CN109100325B - Gas concentration measuring method based on spectral absorption rate second harmonic feature extraction - Google Patents
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Abstract
The invention discloses a gas concentration measuring method based on spectral absorption rate second harmonic feature extraction, which realizes the calculation of integral absorbance by utilizing harmonic features by establishing a second harmonic peak height-peak width feature relation of spectral absorption rate considering a Foritt line type under any modulation coefficient, thereby obtaining gas parameter information; meanwhile, a logarithm processing technology is adopted in the implementation process of the method, so that the influence of residual amplitude modulation on harmonic signal distortion is directly eliminated, and the measurement precision is improved; the measuring method does not need to carry out complex least square iterative fitting calculation and only needs to carry out filtering processing once, thereby reducing the requirement on a hardware system; when the complete harmonic signal cannot be obtained, the waveform characteristic point information can be extracted more accurately, and the lower measurement limit is lower; excessive parameters such as self-broadening coefficients, collision broadening coefficients of various other components, temperature dependence indexes and the like in the database are not needed, the dependence on the database parameters is reduced, and the application range is wider.
Description
Technical Field
The invention relates to a gas concentration measuring method based on spectral absorption rate second harmonic feature extraction, and belongs to the technical field of laser absorption spectroscopy.
Background
Tunable Diode Laser Absorption Spectroscopy (TDLAS) can realize online measurement of multiple parameters such as component concentration, temperature, pressure and speed, has the characteristics of high sensitivity, fast time response, non-contact and the like, and has a wide application prospect in the fields of trace gas detection and combustion diagnosis.
In order to reduce the influence of noise on the measurement result and improve the signal-to-noise ratio, a Wavelength Modulation Spectroscopy (WMS) method is often used as a signal detection method, and second harmonic detection is most often used. In the actual quantitative measurement of the wavelength modulation spectroscopy, the measurement result is usually calibrated by the standard gas, however, because the components of the gas to be measured in the actual field environment are different from those of the standard gas and may change at any time, a certain error may exist in the gas concentration measurement value obtained completely according to the calibration mode. In order to solve the problem, researchers develop a series of calibration-free WMS methods, which mainly comprise a harmonic analysis method based on Hitran database simulation, a WMS-2f/1f waveform fitting method and the like. However, the harmonic analysis method based on Hitran database simulation requires precise spectral line parameters (e.g., self-broadening coefficient, collisional broadening coefficient of various other components, temperature dependent index, etc.) and laser modulation characteristic parameters, and the measurement result is greatly influenced by the spectral line parameters. The WMS-2f/1f waveform fitting method does not need more spectral line parameters, and is widely applied to measurement of gas parameters in recent years, however, the method needs a large amount of iterative fitting calculation, needs filtering processing of multiple harmonics, has a large calculation amount, and has high requirements on hardware and a fitting algorithm. More seriously, when the absorption is weak or the measurement environment is severe, the complete harmonic waveform signal is difficult to extract under the influence of background change and residual amplitude modulation, and at the moment, the WMS-2f/1f waveform fitting method cannot be applied. On the other hand, because the harmonic signal line type contains abundant information about the spectral absorption rate, the spectral absorption rate can be extracted from the waveform characteristics of the harmonic signal, so that the measurement of the gas parameters is realized. However, the existing method for extracting the spectral absorption rate of the waveform features is only suitable for harmonic analysis under a small modulation coefficient or a Lorentz line type, the measurement signal-to-noise ratio is low, and the application range is limited. Therefore, it is important to develop a calibration-free WMS method with high signal-to-noise ratio, independent of spectral line database parameters, and suitable for any modulation factor.
