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一种高效计算各类基于方差重要性指标的方法

员婉莹1,吕震宙2,牟珊珊1   

  1. 1. 西北工业大学航空学院
    2. 西工大航空学院
  • 收稿日期:2015-05-14 修回日期:2015-08-04 发布日期:2015-09-08
  • 通讯作者: 吕震宙
  • 基金资助:
    国家自然科学基金项目;高等学校博士学科点专项科研基金项目

An efficient method for estimating various variance-based importance measures

  • Received:2015-05-14 Revised:2015-08-04 Published:2015-09-08

摘要: 为同时计算各类基于方差的重要性测度指标,本文提出了基于空间分割和无迹变换的计算方法,该方法可以重复利用一组样本点近似计算出基于方差的全局灵敏度指标(Sobol指标)、基于方差的区域重要性指标以及基于方差的W指标。除此之外,本文对基于方差的W指标进行了改进,改进后的W指标除包含原始W指标所提供的信息外,还包含了输入变量取不同实现区间时对输出响应方差影响的变异性,可以更合理地反映调整输入变量的不同取值区间对输出离散程度的平均影响。数值算例以及工程算例的计算结果说明了本文所提方法在计算上的准确性以及改进后的W指标的合理性。

关键词: 空间分割, 无迹变换, Sobol指标, 区域重要性指标, W指标, 改进的W指标

Abstract: In order to simultaneously estimate various variance-based sensitivity indices, a method is proposed by combining space-partition idea and unscented transformation (UT) method, which can estimate variance-based global sensitivity indices, variance-based regional sensitivity indices and variance-based W indices by repeatedly using a set of UT samples. Besides, a modified variance-based W importance measure is proposed, which can analyze the importance of the model input variables comprehensively and reasonably. What's more, the modified variance-based W importance measure includes both the original one and the variability of effect on the variance of model output when the model input variable is fixed in different intervals. Thus, the modified one is more reasonably reflects the average impact on the variance of the model output when model input variable is fixed in different intervals. The results of numerical and engineering examples illustrate the accuracy and efficiency of the proposed method and the reasonability of the modified variance-based W importance measure.

Key words: Space-partition, Unscented transformation(UT), Sobol indices, Variance-based regional sensitivity indices, W indices, Modified W indices

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