinary Design Optimization
,” AIAA J.
0001-1452, 39
(12
), pp. 2233
–2241
.12.
Goovaerts
, P.
, 1997, Geostatistics for Natural Resources Evaluation
, Applied Geostatistics Series
, Oxford University Press
, New York
.13.
Gotway
, C. A.
, 1994, “The Use of Conditional Simulation in Nuclear-Waste-Site Performance Assessment
,” Technometrics
0040-1706, 36
(2
), pp. 129
–141
.14.
Martin
, J. D.
, and Simpson
, T. W.
, 2005, “On the Use of Kriging Models to Approximate Deterministic Computer Models
,” AIAA J.
0001-1452, 43
(4
), pp. 853
–863
.15.
Bayarri
, M. J.
, Berger
, J. O.
, Higdon
, D.
, Kennedy
, M. C.
, Kottas
, A.
, Paulo
, R.
, Sacks
, J.
, Cafeo
, J. A.
, Cavendish
, J. C.
, Lin
, C. H.
, and Tui
, J.
, 2002, “A Framework for Validation of Computer Models
,” Tech. Rep. No. 128, National Institute of Statistical Sciences
, Gaithersburg, MD.16.
Den Hertog
, D.
, Kleijnen
, J.
, and Siem
, A.
, 2005, “The Correct Kriging Variance Estimated by Bootstrapping
,” J. Oper. Res. Soc.
0160-5682, 57
(4
), pp. 400
–409
.17.
Martin
, J. D.
, and Simpson
, T. W.
, 2004, “A Monte Carlo Simulation of the Kriging Model
,” 10th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, AIAA-2004–4483.18.
Robert
, C. P.
, and Casella
, G.
, 1999, Monte Carlo Statistical Methods
, Springer Texts in Statistics
, Springer-Verlag
, New York
.19.
Huang
, B.
, and Du
, X.
, 2006, “Uncertianty Analysis by Dimension Reduction Integration and Saddlepoint Approximations
,” ASME J. Mech. Des.
1050-0472, 128
, pp. 26
–33
.20.
Saltelli
, A.
, Tarantola
, S.
, and Chan
, K.
, 1999, “A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Ouptut
,” Technometrics
0040-1706, 41
(1
), pp. 39
–56
.21.
Martin
, J. D.
, 2005, “A Methodology for Evaluating System-level Uncertainty in the Conceptual Design of Complex Multidisciplinary Systems
,” Ph.D. Dissertation, Dept. of Mechanical Engineering, The Pennsylvania State University, University Park, PA.22.
Saltelli
, A.
, Chan
, K.
, and Scott
, E. M.
, 2000, Mathematical and Statistical Methods: Sensitivity Analysis
, Wiley Series in Probability and Statistics
, Wiley
, Chichester
.23.
Chen
, W.
, Jin
, R.
, and Sudjianto
, A.
, 2005, “Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 875
–886
.24.
Charania
, C. A.
, Bradford
, J. E.
, Olds
, J. R.
, and Graham
, M.
, 2002, “System Level Uncertainty Assessment for Collaborative RLV Design
,” JANNAF 38th Combustion Subcommitte/26th Airbreathing Propulsion Subcommittee/20th Propulsion Systems Hazards Subcommittee/2nd Modeling and Simulation Subcommittee Joint Meeting
, JANNAF-2002–2B-4-MSS.25.
Qu
, X.
, and Haftka
, R. T.
, 2003, “Design Under Uncertainty Using Monte Carlo Simulation and Probabilistic Sufficiency Factor
,” ASME 2003 Design Engineering Technical Conference and Computers and Information in Engineering Conference
, DETC2003/DAC-48704.26.
Radhakrishnan
, R.
, and McAdams
, D. A.
, 2005, “A Methodology for Model Selection in Engineering Design
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 378
–387
.27.
Cooper
, A. B.
, Georgiopoulos
, P.
, Kim
, H. M.
, and Papalambros
, P. Y.
, 2006, “Analytical Target Setting: An Enterprise Context in Optimal Product Design
,” ASME J. Mech. Des.
1050-0472, 128
, pp. 4
–13
.28.
McKay
, M.