Disclosure of Invention
The invention aims to solve the technical problem of providing a gas concentration measuring method based on the second harmonic feature extraction of the spectral absorption rate, which has high signal-to-noise ratio and is independent of spectral line database parameters and suitable for the gas concentration measurement of calibration-free wavelength modulation spectrum under any modulation coefficient.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a gas concentration measuring method based on spectral absorption rate second harmonic feature extraction comprises the following steps:
step 1, the laser scans absorption spectral lines and modulates laser wavelength with high-frequency sinusoidal signals, and photoelectricityThe detector respectively measures background light intensity signals I without absorption0And a transmitted light intensity signal I with absorptiont；
step 3, obtaining a transmission light intensity signal I by measurementtWith background light intensity signal I0Carrying out logarithmic processing to obtain a spectrum absorption rate signal alpha (v);
step 4, performing phase-locked filtering processing on the spectral absorption rate signal alpha (v) to obtain a corresponding second harmonic signal Hα；
Step 5, calculating by utilizing a peak searching algorithm to obtain a second harmonic signal HαHeight of central peak of
Calculating to obtain a second harmonic signal H by combining the variation relation V (t) of laser scanning relative wave numberαA sidelobe width Λ in the frequency domain;
step 6, establishing a second harmonic signal H corresponding to the spectral absorption rate alpha (v) under any modulation coefficientαHeight of central peak of
And the sidelobe width Lambda, the integral absorbance A and the Lorentz broadening Lambda of the absorption spectrum lineLThe relationship of (1);
step 7, initializing Lorentz broadening Lambda of absorption spectral lineL＝λL0The Gaussian broadening lambda of the absorption line is calculated from the known temperatureGAnd calculating to obtain the theoretical side lobe width Lambda by combining the measured modulation depth alpha0；
Step 8, judging the sidelobe width Lambda obtained in the step 5 and the theoretical sidelobe width Lambda obtained in the step 70Whether the following convergence condition is satisfied:
in the formula, s is a preset convergence threshold value;
if so, obtaining the Lorentz broadening Lambda of the absorption lineL＝λL0Combining the harmonic central peak height obtained in step 5
Calculating the integral absorbance A, wherein the integral absorbance A is calculated according to the following formula:
if not, updating lambdaL0＝λnewReturning to the step 7; wherein λ isnewThe optimization algorithm is a new value generated by the adopted optimization algorithm, the optimization algorithm can be randomly selected from various algorithm functions in the MATLAB, and the selected function can generate a random new value;
step 9, calculating a concentration value of the gas according to the calculated integral absorbance A, wherein a calculation formula of the concentration value of the gas is as follows:
wherein P is total gas pressure, S (T) is spectral line intensity at temperature T, and L is absorption optical path length.
In step 3, the expression of the logarithm processing is:
α(v)＝-ln(It/I0)＝Aφ(v)
in the formula: i istAnd I0The laser transmission light intensity and the laser incidence light intensity are respectively; a is the integral absorbance; phi (v) is a linear function.
Wherein, the linear function phi (v) is the convolution of a Lorentzian linear function and a Gaussian linear function, and is described by adopting a Formit linear function, and the approximate expression is as follows:
φ(v)＝cLφL(v)+cGφG(v)
in the formula: phi is aLAnd phiGLorentzian linear function and Gaussian linear function respectively; c. CLAnd cGRespectively Lorentz spread lambdaLAnd a Gaussian spread λGThe weight coefficient of (a); v. of0Is the laser line center frequency; λ is the full width at half maximum of the absorption line; c. CL、cGThe formula for the sum λ is as follows:
d＝(λL-λG)/(λL+λG)
cL＝0.6818817+0.6129331d-0.1838439d2-0.1156844d3
cG＝0.3246017-0.6182531d+0.1768139d2+0.1210944d3
extracting the height of the central peak value of the second harmonic and the width of the minor peak of the side lobe in the frequency domain as characteristic quantities, and establishing a second harmonic signal H corresponding to the spectral absorption rate alpha (v) and suitable for any modulation coefficientαCentral peak height and sidelobe width Λ and integrated absorbance A and Lorentz broadening λ of absorption linesLThe relationship of (1);
