基于Reflected Sigmoid径向基函数插值的温度场重建算法

声学法测温在特殊的温度场环境中有良好的应用,主要是利用有限的超声波传播路径上的飞行时间重构出连续分布的温度场.现有的温度场重建算法中最小二乘法是最常用的方法,但其重建后的温度场会出现边缘信息缺失的现象.针对这一问题,提出在最小二乘法确定温度矩阵的基础上,结合Reflected-Sigmoid函数进行插值,实现了二维平面温度场的无缺失重建.通过两种典型的单峰温度场模型的重建结果及误差分析表明,在补全温度场边缘的条件下,单峰对称温度场的均方根百分误差在1.6%,单峰偏斜温度场的均方根百分误差在3.5%,取得了很好的重建效果.

Temperature field reconstruction algorithm based on Reflected Sigmoid radial basis function interpolation

The acoustic thermometry has a good application in the special temperature field environment. That is, the continuous distribution of temperature field can be reconstructed using the flight time spent on the finite ultrasonic propagation path. The least square method is one of the acoustic temperature field reconstruction algorithms, and the reconstructed temperature field will have the phenomenon of missing edge information using this method. In order to solve this problem, an algorithm based on Reflected Sigmoid radial basis function interpolation is proposed to reconstruct the two dimensional distribution of temperature without information loss. In this algorithm, the least square method is adopted to determine the temperature matrix and the Reflected Sigmoid function is used to interpolate the temperature field. The reconstruction results and error analysis of two typical single peak temperature field models show that the root mean square percentage error of the symmetrical single peak temperature field is 1.6% and the root mean square percentage error of the skewed single peak temperature field is 3.5% after complementing the edge of the temperature field.