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朗伯-比尔定律可以表征待测气体介质对光强的吸收能力。当激光器发出一定频率的光通过待测气体介质时,待测气体介质会吸收部分光强,输出光强可以表示为:
$ \begin{array}{*{20}{c}} {I(\nu ) = {I_0}(\nu )\exp [ - \alpha (\nu )L] = }\\ {{I_0}(\nu )\exp [ - S(T)g(\nu )p\varphi L]} \end{array} $
(1) 式中,I(ν)为透射光强;I0(ν)为入射光强;ν为激光发射频率;α(ν)为气体的吸收系数;S(T)为气体吸收线强, T为温度;g(ν)为谱线的线型函数;p为压强;φ为气体体积分数;L为吸收光程长度。待测气体体积分数可根据上述公式计算[10]。
由于光谱吸收线强非常微弱,一般采用波长调制技术通过低频扫描信号与高频调制信号叠加对激光器的输出波长进行调制。激光器的输入电流变化时,激光频率与光强都受到相应的调制,具体调制公式分别为:
$ \begin{array}{*{20}{c}} {\nu (t) = {\nu _0} + {a_1}{\rm{ sawtooth }}\left( {2{\rm{ \mathsf{ π} }}{f_1}t} \right) + }\\ {{a_2}\sin \left( {2{\rm{ \mathsf{ π} }}{f_2}t} \right)} \end{array} $
(2) $ \begin{array}{*{20}{c}} {{I_0}(t) = {I_0}\left[ {1 + {a_1}{\rm{ sawtooth }}\left( {2{\rm{ \mathsf{ π} }}{f_1}t} \right) + } \right.}\\ {\left. {{a_2}\sin \left( {2{\rm{ \mathsf{ π} }}{f_2}t} \right)} \right]} \end{array} $
(3) 式中,ν0为激光器中心频率,t为采样时间。sawtooth为低频锯齿信号,用于实现波长扫描通过选定范围的气体吸收线,sin为高频正弦信号,目的是提取高频的谐波信号; a1和a2分别为扫描幅度与调制幅度; f1和f2分别为扫描频率与调制频率。从上述公式可以看出, 吸收信号是由低频锯齿信号与高频正弦信号的频率、幅值等因素共同决定的[11-13]。
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TDLAS实验系统原理图见图 1。由调制信号发生器产生的扫描信号和调制信号叠加后通过激光控制器将电压信号转变为电流信号,激光控制器向激光器提供工作所需的电流和温度,使其输出一定波长范围的激光,而后经准直器准直进入气体池被待测气体吸收后,被光电探测器将光信号转换为电信号,再由锁相放大器对其进行解调输出谐波信号。在进行气体检测时,先将动态稀释校准仪配比出一定体积分数的待测气体通入气体池中,待气体体积分数稳定后进行测量。最后用数字示波器与LabVIEW采集程序对所测的信号进行数据采集[14],并由ORIGIN软件对所测信号进行分析处理。本文中所使用的激光器为分布式反馈激光器(distributed feedback,DFB)。
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在分析TDLAS系统的建模原理后,基于MATLAB 2018a中的动态仿真工具建立气体测量仿真模型见图 2。仿真模型由光源模块、气室模块、数据检测模块组成[15-17]。
本文中在常温常压下对CO2体积分数进行检测,因此,碰撞加宽对气体分子吸收谱线影响较大,故气体吸收谱线选用洛伦兹线型, 其模型根据下式构建:
$ {g_{\rm{L}}}\left( {\nu , {\nu _0}} \right) = \frac{{{r_{\rm{L}}}}}{{\rm{ \mathsf{ π} }}} \cdot \frac{1}{{r_{\rm{L}}^2 + {{\left( {\nu - {\nu _0}} \right)}^2}}} $
(4) 式中,gL(ν, ν0)为洛伦兹线型函数,rL为线型函数的半峰全宽。
洛伦兹线型仿真模型见图 3。
半峰全宽rL根据下式计算:
$ {r_{\rm{L}}}(T, p) = {r_0} \cdot {\left( {\frac{{296}}{T}} \right)^n}p $
(5) 式中,激光器中心频率ν0、压力展宽系数r0和温度系数n均可查阅HITRAN数据库可知。气体分子密度根据下式构建:
$ N(T, p) = 2.6868 \times {10^{19}} \times \frac{{273}}{T}p $
(6) 气体分子密度仿真模型见图 4。
一定温度下的气体吸收谱线强度S(T)可以根据下式仿真:
$ \begin{array}{l} S(T) = S\left( {{T_0}} \right)\frac{{Q\left( {{T_0}} \right)}}{{Q(T)}}\exp \left[ { - \frac{{hcE}}{k}\left( {\frac{1}{T} - \frac{1}{{{T_0}}}} \right)} \right] \times \\ \;\;\;\;\;\;\;\;\;\;\;\;\left[ {\frac{{1 - \exp ( - hcE/kT)}}{{1 - \exp \left( { - hcE/k{T_0}} \right)}}} \right] \end{array} $
(7) 式中,S(T0)为在参考温度T0下的吸收谱线强度, h为普朗克常量, k为玻尔兹曼常数, c为光速, E为分子跃迁低态能量,Q为配分函数,在很大程度上决定了谱线吸收线强S(T)与温度的关系。
气体吸收谱线强度仿真模型见图 5。
上述TDLAS仿真系统模型具有很强的通用性,根据HITRAN数据库查阅参量进行设置,可对不同种类的气体进行虚拟监测并观察不同体积分数、温度、压强对气体吸收曲线的影响情况。
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保持气体池压强为101kPa,温度为296K,根据确定的最佳调制参量进行CO2体积分数测量实验。每测量一个体积分数前都将高纯N2通入气体池中,以保证残余气体尽量排出气体池外,使实验结果尽可能准确。将预先配置好的体积分数为0.001, 0.003, 0.005, 0.007, 0.008, 0.009的CO2(背景气体为N2)依次通入气体池,待气体体积分数稳定后进行测量。在对吸收信号进行采集时,应对不同体积分数CO2进行10次测量累加求取平均值以减小噪声的影响。将采集得到的吸收信号进行平滑滤波处理,得到不同体积分数CO2的2f信号, 见图 10。
提取各组数据的最强吸收峰,对吸收峰与不同体积分数CO2进行拟合。由图 11拟合曲线所示,二次谐波信号峰值与实验中选取CO2体积分数具有很好的线性关系[22-23],线性拟合系数R2=0.9998。对二次谐波信号峰值进行体积分数反演并求得其相对误差如表 1所示,测得的最大相对误差为0.7333%。可见,通过调制参量的优化选择可以获得较为理想的二次谐波信号,从而实现待测气体体积分数的精确反演。
