1.Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China 2.University of Science and Technology of China, Hefei 230026, China
Fund Project:Project supported by the National Key R&D Program of China (Grant No. 2019YFB2006003), the National Natural Science Foundation of China (Grant No. 61805286), and the Natural Science Foundation of Anhui Province, China (Grant No. 200808QF317)
Received Date:14 December 2020
Accepted Date:07 January 2021
Available Online:26 June 2021
Published Online:05 July 2021
Abstract:In this paper, a method of selecting the optimal transition lines’ combination is analyzed to measure the absorption spectrum of the non-uniform combustion flow field, which is used to solve the basic two-region distribution, and an improved simulated annealing algorithm (ISA) is proposed for reconstructing the field distribution of the combustion flow field, in order to solve the problems of slow convergence speed and low efficiency of the traditional simulated annealing algorithm. By modifying the model perturbation mode and annealing strategy, the efficiency of the algorithm and the chance to jump out of the local optimal space are further improved. According to the numerical simulation results, more transitions are helpful in improving the accuracy of combustion field reconstruction and making the reconstruction less sensitive to noise. It is worth noting that the optimal transitions’ combination is better than the non-optimal transitions’ combination with more transitions included. In this paper, three different combustion models are constructed to verify the effectiveness of the improved algorithm. A comparison between the reconstruction results of the traditional simulated annealing algorithm and the improved simulated annealing algorithm shows that both algorithms have the same precision but the latter algorithm has a higher operating efficiency, and a faster running time (nearly 40 times faster than the former algorithm). At the same time, the simulation results also show that the reconstruction accuracy will decrease slightly with the complication of combustion flow field. By building the TDLAS-HT measurement system in the laboratory and using 8 × 8 orthogonal optical path arrangement, the two different combustion states formed before and after placing the steel rod in the flat flame furnace are reconstructed, the results show that the reconstruction distribution is basically consistent with the original distribution, and the reconstructed distribution well shows the combustion characteristics of the original distribution of the flame field. The effectiveness of the proposed method is verified by numerical simulation and verification tests. Under the condition of the same reconstruction accuracy as the reconstruction accuracy of the traditional simulated annealing algorithm, the higher operating efficiency is helpful in reconstructing the rapidly changing turbulent field, which has some guiding significance for the hyperspectral reconstruction of temperature and concentration distribution in the combustion flow field. Keywords:combination of transition lines/ field distribution reconstruction/ simulated annealing algorithm/ hyperspectral
4.数值仿真针对燃烧流场中不同的燃烧情况, 构建了三种不同模态的燃烧场, 其中温度分布分别为单峰分布、双峰分布及多峰分布, 范围均为1000—2200 K, 浓度分布范围为0.05—0.21. 燃烧流场温度及水汽浓度分布如图8所示. 图 8 三种不同模态燃烧场分布 (a) 单高斯峰; (b) 双高斯峰; (c) 多高斯峰; (d) 浓度分布 Figure8. Three different modes of combustion field distribution: (a) Single Gaussian peak; (b) two Gaussian peaks; (c) multiple Gaussian peaks; (d) concentration distribution.
利用改进后的算法, 结合之前小节中所述选取的最优谱线组合(5条谱线, 对应于表1谱线中的2, 6, 9, 10和12), 对三种不同模态的燃烧流场进行了反演重建, 重建精度效果以(2)式评判. 为更好地验证其对噪声的敏感性, 在仿真模拟中, 添加了不同水平的高斯噪声(0%, 0.5%, 1%, 1.5%, 2%, 3%, 4%, 5%), 反演结果如图9所示. 图 9 三种不同模态燃烧流场的温度浓度反演精度 Figure9. The inversion accuracy of three different modes of combustion field distribution.
从图9可以看出, 随着燃烧流场分布的复杂化, 温度及水汽浓度的反演精度也会随之略有下降. 为验证纳入多个光谱信息在反演燃烧流场分布时的作用, 采取改进后的算法, 对不同谱线组合反演重建温度浓度场分布的精度进行了对比, 其中最优5条谱线组合对应于表1谱线中的2, 6, 9, 10和12, 最优8条谱线组合对应于表1谱线中的2, 4, 6, 7, 8, 9, 10和12. 同样地, 在对比中添加了不同水平的高斯噪声. 对图8中的三种不同模态燃烧流场均进行了反演对比, 对比结论基本一致, 所以在接下来的内容以图8(c)的多峰分布作为例子进行说明, 对比结果如图10所示. 图 10 最优5条、8条谱线组合和非最优5条、8条谱线组合以及所有12条谱线在不同噪声水平下温度浓度的反演精度 Figure10. The inversion accuracy of the optimal 5, 8 transition lines combinations, the non-optimal 5, 8 transition lines combinations and all 12 transition lines combinations under different noise levels.
从图10的对比结果来看, 纳入更多的光谱信息能提高测量精度和增强对测量噪声的免疫性, 原因在于更多的跃迁谱线提供了更广阔的温度范围. 同时, 对比结果突出了选择最优谱线组合的重要性, 比如, 最优5条谱线组合在测量精度和对噪声的免疫性上甚至优于非最优8条谱线组合. 为比较改进后的算法与传统模拟退火算法重建场分布的差异, 将两种算法得到的重建图像精度和算法运行时间进行对比, 依然以图8(c)中的燃烧场分布举例说明, 两种算法重建结果如图11所示(选取最优5条谱线组合, 零噪声水平下), 上面板为传统模拟退火算法重建, 下面板为本文改进后算法重建. 图 11 零噪声水平下两种算法重建结果对比, 上面板为传统模拟退火算法重建结果, 下面板为改进模拟退火算法重建结果 Figure11. Under zero noise level, the reconstruction results of two algorithms. Top: SA algorithm reconstruction results, Bottom: ISA algorithm reconstruction results.
且为考证不同规模问题下, 两种算法的重建图像精度与算法运行效率是否会有差异, 分别利用前文所述的最优5条谱线组合和最优8条谱线组合去进行反演重建, 重建精度对比结果如图12所示, 改进前后算法运行时间对比如表2所示. 图 12 两种算法的重建精度对比 Figure12. Comparison of reconstruction accuracy between the two algorithms.
Noise level
Simulated annealing algorithm
Improved Simulated annealing algorithm
5 optimal transitions
8 optimal transitions
5 optimal transitions
8 optimal transitions
0%
8704 s
12379 s
231 s
364 s
0.5%
8346 s
12265 s
242 s
372 s
1%
9213 s
12403 s
237 s
384 s
1.5%
9001 s
12608 s
217 s
379 s
2%
8945 s
12337 s
230 s
342 s
3%
8573 s
13151 s
225 s
356 s
4%
8733 s
12726 s
240 s
351 s
5%
8667 s
12516 s
235 s
347 s
表2两种算法应用于高光谱层析成像的运行时间对比 Table2.Comparison of running time of two algorithms applied to hyperspectral tomography.