CN106896191A - A kind of regularization method for improving gas 2-d reconstruction computational efficiency - Google Patents
A kind of regularization method for improving gas 2-d reconstruction computational efficiency Download PDFInfo
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Abstract
The present invention is based on matrix theory and laser absorption spectrum tomography diagnostic techniques, there is provided a kind of regularization method for improving the computational efficiency of gas 2-d reconstruction.The method is first according to the locus of tested region discrete grid block number, secondly discrete grid block is divided into summit, side and three kinds of central area situation, construction regularization equation, the regularization equation of all grids is merged into construction regularization matrix again, and use sparse matrix expression-form, finally, regularization sparse matrix is applied to 2-d reconstruction algorithm, realizes the 2-d reconstruction of gas temperature and concentration of component.The calculating time can substantially be shortened using the present invention, it is to avoid repeat search grid position and calculate regularization coefficient during reconstruction iteration, improve and rebuild efficiency, the method can be widely applied to the two-dimentional on-line measurement of Combustion Flow Field gas distribution.
Description
Technical field
The invention belongs to optics flow field diagnostic field, it is related to Diode Laser Absorption Spectroscopy and computed tomography
Reconstruction technique, can be used to be rebuild in Combustion Flow Field temperature/gas component concentrations 2-d reconstruction measurement the calculating of Flow Field Distribution.
Background technology
Tunable diode laser absorption spectroscopy technology (TDLAS) is combined in time with computerized tomography diagnosis (CT),
Referred to as laser absorption spectrum tomography diagnostic techniques (TDLAT).The technology different angles in same measurement plane by measurement
Projection ray, recycles inversion algorithm to obtain the Two dimensional Distribution information of the temperature and concentration of component in tested region.
Usual tested region by it is discrete be the grid of certain amount, be tested gas parameter of the gas in each grid such as temperature
The physical quantitys such as degree, component, pressure are constant, and the physical message of each grid is exactly the unknown number with solving.In order to realize tested area
The measurement of domain Two dimensional Distribution information, tested region is passed through using a plurality of projection ray along different paths, and projection ray passes through quilt
The distance for surveying region will not be only relevant with the angles and positions of projection ray with gas temperature, the isoparametric change of concentration.Will
Different projected light beams are write as equation group through the absorption equation after tested region, i.e. can be to tested using certain algorithm for reconstructing
Region is solved.
The physical quantity of tested region is generally space continuously, in order to improve reconstruction quality, using regularization method to every
Individual grid is solved.Simultaneously in order to realize the high-acruracy survey of tested region, tested region is separated into more lattice number,
Generally hundreds of or thousands of magnitudes, it is unknown keep count of it is larger, so in 2-d reconstruction calculating using regularization method after
The calculating time is more long, it is impossible to realize stream field real-time online measuring purpose.Therefore, the computational efficiency for improving 2-d reconstruction has ten
Divide important meaning.
Following document reports are related to the phase based on TDLAS method Combustion Flow Field 2-d reconstructions and data processing method inside the Pass
Hold.
1. Clemson University Cai Weiwei et al. are in paper " Hyperspectral tomography based on
proper orthogonal decomposition as motivated by imaging diagnostics of
Unsteady reactive flows " (Applied Optics, 4 phases of volume 29 in 2010) are proposed using ultraphotic spectral method
Solve the Two dimensional Distribution of temperature and concentration, but, the method need to solve the nonlinear equation of temperature in solution procedure, it is necessary to
Take a significant amount of time and post-processed, in computer (X5482,3:36 hours completions, 100 grids are taken around on 2GHz)
The solution of temperature and concentration of component.
2. University of Virginia Bryner E et al. are in paper " Tunable diode laser absorption
technique development for determination of spatially resolved water
concentration and temperature”(48th AIAA Aerospace Sciences Meeting Including
The New Horizons Forum and Aerospace Exposition, AIAA-2010-0299) use filtered back projection
Method measures the temperature and concentration of component Two dimensional Distribution at combustor exit, real due to needing that tested region is projected completely
Test and 72 angles totally 1800 light data are acquired using mobile rotation mode, experimental data collection is time-consuming nearly one hour.
3. paper " Fast Data Processing for of USAF laboratory Kristin M.Busa et al.
Optical Absorption " (54th AIAA Aerospace Sciences Meeting, AIAA-2016-0660) are proposed
A kind of method based on dominant-frequency analysis, Eigenvalues Decomposition is carried out by absorption line, and absorption line shape no longer uses single Voigt lines
Type is fitted, but the combination of a plurality of Voigt line styles, feature Voigt line styles are determined before experiment starts, lead to during data processing
Height, core and the width for calculating different absorption lines are crossed, is contrasted with experimental result, obtain optimal fitting knot
Really.For one group of 50ms size for 1GB experimental data, it is necessary to 1.5 hours obtain average data result.
