基于阻尼LSQR-LMBC的火焰三维温度场重建

Flame 3D temperature field reconstruction based on Damped LSQR-LMBC

光场相机可以解决辐射测温多相机系统光路复杂、同步触发难等问题,在辐射成像三维温度重建时有其独特优势.LSQR是求解基于大型稀疏矩阵最小二乘问题的经典算法,该算法用于重建三维温度场时对温度初值依赖较大,在信噪比较低的情况下重建精度不理想.本文提出阻尼LSQR-LMBC重建算法,通过在LSQR方法中添加阻尼正则化项,提高火焰三维温度场重建的抗噪性能,并结合LMBC算法,实现吸收系数和三维温度场同时求解.在数值模拟部分,随着信噪比逐渐降低,阻尼LSQR的重建效果比LSQR更加稳定,在信噪比达到13.86 dB时,重建精度大约提高30%.阻尼LSQR-LMBC的平均重建误差为6.63%.用丁烷火焰进行了实验,重建的丁烷火焰三维温度场分布符合辐射火焰燃烧的特征,和热电偶的测温数据结果进行对比,相对误差在6.8%左右.

Light field camera can solve the problems of complex optical path and difficult synchronous trigger of radiation temperature measurement multi camera system,which has some unique advantages in three-dimensional temperature reconstruction of radiation imaging.The LSQR is a classical algorithm for solving the least square problem based on large sparse matrix.When the algorithm is used to reconstruct three-dimensional temperature field,it depends on the initial value of temperature,and the reconstruction accuracy is not ideal when the signal-to-noise ratio is low.In this paper,a damped LSQR-LMBC reconstruction algorithm is proposed.By adding a damped regularization term into the LSQR method,the anti noise performance of flame three-dimensional temperature field reconstruction is improved.By combining the LMBC algorithm,the absorption coefficient and three-dimensional temperature field are solved at the same time.In the numerical simulation part,with the gradual reduction of signal-to-noise ratio,the reconstruction effect of Damped LSQR turns more stable than LSQR.When the signal-to-noise ratio reaches 13.86 dB,the reconstruction accuracy is improved by about 30%.The average reconstruction error of damped LSQR-LMBC is 6.63%.The three-dimensional temperature field distribution of butane flame is consistent with the characteristic of radiation flame combustion.Compared with the temperature measurement data of thermocouple,the relative error is about 6.8%.