CN112378883B - TDLAS gas concentration calibration method based on relative error least square method - Google Patents
TDLAS gas concentration calibration method based on relative error least square method Download PDFInfo
- Publication number
- CN112378883B CN112378883B CN202011362264.3A CN202011362264A CN112378883B CN 112378883 B CN112378883 B CN 112378883B CN 202011362264 A CN202011362264 A CN 202011362264A CN 112378883 B CN112378883 B CN 112378883B
- Authority
- CN
- China
- Prior art keywords
- gas concentration
- objective function
- calibration
- relative error
- light intensity
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 47
- 238000000041 tunable diode laser absorption spectroscopy Methods 0.000 title claims abstract description 24
- 238000011088 calibration curve Methods 0.000 claims abstract description 21
- 238000002834 transmittance Methods 0.000 claims abstract description 16
- 238000005259 measurement Methods 0.000 claims abstract description 12
- 238000010521 absorption reaction Methods 0.000 claims description 9
- 238000012937 correction Methods 0.000 claims description 8
- 239000011159 matrix material Substances 0.000 claims description 6
- 238000000862 absorption spectrum Methods 0.000 claims 2
- 239000000463 material Substances 0.000 claims 1
- HBMJWWWQQXIZIP-UHFFFAOYSA-N silicon carbide Chemical compound [Si+]#[C-] HBMJWWWQQXIZIP-UHFFFAOYSA-N 0.000 claims 1
- 229910010271 silicon carbide Inorganic materials 0.000 claims 1
- 238000006467 substitution reaction Methods 0.000 claims 1
- 238000011156 evaluation Methods 0.000 abstract description 2
- 238000005516 engineering process Methods 0.000 description 4
- 238000001514 detection method Methods 0.000 description 3
- 238000012544 monitoring process Methods 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Chemical compound O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- 238000004847 absorption spectroscopy Methods 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 230000031700 light absorption Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 239000013307 optical fiber Substances 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 230000035945 sensitivity Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
- G01N21/39—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using tunable lasers
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2201/00—Features of devices classified in G01N21/00
- G01N2201/12—Circuits of general importance; Signal processing
- G01N2201/127—Calibration; base line adjustment; drift compensation
Landscapes
- Physics & Mathematics (AREA)
- Spectroscopy & Molecular Physics (AREA)
- Analytical Chemistry (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Chemical & Material Sciences (AREA)
- Optics & Photonics (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Investigating Or Analysing Materials By Optical Means (AREA)
Abstract
The invention relates to a TDLAS gas concentration calibration method based on a relative error least square method, which takes a relation between light intensity transmittance and gas concentration as an objective function, and provides a least square fitting method taking the relative error as an evaluation standard. The invention provides a relative error least square method, which solves the problems of larger relative error and measurement misalignment of a TDLAS gas concentration calibration curve under a low concentration range, ensures the stability of the integral error distribution of wide-range calibration of the TDLAS sensor, enlarges the calibration range and improves the measurement precision.
Description
Technical Field
The invention belongs to the technical field of optical fiber sensing, and particularly relates to a TDLAS gas concentration calibration method based on a relative error least square method.
Background
The tunable semiconductor laser spectrum technology (TDLAS, tunable diode laser absorption spectroscopy) utilizes the selective absorption of gas molecules to laser signals to calculate the optical power change of incident light and emergent light, thereby realizing the quantitative detection of the concentration of the gas to be detected. In recent years, a large number of students have studied the TDLAS technology, and compared with other spectrum detection technologies, the TDLAS technology has the advantages of high sensitivity, high resolution, real-time monitoring, good portability, miniaturization and the like, and is widely applied to the fields of industrial environmental protection, medical detection, meteorological monitoring and the like.
