Abstract
Design can be viewed a sequential decision process that increases the detail of modeling and analysis while simultaneously decreasing the space of alternatives considered. In a decision theoretic framework, low-fidelity models help decision-makers identify regions of feasibility and interest in the tradespace and cull others prior to constructing more computationally expensive models of higher fidelity. The method presented herein demonstrates design as a sequence of finite decision epochs through a search space defined by the extent of the set of designs under consideration, and the level of analytic fidelity subjected to each design. Previous work has shown that multi-fidelity modeling can aid in rapid optimization of the design space when high-fidelity models are coupled with low-fidelity models. This paper offers two contributions to the design community: (1) a model of design as a sequential decision process of refinement using progressively more accurate and expensive models, and (2) a connected approach for how conceptual models couple with detailed models. Formal definitions of the process are provided, and several structural design examples are presented to demonstrate the use of sequential multi-fidelity modeling in determining an optimal modeling selection policy.
Similar content being viewed by others
References
Anderson J (2007) Fundamentals of aerodynamics, 4th edn. McGraw-Hill Science/Engineering/Math, Boston
Asher MJ, Croke BFW, Jakeman AJ, Peeters LJM (2015) A review of surrogate models and their application to groundwater modeling. Water Resour Res 51(8):5957–5973
Avigad G, Moshaiov A (2009) Interactive evolutionary multiobjective search and optimization of set-based concepts. IEEE Trans Syst Man Cybern Part B: Cybern 39(4):1013–1027
Bellman R (1957) Dynamic programming. Princeton University Press, Princeton
Brantley MW, Mcfadden WJ, Davis MJ (2002) Expanding the trade space: an analysis of requirements tradeoffs affecting system design. Acquisit Rev Quart 9(1):1–16
Busemeyer JR, Townsend JT (1993) Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment. Psychol Rev 100(3):432–459
Chaudhuri A, Haftka RT (2014) Efficient global optimization with adaptive target setting. AIAA J 52 (7):1573–1578
Choi S, Alonso JJ, Kroo IM, Wintzer M (2004) Multi-fidelity design optimization of low-boom supersonic business jets. In: 10th AIAA/ISSMO Multidisciplinary analysis and optimization conference, AIAA 2004-4371. Albany
Choi S, Alonso JJ, Kroo IM, Wintzer M (2008) Multifidelity design optimization of low-boom supersonic jets. J Aircr 45(1):106–118
Choi S, Alonso JJ, Kroo IM (2009) Two-level multi-fidelity design optimization studies for supersonic jets. J Aircr 46(3):1–37
Choi SH, Lee SJ, Kim TG (2014) Multi-fidelity modeling & simulation methodology for simulation speed up. In: Proceedings of the 2nd ACM SIGSIM/PADS conference on principles of advanced discrete simulation. Denver, pp 139–150
Choi SM, Nguyen NV, Kim WS, Lee JW, Kim S, Byun YH (2010) Multidisciplinary unmanned combat air vehicle system design using multi-fidelity analysis. In: Proceedings of the 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, AIAA 2010-482. Orlando, pp 1–16
Du Q, Faber V, Gunzburger M (1999) Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev 41(4):637–676
Elham A, van Tooren MJL (2016) Coupled adjoint aerostructural wing optimization using quasi-three-dimensional aerodynamic analysis. Struct Multidiscip Optim 43(4):889–906
Evans JH (1959) Basic design concepts. J Amer Soc Naval Eng 71(4):671–678
Finch WW, Ward AC (1997) A set-based system for eliminating design in engineering problems dominated by uncertainty. In: Proceedings of the 1997 ASME design engineering technical conferences, DETC97/DTM-3886. Sacramento, pp 1–12
Finger S, Dixon JR (1989) A review of research in mechanical engineering design. Part I: descriptive, prescriptive, and computer-based models of design processes. Res Eng Des 1:51–67
Finger S, Fox MS, Navlndiandra D, Prins FB, Rinderle JR (1988) Design fusion: a product life-cycle view for engineering designs. Second IFIP WG 52 workshop on intelligent CAD, pp 1–7
Forrester AI, Sȯbester A, Keane AJ (2008) Engineering design via surrogate modeling: a practical guide. Wiley, Chichester
Forsberg K, Mooz H (1992) The relationship of system engineering to the project cycle. Eng Manag J 4 (3):36–43
Frey DD, Herder PM, Wijnia Y, Subrahmanian E, Katsikopoulos K, Clausing DP (2009) The Pugh controlled convergence method: model-based evaluation and implications for design theory. Res Eng Des 20 (1):41–58