wherein, the second harmonic signal H corresponding to the spectral absorption rate alpha (v)αHeight of central peak of
Lorentz broadening Lambda from the integrated absorbance A and absorption lineLThe relational expression of (1) is:
in the formula I1Is a first class of 1 st order deformed Bessel function, parameters m, cL、cGThe calculation formula of (a) is as follows:
d＝(λL-λG)/(λL+λG)
cL＝0.6818817+0.6129331d-0.1838439d2-0.1156844d3
cG＝0.3246017-0.6182531d+0.1768139d2+0.1210944d3
m＝2a/λ；
wherein, the second harmonic signal H corresponding to the spectral absorption rate alpha (v)αSide lobe width Lambda with integrated absorbance A and Lorentz broadening of absorption lines LambdaLThe relational expression of (1) is:
wherein r is cG/cL，p1＝1.966194179，p2＝0.390933340，p3＝3.093996758，p4＝0.388999538，p5＝0.806546476，p6＝-0.289132222，p7＝-1.775513203，p8＝0.017671096，p9＝1.041510614，p10＝-0.146221523，p11＝-1.073806845。
In step 9, the spectral line intensity s (t) is represented by the following formula along with the temperature change:
wherein h is the Planck constant, h is the speed of light in vacuum, k is the Boltzmann constant, E is the low-level energy, T0296K as reference temperature, v0The calculation methods of E and q (T) are obtained by querying a HITRAN2016 database.
Has the advantages that: the method is suitable for extracting the second harmonic peak height-peak width characteristic of the spectral absorption rate considering Voigt line type under any modulation coefficient, and simultaneously adopts a logarithm processing technology to process the measurement signal, thereby achieving the light intensity normalization effect same as WMS-2f/1f, and the result obtained by logarithm processing is irrelevant to the intensity modulation parameter of the laser, directly eliminating the influence of residual amplitude modulation on harmonic signal distortion, and improving the measurement precision; compared with the WMS-2f/1f waveform fitting method, the measuring method does not need to carry out complex least square iterative fitting calculation and only needs to carry out filtering processing once, thereby reducing the requirement on a hardware system, still being capable of accurately extracting waveform characteristic point information when a complete harmonic signal cannot be obtained, and having lower measurement lower limit; excessive parameters such as self-broadening coefficients, collision broadening coefficients of various other components, temperature dependence indexes and the like in the database are not needed, the dependence on the database parameters is reduced, and the application range is wider.
Drawings
FIG. 1 is a flow chart of a gas concentration measurement method according to the present invention;
FIG. 2 is a graph comparing the fitting results of the WMS-2f/1f waveform fitting method with the harmonics obtained by the measurement method of the present invention;
FIG. 3 is a graph of concentration measurements for two gas concentration measurements at different gas distribution concentrations;
FIG. 4 is a comparison of relative errors measured by two gas concentration measurement methods at different gas distribution concentrations.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
Fig. 1 is a flowchart of the measurement method of the present invention, and as shown in fig. 1, the method for measuring gas concentration based on spectral absorption rate second harmonic feature extraction of the present invention specifically includes the following steps:
step 1, respectively measuring background light intensity signals I without absorption0And a transmitted light intensity signal I with absorptiont：
The laser scans absorption spectrum line and modulates laser wavelength with high-frequency sine signal, and the photoelectric detectors measure background light intensity signal I without absorption0And a transmitted light intensity signal I with absorptiont；
measuring an interference peak signal of laser after passing through the solid etalon, and converting a time domain light intensity signal into a frequency domain light intensity signal according to the free spectrum distance FSR of the solid etalon so as to obtain a variation relation V (t) of laser scanning relative wave number and the size a of modulation depth;
step 3, calculating the spectral absorptivity α (v):