Calibration is needed before the TDLAS gas sensor leaves the factory, a corresponding relation curve of the light intensity transmittance logarithm and the calibration concentration is fitted, and the fitting result influences the measurement accuracy of the sensor. The least square method (Least Squares Method, LSA) is a fitting algorithm commonly used at present, and takes the least square sum of absolute errors as an evaluation standard, so that the relative error cannot be restrained, the relative error of a calibration curve of the TDLAS gas sensor under a low concentration range is larger, and the calibration range is limited. In addition, the TDLAS gas sensor is generally calibrated by using a polynomial as an objective function, which can only ensure the measurement accuracy in a smaller concentration range and the measurement error outside the measuring range is increased sharply. For large-range calibration, a complete relation between the light intensity transmittance logarithm and the gas concentration is needed to be deduced, and the relation is used as an objective function for fitting, so that the measurement accuracy in the whole range is improved.
Disclosure of Invention
The invention aims to solve the technical problems that: when the gas concentration in a large range is calibrated in the TDLAS direct absorption spectrometry, and when the calibration curve is fitted by adopting a least square method, the relative error of the calibration curve of the TDLAS gas sensor under a low concentration range is large, and the integral error cannot meet the calibration requirement, so that the measurement accuracy is affected. The invention provides a TDLAS gas concentration calibration curve fitting method based on a relative error least square method, which adopts a Gaussian-Newton iteration method, and uses the relation between the logarithm of light intensity transmittance and gas concentration as an objective function to calibrate a TDLAS gas sensor, thereby improving the fitting relativity of a calibration curve, reducing fitting errors, improving calibration precision and expanding the calibration range.
The technical scheme adopted for solving the technical problems is as follows: a TDLAS gas concentration calibration method based on a relative error least square method comprises the following steps: establishing a fitted objective function by using a relation between the light intensity transmissivity logarithm and the gas concentration Ratio-C, searching an optimal solution of a undetermined coefficient in the objective function by searching the least square sum of relative errors, adopting a Gaussian-Newton iteration method in an iteration mode, optimizing the undetermined coefficient through repeated iteration correction to obtain a fitted calibration curve, and calibrating the TDLAS gas sensor.
The relation between the light intensity transmittance logarithm and the gas concentration Ratio-C is as follows: according to Beer-Lambert law, consider that at the center of the absorption peak, i.e., v=v 0, the gas concentration C is related to the logarithmic transmittance Ratio of light intensity as in (1):
I t is the transmitted light intensity after passing through the gas to be measured, I 0 is the incident light intensity, L is the light absorption path length, N is the temperature coefficient, p 0,T0 is the standard gas pressure and standard temperature, gamma air is the half-width of the air absorption line, gamma self is the half-width of the absorption line of the gas to be measured, K s (T) is the correction coefficient of the absorption line intensity with respect to the temperature, S 0 is the absorption line intensity at the standard gas pressure temperature, and N 0 is the unit volume molecular number at the standard gas pressure temperature;
The objective function: establishing a fitting objective function according to equation (1):
p (1) =s 0·N0·L/π,p(2)＝γself(p0,T0),p(3)＝γair(p0,T0), is the coefficient of uncertainty of the fit, The light intensity transmittance logarithm Ratio after temperature correction is shown, and y is the gas concentration measurement C corresponding to the calibration curve;
The sum of squares of the relative errors S:
Is the calibrated concentration value, r i is the relative error;
The sum of squares of the relative errors, smin: solving an equation with the partial derivative of S to p equal to 0, and in a nonlinear system, approximating and solving by an iteration method by setting an initial value:
k is the number of iterations, Δp is the iteration vector, and each iteration function is linear;
For f (x, p) the Taylor series expansion is performed at p k:
Order the The relative error at this time is:
Δyi＝yi *-f(xi,pk)
Δy i is the residual error of the kth iteration, and formula (7) is substituted into formula (4), resulting in:
(JTJ)Δp＝JTΔyi (8)
The iterative stepping formula: equation (8) is in a matrix form, J is a Jacobian matrix of the objective function, the iteration increment deltap can be obtained by solving equation (8), and the iteration increment deltap is substituted into equation (5) to obtain a final iteration formula:
The relative error least square method flow chart is shown in figure 1;
The implementation steps are as follows:
step one, setting a calibration concentration range, and measuring a gas concentration value C and a light intensity transmissivity logarithmic Ratio value under each calibration concentration.
