A Hierarchical Statistical Sensitivity Analysis Method for Complex Engineering Systems Design
A Hierarchical Statistical Sensitivity Analysis Method for Complex Engineering Systems Design
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DOI：
10.1115/1.2918913
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
X. Yin;Wei Chen-
中科院分区：
文献类型：
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作者：
X. Yin;Wei Chen-
统计灵敏度分析（SSA）在工程设计中发挥着越来越重要的作用，特别是在考虑不确定性的情况下。然而，由于计算和组织方面的困难，将SSA应用于复杂工程系统的设计并不简单。为了将分层统计灵敏度分析方法应用于复杂系统的设计，特别是那些遵循分层建模结构的系统，本文提出了一种分层统计灵敏度分析（HSSA）方法，该方法包含了自上而下的分层统计灵敏度分析策略和全局统计灵敏度指数（GSSI）的聚合评估方法。引入了自顶向下的HSSA策略，根据子模型性能的显著性调用关键子模型的SSA。研究了一种简化的GSSI公式，通过汇总中间水平的子模型SSA结果来表示低水平子模型输入对高水平模型响应的影响。导出了简化式能提供精确解的充分条件。为了提高GSSI公式在一般情况下的准确性，提出了一种修正公式，通过加入调整系数（AC）来捕捉上层模型非线性的影响。为了提高效率，采用与子模型ssa相同的样本集来评估AC。通过数学算例和汽车悬架系统设计中的三层分层模型，对所提出的HSSA方法进行了检验。
Statistical sensitivity analysis (SSA) is playing an increasingly important role in engineering design, especially with the consideration of uncertainty. However, it is not straightforward to apply SSA to the design of complex engineering systems due to both computational and organizational difficulties. In this paper, to facilitate the application of SSA to the design of complex systems especially those that follow hierarchical modeling structures, a hierarchical statistical sensitivity analysis (HSSA) method containing a top-down strategy for SSA and an aggregation approach to evaluating the global statistical sensitivity index (GSSI) is developed. The top-down strategy for HSSA is introduced to invoke the SSA of the critical submodels based on the significance of submodel performances. A simplified formulation of the GSSI is studied to represent the effect of a lower-level submodel input on a higher-level model response by aggregating the submodel SSA results across intermediate levels. A sufficient condition under which the simplified formulation provides an accurate solution is derived. To improve the accuracy of the GSSI formulation for a general situation, a modified formulation is proposed by including an adjustment coefficient (AC) to capture the impact of the nonlinearities of the upper-level models. To improve the efficiency, the same set of samples used in submodel SSAs is used to evaluate the AC. The proposed HSSA method is examined through mathematical examples and a three-level hierarchical model used in vehicle suspension systems design.