Skip to main content
SpringerLink
Log in

An inverse analysis method for design optimization with both statistical and fuzzy uncertainties

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

If the statistical data for the input uncertainties are sufficient to construct the distribution function, the input uncertainties can be treated as random variables to use the reliability-based design optimization (RBDO) method; otherwise, the input uncertainties can be treated as fuzzy variables to use the possibility-based design optimization (PBDO) method. However, many structural design problems include both input uncertainties with sufficient and insufficient data. This paper proposes a new mixed-variable design optimization (MVDO) method using the performance measure approach (PMA) for such design problems. For the inverse analysis, this paper proposes a new most probable/possible point (MPPP) search method called maximal failure search (MFS), which is an integration of the enhanced hybrid mean value method (HMV+) and maximal possibility search (MPS) method. This paper also improves the HMV+ method using an angle-based interpolation. Mathematical and physical examples are used to demonstrate the proposed inverse analysis method and MVDO method.

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

Similar content being viewed by others

References

  • Ben-Haim Y, Elishakoff I (1990) Convex methods of uncertainty in applied mechanics. Elsevier, Amsterdam

    Google Scholar 

  • Choi KK, Youn BD, Du L (2005a) Integration of reliability- and possibility-based design optimizations using performance measure approach. Keynote paper 2005 SAE World Congress, Detroit, MI, 11–14 April 2005also in 2005 SAE Transactions Journal of Passenger Cars, 2005-01-0342

  • Choi KK, Du L, Youn BD, Gorsich D (2005b) Possibility-based design optimization method for design problems with both statistical and fuzzy input data.Sixth World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, 30 May–3 June 2005

  • Du L, Choi KK (2006) Possibility-based design optimization method for design problems with both statistical and fuzzy input data. ASME J 128(4):928–935

    Article  Google Scholar 

  • Du L, Choi KK, Youn BD (2006) An inverse possibility analysis method for possibility-based design optimization. AIAA J 44(11):2682–2690

    Article  Google Scholar 

  • Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic, New York

    MATH  Google Scholar 

  • Dubois D, Prade H (1988) Possibility theory—an approach to computerized processing of uncertainty. Plenum, New York

    MATH  Google Scholar 

  • Hoofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech 100(EMI):111–121

    Google Scholar 

  • Mourelatos ZP, Zhou J (2005) Reliability estimation and design with insufficient data based on possibility theory. AIAA J 43(8):1696–1705

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nikolaidis E, Cudney HH, Chen S, 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 

  • Rosen JB, Suzuki S (1975) Constructions of nonlinear programming test problems. Comm ACM 8:113

    Article  Google Scholar 

  • Schittkowski K (1987) More test examples for nonlinear programming codes. Springer, New York

    MATH  Google Scholar 

  • Vanderplaats GM (1997) DOT User’s Manual. VMA, Colorado Springs

    Google Scholar 

  • Youn BD, Choi KK (2004) Selecting probabilistic approaches for reliability-based design optimization. AIAA J 42(1):124–131

    Article  Google Scholar 

  • Youn BD, Wang PF (2006) Bayesian reliability based design optimization under both aleatory and epistemic uncertainties.11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, VA, 6–8 September 2006

  • Youn BD, Choi KK, Park YH (2001) Hybrid analysis method for reliability-based design optimization. J Mech Des ASME 125(2):221–232 also in Proceedings of 2001 ASME Design Engineering Technical Conferences: 27th Design Automation Conference, Pittsburgh, PA, 2001

    Article  Google Scholar 

  • Youn BD, Choi KK, Gu L, Yang R-J (2004) Reliability-based design optimization for crashworthiness of side impact. Struct Multidisc Optim 26:272–283

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Youn BD, Choi KK, Du L (2005b) Adaptive probability analysis using an enhanced hybrid mean value method. Struct Multidisc Optim 29:134–148

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical & Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA, 52242, USA

    Liu Du & K. K. Choi

Authors
  1. Liu Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. K. Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. K. Choi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Du, L., Choi, K.K. An inverse analysis method for design optimization with both statistical and fuzzy uncertainties. Struct Multidisc Optim 37, 107–119 (2008). https://doi.org/10.1007/s00158-007-0225-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-007-0225-0

Keywords

Search

Navigation