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Nonparametric approach for uncertainty-based multidisciplinary design optimization considering limited data

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Abstract

Uncertainty-based multidisciplinary design optimization (UMDO) has been widely acknowledged as an advanced methodology to address competing objectives and reliable constraints of complex systems by coupling relationship of disciplines involved in the system. UMDO process consists of three parts. Two parts are to define the system with uncertainty and to formulate the design optimization problem. The third part is to quantitatively analyze the uncertainty of the system output considering the uncertainty propagation in the multidiscipline analysis. One of the major issues in the UMDO research is that the uncertainty propagation makes uncertainty analysis difficult in the complex system. The conventional methods are based on the parametric approach could possibly cause the error when the parametric approach has ill-estimated distribution because data is often insufficient or limited. Therefore, it is required to develop a nonparametric approach to directly use data. In this work, the nonparametric approach for uncertainty-based multidisciplinary design optimization considering limited data is proposed. To handle limited data, three processes are also adopted. To verify the performance of the proposed method, mathematical and engineering examples are illustrated.

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References

  • Akaike H (1973) Information theory and an extension of the maximum likelihood principle. Proceedings of the Second Int Symposium on Information Theory pp 267–281

  • Balling RJ, Sobieszczanski-Sobieski J (1996) Optimization of coupled systems: a critical overview of approaches. AIAA J 34(1):6–17

    Article  MATH  Google Scholar 

  • Beyer HG, Sendhoff B (2007) Robust optimization—a comprehensive survey. Comput Method Appl Mech 196(33):3190–3218

    Article  MathSciNet  MATH  Google Scholar 

  • Chi SB, Jung HS, Kim HS, Moon JW (1999) Comparison of vane-shear strength measured by different methods in deep-sea sediments from KODOS area, NE Equatorial Pacific(in Korean). Sea J Korean Soc Ocean Ogr 4(4):390–399

    Google Scholar 

  • Cho S, Park S, Choi SS, Lee M, Choi JS, Kim HW, Lee CH, Hong S, Lee TH (2013) Multi-objective design optimization for manganese nodule pilot miner considering collecting performance and manoeuver of vehicle. Proceeding of the Tenth ISOPE Ocean Mining and Gas Hydrates Symposium, Szczecin, Poland 22–6

  • Cho S, Jang J, Lee SJ, Kim KS, Hong J, Jang WK, Lee TH (2014) Reliability-based optimum tolerance design for industrial electromagnetic devices. IEEE Trans Magn 50(2):713–716

    Article  Google Scholar 

  • Choi JS, Yeu TK, Kim HW, Park SJ, Yoon SM, Hong S (2010) Performance analysis of deep-sea manganese nodule test miner in inshore tests. Ocean Polar Res 32:463–473

    Article  Google Scholar 

  • Choi JS, Hong S, Chi SB, Lee HB, Park CK, Kim HW, Yeu TK, Lee TH (2011) Probability distribution for the shear strength of seafloor sediment in the KR5 area for the development of manganese nodule miner. Ocean Eng 38:2033–2041

    Article  Google Scholar 

  • Christophe A, Nando F, Arnaud D, Michael IJ (2003) An introduction to MCMC for machine learning. Mach Learn 50:5–43

    Article  MATH  Google Scholar 

  • Du X, Chen W (2005) Collaborative reliability analysis under the framework of multidisciplinary systems design. Opt Eng 6(1):63–84

    Article  MathSciNet  MATH  Google Scholar 

  • Elms DG (2004) Structural safety-issues and progress. Prog Struct Eng Mater 6(2):116–26

    Article  Google Scholar 

  • Engmann S, Cousineau D (2011) Comparing distributions: the two-sample Anderson-Darling test as an alternative to the Kolmogorov-Smirnoff test. J Appl Quant Methods 6(3):1–17

    Google Scholar 

  • Gu X, Renaud JE, Batill SM, Brach RM, Budhiraja AS (2000) Worst case propagated uncertainty of multidisciplinary systems in robust design optimization. Struct Multidiscip Optim 20(3):190–213

    Article  Google Scholar 

  • Hong S, Kim HW, Choi JS, Yeu TK, Park SJ, Lee CH, Yoon SM (2010) A self-propelled deep-seabed miner and lessons from shallow water test. ASME 2010 29th Int Conf on Ocean, Offshore and Arctic Eng 3

  • Jang J, Cho S, Lee SJ, Kim KS, Kim JM, Hong J, Lee TH (2015) Reliability-based robust design optimization with kernel density estimation for electric power steering motor considering manufacturing uncertainties. IEEE T Magn 51(3)

  • Ku TL, Broecker WS (1969) Radiochemical studies on manganese nodules of deep-sea origin. Deep-Sea Res 16:625–637

    Google Scholar 

  • Lee KH, Park GJ (2001) Robust optimization considering tolerance of design variables. Comput Struct 79(1):77–86

    Article  Google Scholar 

  • Lee HB, Chi SB, Hyeong K, Park CK, Kim KH, Oh JK (2006) Physical properties of surface sediments from the KR(Korea reserved) 5area, northeastern equatorial pacific(in Korean). Ocean Polar Res 28(4):475–484

    Article  Google Scholar 

  • Lee TH, Jung JJ, Hong S, Kim HW, Choi JS (2007) Prediction for motion of tracked vehicle traveling on soft soil using kriging metamodel. Int J Offshore Polar Eng 17(2):132–138