Giffin M, de Weck OL, Bounova G, Keller R, Eckert C, Clarkson PJ (2009) Change propagation analysis in complex technical systems. J Mech Des 131(8):081,001–1–14
Haftka RT, Villanueva D, Chaudhuri A (2016) Parallel surrogate-assisted global optimization with expensive functions – a survey. Struct Multidiscip Optim 54(1):3–13
Hall EJ (2000) Modular multi-fidelity simulation methodology for multiple spool turbofan engines. In: NASA high performance computing and communications computational aerosciences workshop. NASA Ames Research Centre
Huang D, Allen TT, Notz WI, Miller RA (2006) Sequential kriging optimization using multiple-fidelity evaluations. Struct Multidiscip Optim 32(5):369–382
Jacobs J, Etman L, van Keulen F, Rooda J (2004) Framework for sequential approximate optimization. Struct Multidiscip Optim 27:384–400
Jones DR (2001) A taxonomy of global optimization methods based on response surfaces. J Glob Optim 21:345–383
Jones DR, Schonlau M, William J (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492
Keim DA (2002) Information visualization and visual data mining. IEEE Trans Vis Comput Graph 8(1):1–8
Kitayama S, Srirat J, Arakawa M, Yamazaki K (2013) Sequential approximate multi-objective optimization using radial basis function network. Struct Multidiscip Optim 48(3):501–515
Kuppuraju N, Ittimakin P, Mistree F (1985) Design through selection: a method that works. Des Stud 6(2):91–106
Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multi-objective optimization. Evol Comput 10(3):1–21
Leifsson L, Koziel S (2010) Multi-fidelity design optimization of transonic airfoils using shape-preserving response prediction. Procedia Comput Sci 1(1):1311–1320
Liu GR, Nguyen TT (2010) Smoothed finite element methods. CRC Press, Boca Raton
Logan DL (2007) A first course in the finite element method cengage learning. Mason
Malak RJ, Aughenbaugh JM, Paredis CJJ (2009) Multi-attribute utility analysis in set-based conceptual design. Comput Aided Des 41(3):214–227
Marjanishvili S, Agnew E (2006) Comparison of various procedures for progressive collapse analysis. J Perform Constr Facil 20(4):365–374
Mason WH, Knill DL, Giunta AA, Grossman B, Watson LT, Haftka RT (1998) Getting the full benefits of CFD in conceptual design. In: 16th AIAA applied aerodynamics conference, pp 1–11
Miller SW, Simpson TW, Yukish MA, Bennett LA, Lego SE, Stump GM (2013) Preference construction, sequential decision making, and trade space exploration. In: ASME international design engineering technical conference & computers and information in engineering conference, DETC2013-13098. Portland, pp 1–12
Miller SW, Simpson TW, Yukish MA (2015) Design as a sequential process: a method for reducing design set space using models to bound objectives. In: ASME international design engineering technical conference & computers and information in engineering conference, DETC2015-46909. Boston, pp 1–13
Minisci E, Liqiang H, Vasile M (2010) Multidisciplinary design of a micro-USV for re-entry operations. In: AIAA/AAS astrodynamics specialist conference 2010, AIAA 2010-7968
Moore RA, Paredis CJJ (2009) Variable fidelity modeling as applied to trajectory optimization for a hydraulic backhoe. In: Proceedings of the ASME 2009 international design engineering technical conferences & computers and information in engineering conference, DETC2009-87522. San Diego, pp 1–12
Nahm YE, Ishikawa H (2006) A new 3D-CAD system for set-based parametric design. Int J Adv Manuf Technols 29(1-2):137–150
Pahl G, Beitz W, Feldhusen J, Grote KH (2007) Engineering design: a systematic approach, vol 157, 3rd edn. Springer, London
Payne JW, Bettman JR, Johnson EJ (1993) The adaptive decision maker. Cambridge University Press, New York
Pėrez V, Renaud J, Watson L (2004) An interior-point sequential approximate optimization methodology. Struct Multidiscip Optim 27(5):360–370
Pugh S (1991) Total design - integrated methods for successful product engineering. Addison-Wesley Publishing, New York
Reinertsen DG (1997) Managing the design factory: a product developer’s toolkit. Free Press, New York
Reisenthel PH, Allen TT, Lesieutre DJ, Lee SH (2010) Development of multidisciplinary, multifidelity analysis, integration, and optimization of aerospace vehicles. Tech. Rep. 074, DTIC Document
Rekuc SJ, Aughenbaugh JM, Bruns M, Paredis CJJ (2006) Eliminating design alternatives based on imprecise information. In: SAE technical paper, SAE international, pp 1–13
Roberts CJ, Richards MG, Ross AM, Rhodes DH, Hastings DE (2009) Scenario planning in dynamic multi-attribute tradespace exploration. In: 3rd annual IEEE international systems conference, pp 366–371
