Skip to main content
SpringerLink
Log in

A direct decoupling approach for efficient reliability-based design optimization

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

Abstract

This paper develops an efficient methodology to perform reliability-based design optimization (RBDO) by decoupling the optimization and reliability analysis iterations that are nested in traditional formulations. This is achieved by approximating the reliability constraints based on the reliability analysis results. The proposed approach does not use inverse first-order reliability analysis as other existing decoupled approaches, but uses direct reliability analysis. This strategy allows a modular approach and the use of more accurate methods, including Monte-Carlo-simulation (MCS)-based methods for highly nonlinear reliability constraints where first-order reliability approximation may not be accurate. The use of simulation-based methods also enables system-level reliability estimates to be included in the RBDO formulation. The efficiency of the proposed RBDO approach is further improved by identifying the potentially active reliability constraints at the beginning of each reliability analysis. A vehicle side impact problem is used to examine the proposed method, and the results show the usefulness of the proposed 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

  • Aktas E, Moses F, Gohsn M (2001) Cost and safety optimization of structural design specifications. Reliab Eng Syst Saf 73:205–212

    Article  Google Scholar 

  • Al-Harthy AS, Frangopol DM (1997) Integrating system reliability and optimization in prestressed concrete design. Comput Struct 64(1–4):729–735

    MATH  Google Scholar 

  • Breitung K (1984) Asymptotic approximations for multinormal integrals. J Eng Mech ASCE 110(3):357–366

    Article  Google Scholar 

  • Bucher CG (1988) Adaptive sampling—an iterative fast Monte Carlo procedure. Struct Saf 5:119–126

    Google Scholar 

  • Chen X, Hasselman TK, Neill DJ (1997) Reliability based structural design optimization for practical applications. In: Proceedings, 38th AIAA/ASME/ASCE/AHS/ASC Structures, structural dynamics, and materials conference and exhibit, Orlando, FL

  • Choi KK, Yu X, Chang K (1996) A mixed design approach for probabilistic structural durability. In: 6th AIAA/USAF/NASA/ISSMO Symposium on multidisciplinary analysis and optimization. Bellevue, WA, pp 785–795

    Google Scholar 

  • Cornell CA (1967) Bounds on the reliability of structural systems. J Struct Eng 93(ST1):171–200

    Google Scholar 

  • Dey A, Mahadevan S (1998) Ductile structural system reliability analysis using adaptive importance sampling. Struct Saf 20:137–154

    Google Scholar 

  • Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. ASME J Mech Des 126(2):225–233

    Google Scholar 

  • Gu L, Yang RJ, Tho CH, Makowski M, Faruque O, Li Y (2001) Optimization and robustness for crashworthiness of side impact. Int J Veh Des 26(4):348–360

    Google Scholar 

  • Haldar A, Mahadevan S (2000) Probability statistics and reliability in engineering design. Wiley, New York

    Google Scholar 

  • Hunter D (1976) An upper bound for the probability of a union. J Appl Probab 3(3):597–603

    MathSciNet  Google Scholar 

  • Insurance Institute for Highway Safety, Side Impact Test Program Rating Guidelines, April 2004

  • Karamchandani A, Bjerager P, Cornell CA (1989) Adaptive importance sampling. In: Ang AH-S, Shinozuka M, Schuëller GI (eds) 5th International conference on structural safety and reliability. ASCE, pp 855–862

  • Köylüǧlu HU, Nielsen SRK (1988) New approximations for SORM integrals. Struct Saf 5:119–126

    Google Scholar 

  • Kuschel N, Rackwitz R (2000) A new approach for structural optimization of series systems. In: Melchers RE, Stewart MG (eds) Applications of statistics and probability. Balkema, Rotterdam, pp 987–994

    Google Scholar 

  • Leheta HW, Mansour AE (1997) Reliability-based method for optimal structural design of stiffened panels. Mar Struct 10:323–352

    Google Scholar 

  • Liang J, Mourelatos ZP, Tu J (2004) A single loop method for reliability-based design optimization. Proceedings of the 30th ASME design automation conference, Salt Lake City, UT, September. Paper no. DETC2004/DAC-57255

  • Mahadevan S, Liu X (1998) Probabilistic optimum design of composite laminates. J Compos Mater 32(1):68–82

    Google Scholar 

  • Mahadevan S (1992) Probabilistic optimum design of framed structures. Comput Struct 42(3):365–374

    Article  Google Scholar 

  • Melchers RE (1989) Improved importance sampling methods for structural system reliability calculation. In: Proceedings of ICOSSAR'89, the 5th international conference on structural safety and reliability. ASCE, New York, pp 1185–1192

    Google Scholar 

  • Miki M, Murotsu Y, Tanaka T, Shao S (1997) Reliability-based optimization of fibrous laminated composites. Reliab Eng Syst Saf 56:285–290

    Article  Google Scholar 

  • Nash SG, Sofer A (1996) Linear and nonlinear programming. McGraw-Hill, New York

    Google Scholar 

  • Oakley DR, Sues RH, Rhodes GS (1998) Performance optimization of multidisciplinary mechanical systems subject to uncertainties. Probab Eng Mech 13(1):15–26

    Google Scholar 

  • Pu Y, Das PK, Faulkner D (1997) A strategy for reliability-based optimization. Eng Struct 19:276–282

    Article  Google Scholar 

  • Rackwitz R, Fiessler B (1978) Reliability under combined random load sequences. Comput Struct 9(5):489–494

    Article  MATH  Google Scholar 

  • Royset JO, Der Kiureghian A, Polak E (2001) Reliability-based optimal structural design by the decoupling approach. Reliab Eng Syst Saf 73:213–221

    Article  Google Scholar 

  • Schuëller GI, Pradlwarter HJ, Bucher CG (1991) Efficient computational procedures for reliability estimate of MDOF-systems. Int J Nonlinear Opt Phys 26(6):961–974

    MATH  Google Scholar 

  • Tu J, Choi KK (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564

    Google Scholar 

  • Tu J, Choi KK, Park YH (2001) Design potential method for robust system parameter design. AIAA J 39(4):667–677

    Google Scholar 

  • Tvedt L (1990) Distribution of quadratic forms in normal space-application to structural reliability. J Eng Mech 116(6):1183–1197

    Google Scholar 

  • Wu Y-T (1994) Computational methods for efficient structural reliability and reliability sensitivity analysis. AIAA J 32(8):1717–1723

    Article  MATH  Google Scholar 

  • Zou T, Mahadevan S, Mourelatos Z, Meernik P (2002) Reliability analysis of automotive body-Door Subsystem. Reliab Eng Syst Saf 78(3):315–324

    Article  Google Scholar 

  • Zou T, Mahadevan S (2005) An efficient formulation for multi-objective RBDO. In: Proceedings of SAE World Congress, Detroit, MI.

Download references

Author information

Authors and Affiliations

  1. Vanderbilt University, Nashville, TN, USA

    T. Zou & S. Mahadevan

Authors
  1. T. Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Mahadevan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Mahadevan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zou, T., Mahadevan, S. A direct decoupling approach for efficient reliability-based design optimization. Struct Multidisc Optim 31, 190–200 (2006). https://doi.org/10.1007/s00158-005-0572-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-005-0572-7

Keywords

Search

Navigation