Skip to main content
SpringerLink
Log in

Mixed uncertainty based analytical target cascading: an approach for hierarchical multilevel optimization under probabilistic and interval mixed uncertainties

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Analytical target cascading (ATC) has been extended to the probabilistic formulation to deal with the hierarchical multilevel optimization problem under uncertainty. However, only aleatory uncertainties can be handled by the probabilistic theory. Considering both aleatory and epistemic uncertainties exist in engineering design, a mixed uncertainty based analytical target cascading (MUATC) approach is proposed in this paper. The probability distribution and interval are used to represent the aleatory uncertainties and epistemic uncertainties, respectively. To figure out the mixed uncertainty propagation(MUP) problem, the reliability index approach based MUP (RIA-MUP) and performance measurement approach based MUP (PMA-MUP) are proposed firstly. Based on PMA-MUP, the MUATC method is established. MUATC firstly decouples the mixed uncertainty all-in-one (MUAIO) problem into deterministic optimization problem and mixed uncertainty analysis, and then hierarchically decomposes them into subproblems. All-in-one (AIO) mixed uncertainty analysis and hierarchically mixed uncertainty analysis methods are established to calculate the characteristic of the interrelated responses and shared variables. The accuracy and effectiveness of MUATC are demonstrated with three examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Ahn J, Kwon J (2006) An efficient strategy for reliability-based multidisciplinary design optimization using BLISS. Struct Multidiscip Optim 31:363–372

    Article  Google Scholar 

  • Bailing RJ, Sobieszczanski-Sobieski J (1994) An algorithm for solving the system-level problem in multilevel optimization. Institute for Computer Applications in Science and Engineering (ICASE), Hampton

  • Beyer H, Sendhoff B (2007) Robust optimization – a comprehensive survey. Comput Methods Appl Mech 196:3190–3218. https://doi.org/10.1016/j.cma.2007.03.003

    Article  MathSciNet  MATH  Google Scholar 

  • Chiralaksanakul A, Mahadevan S (2007) Decoupled approach to multidisciplinary design optimization under uncertainty. Optim Eng 8:21–42

    Article  MathSciNet  MATH  Google Scholar 

  • Choi S, Grandhi RV, Canfield RA (2007) Reliability-based structural design. Springer London. https://doi.org/10.1007/978-1-84628-445-8

  • Du X (2008) Unified uncertainty analysis by the first order reliability method. J Mech Des 130:1404

    Google Scholar 

  • Du X, Sudjianto A, Huang B (2005) Reliability-based design with the mixture of random and interval variables. J Mech Des 127:1068–1076

    Article  Google Scholar 

  • Du X, Guo J, Beeram H (2008) Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip Optim 35:117–130

    Article  MathSciNet  MATH  Google Scholar 

  • He L, Huang H, Du L, Zhang X, Miao Q (2007) A review of possibilistic approaches to reliability analysis and optimization in engineering design. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Helton JC, Oberkampf WL (2004) Alternative representations of epistemic uncertainty. Reliab Eng Syst Saf 85:1–10

    Article  Google Scholar 

  • Helton JC, Johnsonb JD, Oberkampf WL (2004) An exploration of alternative approaches to the representation of uncertainty in model predictions. Reliab Eng Syst Saf 85:39–71

    Article  Google Scholar 

  • Kim HM (2001) Target cascading in optimal system design. Ph.D Dissertation, University of Michigan

  • Kim HM, Michelena NF, Papalambros PY, Jiang T (2003) Target cascading in optimal system design. J Mech Des 125:474–480

    Article  Google Scholar 

  • Klir GJ, Smith RM (2001) On measuring uncertainty and uncertainty-based information: recent developments. Ann Math Artif Intell 32:1012–2443

    Article  MathSciNet  MATH  Google Scholar 

  • Li Y, Jiang P, Gao L, Shao X (2013) Sequential optimisation and reliability assessment for multidisciplinary design optimisation under hybrid uncertainty of randomness and fuzziness. J Eng Des 24:363–382

    Article  Google Scholar 

  • Liu P, Der Kiureghian A (1991) Optimization algorithms for structural reliability. Struct Saf 9:161–177

    Article  Google Scholar 

  • Liu H, Chen W, Kokkolaras M et al (2006) Probabilistic analytical target cascading: a moment matching formulation for multilevel optimization under uncertainty. J Mech Des 128:503–508

    Article  Google Scholar 

  • McAllister CD, Simpson TW (2003) Multidisciplinary robust design optimization of an internal combustion engine. J Mech Des 125:124–130

    Article  Google Scholar 

  • Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to interval analysis. SIAM Press, Philadelphia

    Book  MATH  Google Scholar 

  • Mourelatos Z, Zhou J (2006) A design optimization method using evidence theory. J Mech Des 128:901–908

    Article  Google Scholar 

  • Nikolaidis E, Chen S, Cudney H, Haftka RT, Rosca R (2004) Comparison of probability and possibility for design against catastrophic failure under uncertainty. J Mech Des 126:386–394

    Article  Google Scholar 

  • Ouyang Q, Chen X, Yao W (2014) Sequential probabilistic analytical target cascading method for hierarchical multilevel optimization under uncertainty. Struct Multidiscip Optim 49:267–280

    Article  MathSciNet  Google Scholar 

  • Padmanabhan D, Batill S (2002) Reliability based optimization using approximations with applications to multi-disciplinary system design. In: 40th Aerospace Sciences Meeting and Exhibit, Reno, Nevada. AIAA-2002-0449

  • Padula SL, Alexandrov N, Green LL (1996) MDO test suite at nasa langley research center. In: 6th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization. AIAA-1996-4028

  • Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23:470–472

    Article  MathSciNet  MATH  Google Scholar 

  • Xiong F, Yin X, Chen W, Yang S (2010) Enhanced probabilistic analytical target cascading with application to multi-scale design. Eng Optim 42:581–592

    Article  Google Scholar 

  • Yao W (2013) Sequential optimization and mixed uncertainty analysis method for reliability-based optimization. AIAA J 51:2266–2277

    Article  Google Scholar 

  • Yao W, Chen X, Ouyang Q, van Tooren M (2013a) A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory. Struct Multidiscip Optim 48:339–354. https://doi.org/10.1007/s00158-013-0901-1

    Article  MathSciNet  Google Scholar 

  • Yao W, Chen X, Huang Y, van Tooren M (2013b) An enhanced unified uncertainty analysis approach based on first order reliability method with single-level optimization. Reliab Eng Syst Saf 116:28–37. https://doi.org/10.1016/j.ress.2013.02.014

    Article  Google Scholar 

  • Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang X, Huang HZ (2009) Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties. Struct Multidiscip Optim 40:165–175

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Natural Science Foundation of China under Grant No. 51675525.

Author information

Authors and Affiliations

  1. Beijing Aerospace Control Center, Beijing, 100094, China

    Qi Ouyang

  2. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China

    Wen Yao & Xiaoqian Chen

Authors
  1. Qi Ouyang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoqian Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qi Ouyang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ouyang, Q., Yao, W. & Chen, X. Mixed uncertainty based analytical target cascading: an approach for hierarchical multilevel optimization under probabilistic and interval mixed uncertainties. Struct Multidisc Optim 57, 1475–1493 (2018). https://doi.org/10.1007/s00158-017-1820-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-017-1820-3

Keywords

Search

Navigation