Robertson B, Radcliffe D (2009) Impact of CAD tools on creative problem solving in engineering design. Comput Aided Des 41(3):136–146
Robinson TD, Eldred MS, Willcox KE, Haimes R (2008) Surrogate-based optimization using multifidelity models with variable parameterization and corrected space mapping. AIAA J 46(11):2814–2822
Rodri̇guez J F, Pėrez V, Padmanabhan D, Renaud JE (2001) Sequential approximate optimization using variable fidelity response surface approximations. Struct Multidiscip Optim 22(1):24–34
Ross AM, Hastings DE (2005) The tradespace exploration paradigm. INCOSE International Symposium, pp 1–13
Ross AM, Rhodes DH (2008) Using natural value-centric time scales for conceptualizing system timelines through epoch-era analysis. INCOSE Int Symp 18(1):1186–1201
Royce WW (1970) Managing the development of large software systems. Proc IEEE WESCON 26(8):328–338
Shai O, Reich Y, Rubin D (2009) Creative conceptual design: extending the scope by infused design. Comput Aided Des 41(3):117– 135
Shames IH, Dym CL (1985) Energy and finite element methods in structural mechanics. Hemisphere Pub. Corp, Washington, DC
Shan S, Wang GG (2010) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multidiscip Optim 41(2):219–241
Shewchuk JR (1996) Triangle: engineering a 2D quality mesh generator and Delaunay triangulator. In: Applied computational geometry, towards geometric engineering. Springer, pp 203–222
Shewchuk JR (2002) Delaunay refinement algorithms for triangular mesh generation. Comput Geom 22 (1):21–74
Shocker AD, Ben-Akiva M, Boccara B, Nedungadi P (1991) Consideration set influences on consumer decision making and choice: issues, models, and suggestions. Mark Lett 2(3):181–197
Singer DJ, Doerry N, Buckley ME (2009) What is set-based design? Nav Eng J 121(4):31–43
Sobek DKI, Ward AC, Liker JK (1999) Toyota’s principles of set-based concurrent engineering. Sloan Manage Rev 40(2):67–83
Stander JN, Venter G, Kamper MJ (2016) High fidelity multidisciplinary design optimisation of an electromagnetic device. Struct Multidiscip Optim 53(5):1113–1127
Stump GM, Lego SE, Yukish MA, Simpson TW, Donndelinger JA (2009) Visual steering commands for trade space exploration: user-guided sampling with example. ASME J Comput Inf Sci Eng 9(4):1–10
Takagi H (2001) Interactive evolutionary computation: fusion of the capabilitiesof EC optimization and human evaluation. Proc IEEE 89(9):1275–1296
Tsetsos K, Usher M, Chater N (2010) Preference reversal in multiattribute choice. Psychol Rev 117 (4):1275–1293
Ulrich KT, Eppinger SD (2004) Product design and development, 3rd edn. McGraw-Hill/Irwin, Boston
Venkataraman S, Haftka RT (2004) Structural optimization complexity: what has Moore’s law done for us? Struct Multidiscip Optim 28(6):375–387
Viana FAC, Simpson TW, Balabanov V, Toropov V (2014) Metamodeling in multidisciplinary design optimization: how far have we really come? AIAA J 52(4):670–690
Ward AC (1989) A theory of quantitative inference for artifact sets, applied to a mechanical design compiler. Doctor of science Massachusetts Institute of Technology, Cambridge
Willis DJ, Persson PO, Israeli ER (2008) Multifidelity approaches for the computational analysis and design of effective flapping wing vehicles. In: 46th AIAA Aerospace sciences meeting and exhibit, AIAA 2008–518. Reno, pp 1-17
Xu X, Dajun X, Guobiao C (2005) Optimization design for scramjet and analysis of its operation performance. Acta Astronaut 57(2-8):390–403
Yukish MA (2005) Research topics in trade space exploration. In: IEEE Aerospace conference, #1001. New York, pp 1–7
Acknowledgements
The authors wish to acknowledge the support provided by the Defense Advanced Research Projects Agency (DARPA / TTO) under contract HR0011-12-C-0075 iFAB Foundry for making this work feasible.
The authors also acknowledge support from the National Science Foundation (Grant No. 1436236). This material is also supported by the U.S. Department of Defense through the Systems Engineering Research Center (SERC) under Contract H98230-08-D-0171. SERC is a federally funded University Affiliated Research Center managed by the Stevens Institute of Technology. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of DARPA, or the U.S. Government, or the National Science Foundation.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Miller, S.W., Yukish, M.A. & Simpson, T.W. Design as a sequential decision process. Struct Multidisc Optim 57, 305–324 (2018). https://doi.org/10.1007/s00158-017-1756-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-017-1756-7