在模糊随机因素影响下的多层圆筒结构的稳态热传导问题的区间数解法

Interval Analysis of the Fuzzy-Random Heat Conduction in the Composite Tubes

在多层圆筒结构稳态热传导分析中,根据给定固体壁两侧表面温度总传热量公式,首先推导出当边界温度为随机变量情况下总传热量函数统计参数的均值和方差;然后推导出在导热系数为模糊数,边界温度为随机数下的总传热量的区间表达式.通过比较可以知道由区间数算法得到的区间最大,由概率统计算法得到的区间最小.并给出了两者的相对误差公式.最后引进粗糙集中的上、下近似集,提出用一个参数来统一定义模糊和随机区间进行稳态结构的热传导分析.

During the analysis of stability heat conduction in the composite tubes and when the temperature boundary conditions were the randorn conditions,first equations of the mean values and variances of the random thermal function were transformed.Secondly when the heat conduct parameters were the fuzzy numbers and the temperature boundary conditions were the random numbers,interval equations of the heat conduction were presented.Thirdly compared with the interval results between in the interval analysis and in the confidence interval,the result in the interval analysis is larger than that in the confidence interval.Moreover the error expecting equation was presented.Finally,with upper （lower） approximation in rough set theory,a new method of the interval analysis to deal with the stability heat conduction was presented.