A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

中文翻译：

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具有区间不确定性的非线性瞬态传热问题的满量程边界估计

提出了一种用于在具有小或大不确定性的非线性瞬态传热问题中对温度进行全面边界估计的一揽子解决方案。当区间尺度相对较小时，基于泰勒级数展开的有效温度边界估计强调获得高保真温度的一阶和二阶导数。当区间尺度相对较大时，基于优化的方法结合维度自适应稀疏网格 (DSG) 代理被开发用于温度的边界估计，以及非线性瞬态传热问题的重复确定性解的繁重计算负担可以通过 DSG 代理有效缓解。采用具有高保真度的时间分段自适应算法来获得温度的确定性解，并进一步发展用于温度的一阶和二阶导数的递归自适应计算。因此，泰勒级数展开的实施和DSG代理的构建都需要一个可靠的数值平台。并行化用于构建 DSG 代理以进一步加速。两个数值例子证明了所提出方法的准确性和效率。泰勒级数展开的实施和 DSG 代理的构建以可靠的数值平台为基础。并行化用于构建 DSG 代理以进一步加速。两个数值例子证明了所提出方法的准确性和效率。泰勒级数展开的实施和 DSG 代理的构建以可靠的数值平台为基础。并行化用于构建 DSG 代理以进一步加速。两个数值例子证明了所提出方法的准确性和效率。