, Conover
, W.
, and Beckman
, R.
, 1979, “A Comparison of Three Methods for Selecting Values of Input in the Analysis of Output from a Computer Code
,” Technometrics
0040-1706, 21
(1
), pp. 239
–245
.29.
Simpson
, T. W.
, Peplinski
, J.
, Koch
, P. N.
, and Allen
, J. K.
, 2001, “Metamodels for Computer-Based Engineering Design: Survey and Recommendations
,” Eng. Comput.
0177-0667, 17
(2
), pp. 129
–150
.30.
Simpson
, T. W.
, Lin
, K. J.
, and Chen
, W.
, 2001, “Sampling Stategies for Computer Experiments: Design and Analysis
,” Int. J. Reliab. Appl.
1598-0073, 2
(3
), pp. 209
–240
.31.
Martin
, J. D.
, and Simpson
, T. W.
, 2005, “On Using Kriging Models as Probabilistic Models in Design
,” SAE Trans.
0096-736X, 5
, pp. 129
–139
.32.
Martin
, J. D.
, and Simpson
, T. W.
, 2005, “On the Use of Kriging Models to Approximate Deterministic Computer Models
,” AIAA J.
0001-1452, 43
(4
), pp. 853
–863
.33.
Myers
, R. H.
, and Montgomery
, D. C.
, 2002, Response Surface Methodology: Process and Product Optimization Using Designed Experiments
, Wiley Series in Probability and Statistics
, 2nd ed., Wiley
, New York
.34.
Burnham
, K. P.
, and Anderson
, D. R.
, 2002, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach
, 2nd ed., Springer-Verlag
, New York
.35.
Du
, X.
, Sudjianto
, A.
, and Huang
, B.
, 2005, “Reliability-Based Design with the Mixture of Random and Interval Variables
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 1068
–1076
.36.
Xiong
, Y.
, and Rao
, S. S.
, 2005, “A Fuzzy Dynamic Programming Approach for the Mixed-Discrete Optimziation of Mechanical Systems
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 1088
–1099
.37.
Helton
, J. C.
, and Davis
, F. J.
, 2000, “Sampling-Based Methods
,” Sensitivity Analysis
, A.
Saltelli
, K.
Chan
, and E. M.
Scott
, eds., Wiley
, Chichester
, pp. 101
–153
.38.
Mawardi
, A.
, and Pitchumani
, R.
, 2005, “SAMS: Stochastic Analysis With Minimal Sampling—A Fast Algorithm for Analysis and Design Under Uncertainty
,” ASME J. Mech. Des.
1050-0472, 127
, pp. 558
–571
.39.
Yukish
, M.
, 2004, “Algorithms to Identify Pareto Points in Multi-Dimensional Data Sets
,” Ph.D. Dissertation, Dept. of Mechanical Engineering, The Pennsylvania State University, University Park, PA.40.
McKay
, M.
, 1995, “Evaluating Prediction Uncertainty
,” NUREG/CR-6311, Los Alamos National Laboratory.41.
Abell
, M. L.
, Braselton
, J. P.
, and Rafter
, J. A.
, 1999, Statistics with Mathematica
, Academic Press
, San Diego
.42.
Booker
, A. J.
, 2000, “Well-Conditioned Kriging Models for Optimization of Computer Simulations
,” M&CT-TECH-00–002
, The Boeing Company
, Bellevue, WA
.43.
Kleijnen
, J. P. C.
, and Van Beers
, W. C. M.
, 2004, “Application-Driven Sequential Designs for Simulation Experiments: Kriging Metamodeling
,” J. Oper. Res. Soc.
0160-5682, 55
(8
), pp. 876
–883
.44.
Spall
, J. C.
, 2003, Introduction to Stochastic Search and Optimization; Estimation, Simulation, and Control
, Wiley
, Hoboken, NJ
.45.
Lophaven
, S. N.
, Nielsen
, H. B.
, and Sondergaard
, J.
, 2002, “DACE: A MATLAB Kriging Toolbox, Version 2.0
,” IMM Technical Unversity of Denmark, Lyngby.Copyright © 2006
by American Society of Mechanical Engineers
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