Skip to main content
Log in

A new reliability analysis method based on the conjugate gradient direction

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

Abstract

Reliability-based design optimization (RBDO) is an important area in structural optimization. A principal step of the RBDO process is to solve a reliability analysis problem. This problem has been considered in inner loop of double-loop RBDO approaches. Although many algorithms have been developed for solving this problem, there are still some challenges. Existing algorithms do not have good convergence rates and often diverge. There is a need to develop more efficient and stable algorithms that can be used for evaluating all performance functions sufficiently. In this paper, a new method, called “Conjugate Gradient Analysis (CGA) Method”, is proposed to apply in the reliability analysis problems. This method is based on the conjugate gradient method. Some mathematical problems are provided in order to demonstrate the advantages of the proposed method compared with the existing methods.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Aoues Y, Chateauneuf A (2010) Benchmark Study of Numerical Methods for Reliability-Based Design Optimization. Structual Multidiscip Optim 41:227–294

    MathSciNet  Google Scholar 

  • Arora JS (2012) Introduction to Optimum Design. Acad Press, Waltham

    Google Scholar 

  • Axelsson O (1996) Iterative Solution Methods. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Ayyub BM, McCuen RH (2011) Probability, Statistics and Reliability for Engineers and Scientists. CRC Press, Boca Raton

    Google Scholar 

  • Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming theory and algorithms. Wiley InterScience, Hoboken

    Book  MATH  Google Scholar 

  • Chen D, Hasselman TK, Neill FJ (1997) Reliability-Based Structural Design Optimization for Practical Application, 38th AIAA/ASME/ASCE/AHA/ASC Structures, Structural Dynamics and Material Conference

  • Cheng G, Xu L, Jiang L (2006) A Sequential Approximate Programming Strategy for Reliability-Based Structural Optimization. Comput Struct 84(21):1353–1367

    Article  Google Scholar 

  • Choi KK, Youn BD (2002) On Probabilistic Approaches for Reliability-Based Design Optimization, 9th AIAA/NASA/USA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, USA

  • Crowder H, Wolfe Ph (1972) Linear Convergence of the Conjugate Gradient Method. IBM Research Center, New York

    Google Scholar 

  • Du X, Chen W (2004) Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design. J Mech Des 126:225–233

    Article  Google Scholar 

  • Enevoldsen I, Sorensen JD (1994) Reliability-Based Optimization in Structural Engineering. Struct Saf 15(3):169–196

    Article  Google Scholar 

  • Frangopol DM, Tsompanakis Y, Lagaros ND, Papadrakakis M (2008), Structural Design Optimization Considering Uncertainties, Taylor and Francis

  • Guo X, Bai W, Zhang W (2009a) Confidence Extremal Structural Response Analysis of Truss Structures under Static Load Uncertainty via SDP Relaxation. Comput Struct 87:246–253

    Article  Google Scholar 

  • Guo X, Bai W, Zhang W, Gao X (2009b) Confidence Structural Robust Design and Optimization under Stiffness and Load Uncertainties. Comput Methods Appl Mech Eng 198:3378–3399

    Article  MATH  MathSciNet  Google Scholar 

  • Hasofer AM, Lind NC (1974) Exact and Invariant Second-Moment Code Format. J Eng Mech 100(1):111–121

    Google Scholar 

  • Hohenbichler M, Rackwitz R (1981) Nonnormal Dependent Vectors in Structural Reliability, Journal of Engineering Mechanics Division. ASCE 107(6):1227–1238

    Google Scholar 

  • Lee TW, Kwak BM (1987) A Reliability Based Optimal Design Using Advanced First Order Second Moment Method. Mech Struct Mach 15(4):523–542

    Article  Google Scholar 

  • Liu PL, Kiureghian AD (1991) Optimization Algorithms for Structural Reliability. Struct Saf 9:161–177

    Article  Google Scholar 

  • Madsen HO, Krenk S, Lind NC (1986) Methods of Structural Safety. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Madsen HO, Friis Hansen F (1992) A Comparison of Some Algorithms of reliability-based design optimization, 4th IFIP WG 7.5 Conference. Springer-Verlag, Munich, pp 443–451

    Google Scholar 

  • Nikoladis E, Burdisso R (1988) Reliability-Based Optimization: a Safety Index Approach. Comput Struct 28(6):781–788

    Article  Google Scholar 

  • Powell MJD (1976) Some Convergence Properties of the Conjugate Gradient Method. Math Program 11(1):42–49

    Article  MATH  Google Scholar 

  • Rackwitz R, Fiessler B (1978) Structural Reliability Under Combined Load Sequences. Comput Struct 9:489–494

    Article  MATH  Google Scholar 

  • Snyman JA (2005) Practical Mathematical Optimization. Springer

  • Sun W, Yuan YX (2006) Optimization Theory and Methods: Nonlinear Programming, Springer Optimization and Its Applications

  • Tu J, Choi KK (1997) A performance measure approach in reliability based structural optimizatioin, University of Iowa

  • Tu J, Choi KK (1999) A New Study on Reliability-Based Design Optimization, Journal of Mechanical Design. ASME 121(4):557–564

    Article  Google Scholar 

  • Wang H, Gong Z, Huang HZ, Zhang Z, Lv Z (2012) System Reliability Based Design Optimization with Monte Carlo Simulation. IEEE J 12:1143–1147

    Google Scholar 

  • Wolfe PH (1969) Convergence Conditions for Ascent Methods. SIAM Rev 11(2):226–235

    Article  MATH  MathSciNet  Google Scholar 

  • Wolfe PH (1971) Convergence Conditions for Ascent Methods: II. Some Corrections. SIAM Rev 13(2):185–188

    Article  MATH  MathSciNet  Google Scholar 

  • Youn BD, Choi KK, Park YH (2003) Hybrid analysis method for reliability-based design optimization. J Mech Des ASME 125:221–232

    Article  Google Scholar 

  • Youn BD, Choi KK (2004a) An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches, Journal of Mechanical Design. ASME 126:403–411

    Article  Google Scholar 

  • Youn BD, Choi KK (2004b) Selecting Probabilistic Approaches for Reliability-Based Design Optimization. AIAA J 42(1):124–131

    Article  Google Scholar 

  • Zhang J, Du X (2010) A Second-Order Reliability Method with First-Order Efficiency. J Mech Des:132

  • Zhang J, Du X (2011) Time-Dependent Reliability Analysis for Function Generator Mechanisms. J Mech Des:133

Download references

Acknowledgments

This research is partially supported by National ICT Australia (NICTA).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ghasem Ezzati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ezzati, G., Mammadov, M. & Kulkarni, S. A new reliability analysis method based on the conjugate gradient direction. Struct Multidisc Optim 51, 89–98 (2015). https://doi.org/10.1007/s00158-014-1113-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-014-1113-z

Keywords

Navigation