Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1625–1641 | Cite as

A modified importance sampling method for structural reliability and its global reliability sensitivity analysis

  • Wanying Yun
  • Zhenzhou Lu
  • Xian Jiang


The importance sampling method is an extensively used numerical simulation method in reliability analysis. In this paper, a modification to the importance sampling method (ISM) is proposed, and the modified ISM divides the sample set of input variables into different subsets based on the contributive weight of the importance sample defined in this paper and the maximum super-sphere denoted by β-sphere in the safe domain defined by the truncated ISM. By this proposed modification, only samples with large contributive weight and locating outside of the β-sphere need to call the limit state function. This amelioration remarkably reduces the number of limit state function evaluations required in the simulation procedure, and it doesn’t sacrifice the precision of the results by controlling the level of relative error. Based on this modified ISM and the space-partition idea in variance-based sensitivity analysis, the global reliability sensitivity indices can be estimated as byproducts, which is especially useful for reliability-based design optimization. This process of estimating the global reliability sensitivity indices only needs the sample points used in reliability analysis and is independent of the dimensionality of input variables. A roof truss structure and a composite cantilever beam structure are analyzed by the modified ISM. The results demonstrate the efficiency, accuracy, and robustness of the proposed method.


Reliability analysis Sensitivity analysis Contributive weight Modification Importance sampling Sample subset Sample reduction 



This work was supported by the Natural Science Foundation of China (Grant 51475370, 51775439) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant CX201708).


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Aircraft Flight Test Technology InstituteChinese Flight Test EstablishmentXi’anChina

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