CN109100045B - Gas temperature probability density distribution reconstruction method based on single light path multispectral - Google Patents
Gas temperature probability density distribution reconstruction method based on single light path multispectral Download PDFInfo
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Abstract
The invention provides a gas temperature probability density distribution reconstruction method based on single light path multispectral, which comprises the following steps: enabling laser of a plurality of absorption spectrum sections capable of covering certain absorption molecules in the gas to be detected to pass through the region of the gas to be detected along a single light path to obtain absorption rate integral measurement data corresponding to the plurality of absorption spectrum sections; an integral equation set for solving the gas temperature probability density distribution is constructed by utilizing the line intensity and the absorption rate integral of the absorption spectrum section; and carrying out normalization and discretization treatment on the integral equation set, solving to obtain polynomial fitting parameters of the gas temperature probability density distribution, and calculating the gas temperature probability density distribution. Compared with a multi-view multispectral imaging system, the multi-view multispectral imaging system has the advantages of simple structure, few required optical windows, capability of reconstructing gas temperature probability density distribution by using a limited number of discrete absorption spectrum segments without temperature distribution prior information, high reconstruction speed, excellent effect and wide application prospect in the field of non-contact non-uniform temperature distribution measurement.
Description
Technical Field
The invention relates to a single-light path multispectral-based gas temperature probability density distribution reconstruction method, in particular to a single-light path multispectral gas temperature probability density distribution reconstruction method capable of achieving high precision when measured temperature parameters are unevenly distributed. The intensity of the spectral line is not required to be continuous, and the application range is wide.
Background
The tunable laser absorption spectroscopy (TDLAS) is an effective method in the field of accurate measurement of temperature and substance concentration due to the advantages of rapidness, non-invasion and sensitivity and capability of measuring a plurality of flow field parameters on site, is widely applied to the aspects of combustion diagnosis, combustion control and the like, and has huge application potential and considerable prospect.
The single-path laser absorption spectrum technology of the two absorption spectral lines is used for acquiring the average temperature and component concentration of the flow field along the laser path. For example, in the patent "TDLAS gas temperature measurement detection method" (patent No. CN201510410013.0), based on computer temperature measurement processing software, the area of two paths of electrical signals in sawtooth waveform absorption peak region is extracted, and comparison processing operation is performed to obtain the average temperature value of the combustion flow field. Laser absorption spectroscopy of multiple absorption lines reconstructs the absorption distribution by solving a system of linear equations. For example, in the patent "apparatus for pyrometry and temperature field reconstruction based on laser absorption spectroscopy" (patent No. CN201320136230.1), the laser absorption spectroscopy technology and the computed tomography technology are combined by using a plurality of detectors and a plurality of absorption lines simultaneously, so as to realize the reconstruction of the temperature field.
Direct measurements of single-path laser absorption spectroscopy techniques reflect the average absorbance across the path. Using a two-wire direct absorption thermometry method, the ratio of the absorption integrals of the two absorption lines is a function of temperature only. As the paper "Development of a tunable diode sensor for a turbine system of gas turbine absorption, Applied Physics B82, 469-478 (2006)", is verified in a large industrial gas turbine for power generation, the ratio of the average temperature along the laser path to the absorbance measured by two water absorption lines in the near infrared region is converted and a multiline strategy is being developed to solve the problem of uneven temperature distribution.
Measuring the temperature distribution of the combustion gas along single-path multi-absorption line conversion by using a laser absorption spectrum technology, such as the Applied Optics,2001.40(24) and p.4404, the Applied Optics proposes that a column density value reflecting temperature and concentration distribution information is obtained by using a discretization technology under the condition of known upper and lower temperature limits, and has the advantages of rapidness and wide application range; while the distribution fitting technique reconstructs the results more accurately but requires a known temperature distribution profile. Similarly, Liu et al propose two measurement strategies, curve fitting and temperature grading, respectively. For example, the paper "Measurement of Non-Uniform temperature distributions Using Line-of-signal Absorption Spectroscopy" (AIAA Journal,2007.45(2): p.411-419.) uses two Measurement strategies to achieve reconstruction of a binary temperature distribution of low temperature 300K and high temperature 1500K, and illustrates that Using known physical constraints, reducing the degree of freedom improves the Measurement accuracy.
However, in the field of combustion diagnostics, where the temperature distribution is more complex than a binary distribution, the laser path should be discretized into multiple temperature segments during temperature grading, but this would increase the number of steps of the linear intensity matrix and further worsen the problem of ill-qualification. For example, in the paper "Measurement of non-uniform temperature distribution and concentration distribution combining line-of-sight tunable diode absorption spectrum with regularization method" (Appl Opt,2013.52(20): p.4827-42.) Liuchang, etc., a regularization method is used to measure the non-uniform temperature distribution and concentration distribution along the optical path, so that the ill-conditioned problem of matrix solution is well improved, prior information is obtained under the condition of using fluid dynamics simulation or thermocouple single-point temperature Measurement, the correspondence between the temperature box and the probability density is completed, and the reconstruction of the parabolic temperature distribution is realized. But this has the problem of requiring a priori information.
