CN106896191B - It is a kind of for improving the regularization method of gas 2-d reconstruction computational efficiency - Google Patents
It is a kind of for improving the regularization method of gas 2-d reconstruction computational efficiency Download PDFInfo
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Abstract
The present invention is based on matrix theories and laser absorption spectrum tomography diagnostic techniques, provide a kind of for improving the regularization method of the computational efficiency of gas 2-d reconstruction.This method is first according to the spatial position of tested region discrete grid block number, secondly discrete grid block is divided into vertex, side and three kinds of central area situation, construct 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, the 2-d reconstruction of gas temperature and concentration of component is realized.It can be obviously shortened using the present invention and calculate the time, avoid repeat search grid position during reconstruction iteration and calculate regularization coefficient, improved and rebuild efficiency, this 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 fields, are related to Diode Laser Absorption Spectroscopy and computed tomography
Reconstruction technique can be used for rebuilding the calculating of Flow Field Distribution in Combustion Flow Field temperature/gas component concentrations 2-d reconstruction measurement.
Background technique
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).Technology different angle in same measurement plane by measurement
Projection ray recycles inversion algorithm to obtain the Two dimensional Distribution information of temperature and concentration of component in tested region.
Usual tested region is tested gas parameter of the gas in each grid such as temperature by the discrete grid for certain amount
The physical quantitys such as degree, component, pressure are constant, and the physical message of each grid is exactly with the unknown number solved.In order to realize tested area
The measurement of domain Two dimensional Distribution information passes through tested region along different paths using a plurality of projection ray, and projection ray passes through quilt
The distance for surveying region will not be only related with the angles and positions of projection ray with the variation of the parameters such as gas temperature, concentration.It will
Absorption equation of the different projected light beams after tested region is write as equation group, can be to tested using certain algorithm for reconstructing
Region is solved.
It is continuous that the physical quantity of tested region is generally space, in order to improve reconstruction quality, using regularization method to every
A grid is solved.While the high-acruracy survey in order to realize tested region, tested region are separated into more lattice number,
Usually in several hundred or thousands of magnitudes, it is unknown keep count of it is larger, in this way in 2-d reconstruction calculating using regularization method after
The calculating time is longer, can not achieve 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 reconstruction and data processing method inside the Pass
Hold.
1. Clemson University Cai Weiwei et al. is 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), which is proposed, utilizes ultraphotic spectral method
The Two dimensional Distribution of temperature and concentration is solved, still, the method needs to solve the nonlinear equation of temperature in solution procedure, needs
It takes a significant amount of time and is post-processed, 36 hours completions, 100 grids are taken around on computer (X5482,3:2GHz)
The solution of temperature and concentration of component.
2. University of Virginia Bryner E et al. is 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 temperature and concentration of component Two dimensional Distribution at combustor exit, real due to needing to project completely to tested region
It tests and 72 angles totally 1800 light data is acquired using mobile rotation mode, experimental data acquisition is nearly one hour time-consuming.
3. paper " the Fast Data Processing for of United States Air Force laboratory Kristin M.Busa et al.
Optical Absorption " (54th AIAA Aerospace Sciences Meeting, AIAA-2016-0660) is proposed
A method of based on dominant-frequency analysis, absorption line being subjected to Eigenvalues Decomposition, absorption line shape no longer uses single Voigt line
Type is fitted, but the combination of a plurality of Voigt line style, and feature Voigt line style is determined before experiment starts, logical when data processing
The height for calculating different absorption lines, core and width are crossed, is compared with experimental result, optimal fitting knot is obtained
Fruit.The experimental data for being 1GB for one group of 50ms size, needs obtain average data result within 1.5 hours.
4. Tokushima Japan university Yoshihiro Deguchi et al. is 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) using 8 optical path TDLAT reconstructing systems of fixed optical path conceptual design, for measuring burning
The temperature and H of device and diesel engine exhaust exit2The distribution of O concentration of component, and related experiment has been carried out, demonstrating this is
The rapid survey ability of system, so as to the combustion state of real-time measurement internal combustion engine.
