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为探究基于激光吸收光谱技术的燃烧场二维测量光路布置方式, 实现有限投影下更精确的燃烧场二维重建, 根据分数阶微积分理论, 提出一种基于分数阶Tikhonov正则化的光路优化方法. 将经典的整数阶Tikhonov正则化推广到分数阶模式, 建立了基于分数阶Tikhonov正则化的光路设计目标函数. 利用遗传算法分析(0, 1)范围内不同阶数的计算结果, 得到最佳光路布置方式. 采用近红外波段7185.6 cm
–1
的H
2
O特征吸收谱线结合20条测试光路对10×10离散化网格区域进行计算, 对比分析五种光路布置方式对多种分布模型的重建结果, 结果表明, 基于分数阶Tikhonov正则化的光路布置方式具有最佳重建效果. 研究结果对有限投影条件下激光吸收光谱二维测量光路的优化设计理论研究具有重要意义, 可以促进激光吸收光谱技术在复杂发动机燃烧场二维重建及燃烧效率提升方面的应用.
激光吸收光谱 /
二维重建 /
分数阶Tikhonov正则化 /
Beam arrangement with limited projections based on tunable diode laser absorption spectroscopy is the key to achieving a more accurate two-dimensional reconstruction of the combustion. Using fractional calculus theory, a beam optimization method based on fractional Tikhonov regularization is proposed. The beam arrangement function based on fractional Tikhonov regularization is established by extending the standard Tikhonov regularization to fractional modes. The genetic algorithm is used to analyze the calculation results of different orders in a range of (0, 1), and the beam arrangement is obtained. Using 20 laser beams to scan the characteristic absorption spectrum of H
2
O in the near-infrared band 7185.6 cm
–1
, modeling the calculations in a 10×10 element discrete tomography domain, and comparing the reconstruction results of the five beam arrangements for different Gaussian distribution models, the beam arrangement based on fractional Tikhonov regularization shows more obvious advantages. This design method proposed in this work is valuable for the theoretical study of the optimal design of two-dimensional measurement beams based on the tunable diode laser absorption spectroscopy technique, which can promote the application of this technique in the two-dimensional reconstruction of complex engine combustion and combustion efficiency improvement.
Keywords:
laser absorption spectroscopy /
two-dimensional reconstruction /
fractional Tikhonov regularization /
beam arrangement optimization
Funds:
Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant Nos. BK20220952, BK20220919), the National Key Laboratory of Transient Physics Found Project, China (Grant Nos. 6142604210204, 6142604210203), and the Shuangchuang Doctoral Program of Jiangsu Province, China (Grant No. JSSCBS20210207).
Fig. 7
.
Spatial distribution and projection point distribution diagram of five beam arrangements: (a) 2×10 orthogonal optical path arrangement; (b) 4×5 fan-shaped optical path arrangement; (c) cross optical path arrangement; (d) beam arrangement based on standard Tikhonov regularization design; (e) beam arrangement based on fractional Tikhonov regularization design.
Fig. 8
.
Reconstruction results of unimodal distribution model and different beam arrangements: (a) reconstruction model; (b) 2×10 orthogonal beam arrangement; (c) 4×5 fan-shaped beam arrangement; (d) cross beam arrangement (e) beam arrangement based on standard Tikhonov regularization design; (f) beam arrangement based on fractional Tikhonov regularization design.
Fig. 9
.
Reconstruction results of bimodal distribution model and different beam arrangements: (a) Reconstruction model; (b) 2×10 orthogonal beam arrangement; (c) 4×5 fan-shaped beam arrangement; (d) cross beam arrangement; (e) beam arrangement based on standard Tikhonov regularization design; (f) beam arrangement based on fractional Tikhonov regularization design.