With TDLAS tomography, projections of optical paths from several different directions can be applied to reconstruct two-dimensional spatial parameter distribution images. For example, the paper "Application of related analysis for multi-specific modeling." (Computer Physics Communications,2008.179(4): p.250-255.) reconstructs the two-dimensional distribution of temperature and concentration of the flow field using multi-directional projection results and simulated annealing algorithms. In order to obtain more projections with reduced time and equipment investment, the paper "Two-dimensional morphology for concentration and temperature distribution based on tunable laser spectroscopy" (Measurement Science and Technology,2010.21(4): p.045301.) adopts four platforms to mount four lasers for rotation scanning to dynamically obtain projection information, and uses algebraic reconstruction Technology to reconstruct temperature distribution and concentration distribution. However, this method of achieving temperature field reconstruction requires multiple optical windows to acquire multiple sets of multiple projection measurements, which is a limitation for some system devices that do not suggest or allow for open optical windows.
Based on the background, the invention discloses a gas temperature probability density distribution reconstruction method based on single-light-path multispectral, which covers a measured gas parameter distribution field through single-light-path multispectral to obtain absorption rate integral data, so that an integral equation set is constructed and converted into a matrix equation for solving. On the basis of relatively simplifying the system structure, the temperature distribution detection with less prior information, no need of opening a plurality of optical windows, only use of limited absorption spectral lines, high precision and high resolution is realized. The requirement for spectral line selection is relaxed, the line intensity of the spectral line is not required to be continuous, and the method is suitable for various gases to be measured.
Disclosure of Invention
Aiming at a measured area with non-uniform parameter distribution, the invention provides a gas temperature probability density distribution reconstruction method based on single light path multispectral, which aims to reduce an optical window and simplify equipment complexity.
The technical scheme adopted by the invention is as follows:
the method comprises the following steps of firstly, obtaining measurement data of a plurality of absorption spectrum sections of a laser single light path: dividing a laser beam with scanning wavelength covering the absorption spectrum into two beams by utilizing a plurality of laser absorption spectrum sections of a gas molecule, wherein one beam passes through a temperature distribution field of a measured gas to be used as an absorption signal, the other beam passes through an etalon to be used as a reference signal, and measuring data of absorption rate integral corresponding to each absorption spectrum section is obtained through Voigt line type fitting;
step two, constructing an integral equation system for solving the temperature probability density distribution of the measured gas according to the linear intensities and the corresponding absorption rate integral measurement data of a plurality of absorption spectrum sections of the gas at different temperatures: the laser is utilized to emit laser spectral bands with different central wavelengths, laser passes through the temperature distribution field of the gas to be measured along the same path to obtain a measurement signal, and N corresponding absorption rate integrals are selected as measurement data:
wherein i is the number of the absorption spectrum band, ranging from one to the total number of the selected absorption spectrum band. A. theiRepresents the integral measurement data of the absorbance corresponding to the ith absorption spectrum band. P representing the gas to be measuredThe total pressure is in atm. L represents the path length of the gas to be measured in centimeters cm. T is the temperature of the gas to be measured in Kelvin K. T is1And T2Respectively, the lower limit and the upper limit of the temperature of the gas to be measured, and the unit is Kelvin K. Si(T) represents the linear intensity value of the laser in the ith absorption spectrum at the temperature T in cm-2atm-1. X (T) represents the mole fraction of the gas component at temperature T. And f (T) represents the temperature T corresponding to the path fraction of the gas. Considering that the concentration distribution of the gas component is approximately uniform in the measurement, the formula (1) can be simplified as follows:
step three, carrying out normalization processing on the integral equation set: normalizing T on the left and right sides of the expression (2), wherein the normalization expression is T ═ u (T) ═ T (T)2-T1)/(t2-t1)×(t-t1)+T1Wherein T is1、T2Respectively the lowest temperature and the highest temperature, t, of the gas temperature distribution field to be determined1、t2Respectively, the lowest temperature and the highest temperature after normalization, thereby obtaining an expression equivalent to the formula (2)
Wherein A (v)i) I.e. AiRepresents the integral measurement data of the absorption rate corresponding to the ith absorption spectrum band, wherein the central wave number is vi。S(u(t),vi) I.e. Si(T) the linear intensity value of the laser in the ith absorption spectrum band at the temperature T, wherein the central wave number is vi。
Step four, polynomial fitting to the probability density distribution of the temperature of the gas to be measured, and decomposing the integral equation set into a matrix equation: the probability density distribution of the temperature of the gas to be measured is expressed by a polynomial form
f(u(t))=d0'+d1't+d2't2+…+dn'tn(4)
Thus, an expression equivalent to the expression (3) is obtained,
decomposing the system of integral equations by using information of a plurality of laser absorption spectrum bands, including
Note the bookIs a column vector a, of length M,is matrix C, size M x (N +1),is a column vector D of length N, thus having a matrix equation AM×1=CM×(N+1)·D(N+1)×1. Wherein the matrix C reflects a coefficient matrix formed by specific absorption spectrum bands; the vector D represents a fitting parameter of the temperature probability density distribution to be solved; vector a reflects the absorbance integral measurement.