4. Tokushima Japan university Yoshihiro Deguchi et al. are in paper " Two-dimensional tomography
for gas concentration and temperature distributions based on tunable diode
laser absorption spectroscopy”(Journal of Mechanics Engineering and
Automation, the 2nd phase in 2012) 8 light path TDLAT reconstructing systems of fixed light path conceptual design are used, for measuring burning
Device and the temperature and H in diesel engine exhaust exit2O concentration of component is distributed, and has carried out related experiment, and demonstrating this is
The quick measurement capability of system such that it is able to measure the fired state of internal combustion engine in real time.
Above-mentioned document is demonstrated rebuilds Combustion Flow Field gas parameter based on TDLAS technologies and computed tomography
Feasibility, but because discrete grid block number is more, projection ray's number is more, the calculating time of Data Post is more long, typically exists
A few minutes to a few houres magnitude, therefore, for improve 2-d reconstruction computational efficiency research tool be of great significance.
The content of the invention
It is an object of the invention to provide a kind of regularization method for improving gas 2-d reconstruction computational efficiency.The invention
Propose for sparse matrix computational methods to be used for the regularization process based on TDLAS Combustion Flow Field gas 2-d reconstructions first.Invention
Regularization method be that regularization process is rewritten as matrix computations process, while more using regularization matrix nonzero element
Feature, sparse matrix form is rewritten as by regularization matrix, nonzero element and non-zero entry in a preservation matrix in storing process
Element position in a matrix, in calculating process, by eliminating neutral element and then shortening the calculating time.Using the method, can be with
The computational efficiency of gas 2-d reconstruction is effectively improved, can be used for the burning such as scramjet engine, aero-engine, combustion furnace
The Two dimensional Distribution measurement of gas parameter in environment.
Present invention description regularization method, the implementation for setting up initial distribution information is as follows：
(1) assume that gas is distributed in tested region in certain function, tested region is separated into N=m × n grids, and
Assuming that gas parameter property keeps constant in discrete net region；
(2) projection ray's distribution form is preset, the information such as projection ray's number, projection angle are given, light is calculated and is passed through
The length of each grid, sets up projection matrix；
(3) temperature range according to tested gas selects two absorption lines, with reference to projection matrix and absorption line information
Calculate every projection value of light.
The present invention establishes the regularization method for improving gas 2-d reconstruction computational efficiency, and implementation is as follows：
(1) according to the information of discrete grid block, locus where grid is judged；
(2) locus is divided into summit, side and three kinds of central area situation, with reference to the regularization factors of setting, construction
Regularization equation；
(3) the regularization equation of all grids is merged into construction regularization matrix, and regularization matrix is used into sparse square
Battle array expression-form.
The present invention establishes the gas 2-d reconstruction method based on algebraic reconstruction algorithm, and implementation is as follows：
(1) regularization matrix (sparse matrix), ray cast value, projection matrix are brought into gas two dimension as initial parameter
Process of reconstruction.
(2) algebraic reconstruction algorithm initiation parameter is set, flow field gas temperature and component is realized using algebraic reconstruction algorithm
The 2-d reconstruction of concentration.
(3) reconstructed results are visualized, is calculated reconstruction error.
It is of the invention improve gas 2-d reconstruction computational efficiency the advantage of regularization method be：
(1) method for reconstructing computational efficiency is high.The present invention improves the computational efficiency of 2-d reconstruction, has saved time cost.
In discrete grid block number and the timing of projection ray's number one, gas 2-d reconstruction is carried out using the method for the present invention, ensureing weight
Build outcome quality it is constant in the case of, can effectively shorten the calculating time.
(2) regularization process committed memory space is small.Matrix form is rewritten as present invention firstly provides by regularization process,
And stored using sparse matrix and calculated, the advantage that sparse matrix only preserves nonzero element position in a matrix has been played,
Neutral element can be directly eliminated in calculating, the occupancy to memory headroom in calculating process is greatly reduced.
(3) regularization method highly versatile, it is easy to improve.Self-editing function interface, Ke Yiyong are left in regularization method
In the expression-form for adding and changing regularization equation.The present invention can be used for arbitrary mess number and projection ray's number just
Then change process, at the same time it can also be directed to special Flow Field Distribution form, in addition prior information to regularization matrix, improve and rebuild
Outcome quality.
Brief description of the drawings
Fig. 1 is the specific embodiment figure for realizing the method for the invention.
Fig. 2 is gas initial temperature of the invention and concentration profile.
