Abstract This article devotes to the uncertain analysis of steady-state convection-diffusion heat transfer problems with interval input parameters in material properties, thermal source and boundary conditions. The optimization strategy is adopted to ensure a reliable bounds estimation when scales of interval width is larger, and a Galerkin system is derived to construct a Legendre Series Expansion (LSE) to surrogate FE solutions of deterministic problems, so as to reduce the computational expense in the optimization based bounds estimation with sufficient accuracy. A LSE-GS (global search), and a LSE-CM (combinatorial method) are presented to solve uncertain steady-state convection-diffusion heat transfer problems with multiple interval variables, and are extended to the fuzzy analysis. Various numerical examples are provided to verify the performance of the proposed method, and evidence the accuracy and effectiveness of the proposed methods for interval prediction of steady-state convection-diffusion heat transfer problems.

中文翻译：

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一种使用 LSE 和优化算法对对流-扩散传热问题进行区间分析的新数值技术

摘要 本文致力于材料特性、热源和边界条件等输入参数区间的稳态对流传热问题的不确定性分析。采用优化策略保证区间宽度尺度较大时的可靠边界估计，并推导出伽辽金系统构造勒让德级数展开（LSE）来替代确定性问题的有限元解，从而降低计算开销基于优化的边界估计具有足够的准确性。提出了 LSE-GS（全局搜索）和 LSE-CM（组合方法）来解决具有多个区间变量的不确定稳态对流扩散传热问题，并将其扩展到模糊分析。