    Google Scholar 

  • Lee M, Cho S, Choi JS, Kim HW, Hong S, Lee TH (2012) Metamodel-based multidisciplinary design optimization of a deep-sea manganese nodules test miner. J Appl Math: 18

  • Lee SJ, Kim KS, Cho S, Jang J, Lee TH, Hong J (2014) Optimal design of interior permanent magnet synchronous motor considering the manufacturing tolerances using Taguchi robust design. IET Electr Power Appl 8(1):23–8

    Article  Google Scholar 

  • Liang C, Sankararaman S, Mahadevan S (2015) Stochastic multidisciplinary analysis under epistemic uncertainty. J Mech Des 137(2):021404

    Article  Google Scholar 

  • Massey FJ (1951) The Kolmogorov-Smirnov test of goodness of fit. J Am Stat Assoc 46(253):68–78

    Article  MATH  Google Scholar 

  • Murakami H, Watanabe K, Kitano M (1992) A mathematical model for spatial motion of tracked vehicles on soft ground. J Terramech 29:71–81

    Article  Google Scholar 

  • Muro T (1983) Trafficability of tracked vehicle on super weak ground (in Japanese). Mem Fac Eng 10(2):329–338

    Google Scholar 

  • Neal RM (2003) Slice sampling. Ann Stat 31(3):705–767

    Article  MathSciNet  MATH  Google Scholar 

  • Nguyen TH, Song JH, Paulino GH (2009) Single-loop system reliability-based design optimization using matrix-based system reliability method theory and applications. J Mech Des 132(1):11005–11

    Article  Google Scholar 

  • Padmanabhan D, Batill S (2002) Decomposition strategies for reliability based optimization in multidisciplinary system design. In: Proceedings of the ninth AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, Georgia 77–83

  • Park GJ (2006) Analytic methods for design practice. Springer, New York

    Google Scholar 

  • Parkinson A, Sorensen C, Pourhassan N (1993) A general approach for robust optimal design. J Mech Des 115(1):74–80

    Article  Google Scholar 

  • Rao SS (1992) Reliability-based design. McGraw-Hill, New York

    Google Scholar 

  • Sankararaman S, Mahadevan S (2011) Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data. Reliab Eng Syst Saf 96(7):814–824

    Article  Google Scholar 

  • Scott F, Cliff AJ, Jon CH, William LO, Kari S (2004) Summary from the epistemic uncertainty workshop: consensus amid diversity. Reliab Eng Syst Saf 85:355–369

    Article  Google Scholar 

  • Taguchi G, Yokoyama Y, Wu Y (1983) Taguchi methods: design of experiments. American Supplier Institute Press, Michigan

    Google Scholar 

  • Tang Y, Chen J, Wei J (2012) A sequential algorithm for reliability-based robust design optimization under epistemic uncertainty. J Mech Des 134(1)

  • Thunnissen DP (2005) Propagating and mitigating uncertainty in the design of complex multidisciplinary systems, PhD dissertation, California Institute of Technology

  • Yao W, Chen X, Luo W, Tooren M, Guo J (2011) Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles. Prog Aerosp Sci 47(6):450–479

    Article  Google Scholar 

  • Yi SI, Shin JK, Park GJ (2008) Comparison of MDO methods with mathematical examples. Struct Multidiscip Optim 35(5):391–402

    Article  Google Scholar 

  • Youn BD, Choi KK (2004) An investigation of nonlinearity of reliability-based design optimization approaches. J Mech Des 126:403–411

    Article  Google Scholar 

  • Youn BD, Choi KK and Du L (2005) Enriched performance measure approach for reliability-based design optimization. J AIAA 43(4): 874–884

Download references

Acknowledgments

This study was initiated from an R&D Project, “Development of CAE technology for topside equipment of offshore plant”, sponsored by the Korea Research Institute of Ships & Ocean Engineering (KRISO). The authors are grateful for the full support shown for this research work.

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Authors and Affiliations

  1. Department of Automotive Engineering, College of Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul, 04763, South Korea

    Su-gil Cho, Junyong Jang, Shinyu Kim, Sanghyun Park, Tae Hee Lee & Minuk Lee

  2. Offshore Plant Research Division, Korea Research Institute Ships and Ocean Engineering, Daejeon, 305-343, South Korea

    Jong-Su Choi

  3. Technology Center for Offshore Plant Industries, Korea Research Institute Ships and Ocean Engineering, Daejeon, 305-343, South Korea

    Su-gil Cho, Sanghyun Park, Hyung-Woo Kim & Sup Hong

Authors
  1. Su-gil Cho
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  2. Junyong Jang
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  3. Shinyu Kim
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  4. Sanghyun Park
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  5. Tae Hee Lee
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  6. Minuk Lee
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  7. Jong-Su Choi
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  8. Hyung-Woo Kim
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  9. Sup Hong
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Correspondence to Tae Hee Lee.

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This paper will be submitted to Structural and Multidisciplinary Optimization

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Cho, Sg., Jang, J., Kim, S. et al. Nonparametric approach for uncertainty-based multidisciplinary design optimization considering limited data. Struct Multidisc Optim 54, 1671–1688 (2016). https://doi.org/10.1007/s00158-016-1540-0

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  • DOI: https://doi.org/10.1007/s00158-016-1540-0

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