for the measured transmitted light intensity signal ItWith background light intensity signal I0Logarithmic processing is carried out to obtain a spectral absorption rate signal alpha (v) ═ ln (I)t/I0)＝Aφ(v)；
Step 4, analyzing to obtain a second harmonic signal H of the spectrum absorption rate signalα：
Processing the spectral absorbance signal α (v) using a digital phase-locking process to obtain an x-component and a y-component comprising a second harmonic signal:
x2f＝α(v)·cos(4πfmt) y2f＝α(v)·sin(4πfmt)
in the formula (f)mTo modulate frequency, x2f、y2fAn x component and a y component corresponding to the spectral absorptance signal α (v), respectively;
then, the second harmonic X component and the second harmonic Y component of each signal are extracted through a low-pass filter:
X2f＝lowpass filter(x2f) Y2f＝lowpass filter(y2f)
the second harmonic of the spectral absorbance signal α (v) is shown below;
step 5, analyzing to obtain a second harmonic signal H of the spectrum absorption rate signalαCentral peak height and side lobe width of (d):
calculating to obtain a second harmonic signal H by utilizing a peak searching algorithmαHeight of central peak of
Calculating to obtain a second harmonic signal H by combining the variation relation V (t) of laser scanning relative wave numberαA sidelobe width Λ in the frequency domain;
step 6, establishing a second harmonic signal H corresponding to the spectral absorption rate alpha (v) under any modulation coefficientαHeight of central peak of
And the sidelobe width Lambda, the integral absorbance A and the Lorentz broadening Lambda of the absorption spectrum lineLThe relationship of (1):
second harmonic signal H corresponding to spectral absorptivity alpha (v)αHeight of central peak of
Lorentz broadening Lambda from the integrated absorbance A and absorption lineLThe expression of the relationship of (1) is:
in the formula I1Is a first class of 1 st order deformed Bessel function, parameters m, cL、cGThe calculation formula of (a) is as follows:
d＝(λL-λG)/(λL+λG)
cL＝0.6818817+0.6129331d-0.1838439d2-0.1156844d3
cG＝0.3246017-0.6182531d+0.1768139d2+0.1210944d3
m＝2a/λ
second harmonic signal H corresponding to spectral absorptivity alpha (v)αSide lobe width Lambda with integrated absorbance A and Lorentz broadening of absorption lines LambdaLThe expression of the relationship of (1) is:
wherein r is cG/cLParameter piThe values of (i ═ 1, 2.., 11) are shown in table 1:
TABLE 1 parameter piValue taking
Step 7, calculating a harmonic side lobe width theoretical value Lambda0：
Firstly, the Lorentz broadening Lambda of the absorption line needs to be initializedL＝λL0；
The Gaussian broadening lambda of the absorption line can be calculated from the known temperatureGThe calculation formula is as follows:
λG＝7.1623×10-7v0(T/M)1/2
in the formula, M is the molar mass of the gas to be detected;
combining the measured modulation depth a and utilizing the second harmonic signal H corresponding to the spectral absorption rate alpha (v) established in step 6αSide lobe width Lambda with integrated absorbance A and Lorentz broadening of absorption lines LambdaLThe theoretical harmonic sidelobe width Lambda can be calculated by the relationship (A)0；
Step 8, judging the sidelobe width Lambda obtained in the step 5 and the theoretical sidelobe width Lambda obtained in the step 70Whether the following convergence condition is satisfied:
wherein, the convergence threshold is preset;
if so, obtaining the Lorentz broadening Lambda of the absorption lineL＝λL0Combining the harmonic central peak height obtained in step 5
The integral absorbance A can be calculated according to the following formula:
if not, updating lambdaL0＝λnewReturning to the step 7; wherein λ isnewIs a new value generated by the adopted optimization algorithm, the optimization algorithm can be randomly selected from various algorithm functions in the MATLAB, and the selected function can generate a random new value.
Step 9, calculating to obtain a gas concentration value:
the gas concentration value can be calculated according to the integral absorbance A by the following formula:
wherein P is total gas pressure, S (T) is spectral line intensity at temperature T, and L is absorption optical path length.
The variation of the absorption line intensity s (t) with temperature can be expressed as:
wherein h is the Planck constant, h is the speed of light in vacuum, k is the Boltzmann constant, E is the low-level energy, T0296K as reference temperature, v0Is a music scoreThe line center frequency, Q (T), is the partition function value at temperature T, and the calculation of E and Q (T) can be found in the HITRAN2016 database.
