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A novel fractional moments-based maximum entropy method for high-dimensional reliability analysis

机译：高维可靠性分析的基于分数阶矩的最大熵新方法

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摘要

High-dimensional reliability analysis is still an open challenge in structural reliability community. To address this problem, a new sampling approach, named the good lattice point method based partially stratified sampling is proposed in the fractional moments-based maximum entropy method. In this approach, the original sample space is first partitioned into several orthogonal low-dimensional sample spaces, say 2 and 1 dimensions. Then, the samples in each low-dimensional sample space are generated by the good lattice point method, which are deterministic points and possess the property of large variance reduction. Finally, the samples in the original space can be obtained by randomly pairing the samples in low-dimensions, which may also significantly reduce the variance in high-dimensional cases. Then, this sampling approach is applied to evaluate the low-order fractional moments in the maximum entropy method with the tradeoff of efficiency and accuracy for high-dimensional reliability problems. In this regard, the probability density function of the performance function involving a large number of random inputs can be derived accordingly, where the reliability can be straightforwardly evaluated by a simple integral over the probability density function. Numerical examples are studied to validate the proposed method, which indicate the proposed method is of accuracy and efficiency for high-dimensional reliability analysis. Keywords: High-dimensional model Good lattice point method Partially stratified sampling Variance reduction Maximum entropy method Fractional moments. (C) 2019 Elsevier Inc. All rights reserved.
机译：高维可靠性分析仍然是结构可靠性界的一个开放挑战。为了解决这个问题，在基于分数矩的最大熵方法中，提出了一种新的采样方法，即基于良好格点法的部分分层采样法。在这种方法中，首先将原始样本空间划分为几个正交的低维样本空间，例如2维和1维。然后，通过良好的晶格点法生成每个低维样本空间中的样本，这些点是确定性点，并具有减少大方差的特性。最后，可以通过将低维样本随机配对来获得原始空间中的样本，这也可以显着减少高维情况下的方差。然后，该采样方法被用于评估最大熵方法中的低阶分数矩，同时权衡了高维可靠性问题的效率和精度。在这方面，可以相应地导出涉及大量随机输入的性能函数的概率密度函数，其中可以通过概率密度函数上的简单积分来直接评估可靠性。数值算例验证了该方法的有效性，表明该方法对高维可靠性分析具有较高的准确性和效率。关键词：高维模型良好格点法部分​​分层采样方差降低最大熵法分数矩。 （C）2019 Elsevier Inc.保留所有权利。

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