带随机Robin边界数据的三层热传递模型及参数识别反问题

Three-layer heat transfer model with random Robin boundary data and the inverse problem of parameter identification

为描述带随机数据的环境-热防护服-空气层-皮肤系统的热传递过程,建立了带随机Robin边界条件的一类三层抛物型方程定解问题,对方程进行数值求解,得到了温度随时间、空间的分布情况。提出了概率意义下的厚度参数识别反问题,并基于区间算法思想构建了反问题的一种随机搜索算法,通过数值计算获得了给定设计目标下的厚度参数置信区间。将计算结果代入正问题模型,并结合皮肤烧伤评估系统进行验证,结果表明置信区间下选取的厚度参数可以尽可能减轻烧伤程度。

In this paper,a class of three-layer parabolic equation finite solution problems with random Robin boundary conditions was established to describe the heat transfer process of environment-heat protective clothing-air layer-skin system with random data.The distribution of temperature with time and space was derived by solving the equation.An inverse problem of thickness parameter identification in the sense of probability was presented.Based on the idea of interval algorithm,a random search algorithm for inverse problem was constructed.The confidence interval of the thickness parameter under the given design objective was obtained through numerical calculation.The calculation results were substituted into the direct problem model and verified using the skin burn evaluation system.The results show that the thickness parameter selected under the confidence interval can reduce the degree of burn as far as possible.