Abstract
The high-pressure absorption spectrum at 6046.96 c
High-pressure gas detection is required urgently in the fields of natural gas pipeline transportation monitoring， deep submergence detection， aircraft engine diagnosis and other industries and national defense fields. Traditional semiconductor and electrochemical sensors which use contact measurement methods are prone to false alarm in high-pressure environment as the poor adaptability and difficult to meet on-line detection needs at high-pressure. In recent years， a new spectroscopy detection technology represented by Tunable Diode Laser Absorption Spectroscopy （TDLAS） technology has become a research focus in gases diagnosis under extreme conditions such as high temperature and high-pressure environment because of its high sensitivity， high selectivity， non-contact detection and strong adaptability to harsh environment
In high-pressure environment， due to the molecular collision aggravation the absorption spectral line broadened obviously， which led to the change of characteristic absorption spectrum. So， the spectral characteristic parameters must be accurately obtained for inverting gas concentration. At present， the study of spectral characteristic parameters at normal pressure is comprehensive. For example， Rieker et al.
As an important fuel and chemical raw material， methane has been widely used in civil and industrial fields. In this paper， the research experiment of spectrum broadening characteristics of methane at 6 046.96 c
Based on Lambert-Beer's law， a monochromatic laser with the emitting frequency of and the initial intensity of passes through an absorption medium of L in length， and the laser intensity at the receiving end is ， so the absorbance used to represent the absorption intensity can be expressed as Eq.1：
| , | （1） |
where S（T） is the line strength， P is the pressure， x is the gas concentration， and is normalized linear function. As the spectral frequency of molecular absorption or molecular emission is not strictly monochromatic， the molecular absorption spectrum has linewidth and line-type
Linewidth is proportional to pressure P at a certain temperature which expressed as Eq.2：
| , | （2） |
where xB is the mole fraction of collision gas， is the binary collision broadening coefficient between components B and A which is a function of temperature. Each collision pairs and specific radiation transition is corresponding to a broadening coefficient. Hitran database gives the collision broadening coefficient in the normal atmospheric environment including the self-broadening coefficient and the air broadening coefficient （at 296 K as the reference temperature， 1 atm as the reference pressure）. The relationship between collision broadening coefficient and temperature T can be expressed as Eq.3：
| , | （3） |
where T0 is the reference temperature， is the broadening coefficient at T0， and n is the temperature dependent coefficient （usually < 1， typical value is 0.5）.
The center frequency of the corresponding absorption line at different pressures is obtained by linear fitting of the absorbance curves， and the corresponding relation can be expressed as Eq.4：
| , | （4） |
where is the original center frequency， is the self-induced pressure shift coefficient， and is the nitrogen-induced pressure shift coefficient.
The high-pressure experimental platform for spectrum detection with TDLAS was built， as shown in
Fig.1 （a） Spectrum measurement experimental platform, （b） gas path connection of experimental device
图1 （a） 光谱测量实验平台，（b） 实验装置气路连接
In this experiment， the absorption line of methane molecule at 1653.7 nm in the overtone band 2ν3 was selected， and the specific parameters of methane absorption line were shown in
In the experiment， the temperature and current operating parameters of the laser controller were firstly tuned to the position of the goal absorption line， and a saw-tooth signal of 100 Hz was used with the wavelength scanning range of about 0.25 nm. It is necessary to maintain air tightness in the experiment. First， 99.99% nitrogen was introduced into the high-pressure absorption cell to remove any residual gas adsorbed， and then the above step was repeated three times with the lasting time of 2∼3 minutes. Subsequently， the methane standard gas （1.0% volume concentration mixed nitrogen） was transmitted into the high-pressure absorption cell， and the valve was closed after 2 minutes. The spectrum measurement was carried out after the gas fully stabilizing about 30 seconds， and the pressure data was synchronously observed by EN837-1 gauge. Thus， a group of methane measurement spectrum was obtained respectively at different pressures （1.5∼5 atm） for analyzing. The uncertainty of the standard gas used here was about 2.0% which produced by Nanjing Special Gas Corporation. The collected detection spectral signals can be converted from time domain to frequency domain by etalon signal （FSR = 3 GHz） collected synchronously.
