温度场的非概率凸集合理论模型的摄动数值解法

Perturbed Numerical Algorithm of Nonprobabilistic Convex Set Theoretical Models for Temperature Field

采用凸模型描述结构温度场的物理参数、初始条件和边界条件的不确定性,探讨热传导的不确定性问题.将矩阵摄动理论与凸模型方法相结合,导出了有界不确定性参数瞬态温度场响应上、下界的摄动计算公式,并通过数值算例对凸模型方法和区间分析法的计算结果进行了比较.结果表明,凸模型求得的温度场响应的范围比区间分析法求得的大.

Abstract： In order to investigate the uncertainties of heat conduction, the uncertainties of physical parameters and initial and boundary conditions of structural temperature fields were described using convex models. The perturbation formulas of the upper and lower bounds of responses of temperature fields with unknown-but-bounded parameters were derived via the ＂combination of the matrix perturbation theory and the convex models. A comparison between the results obtained respectively by the convex models and the interval analysis method was made by a numerical example. The results show that the width of the upper and lower bounds of temperature field responses calculated by the convex models is greater than that calculated by the interval analysis method.