Example 1
Following is CH4Molecule 6046.95cm-4Spectral line to proceed CH4Measurement of the volume concentration, CH4The gas distribution concentrations are respectively as follows: 2.10X 10-2、1.57×10-2、1.05×10-2、5.28×10-3、2.08×10-3、1.10×10-3、5.01×10-4、2.54×10-4. The fitting result of the WMS-2f/1f waveform fitting method and the harmonic comparison result obtained by the measuring method of the invention are shown in FIG. 2. As can be seen from FIG. 2, when CH is present4At higher volume concentrations (> 1.10X 10)-3) The WMS-2f/1f waveform is complete and the fit residual is small. But with CH4The volume concentration is reduced, the signal to noise ratio of measurement is reduced, the WMS-2f/1f waveform is obviously distorted, and the WMS-2f/1f waveform fitting method is not suitable for calculating CH4Volume concentration. Different from the WMS-2f/1f waveform fitting method, the second harmonic feature extraction method based on the spectral absorption rate does not need complete waveform information, and only needs to extract the second harmonic signal HαThe center peak height and the harmonic width of the filter can be obtained. Due to H in factαThe signal-to-noise ratio of the harmonic wave at the center height is highest, and the side peak height is HαThe influence of the width is not large, so the method provided by the invention has higher signal-to-noise ratio. Even when CH is present4The volume concentration is 2.54 multiplied by 10-4When H is presentαThe harmonics still have a more pronounced peak height-peak width characteristic. Different CH4Under the gas distribution concentration, the concentration measurement results of the two methods are shown in figures 3-4. When CH is present4Volume concentration of more than 2.08X 10-3When the relative deviation measured by the two methods is less than 2%, when the concentration is further reduced (< 1.10 multiplied by 10)-3) And along with the reduction of the measurement signal-to-noise ratio, the measurement deviation of the two methods is increased, but the measurement result of the harmonic feature extraction method is closer to the gas distribution concentration.
It can be seen that the method provided by the invention does not need to perform complex least square iterative fitting calculation and only needs to perform filtering processing once, thereby reducing the requirements on a hardware system; when the complete harmonic signal cannot be obtained, the waveform characteristic point information can be accurately extracted, and the lower limit of measurement is lower; excessive parameters such as self-broadening coefficients, collision broadening coefficients of various other components, temperature dependence indexes and the like in the database are not needed, the dependence on the database parameters is reduced, and the application range is wider. The measurement result is more accurate, and compared with a WMS-2f/1f waveform fitting method, the calculation result of the method provided by the invention is more reliable.
Claims (3)
1. A gas concentration measuring method based on spectral absorption rate second harmonic feature extraction is characterized by comprising the following steps:
step 1, a laser scans absorption spectral lines and modulates laser wavelength with high-frequency sinusoidal signals, and a photoelectric detector respectively measures background light intensity signals I without absorption0And a transmitted light intensity signal I with absorptiont；
Step 2, measuring an interference peak signal of laser after passing through the solid etalon, and converting a time domain light intensity signal into a frequency domain light intensity signal according to the free spectrum distance FSR of the solid etalon, thereby obtaining a variation relation V (t) of laser scanning relative wave number and the size a of modulation depth;
step 3, obtaining a transmission light intensity signal I by measurementtWith background light intensity signal I0Carrying out logarithmic processing to obtain a spectrum absorption rate signal alpha (v);
wherein, the expression of the logarithm processing is:
α(v)＝-ln(It/I0)＝Aφ(v)
in the formula: i istAnd I0The laser transmission light intensity and the laser incidence light intensity are respectively; a is the integral absorbance; phi (v) is a linear function;