Step two, establishing a fitting objective functionSetting an initial value of a coefficient p (1), p (2) and p (3) to be determined; the initial value setting can be calculated according to Hitran data ,p(1)＝S0·N0·L/π,p(2)＝γself(p0,T0),p(3)＝γair(p0,T0).The light intensity transmittance log Ratio after temperature correction is shown, and y is a gas concentration measurement value C corresponding to a calibration curve;
step three, solving a Jacobian matrix J of an objective function, and calculating a residual error delta y i＝yi *-f(xi,pk),yi * of the kth iteration as an ith calibration concentration value and f (x i,pk) as a measurement value of the ith calibration curve;
Step four, solving equation (J TJ)Δp＝JTΔyi) to obtain iteration increment delta p, if f (x i,pk)-f(xi,pk-1) < epsilon, epsilon is a set error rate threshold, finishing iteration, and if f (x i,pk)-f(xi,pk-1) > epsilon, delta p is substituted into the iteration formula, wherein the undetermined parameter is the optimal solution Updating the undetermined parameters, and repeating the fourth step;
and fifthly, substituting the optimized undetermined parameters into an objective function to obtain a calibration curve, and substituting the measured light intensity transmittance logarithm Ratio into the calibration curve to obtain the measured gas concentration value.
Compared with the prior art, the invention has the advantages that: the method fits the TDLAS gas concentration calibration curve based on the relative error least square method, solves the problems that the relative error of the TDLAS sensor is large under low concentration and the calibration range is limited when the TDLAS sensor is calibrated in a large range, can effectively reduce the relative error of the calibration curve, improves the fitting relativity of the calibration curve, and enables the measured value to be more accurate.
Drawings
FIG. 1 is a flow chart of the relative error least squares method of the present invention;
FIG. 2 is a fitted curve of the least squares method and the least squares method of the relative error with the Ratio-C relation as the objective function in the embodiment of the present invention;
FIG. 3 is a graph showing the error distribution of a fitted curve using the Ratio-C relation as the objective function least squares method and the relative error least squares method in an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to examples.
According to the invention, water vapor is selected as a measuring gas, the concentration range is calibrated to be 0.7% -50% VOL, the objective function selects a Ratio-C relation, and the fitting results of a least square method (LSA) and a relative error least square method (RELSA) are compared.
The respective calibration concentrations C and the light intensity transmittance logarithmic Ratio were measured, and the results are shown in table 1:
TABLE 1 calibration results of 0.7% -50% VOL Water vapor concentration
Fitting the data in table 1, wherein the objective function is a Ratio-C relation derived by the invention, the initial value is set to be p (1) =0.85, p (2) =0.093, and p (3) =0.51, the fitting algorithm adopts a least square method and a relative error least square method, error analysis is carried out on the fitting results of the two methods, fig. 2 is a fitting curve of the two methods, fig. 3 is an error distribution diagram of the two methods, and table 2 is error fitting statistics of the two methods.
Table 2 Ratio-C fit error statistics for two algorithms with objective function
As shown in fig. 3, from the fitting error distribution result of the Ratio-C relation as the objective function, a larger relative error occurs under a low concentration range by using a least square method, and the relative error gradually decreases under a high concentration range; the whole error distribution tends to be stable by adopting a relative error least square method, and the method is similar to a fitting result with a polynomial as an objective function. As can be seen from table 2, the maximum relative error of the relative error least square method is 0.0494, the relative error standard deviation is 0.0237, and both the maximum relative error 0.1604 and the relative error standard deviation are better than those of the least square method by 0.0572. And combining polynomial fitting results, taking a Ratio-C relation as an objective function, wherein the fitting result by adopting a relative error least square method is best, the relative error is within +/-5%, the maximum relative error and the relative error standard deviation are minimum, and the fitting result is optimal.
