基于三维变分的声学法三维温度场重建

Reconstruction of three-dimensional temperature field using 3DVAR-based acoustic method

在声学层析成像方法测量锅炉温度场的应用中,温度场重建算法的精度和速度起着重要作用。本文在分析基于像素分割的声学法温度场重建原理的基础上,将三维变分方法用于锅炉炉膛的三维温度场重建,将温度场重建的反问题求解归结为一个表征分析场与观测场和分析场与背景场偏差的二次泛函极小值问题。按照不同权重扩展目标函数,并采用共轭梯度法求解目标函数。分别对4种温度场模型实现了模拟重建,结果表明,基于三维变分的重建算法与最小二乘法和代数重建算法相比,重建精度高,并对测量噪声有很好的数值稳定性。

During the temperature field measurement for boilers using acoustic tomography method, the accuracy and speed of the reconstruction algorithm plays an important role in reconstructing the temperature field. The principle of reconstructing temperature field based on pixel segmentation was analyzed and the three-dimensional variational algorithm （3DVAR） was adopted in temperature field reconstruction. The solving of inverse problem of the temperature field reconstruction was come down to a minimum problem of a quadratic function characterizing the deviation between the analysis field and observation field as well as the analysis field and background field. The objective function was extended according to different weights. The objective function was solved by conjugate gradient method. Numerical simulation was realized in four temperature models respectively. The results show that, the precision and numerical stability of the 3DVAR-based reconstruction method are higher than that of the least squares and algebra reconstruction technique.