Fig. 3 is original light distribution map of the invention.
Fig. 4 is regularization matrix element ratio schematic diagram of the invention.
Fig. 5 is temperature of the invention and concentration Two dimensional Distribution reconstructed results.
Specific embodiment
The present invention is done for improving the regularization method of gas 2-d reconstruction computational efficiency in conjunction with drawings and Examples
Describe in further detail.
Implementation of the invention is as follows：On the basis of the gas 2-d reconstruction calculating time has been analysed in depth, it is proposed that
A kind of regularization method for improving gas 2-d reconstruction computational efficiency.The present invention is specifically divided into three steps, i.e. discretization
Step, regularizing step and 2-d reconstruction step.Specific embodiment is as follows, participates in Fig. 1：
Step 1：Discrete region
Discrete regionization includes discrete tested region, calculates projection matrix and calculates projection value.Comprise the following steps that：
(1) assume that gas is distributed in tested region in certain function, tested region is separated into N=m × n grids, and
Assuming that gas parameter property keeps constant in discrete net region；
Discrete grid block number 20 × 20 is chosen in text, Temperature Distribution is distributed for double gauss, distribution is 500~1300K,
Concentration distribution is single Gaussian Profile, and distribution is 0.02~0.1, and Flow Field Distribution is as shown in Figure 2；
(2) projection ray's distribution form is preset, the information such as projection ray's number, projection angle are given, light is calculated and is passed through
The length of each grid, sets up projection matrix；
Light is designed in text and is distributed as ray fans distribution, launch point is located at 4 summits of tested region, and total light number is
160, light distribution form is as shown in Figure 3；
(3) temperature range according to tested gas selects two absorption lines, with reference to projection matrix and absorption line information
Calculate every projection value of light.
Projection value is that integration absorption area A can be expressed as
Wherein P is gas stagnation pressure, and χ is under test gas concentration of component, and L is the light path for absorbing gas, Sν(T) it is absorption line
Intensity, is the function of temperature T, be can be written as
Wherein T0Be reference temperature 296K, E " be lower state energy level, h be Planck constants, k be Boltzmann constants, c
It is the light velocity, partition function value when Q (T) is temperature T, the partition function in certain temperature range can use polynomial repressentation.
Being write projection ray's matrix and projection result as matrix form is
Wherein N represents tested region by discrete lattice number, and M is the number of projection ray, AiExpression centre frequency is v
I-th light integration absorptivity, f is flow field parameter to be measured, here fj=[PS (T) χ]j, LijRepresent that i-th light is passed through
J-th length of grid, and locus only with projection ray is relevant.
Step 2：Regularization is calculated
(1) according to the information of discrete grid block, locus where grid is judged；
(2) regularization equation is constructed, the physical quantity f that reconstruction regions are represented is separated into N=m × n grids, m, n difference table
Show zone of dispersion x directions and y directions lattice number, its dimension is m × n, wherein the physical quantity that the grid of the i-th row jth row is represented
It is expressed as f(i,j), according to the position of mesh space, each f(i,j)It is expressed as by regularization：
In formula, δ is regularization factors, when δ is 0, is indicated without regularization, when δ is 1, represents Complete regularization of L fuzzy.
(3) the regularization equation of all grids is merged into construction regularization matrix, and regularization matrix is used into sparse square
Battle array expression-form.
Regularization matrix is expressed as T, its dimension be N × N, wherein N=m × n, m, n represent respectively zone of dispersion x directions and
Y directions lattice number, it is the matrix F of N × 1, canonical that the physical quantity f that the step reconstruction regions of step 2 (2nd) are represented is rewritten as into dimension
Matrix F after changemodifyIt is expressed as
Fmodify=TF (8)
More neutral element is included in regularization matrix T, so regularization matrix T is rewritten as sparse matrix form, i.e.,
Nonzero element and nonzero element position in a matrix, element schematic diagram such as Fig. 4 institutes of regularization matrix T in preservation matrix
Show, dot represents element position in a matrix wherein in figure.In calculating matrix FmodifyWhen, by eliminating nonzero element, reduce
The calculating time.
Step 3：Gas parameter 2-d reconstruction
(1) regularization matrix (sparse matrix), ray cast value, projection matrix are brought into gas two dimension as initial parameter
Process of reconstruction.
(2) algebraic reconstruction algorithm initiation parameter is set, flow field gas temperature and component is realized using algebraic reconstruction algorithm
The 2-d reconstruction of concentration.Can be wherein expressed as using solving equation (6) algebraic reconstruction algorithm
Wherein k be iterations, α is relaxation factor, due to temperature field and concentration field be on the occasion of, in an iterative process plus
Enter nonnegativity limitation.
