A decoupling approach for evidence-theory-based reliability design optimization

For the problem of evidence-theory-based reliability design optimization (EBDO), this paper presents a decoupling approach which provides an effective tool for the reliability design of some complex structures with epistemic uncertainty. The approach converts the original nested optimization into a sequential iterative process including design optimization and reliability analysis. In each iteration step, through the uniformity algorithm, the original EBDO is firstly transformed to a conventional reliability-based design optimization (RBDO) and an optimal solution is obtained by solving it. At the solution, the first-order approximate reliability analysis method (FARM) is then used to perform the evidence-theory-based reliability analysis for each constraint. In addition, the RBDO solving and the evidence-theory-based reliability analysis are carried out alternately until reaching the convergence. Finally, two numerical examples and a practical engineering application show the effectiveness of the proposed method.

[1]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[2]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[3]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[4]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[5]  L. A. Zadeh,et al.  A note on prototype theory and fuzzy sets , 1982, Cognition.

[6]  W. Dong,et al.  Vertex method for computing functions of fuzzy variables , 1987 .

[7]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[8]  T. Cruse,et al.  Advanced probabilistic structural analysis method for implicit performance functions , 1990 .

[9]  Arie Tzvieli.  Possibility theory: An approach to computerized processing of uncertainty , 1990, J. Am. Soc. Inf. Sci..

[10]  William F. Caselton,et al.  Decision making with imprecise probabilities: Dempster‐Shafer Theory and application , 1992 .

[11]  I. Elishakoff,et al.  Combination of probabilistic and convex models of uncertainty when scarce knowledge is present on acoustic excitation parameters , 1993 .

[12]  F. O. Hoffman,et al.  Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[13]  J. Kacprzyk,et al.  Advances in the Dempster-Shafer theory of evidence , 1994 .

[14]  George J. Klir,et al.  Uncertainty-Based Information , 1999 .

[15]  Woodrow Barfield,et al.  Fundamentals of Wearable Computers and Augumented Reality , 2000 .

[16]  Kari Sentz,et al.  Combination of Evidence in Dempster-Shafer Theory , 2002 .

[17]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[18]  Ramana V. Grandhi,et al.  Structural Design Optimization Based on Reliability Analysis Using Evidence Theory , 2003 .

[19]  John E. Renaud,et al.  Uncertainty quantification using evidence theory in multidisciplinary design optimization , 2004, Reliab. Eng. Syst. Saf..

[20]  J. Tu,et al.  A Single-Loop Method for Reliability-Based Design Optimization , 2004, DAC 2004.

[21]  George J. Klir,et al.  On Measuring Uncertainty and Uncertainty-Based Information: Recent Developments , 2001, Annals of Mathematics and Artificial Intelligence.

[22]  Wei Gao,et al.  Reliability-Based Optimization of Active Nonstationary Random Vibration Control , 2005 .

[23]  G. Cheng,et al.  A sequential approximate programming strategy for reliability-based structural optimization , 2006 .

[24]  Z. Mourelatos,et al.  A Design Optimization Method Using Evidence Theory , 2006, DAC 2005.

[25]  Xiaoping Du,et al.  Uncertainty Analysis With Probability and Evidence Theories , 2006, DAC 2006.

[26]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

[27]  Xiaoping Du,et al.  Sensitivity Analysis with Mixture of Epistemic and Aleatory Uncertainties , 2007 .

[28]  Ramana V. Grandhi,et al.  Gradient projection for reliability-based design optimization using evidence theory , 2008 .

[29]  G. Gary Wang,et al.  Reliable design space and complete single-loop reliability-based design optimization , 2008, Reliab. Eng. Syst. Saf..

[30]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[31]  Xu Guo,et al.  Confidence extremal structural response analysis of truss structures under static load uncertainty via SDP relaxation , 2009 .

[32]  Xu Guo,et al.  Confidence structural robust design and optimization under stiffness and load uncertainties , 2009 .

[33]  Z. Kang,et al.  Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models , 2009 .

[34]  A. Kiureghian,et al.  Aleatory or epistemic? Does it matter? , 2009 .

[35]  Baoding Liu.  Uncertain Risk Analysis and Uncertain Reliability Analysis , 2010 .

[36]  F. Tin-Loi,et al.  Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method , 2011 .

[37]  C. Jiang,et al.  Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique , 2011 .

[38]  Kalyanmoy Deb,et al.  An EA-based approach to design optimization using evidence theory , 2011, GECCO '11.

[39]  Liping Chen,et al.  Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions , 2013 .

[40]  Qiu Zhiping,et al.  Structural reliability analysis and reliability-based design optimization: Recent advances , 2013 .

[41]  Xiaoqian Chen,et al.  A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory , 2013 .

[42]  Masoud Rais-Rohani,et al.  Optimization of structures under material parameter uncertainty using evidence theory , 2013 .

[43]  Xu Han,et al.  A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty , 2013 .

[44]  Nong Zhang,et al.  Interval multi-objective optimisation of structures using adaptive Kriging approximations , 2013 .

[45]  Xue Han,et al.  First and second order approximate reliability analysis methods using evidence theory , 2015, Reliab. Eng. Syst. Saf..

[46]  Zhen Luo,et al.  An incremental shifting vector approach for reliability-based design optimization , 2016 .

[47]  Chao Jiang,et al.  A reliability-based design optimization method for structures using evidence theory , 2016 .