Table 1. Gas volume fraction measurement and inversion results
gas volume
fractionpeak of main
absorptionlinear fitting inversion
volume fractionrelative
error/%0.001 5.5318 0.000998 0.2000 0.003 12.4169 0.002978 0.7333 0.005 19.4887 0.005011 0.2200 0.007 26.5009 0.007028 0.4000 0.008 30.0577 0.008050 0.6250 0.009 33.1322 0.008935 0.7222 -
为测量系统检测限,测得体积分数为0.001的CO2的二次谐波信号见图 12。根据2f信号峰值均值(USV=5.5381V)和无吸收处的噪声幅值(USD=0.1365V)之比计算出该系统二次谐波信噪比RSNR[24]≈40.5722,检测限[25]计算公式为:
$ D = 3Q \times N/I = 3Q/{R_{{\rm{SNR}}}} $
(8) 式中,Q为测量系统进样量,N为测量过程中的噪音,I为信号响应值。I/N即为该进样量下的信噪比RSNR。利用以上公式对体积分数为0.001时系统的检测限进行估算,其中进样量即气体体积分数,此时系统信噪比RSNR=40.5722,可获得系统检测限为:D=3×0.001/40.5722≈0.0074%。
TDLAS技术调制参量的优化及实验研究
Optimization and experimental research on modulation parameters of TDLAS technology
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摘要: 为了研究激光调制参量对二次谐波信号峰值、信噪比、峰宽、对称性以及信号完整性的影响, 基于硬件实验系统与Simulink仿真模型进行分析, 验证了理论模拟结果与此硬件系统下信号变化趋势的一致性, 同时确定了CO2检测系统的最佳调制参量。通过实验系统对不同体积分数的CO2在1432.04nm处的吸收光谱进行了测量, 建立主吸收峰处信号强度与不同体积分数CO2的反演模型, 分析了系统性能及测量精度。结果表明, 线性拟合系数R2=0.9998, 气体体积分数反演最大相对误差为0.7333%, 系统检测限为0.0074%;通过调制参量的优化选择可以获得较为理想的二次谐波信号, 从而实现待测气体体积分数的精确反演。该研究为检测系统中调制参量的优化提供了重要参考, 为系统测量精度的改善提供了指导。
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关键词:
- 光谱学 /
- 调制参量优化 /
- 建模仿真 /
- 可调谐二极管激光吸收光谱 /
- 体积分数反演模型
Abstract: In order to study the effect of laser modulation parameters on the peak, signal-to-noise ratio, peak width, symmetry, and signal integrity of second harmonic signals, the analysis based on the hardware system and the Simulink analogue model were verified that the theoretical simulation results were consistent with the signal variation trend of the hardware system, and at the same time the optimal modulation parameters of the CO2 detection system were determined. Through the experimental system, the absorption spectra of different volume fraction of CO2 at 1432.04nm were measured, the inversion model of the signal intensity at the main absorption peak and CO2 volume fraction was established, and the system performance and measurement accuracy were analyzed. The results show that the linear fitting coefficient R2 is 0.9998, the maximum relative error of gas volume fraction inversion is 0.7333%, and the detection limit of the system is 0.0074%. The ideal second harmonic signal can be obtained through the optimal selection of modulation parameters, so as to achieve accurate inversion of the gas volume fraction to be measured. The study provides an important reference for the optimization of modulation parameters in the detection system and provides guidance for the improvement of the measurement accuracy of the system. -
Table 1. Gas volume fraction measurement and inversion results
gas volume
fractionpeak of main
absorptionlinear fitting inversion
volume fractionrelative
error/%0.001 5.5318 0.000998 0.2000 0.003 12.4169 0.002978 0.7333 0.005 19.4887 0.005011 0.2200 0.007 26.5009 0.007028 0.4000 0.008 30.0577 0.008050 0.6250 0.009 33.1322 0.008935 0.7222 -
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