In an iterative process, regularization equation (8) is brought into iterative process, is smoothed, weaken reconstruction regions
Adjacent point mutation response.
(3) reconstructed results are visualized, is calculated reconstruction error, wherein reconstruction error computing formula can be expressed as
Wherein subscript ' cal ' represents result of calculation, and ' orig ' represents initial value.M and N represent the line number of discrete grid block respectively
And columns.
The reconstruction error of temperature field and concentration field is respectively 0.0264,0.0451, reconstructed results as shown in figure 5, when calculating
Between shorten to 6.89s by 141.31, the run time of each program is as shown in the table, wherein table (a) be use the present invention propose
The calculating time of algorithm, table (b) is the original calculation time.Thus regularization method proposed by the present invention is illustrated, before amendment
Regularization method program regulation2 so that computational efficiency is obviously improved.
The list procedure Operational Timelines
Claims (5)
1. a kind of regularization method for improving gas 2-d reconstruction technical efficiency, it is characterised in that：
According to the locus of tested region discretization grid, it is divided into summit, side and three kinds of central area situation, constructs regularization
Equation, construction regularization matrix is merged further according to by the regularization equation of all grids, and using the expression-form of sparse matrix,
Finally, by rarefaction matrix application to 2-d reconstruction algorithm, the 2-d reconstruction of gas temperature and concentration of component is realized.
2. a kind of regularization method for improving gas 2-d reconstruction technical efficiency as claimed in claim 1, its feature exists
In：
During construction regularization equation, the physical quantity f that reconstruction regions are represented is separated into N=m × n grids, and m, n represent discrete regions respectively
Domain x directions and y directions lattice number, its dimension are m × n, wherein the physical quantity that the grid of the i-th row jth row is represented is expressed as
f(i,j), mesh space position is divided into three kinds of situations, i.e. summit, side and central area, f(i,j)It is expressed as by regularization：
In formula, δ is regularization factors, when δ is 0, is indicated without regularization, when δ is 1, represents Complete regularization of L fuzzy.
3. a kind of regularization method for improving gas 2-d reconstruction technical efficiency as claimed in claim 1, its feature exists
In：
Regularization matrix is expressed as T, and its dimension is N × N, and wherein N=m × n, m, n represent zone of dispersion x directions and y side respectively
To lattice number, it is the matrix F of N × 1 that the physical quantity f that reconstruction regions in claim 2 are represented is rewritten as dimension, after regularization
Matrix FmodifyIt is expressed as
Fmodify=TF (2).
4. a kind of regularization method for improving gas 2-d reconstruction technical efficiency as claimed in claim 1, its feature exists
In：
More neutral element is included in regularization matrix T, so regularization matrix T is rewritten as into sparse matrix form, i.e., is only protected
Nonzero element and nonzero element position in a matrix in matrix are deposited, in claim 3 calculating matrix FmodifyWhen, by eliminating
Nonzero element, reduces the calculating time.
5. a kind of regularization method for improving gas 2-d reconstruction technical efficiency as claimed in claim 1, its feature exists
In：
Computing formula in claim 3 is brought into gas 2-d reconstruction algorithm, wherein 2-d reconstruction algorithm is using amendment generation
Number alternative manner, calculates the two-dimensional space distribution of gas temperature and concentration of component.
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| CN107870159A (en) * | 2017-11-01 | 2018-04-03 | 中国矿业大学(北京) | Two-dimensional reconstruction method of gas concentration for tunable semiconductor laser absorption spectrum |
| CN108627272A (en) * | 2018-03-22 | 2018-10-09 | 北京航空航天大学 | A kind of two-dimension temperature distribution method for reconstructing based on four angle laser absorption spectrums |
| CN108801496A (en) * | 2018-04-26 | 2018-11-13 | 北京航空航天大学 | A kind of path temperature histogram measurement System and method for based on overlapping absorption spectra |
| CN111157139A (en) * | 2020-02-06 | 2020-05-15 | 北京航空航天大学 | Visual measurement method for temperature distribution of single-connected combustion field |
| CN112304897A (en) * | 2020-09-14 | 2021-02-02 | 中国人民解放军战略支援部队航天工程大学 | Spectrum selection method and system for combustion field two-dimensional reconstruction |
| CN114034653A (en) * | 2021-11-17 | 2022-02-11 | 清华大学 | Wavelength modulation absorption spectrum tomography reconstruction system based on deep learning |
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| CN114034653B (en) * | 2021-11-17 | 2023-08-15 | 清华大学 | Wavelength modulation absorption spectrum tomography reconstruction system based on deep learning |
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