the linear function phi (v) is the convolution of a Lorentzian linear function and a Gaussian linear function, and is described by a Formit linear function, and the approximate expression of the linear function phi (v) is as follows:
φ(v)＝cLφL(v)+cGφG(v)
in the formula: phi is aLAnd phiGLorentzian linear function and Gaussian linear function respectively; c. CLAnd cGRespectively Lorentz spread lambdaLAnd a Gaussian spread λGThe weight coefficient of (a); v. of0Is the laser line center frequency; λ is the full width at half maximum of the absorption line; c. CL、cGThe formula for the sum λ is as follows:
d＝(λL-λG)/(λL+λG)
cL＝0.6818817+0.6129331d-0.1838439d2-0.1156844d3
cG＝0.3246017-0.6182531d+0.1768139d2+0.1210944d3
step 4, performing phase-locked filtering processing on the spectral absorption rate signal alpha (v) to obtain a corresponding second harmonic signal Hα；
Step 5, calculating by utilizing a peak searching algorithm to obtain a second harmonic signal HαHeight of central peak of
Calculating to obtain a second harmonic signal H by combining the variation relation V (t) of laser scanning relative wave numberαA sidelobe width Λ in the frequency domain;
step 6, establishing a second harmonic signal H corresponding to the spectral absorption rate alpha (v) under any modulation coefficientαHeight of central peak of
And the sidelobe width Lambda, the integral absorbance A and the Lorentz broadening Lambda of the absorption spectrum lineLThe relationship of (1);
wherein, the second harmonic signal H corresponding to the spectral absorption rate alpha (v)αHeight of central peak of
Lorentz broadening Lambda from the integrated absorbance A and absorption lineLThe relational expression of (1) is:
in the formula I1Is a first class of 1 st order deformed Bessel function, parameters m, cL、cGThe calculation formula of (a) is as follows:
d＝(λL-λG)/(λL+λG)
cL＝0.6818817+0.6129331d-0.1838439d2-0.1156844d3
cG＝0.3246017-0.6182531d+0.1768139d2+0.1210944d3
m＝2a/λ；
step 7, initializing Lorentz broadening Lambda of absorption spectral lineL＝λL0The Gaussian broadening lambda of the absorption line is calculated from the known temperatureGAnd calculating to obtain the theoretical side lobe width Lambda by combining the measured modulation depth alpha0；
Step 8, judging the sidelobe width Lambda obtained in the step 5 and the theoretical sidelobe width Lambda obtained in the step 70Whether the following convergence condition is satisfied:
wherein, the convergence threshold is preset;
if so, obtaining the Lorentz broadening Lambda of the absorption lineL＝λL0Combining the harmonic central peak height obtained in step 5
Calculating the integral absorbance A, wherein the integral absorbance A is calculated according to the following formula:
if not, updating lambdaL0＝λnewReturning to the step 7; wherein λ isnewThe optimization algorithm is a new value generated by the adopted optimization algorithm, the optimization algorithm can be randomly selected from various algorithm functions in the MATLAB, and the selected function can generate a random new value;
step 9, calculating a concentration value of the gas according to the calculated integral absorbance A, wherein a calculation formula of the concentration value of the gas is as follows:
wherein P is total gas pressure, S (T) is spectral line intensity at temperature T, and L is absorption optical path length.
2. The method for measuring gas concentration based on spectral absorption rate second harmonic feature extraction according to claim 1, characterized in that: in step 6, the second harmonic signal H corresponding to the spectral absorption rate alpha (v)αSide lobe width Lambda with integrated absorbance A and Lorentz broadening of absorption lines LambdaLThe relational expression of (1) is:
wherein r is cG/cL，p1＝1.966194179，p2＝0.390933340，p3＝3.093996758，p4＝0.388999538，p5＝0.806546476，p6＝-0.289132222，p7＝-1.775513203，p8＝0.017671096，p9＝1.041510614，p10＝-0.146221523，p11＝-1.073806845。
3. The method for measuring gas concentration based on spectral absorption rate second harmonic feature extraction according to claim 1, characterized in that: in step 9, the spectral line intensity s (t) is represented by the following formula with temperature:
wherein h is the Planck constant, c is the speed of light in vacuum, k is the Boltzmann constant, E is the low-level energy, T0296K as reference temperature, v0The calculation methods of E and q (T) are obtained by querying a HITRAN2016 database.
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