Above-mentioned document, which is demonstrated, rebuilds Combustion Flow Field gas parameter based on TDLAS technology and computed tomography
Feasibility, but since discrete grid block number is more, projection ray's number is more, the calculating time of Data Post is longer, generally exists
A few minutes to a few houres magnitude, therefore, have a very important significance for the research for improving 2-d reconstruction computational efficiency.
Summary of the invention
The object of the present invention is to provide a kind of for improving the regularization method of gas 2-d reconstruction computational efficiency.The invention
It is put forward for the first time and sparse matrix calculation method is used for the regularization process based on TDLAS Combustion Flow Field gas 2-d reconstruction.Invention
Regularization method be regularization process is rewritten as to matrix calculating process, while using regularization matrix nonzero element it is more
Regularization matrix is rewritten as sparse matrix form by feature, nonzero element and non-zero entry in preservation matrix in storing process
Shorten the calculating time by eliminating neutral element in calculating process in the position of element in a matrix.It, can be with using this method
The computational efficiency for effectively improving gas 2-d reconstruction can be used for the burning such as scramjet engine, aero-engine, combustion furnace
The Two dimensional Distribution measurement of gas parameter in environment.
The present invention describes regularization method, and the implementation for establishing 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 grid, and
Assuming that gas parameter property is kept 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 passes through
The length of each grid, establishes projection matrix；
(3) two absorption lines are selected according to the temperature range for being tested gas, in conjunction with projection matrix and absorption line information
Calculate the projection value of every 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, judge spatial position where grid；
(2) spatial position is divided into vertex, side and three kinds of central area situation, in conjunction with 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) gas two dimension is brought into using regularization matrix (sparse matrix), ray cast value, projection matrix as initial parameter
Reconstruction process.
(2) algebraic reconstruction algorithm initiation parameter is set, realizes flow field gas temperature and component using algebraic reconstruction algorithm
The 2-d reconstruction of concentration.
(3) reconstructed results are visualized, calculates reconstruction error.
The advantages of regularization method of raising gas 2-d reconstruction computational efficiency of the invention, is:
(1) method for reconstructing computational efficiency is high.The present invention improves the computational efficiency of 2-d reconstruction, has saved time cost.
In one timing of discrete grid block number and projection ray's number, gas 2-d reconstruction is carried out using method of the invention, is guaranteeing weight
Build outcome quality it is constant in the case where, can effectively shorten calculate the time.
(2) regularization process committed memory space is small.Present invention firstly provides regularization process is rewritten as matrix form,
And stored and calculated using sparse matrix, played sparse matrix only save nonzero element in a matrix position the advantages of,
Neutral element can be directly eliminated in calculating, greatly reduce the occupancy in calculating process to memory headroom.
(3) regularization method is versatile, is easily modified.There are self-editing function interface, Ke Yiyong 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, adds prior information into regularization matrix, improve and rebuild
Outcome quality.
Detailed description of the invention
The specific embodiment figure of Fig. 1 the method to realize the present invention.
Fig. 2 is gas initial temperature and concentration profile of the invention.
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 now in conjunction with drawings and examples
It is described in further detail.
Implementation of the invention is as follows: on the basis of having analysed in depth the gas 2-d reconstruction calculating time, proposing
It is a kind of for improving the regularization method of 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 region includes discrete tested region, calculates projection matrix and calculate projection value.Specific step is as follows:
(1) assume that gas is distributed in tested region in certain function, tested region is separated into N=m × n grid, and
Assuming that gas parameter property is kept constant in discrete net region；
Discrete grid block number 20 × 20 is chosen in text, Temperature Distribution is double gauss distribution, and 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 passes through
The length of each grid, establishes projection matrix；
Light is designed in text and is distributed as ray fans distribution, and launch point is located at 4 vertex of tested region, and total light number is
160, light distribution form is as shown in Figure 3；
(3) two absorption lines are selected according to the temperature range for being tested gas, in conjunction with projection matrix and absorption line information
Calculate the projection value of every light.