When TDLAS technology was used to gas detection， the noise caused by electronic components， window deformation in high-pressure environment and other factors will affect the measurement accuracy. Therefore， according to the non-linear and non-stationary characteristics of spectral signals， the empirical mode decomposition algorithm was selected to filter the detected spectral signals according to the advantages and disadvantages of various de-noising algorithms. Then， the Lorentz line-type fitting algorithm was used to obtain the absorbance signal and extract the characteristic absorption spectrum. The spectral analysis algorithm was as follows
（i）Firstly， all the extreme points in the specific signal X（t） were founded out， then， the upper envelope and the lower envelope were formed by cubic spline curve method with all of the extreme points. Supposing the average value of the upper and lower envelopes were m1， and the difference H1 can be expressed as Eq.5：
| . | （5） |
At the same time， H1 was regarded as a new X（t）， and the above steps were repeated until H1 satisfying the two conditions of the eigenmode function IMF. Then H1 was defined as the first-order IMF， denoted as IMF1. In general， the highest frequency component of the original signal was located in IMF1.
（ii） Secondly， the IMF1 was separated from X（t） to obtain the difference signal r1 which was expressed as Eq.6：
| ， | （6） |
where r1 was regarded as a new signal and the above steps were also repeated until the residual signal of the n order became a monotone function when the IMF variables which satisfied the eigenmode function cannot be generated. The residual signal of the n order was regarded as Eq.7：
| . | （7） |
Mathematically， X（t） can be expressed as the sum of IMF components and a residual function， i.e.：
| ， | （8） |
where was the residual function representing the average trend which contained different frequencies components arranged from high to low.
（iii） Thirdly， the IMF of each order was separated by a preset threshold value to generate the de-noised IMF components which were accumulated together with the residual function and to realize the de-noised signal reconstruction.
（iv）The de-noised signal was subjected to background baseline fitting to extract the absorbance signal. In general， the signal de-noising effect is evaluated by the signal-to-noise ratio （SNR） or root- -mean-square error （RMSE）
Fig. 2 （a） Absorbance signal before and after filtering, （b） line-type fitting and residual result
图2 （a）滤波前后的吸光度信号, （b）线型拟合和残差结果
（v）The Lorentz line-type function was used to fit absorbance spectral signal after time domain to frequency domain converting， and the fitting residual error was calculated within ±1%， as shown in
A group of spectral signals at different pressures were measured. The absorption linewidth showed obvious broadening characteristics that it increased with pressure increasing but the peak values of the signals decreased， so the line shape tended to be flat. The integrated absorbance spectral signals were shown in
Fig.3 Absorbance spectral signals after Lorentz line-type fitting
图3 洛伦兹线型拟合后的吸光度光谱信号
The line-type change of gas absorption lines was mainly due to the gas molecule collision intensifying in high pressure environment which enhanced the collision broadening effect. The actual broadening coefficient of absorption line was obtained by calculating the slope of linear fitting of the line-width result at different pressures， as shown in
| . | （9） |
Fig.4 Nitrogen broadening coefficient at 6 046.96 c
图4 6 046.96 cm-1处的氮气展宽系数
In this experiment， the methane concentration was 1.0%， so the content of N2 molecules in unit volume was much larger than that of methane molecules. Therefore， self-broadening caused by collision between the same molecules can be ignored， only the nitrogen broadening of the collision between methane molecules in excited state and N2 molecules needed to be considered. The nitrogen broadening coefficient was calculated to be 0.062 4 c
A group of center frequency of absorption line at different pressures was obtained by linear fitting of absorbance signals， as shown in
| . | （10） |
Fig.5 Center frequency drift phenomenon
图5 中心频率漂移现象
According to the above analysis， the unknown low concentration x can be measured as Eq.11 when the frequency corresponding to the peak value of the absorbance signal and the current pressure were known：
| . | （11） |
Fig.6 Calculated the pressure shift coefficient of nitrogen-induced
图6 计算的氮气诱导压力频移系数
In TDLAS system， the amplitude of the wavelength scanning signal was within a certain range to ensure the normal operation of the laser. As the pressure increased， the absorption signal linewidth had gradually increased， while the proportion of the directly detected signal without absorption part gradually decreased. Therefore， Lorentz line-type fitting results of absorbance signal were incomplete （as shown of dotted line in
Fig.7 Absorbance signals of different concentration at high pressure
图7 不同浓度的高压下吸光度信号
In the experiment， a group of methane standard gases with different concentrations were transported into the high-pressure absorption cell， and the absorbance signals after air pressure stabilizing were obtained as shown in
In Conclusion， the methane absorption spectrum at 6 046.96 c
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