Dimension reduction for constructing high-dimensional response distributions by accounting for unimportant and important variables

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL
Yongyong Xiang , Te Han , Yifan Li , Luojie Shi , Baisong Pan
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引用次数: 0

Abstract

Probability distributions of responses have been widely used in structural analysis and design because of their complete statistical information. In practice, the dimensionality of input variables could easily reach hundreds or thousands, making it computationally expensive to obtain accurate distributions. In this paper, a generalized most probable point (MPP) method is developed to effectively build the response distributions of high-dimensional problems. First, a global index based on one-iteration MPPs is presented for dimension reduction, which is to divide the input variables into important and unimportant variables. After fixing the unimportant variables at their one-iteration MPP components, the MPP components of the important variables are obtained by performing the inverse first-order reliability method (FORM) in the reduced space. Predictive models of the all MPP components are then established to quickly estimate the MPPs of other cumulative distribution function (CDF) values. To accurately calculate CDF points of limit state functions with different shapes, a comprehensive uncertainty analysis method that accommodates the contributions of the important and unimportant variables is proposed by multiple combinations of FORM, second-order reliability method, and second-order saddlepoint approximation. Finally, the response distributions are generated based on Gaussian mixture distribution and all CDF points. The effectiveness of the proposed method is verified by a mathematical example and two engineering cases.

通过考虑不重要和重要变量,构建高维响应分布的降维方法
响应的概率分布因其完整的统计信息而被广泛应用于结构分析和设计中。在实际应用中,输入变量的维数动辄成百上千,要获得精确的分布需要耗费大量的计算资源。本文提出了一种广义的最可能点(MPP)方法,以有效建立高维问题的响应分布。首先,本文提出了一种基于一次迭代 MPP 的全局指数,用于降维,即将输入变量分为重要变量和不重要变量。在将不重要变量固定在其一次迭代 MPP 分量上后,通过在缩减空间中执行反一阶可靠性方法(FORM),得到重要变量的 MPP 分量。然后建立所有 MPP 分量的预测模型,以快速估算其他累积分布函数 (CDF) 值的 MPP。为了准确计算不同形状的极限状态函数 CDF 点,通过 FORM、二阶可靠性方法和二阶鞍点近似的多重组合,提出了一种兼顾重要变量和不重要变量贡献的综合不确定性分析方法。最后,根据高斯混合分布和所有 CDF 点生成响应分布。通过一个数学实例和两个工程案例验证了所提方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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