Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1593–1610 | Cite as

A novel first–order reliability method based on performance measure approach for highly nonlinear problems

  • Gang Li
  • Bin Li
  • Hao Hu


The first–order reliability method (FORM) is widely used in structural reliability analysis for its simplicity and efficiency. It can be solved by gradient–based algorithms, on which the nonlinear degree of performance functions may have a great influence. On the other hand, evolutionary algorithms could achieve convergence solutions even for highly nonlinear performance function, usually with expensive computational cost. To overcome their drawbacks, we propose a new reliability analysis method called PMA–IACC to search the most probable failure point (MPP). As the inverse reliability analysis and reliability analysis are reversible each other, the performance measure approach (PMA) of the inverse reliability analysis could be used for the reliability analysis based on the multi–objective optimization theory. To enhance the efficiency and robustness of the inverse reliability, the improved adaptive chaos control (IACC) method is proposed and then it is integrated into the PMA reliability analysis strategy. Five illustrative examples, including three two–dimensional problems and two multi–dimensional problems, demonstrate the outstanding efficiency and robustness of the PMA–IACC over other prevalent approaches.


Reliability analysis First–order reliability method Performance measure approach Improved adaptive chaos control High nonlinearity 



The support of the National Basic Research Program of China (Grant Nos. 2014CB046506 and 2014CB046803) and the National Natural Science Foundation of China of 11372061 is greatly appreciated. The authors also thank Professor Gengdong Cheng, Professor Dixiong Yang for their comments and discussion to guarantee the quality of this paper.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina
  2. 2.School of Civil EngineeringYancheng Institute of TechnologyYanchengChina

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