基于维自适应算法的多项式混沌展开方法
首发时间:2018-09-25
摘要:为缓解多项式混沌展开(PCE)代理模型映射求解过程中的"维数灾难"问题,本文提出了基于维自适应算法的多项式混沌展开技术,并以固体火箭发动机低温点火过程为例,验证所提方法的可行性。本文的主要贡献如下:(1)提出了基于全局灵敏度分析(GSA)的维自适应算法(Dimension-adaptive)。(2)通过建立基于全局灵敏度分析的非均匀网格,发展了基于伽辽金投影的非侵入式求解技术。(3)将所提方法应用于固体火箭发动机低温点火加压不确定性分析。结果表明:与一些传统非侵入式随机分析方法相比,对于多参数不确定性问题的求解,本文所提方法能够在服从精度要求的条件下,明显提高计算效率。
关键词: 多项式混沌展开 全局灵敏度分析 不确定性量化 维自适应算法
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Polynomial Chaos Expansion Based on Dimension-adaptive Algorithm
Abstract:To alleviate the dimension curse during the projection solving of polynomial chaos expansion (PCE), this paper presents a PCE technique based on Dimension-adaptive algorithm, and verifies the feasibility of the proposed method through taking solid rocket motor ignition under low temperature as an example. The main contributions of this work are as follows: (1) Presenting the Dimension-adaptive algorithm based on global sensitivity analysis (GSA). (2) Through establishing a non-uniform grid based on GSA, developing non-invasive solution method based on Galerkin projection. (3) Applying the proposed method to uncertainty quantification (UQ) of solid rocket motor ignition under low temperature. The result indicates that by means of comparing with some conventional non-invasive method , the proposed method is able to raise the computational efficiency significantly and meet the accuracy requirement for high-dimension uncertainty problem.
Keywords: Polynomial chaos expansion Global sensitivity analysis Uncertainty quantification (UQ) Dimension-adaptive
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