The above examples are provided for the purpose of describing the present invention only and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalents and modifications that do not depart from the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (1)
1. A TDLAS gas concentration calibration method based on a relative error least square method is characterized in that: comprising the following steps: establishing a fitted objective function by using a relation between the light intensity transmissivity logarithm and the gas concentration Ratio-C, searching an optimal solution of a undetermined coefficient in the objective function by searching the least square sum of relative errors, adopting a Gaussian-Newton iteration method in an iterative mode, and optimizing the undetermined coefficient through repeated iterative correction to obtain a fitted calibration curve, and calibrating the TDLAS gas sensor;
The relation between the light intensity transmittance logarithm and the gas concentration Ratio-C is as follows: according to Beer-Lambert law, consider the position at the center of the absorption peak, i.e The relation between the gas concentration C and the light intensity transmittance logarithm Ratio is as shown in the formula (1):
（1）
To transmit the light intensity after passing through the gas to be measured, For the intensity of the incident light,For the length of the light-absorbing path,Is a temperature coefficient of the silicon carbide material,Is a standard gas pressure and a standard temperature,Is the half-width of the air absorption spectrum line,Is the half-width of the absorption spectrum line of the gas to be measured,Is the correction factor of the absorption line intensity with respect to temperature,Is the absorption line intensity at standard air pressure temperature,Is the number of molecules per unit volume at standard atmospheric pressure temperature;
the objective function: establishing a fitting objective function according to equation (1):
（2）
，， is the undetermined coefficient of the fitting, The light intensity transmittance logarithm Ratio after temperature correction is shown, and y is the gas concentration measurement C corresponding to the calibration curve;
The sum of squares of the relative errors S:
（3）
Is the value of the calibrated concentration, Is the relative error;
the sum of squares of the relative errors Minimum: solving forFor a pair ofEquation with partial derivative equal to 0, in a nonlinear system, by setting an initial value, approximating and solving by an iterative method:
（4）
（5）
is the number of iterations that are performed, Is an iteration vector, and each iteration function is linear;
For a pair of At the position ofThe processing uses Taylor series expansion:
（6）
Order the The relative error at this time is:
，
（7）
Is the first Residual error of the next iteration, substituting formula (7) into formula (4), and obtaining:
，
（8）
the iterative stepping formula: the formula (8) is in the form of a matrix, Jacobian matrix, which is the objective function, can be solved to obtain iteration increment (8)Substituting formula (5) to obtain a final iteration formula:
（9）
The relative error least square method implementation step:
Step one, setting a calibration concentration range, and measuring a gas concentration value C and a light intensity transmittance logarithmic Ratio value under each calibration concentration;
Step two, establishing a fitting objective function Setting undetermined coefficient，，Is the initial value of (2); the initial value setting may be calculated from Hitran data,，，，The light intensity transmittance log Ratio after temperature correction is shown, and y is a gas concentration measurement value C corresponding to a calibration curve;
step three, solving Jacobian matrix of objective function Calculate the firstResidual error of multiple iterations，For the i-th calibration concentration value,Is the measured value of the ith calibration curve;
Step four, solving the equation Obtaining iteration incrementIf (3)，If the error rate threshold is set, iteration is completed, and the undetermined parameter is an optimal solution; if it is，Substitution into iterative formulaUpdating the undetermined parameters, and repeating the fourth step;
and fifthly, substituting the optimized undetermined parameters into an objective function to obtain a calibration curve, and substituting the measured light intensity transmittance logarithm Ratio into the calibration curve to obtain the measured gas concentration value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011362264.3A CN112378883B (en) | 2020-11-27 | 2020-11-27 | TDLAS gas concentration calibration method based on relative error least square method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011362264.3A CN112378883B (en) | 2020-11-27 | 2020-11-27 | TDLAS gas concentration calibration method based on relative error least square method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112378883A CN112378883A (en) | 2021-02-19 |
| CN112378883B true CN112378883B (en) | 2024-07-02 |
Family
ID=74589053
