Enhanced high‐dimensional model representation for reliability analysis
Enhanced high‐dimensional model representation for reliability analysis
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DOI：
10.1002/nme.2440
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发表时间：
2009-01
影响因子：
2.9
通讯作者：
B. Rao;R. Chowdhury
中科院分区：
文献类型：
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作者：
B. Rao;R. Chowdhury
本文提出了一种新的替代计算工具，用于预测结构/机械系统在随机载荷、材料特性和几何形状下的失效概率，该工具基于从低阶函数分量生成的高维模型表示（HDMR）。HDMR是一套通用的定量模型评估和分析工具，用于捕获输入和输出模型变量集之间的高维关系。如果高阶变量的相关性很弱，这是一个非常有效的系统响应公式，允许物理模型被低阶项捕获，并便于原始高维隐式极限状态/性能函数的低维近似。当原始高维隐式极限状态/功能函数的一阶HDMR近似不足以提供预测失效概率所需的精度时，本文提出了一种增强的HDMR（eHDMR）方法，该方法通过类似于具有单项乘子的低阶项的表达式来表示HDMR展开的高阶项。HDMR展开的准确性可以通过使用最少数量的额外输入-输出样本进行预处理来显着提高，而无需直接调用二阶和高阶项的确定。给出了eHDMR的数学基础沿着，以及其在后续可靠性分析中近似原始高维隐式极限状态/性能函数的适用性，因为传统的可靠性分析方法在与复杂的有限元模型结合使用时计算量很大。本研究旨在评估eHDMR近似技术如何准确有效地捕获复杂的模型输出不确定性。通过eHDMR展开的分量函数，采用移动最小二乘插值公式构造极限状态/性能函数代理。一旦定义了隐式响应函数的近似形式，就可以通过统计模拟得到失效概率。涉及初等数学函数和结构/固体力学问题的五个数值例子的结果表明，与传统的Monte Carlo方法相比，使用eHDMR近似方法获得的隐式极限状态/性能函数的失效概率提供了显着的准确性，同时需要更少的原始模型模拟。版权所有© 2008约翰威利父子有限公司.
This paper presents a new and alternative computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry based on high‐dimensional model representation (HDMR) generated from low‐order function components. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high‐dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher‐order variable correlations are weak, allowing the physical model to be captured by the lower‐order terms and facilitating lower‐dimensional approximation of the original high‐dimensional implicit limit state/performance function. When first‐order HDMR approximation of the original high‐dimensional implicit limit state/performance function is not adequate to provide the desired accuracy to the predicted failure probability, this paper presents an enhanced HDMR (eHDMR) method to represent the higher‐order terms of HDMR expansion by expressions similar to the lower‐order ones with monomial multipliers. The accuracy of the HDMR expansion can be significantly improved using preconditioning with a minimal number of additional input–output samples without directly invoking the determination of second‐ and higher‐order terms. The mathematical foundation of eHDMR is presented along with its applicability to approximate the original high‐dimensional implicit limit state/performance function for subsequent reliability analysis, given that conventional methods for reliability analysis are computationally demanding when applied in conjunction with complex finite element models. This study aims to assess how accurately and efficiently the eHDMR approximation technique can capture complex model output uncertainty. The limit state/performance function surrogate is constructed using moving least‐squares interpolation formula by component functions of eHDMR expansion. Once the approximate form of implicit response function is defined, the failure probability can be obtained by statistical simulation. Results of five numerical examples involving elementary mathematical functions and structural/solid‐mechanics problems indicate that the failure probability obtained using the eHDMR approximation method for implicit limit state/performance function, provides significant accuracy when compared with the conventional Monte Carlo method, while requiring fewer original model simulations. Copyright © 2008 John Wiley & Sons, Ltd.