Solving a matrix equation to obtain a gas temperature probability density distribution fitting parameter: and solving the linear equation set of which the CD is A, solving to obtain a fitting parameter D of the temperature probability density distribution to be solved, further obtaining a polynomial expression of the temperature probability density distribution to be solved, and reflecting the temperature distribution condition of the gas to be measured.
The invention has the following effects: through the multispectral measurement data of the single light path, a plurality of optical windows are not required to be opened, the system is simplified, the integral equation is organized into a matrix equation, and the reconstruction speed and the precision and the resolution of the reconstructed parameter distribution image are improved. In the aspect of practical application, the method is suitable for various gases to be measured, and has no requirement on the continuity of the intensity of the spectral line.
Drawings
FIG. 1 is a schematic diagram of a single-path multi-spectral laser thermometry system.
FIG. 2 is a given raw temperature probability density distribution, (a) a unimodal probability density distribution; (b) a bimodal probability density distribution.
FIG. 3 is a simulation result of temperature probability density distribution reconstruction, (a) a unimodal reconstruction result; (b) bimodal reconstruction results.
Detailed Description
In the present embodiment, given a gas with a monomodal temperature probability density distribution and a bimodal temperature probability density distribution, the effectiveness of the method is demonstrated by numerical simulation of single-path multispectral spectra.
The invention is further described with reference to the accompanying drawings in which:
step one, aiming at gas H to be measured2O, selecting wave numbers of 6804.342cm respectively-1、6806.032cm-1、7181.156cm-1、7185.597cm-1、7444.352cm-1、7447.483cm-1、7450.932cm-1Carrying out verification simulation on the 7 spectral lines;
and step two, dividing the laser emitted by the laser into two beams of laser with equal light intensity through the optical fiber beam splitter, wherein one beam passes through the area to be detected, the other beam passes through the etalon, and then is received by the detector to obtain one path of absorption signal and one path of reference signal, as shown in fig. 1.
And step three, obtaining 7 absorption peaks in the scanning range of the laser, and calculating to obtain corresponding absorption rate integral data:
where i is the number of the absorption line, i is 1,2, … 7 in this example. A. theiRepresents the integral measurement data of the absorption rate corresponding to the ith absorption line, P represents the total pressure of the gas to be measured, P is 1atm in the embodiment, L represents the path length of the gas to be measured, and L is 48cm in the embodiment. T is1And T2Respectively, the lower limit and the upper limit of the temperature of the gas to be measured, in this caseExamples of T1=800K,T2=1300K。Si(T) represents the linear intensity value of the i-th absorption line at the temperature T, and the unit is cm-2atm-1. And f (T) is the given temperature probability density distribution, in this example a unimodal and a bimodal probability density distribution, respectively.
Step four, carrying out normalization processing on the integral equation set: normalizing T in the left side and the right side of the formula (1), wherein the normalization formula isWherein T is1、T2Respectively the lowest temperature and the highest temperature, t, of the gas temperature distribution field to be determined1、t2Respectively, the lowest temperature and the highest temperature after normalization, t in this example1=1K,t24K. Thereby obtaining an expression equivalent to the formula (1)
Wherein A (v)i) I.e. AiRepresents the integral measurement data of the absorption rate corresponding to the ith absorption spectrum band, wherein the central wave number is vi。S(u(t),vi) I.e. Si(T) the linear intensity value of the laser in the ith absorption spectrum band at the temperature T, wherein the central wave number is vi。
Step five, polynomial fitting to the probability density distribution of the temperature of the gas to be measured, and decomposing the integral equation set into a matrix equation: the probability density distribution of the temperature of the gas to be measured is expressed by a polynomial form
f(u(t))=d0'+d1't+d2't2+…+d6't6(3)
Thus, an expression equivalent to the expression (2) is obtained,
decomposing the system of integral equations by using information of a plurality of laser absorption spectrum bands, including
Note the bookIs a column vector a, of length 7,is a matrix C, with a size of 7 x 7,is a column vector D of length 7, and thus has a matrix equation A7×1=C7×7·D7×1. Wherein the matrix C reflects a coefficient matrix formed by specific absorption spectrum bands; the vector D represents a fitting parameter of the temperature probability density distribution to be solved; vector a reflects the absorbance integral measurement.