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202011362264.3A Active CN112378883B (en) | 2020-11-27 | 2020-11-27 | TDLAS gas concentration calibration method based on relative error least square method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112378883B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113758899B (en) * | 2021-11-11 | 2022-04-08 | 国网湖北省电力有限公司超高压公司 | Micro-water measuring method and device based on TDLAS technology |
| CN115266619A (en) * | 2022-07-21 | 2022-11-01 | 北京九强生物技术股份有限公司 | Calibration model and method for determining the concentration of a substance to be measured |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109557045A (en) * | 2018-12-10 | 2019-04-02 | 中国科学院电工研究所 | It is a kind of for extracting the approximating method of direct absorption line in TDLAS technology |
| CN110057779A (en) * | 2019-04-28 | 2019-07-26 | 西北核技术研究所 | Method and apparatus based on temperature self-compensation TDLAS technology measurement gas concentration |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6518562B1 (en) * | 2000-01-20 | 2003-02-11 | Gas Research Institute | Apparatus and method of remote gas trace detection |
| GB2532088B (en) * | 2014-11-10 | 2017-10-11 | Optosci Ltd | Multipoint gas sensing apparatus |
| US10643008B2 (en) * | 2014-11-11 | 2020-05-05 | Spectrasensors, Inc. | Target analyte detection and quantification in sample gases with complex background compositions |
| CN110736719A (en) * | 2019-11-27 | 2020-01-31 | 中国科学院电工研究所 | gas concentration calibration and measurement method based on TDLAS direct absorption spectrum |
-
2020
- 2020-11-27 CN CN202011362264.3A patent/CN112378883B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109557045A (en) * | 2018-12-10 | 2019-04-02 | 中国科学院电工研究所 | It is a kind of for extracting the approximating method of direct absorption line in TDLAS technology |
| CN110057779A (en) * | 2019-04-28 | 2019-07-26 | 西北核技术研究所 | Method and apparatus based on temperature self-compensation TDLAS technology measurement gas concentration |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112378883A (en) | 2021-02-19 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112378883B (en) | TDLAS gas concentration calibration method based on relative error least square method | |
| CN104198416B (en) | The measurement error real-time compensation method that the drift of a kind of spectrometer wavelength causes | |
| US10241038B2 (en) | Spectrophotometer and spectrophotometry method | |
| CN107490397B (en) | High-accuracy self-adaptation filters the quick Peak Search Method of FBG spectrum | |
| CN102788643B (en) | Method for calibrating ontrack high-precision optical spectrum of space remote sensing optical spectrum instrument | |
| CN105424180B (en) | Calibration method for terahertz laser power meter | |
| CN110736719A (en) | gas concentration calibration and measurement method based on TDLAS direct absorption spectrum | |
| CN106679817A (en) | Method for calibrating thermal infrared imager | |
| CN104677495A (en) | Method for measuring flame temperature and emissivity distribution based on spectral radiance intensity | |
| CN113607686B (en) | Gas concentration detection method, system and computer readable storage medium based on correction TDLAS background signal drift | |
| CN112113928B (en) | Molecular spectroscopy and experimental data based mid-infrared methane sensor correction method | |
| CN108333143B (en) | Water vapor concentration measurement correction method based on tunable laser absorption spectrum | |
| CN103256999B (en) | Distributed type optical fiber temperature measuring method | |
| CN107144345B (en) | A kind of calibration method of multi-wavelength and wide temperature thz laser power meter | |
| CN116008308A (en) | Improved sky-tilt curve calibration method and calibration device for microwave radiometer | |
| CN112098365B (en) | Multi-spectral line gas absorption spectrum line type fitting measurement method based on orthogonal decomposition | |
| CN113390826B (en) | Integral absorbance measurement error estimation method for sight line non-uniform absorption spectrum measurement | |
| CN114646609B (en) | Correction method based on TDLAS absorption method pressure measurement under high mole fraction | |
| CN114878515A (en) | Tunable diode laser absorption signal time-frequency conversion method | |
| Gaynullin et al. | A practical solution for accurate studies of NDIR gas sensor pressure dependence. Lab test bench, software and calculation algorithm | |
| CN114235155B (en) | Method for measuring two-dimensional distribution of wide-range temperature based on multiple absorption spectral lines | |
| CN110657833A (en) | Novel calibration method for high-precision source meter integrated measuring equipment | |
| CN110702236B (en) | High-precision spectrum calibration method for optical fiber wavelength standard device | |
| CN116576974B (en) | Self-calibration method of multichannel microwave radiometer | |
| CN112986180B (en) | Spectrum type gas sensing data processing method and system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant |