边值传热反问题误差评估的正则化仿真模型

Regularized Simulation Model of Error Assessment for Boundary Value Inverse Heat Conduction Problem

传热反问题数值解误差的准确评估一直是制约它应用于工业测量的一个难点。以淬火测试探头冷却过程的非稳态一维线性传热反问题为例,以位于探头中心热电偶所测的温度数据为基础,通过引入正则化参数,抑制了反问题对测量误差的放大作用,根据特殊情况下的非级数形式的解析解,建立了数值解计算误差评估的正则化仿真模型。仿真实验获得了模型的最优正则参数,提高了反问题数值解误差评估的准确性,验证了该模型的有效性。

Accurate assessment of error in numerical solution is always a difficult part for the inverse heat conduction problem which restricts its applications in industrial measurements. Taking a one-dimensional linear inverse heat conduction problem of the cooling process of a quenching probe as an example, based on the measured temperature data of the thermocouple in the center of the probe, the magnifying effect for measurement error of the inverse problem was hem back by introducing a regularized parameter. According to the closed-form analytical solution in a special case, a regularized simulation model of error assessment in numerical solution was designed. The best regularized parameter was obtained, and the precision of error assessment in IHCP numerical solution was heightened. The validity of this method was verified in the simulation experiments.