Solving a matrix equation to obtain a gas temperature probability density distribution fitting parameter: and iteratively solving the linear equation set of CD (total differential) A by adopting a generalized minimum residual error method, solving to obtain a fitting parameter D of the temperature probability density distribution to be solved, further obtaining a polynomial expression of the temperature probability density distribution to be solved, and reflecting the temperature distribution condition of the gas to be measured.
The probability density distribution of known single peak and double peaks is shown in fig. 2, and the simulation is performed through the above steps, and as a result, as shown in fig. 3, it can be seen that the reconstructed temperature probability density is well matched with the original distribution, and can reflect the temperature distribution situation on the path.
The above description of the invention and its embodiments is not intended to be limiting, and the illustrations in the drawings are intended to represent only one embodiment of the invention. Without departing from the spirit of the invention, it is within the scope of the invention to design structures or embodiments similar to the technical solution without creation.
Claims (1)
1. A gas temperature probability density distribution reconstruction method based on single light path multispectral comprises the following steps:
the method comprises the following steps of firstly, obtaining measurement data of a plurality of absorption spectrum sections of a laser single light path: dividing a laser beam with scanning wavelength covering the absorption spectrum into two beams by utilizing a plurality of laser absorption spectrum sections of a gas molecule, wherein one beam passes through a temperature distribution field of a measured gas to be used as an absorption signal, the other beam passes through an etalon to be used as a reference signal, and measuring data of absorption rate integral corresponding to each absorption spectrum section is obtained through Voigt line type fitting;
step two, constructing an integral equation system for solving the temperature probability density distribution of the measured gas according to the linear intensities and the corresponding absorption rate integral measurement data of a plurality of absorption spectrum sections of the gas at different temperatures: the laser is utilized to emit laser spectral bands with different central wavelengths, laser passes through the temperature distribution field of the gas to be measured along the same path to obtain a measurement signal, and N corresponding absorption rate integrals are selected as measurement data:
wherein i is the number of the absorption spectrum band ranging from one to the total number of the selected absorption spectrum band, AiRepresents the integral measurement data of the absorption rate corresponding to the ith absorption spectrum band, P represents the total pressure of the gas to be measured in one atmosphere atm, L represents the path length of the gas to be measured in cm, T is the temperature of the gas to be measured in Kelvin K and T1And T2Respectively the lower and upper temperature limits of the gas to be measured in Kelvin K, Si(T) represents the linear intensity value of the laser in the ith absorption spectrum at the temperature T in cm-2atm-1X (T) represents the mole fraction of the gas component at temperature T, and f (T) represents the path fraction of the gas corresponding to temperature T, and considering that the concentration distribution of the gas component is approximately uniform in the measurement, equation (1) can be simplified as:
step three, carrying out normalization processing on the integral equation set: normalizing T on the left and right sides of the expression (2), wherein the normalization expression is T ═ u (T) ═ T (T)2-T1)/(t2-t1)×(t-t1)+T1Wherein T is1、T2Respectively the lowest temperature and the highest temperature, t, of the gas temperature distribution field to be determined1、t2Respectively, the lowest temperature and the highest temperature after normalization, thereby obtaining an expression equivalent to the formula (2)
Wherein A (v)i) I.e. AiRepresents the integral measurement data of the absorption rate corresponding to the ith absorption spectrum band, wherein the central wave number is vi,S(u(t),vi) I.e. Si(T) the linear intensity value of the laser in the ith absorption spectrum band at the temperature T, wherein the central wave number is vi;
Step four, polynomial fitting to the probability density distribution of the temperature of the gas to be measured, and decomposing the integral equation set into a matrix equation: the probability density distribution of the temperature of the gas to be measured is expressed by a polynomial form
f(u(t))=d0'+d1't+d2't2+…+dn'tn(4)
Thus, an expression equivalent to the expression (3) is obtained,
decomposing the system of integral equations by using information of a plurality of laser absorption spectrum bands, including
Note the bookIn order to be the column vector a,the length of the glass is M,is matrix C, size M x (N +1),is a column vector D of length N, thus having a matrix equation AM×1=CM×(N+1)·D(N+1)×1Wherein the matrix C reflects a coefficient matrix formed by specific absorption spectrum bands; the vector D represents a fitting parameter of the temperature probability density distribution to be solved; vector a reflects the absorbance integral measurement;
solving a matrix equation to obtain a gas temperature probability density distribution fitting parameter: and solving the linear equation set of which the CD is A, solving to obtain a fitting parameter D of the temperature probability density distribution to be solved, further obtaining a polynomial expression of the temperature probability density distribution to be solved, and reflecting the temperature distribution condition of the gas to be measured.
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