基于LSMR算法的火焰三维温度场重建

doi:10.16085/j.issn.1000-6613.2023-1323

摘要/Abstract

摘要：

光场成像技术可以同时记录入射光线的空间分布信息和传播方向信息，结合相关反演算法，可以进行火焰三维温度场的重建。最小二乘QR分解算法（least squares via QR factorization，LSQR）可以有效求解基于大型稀疏矩阵的线性问题，但是在对火焰辐射强度求解的过程中，难以保证求解的非负性和准确性。非负最小二乘算法（non-negative least squares，NNLS）可以保证求解的非负性，但是计算效率太低。本文提出将最小二乘残差方法（least square minimal residual，LSMR）用于火焰光场成像三维温度场重建，并研究其重建精度、计算效率、抗噪性能等指标。仿真实验表明，LSMR和NNLS算法可以在不同噪声水平下保证求解火焰辐射强度的非负性。在噪声为5%、10%、15%和20%的情况下，LSMR和NNLS算法对辐射强度的求解精度均比LSQR提高了10%以上，且LSMR算法的求解时间比LSQR和NNLS分别降低了一个数量级和四个数量级。可见，LSMR算法可以在保证求解精度的情况下大幅提高运算效率。最后用LSMR算法对模拟光场火焰进行温度场重建，在不同噪声水平下，平均相对误差都保持在1.2%以内，验证了LSMR算法在重建时的准确性和可靠性。

关键词: 光场, 成像, 火焰, LSMR算法, 三维温度场重建

Abstract:

The light field imaging technique can simultaneously record the spatial distribution information and propagation direction information of the incident light, and combined with relevant inversion algorithms, it can be used for the reconstruction of the three-dimensional temperature field of the flame. The least squares via QR factorization (LSQR) algorithm can effectively solve linear problems based on large sparse matrices, but it is difficult to ensure the nonnegativity and accuracy of the solution in the process of solving the flame radiation intensity. The non-negative least squares (NNLS) algorithm can guarantee the non-negativity of the solution, but the computational efficiency is too low. In this paper, we proposed to use the least square minimal residual (LSMR) method for three-dimensional temperature field reconstruction of flame light field imaging, and studied its reconstruction accuracy, computational efficiency, anti-noise performance and other indicators. Simulation experiments showed that the LSMR and NNLS algorithms can guarantee the non-negativity of solving the flame radiation intensity under different noise levels. In the case of noise of 5%, 10%, 15% and 20%, both LSMR and NNLS algorithms improved the accuracy of solving the radiation intensity by more than 10% compared with LSQR, and the solution time of LSMR algorithm was reduced by one order of magnitude and four orders of magnitude compared with LSQR and NNLS, respectively. It could be seen that the LSMR algorithm can significantly improve the computational efficiency while ensuring the solution accuracy. Finally, the LSMR algorithm was used to reconstruct the temperature field of the simulated light field flame, and the average relative errors were kept within 1.2% under different noise levels, which verified the accuracy and reliability of the LSMR algorithm in reconstruction.

Key words: light field, imaging, flame, LSMR algorithm, 3D temperature field reconstruction

中图分类号:

TK311

单良, 仰文淇, 洪波, 周荣幸, 孔明. 基于LSMR算法的火焰三维温度场重建[J]. 化工进展, 2024, 43(2): 659-666.

SHAN Liang, YANG Wenqi, HONG Bo, ZHOU Rongxing, KONG Ming. Three-dimensional temperature field reconstruction of flame based on LSMR algorithm[J]. Chemical Industry and Engineering Progress, 2024, 43(2): 659-666.

图/表 9

图1 光场相机成像

图2 火焰数值模拟模型

表1 辐射强度重建时出现负值点的数量及百分比

噪声/%	负值的数量			负值所占的百分比/%
噪声/%	LSQR	NNLS	LSMR	LSQR	NNLS	LSMR
1	0	0	0	0	0	0
5	14	0	0	0.04	0	0
10	87	0	0	0.24	0	0
15	166	0	0	0.46	0	0
20	261	0	0	0.72	0	0

图3 中心层内焰区域辐射强度重建对比

图4 LSQR、NNLS 和LSMR算法计算火焰辐射强度的平均相对误差

表2 不同噪声下计算时间的对比

噪声/%	LSQR/s	NNLS/s	LSMR/s
1	2.91	2201	0.14
5	2.90	2215	0.14
10	2.90	2246	0.15
15	2.96	2255	0.15
20	3.05	2278	0.16

图5 LSMR算法在不同噪声下温度的重建效果

图6 LSMR算法在不同噪声下温度重建的绝对误差分布

表3 LSMR算法温度重建的误差

噪声/%	平均相对误差/%	最大相对误差/%
1	0.03	0.21
5	0.18	1.53
10	0.44	3.09
15	0.74	8.28
20	1.12	14.34

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