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A new method for evaluating Borgonovo moment-independent importance measure with its application in an aircraft structure

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  • Zhang, Leigang
  • Lu, Zhenzhou
  • Cheng, Lei
  • Fan, Chongqing

Abstract

The moment-independent importance measure proposed by Borgonovo, which is defined as the average shift between the unconditional and conditional probability density functions (PDFs) of model output, is widely used to evaluate the influence of input uncertainty on the entire output distribution. And how to exactly and efficiently estimate the PDFs remains a crucial and challenging problem. In this paper, a novel PDF estimation based method is proposed to efficiently evaluate the moment-independent index. Firstly, the PDF of the model output is obtained based on the concepts of maximum entropy, fractional moment and high dimensional model representation. Secondly, the Nataf transformation is utilized to estimate the joint PDF of the output and input variable. Finally, the index can be easily computed using the generated correlated standard normal samples. Thus the importance measure can be calculated with high efficiency and accuracy using this proposed composited method. Several examples are employed to demonstrate the advantages of the proposed method. Meanwhile, the importance analysis of a stiffening rib of the wing leading edge in a certain aircraft also verifies its good engineering applicability.

Suggested Citation

  • Zhang, Leigang & Lu, Zhenzhou & Cheng, Lei & Fan, Chongqing, 2014. "A new method for evaluating Borgonovo moment-independent importance measure with its application in an aircraft structure," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 163-175.
    • Handle: RePEc:eee:reensy:v:132:y:2014:i:c:p:163-175
    DOI: 10.1016/j.ress.2014.07.011
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    References listed on IDEAS

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    1. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    2. Liu, Qiao & Homma, Toshimitsu, 2009. "A new computational method of a moment-independent uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1205-1211.
    3. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    4. Wei, Pengfei & Lu, Zhenzhou & Yuan, Xiukai, 2013. "Monte Carlo simulation for moment-independent sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 60-67.
    5. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
    6. Andrea Saltelli, 2002. "Sensitivity Analysis for Importance Assessment," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 579-590, June.
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    1. Derennes, Pierre & Morio, Jérôme & Simatos, Florian, 2021. "Simultaneous estimation of complementary moment independent and reliability-oriented sensitivity measures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 721-737.
    2. Liu, Jie & Hu, Yifeng & Xu, Can & Jiang, Chao & Han, Xu, 2016. "Probability assessments of identified parameters for stochastic structures using point estimation method," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 51-58.
    3. López-Benito, Alfredo & Bolado-Lavín, Ricardo, 2017. "A case study on global sensitivity analysis with dependent inputs: The natural gas transmission model," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 11-21.
    4. Xing Pan & Lunhu Hu & Ziling Xin & Shenghan Zhou & Yanmei Lin & Yong Wu, 2018. "Risk Scenario Generation Based on Importance Measure Analysis," Sustainability, MDPI, vol. 10(9), pages 1-18, September.
    5. Yun, Wanying & Lu, Zhenzhou & Jiang, Xian, 2019. "An efficient method for moment-independent global sensitivity analysis by dimensional reduction technique and principle of maximum entropy," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 174-182.
    6. Wei, Pengfei & Song, Jingwen & Lu, Zhenzhou & Yue, Zhufeng, 2016. "Time-dependent reliability sensitivity analysis of motion mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 107-120.
    7. Yun, Wanying & Lu, Zhenzhou & Feng, Kaixuan & Li, Luyi, 2019. "An elaborate algorithm for analyzing the Borgonovo moment-independent sensitivity by replacing the probability density function estimation with the probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 99-108.
    8. Cai, Zhiqiang & Si, Shubin & Sun, Shudong & Li, Caitao, 2016. "Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 248-258.
    9. Cheng, Lei & Lu, Zhenzhou & Zhang, Leigang, 2015. "Application of Rejection Sampling based methodology to variance based parametric sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 9-18.
    10. Yicheng Zhou & Zhenzhou Lu & Yan Shi & Kai Cheng, 2019. "A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output," Journal of Risk and Reliability, , vol. 233(3), pages 338-354, June.
    11. Weng, Ye-Yao & Liu, Teng & Zhang, Xuan-Yi & Zhao, Yan-Gang, 2025. "Probability density estimation of polynomial chaos and its application in structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
    12. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    13. Derennes, Pierre & Morio, Jérôme & Simatos, Florian, 2019. "A nonparametric importance sampling estimator for moment independent importance measures," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 3-16.
    14. Rongyao Song & Tong Yan & Xiaoyi Wang & Wenxuan Wang, 2024. "An efficient approximate optimization algorithm and its application to non-probabilistic reliability importance measures," Journal of Risk and Reliability, , vol. 238(2), pages 401-416, April.
    15. Zhao, Yan-Gang & Zhang, Xuan-Yi & Lu, Zhao-Hui, 2018. "A flexible distribution and its application in reliability engineering," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 1-12.

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