Projection value integrates absorption area A and 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, SνIt (T) is absorption line
Intensity is the function of temperature T, can be written as
Wherein T0It is lower state energy level for reference temperature 296K, E ", h is Planck constant, and k is Boltzmann constant, c
For 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 as matrix form with projection result is
Wherein N indicates tested region by discrete lattice number, and M is the number of projection ray, AiExpression centre frequency is v
I-th light integral absorptivity, f is flow field parameter to be measured, here fj=[PS (T) χ]j, LijIndicate that i-th light passes through
The length of j-th of grid, and it is only related with the spatial position of projection ray.
Step 2: regularization calculates
(1) according to the information of discrete grid block, judge spatial position where grid；
(2) regularization equation is constructed, the physical quantity f that reconstruction regions represent is separated into N=m × n grid, m, n distinguish table
Show the direction zone of dispersion x and the direction y lattice number, dimension is m × n, wherein the physical quantity that the grid of the i-th row jth column represents
It is expressed as f(i,j), according to the position of mesh space, each f(i,j)It is indicated by regularization are as follows:
In formula, δ is regularization factors, when δ is 0, indicates no regularization, when δ is 1, indicates 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, and dimension is N × N, wherein N=m × n, m, n respectively indicate the direction zone of dispersion x and
The direction y lattice number, the matrix F that the physical quantity f that step 2 (2) step reconstruction regions represent is rewritten as dimension as N × 1, canonical
Matrix F after changemodifyIt is expressed as
Fmodify=TF (8)
It include more neutral element in regularization matrix T, so regularization matrix T is rewritten as sparse matrix form, i.e.,
The position of nonzero element and nonzero element in a matrix in preservation matrix, element schematic diagram such as Fig. 4 institute of regularization matrix T
Show, wherein dot indicates the position of element in a matrix in figure.In calculating matrix FmodifyWhen, by eliminating nonzero element, reduce
Calculate the time.
Step 3: gas parameter 2-d reconstruction
(1) gas two dimension is brought into using regularization matrix (sparse matrix), ray cast value, projection matrix as initial parameter
Reconstruction process.
(2) algebraic reconstruction algorithm initiation parameter is set, realizes flow field gas temperature and component using algebraic reconstruction algorithm
The 2-d reconstruction of concentration.It can be wherein expressed as using solution equation (6) algebraic reconstruction algorithm
Wherein k be the number of iterations, α is relaxation factor, since temperature field and concentration field are positive value, 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, calculates reconstruction error, wherein reconstruction error calculation formula can be expressed as
Wherein subscript ' cal ' represents calculated result, and ' orig ' represents initial value.M and N respectively represents the line number of discrete grid block
And columns.
The reconstruction error of temperature field and concentration field is respectively 0.0264,0.0451, and reconstructed results are as shown in figure 5, when calculating
Between by 141.31 shorten to 6.89s, the runing time of each program is as shown in the table, and wherein table (a) is to be proposed using the present invention
The calculating time of algorithm, table (b) are the original calculation time.Thus illustrate regularization method proposed by the present invention, before correcting
Regularization method program regulation2, so that computational efficiency is obviously improved.
The list procedure Operational Timelines
Claims (1)
1. a kind of for improving the regularization method of gas 2-d reconstruction technical efficiency, it is characterised in that:
Step 1, according to the spatial position of tested region discretization grid, it is divided into vertex, side and three kinds of central area situation；Step
2, regularization equation is constructed, the regularization equation of all grids is merged into construction regularization matrix, by regularization matrix using dilute
Dredge the expression-form of matrix；Step 3, by rarefaction matrix application into 2-d reconstruction algorithm, realize that gas temperature and component are dense
The 2-d reconstruction of degree；
The construction regularization equation specifically includes: the physical quantity f that reconstruction regions represent being separated into N=m × n grid, m, n divide
Not Biao Shi the direction zone of dispersion x and the direction y lattice number, dimension be m × n, wherein the i-th row jth column grid represent object
Reason amount is expressed as f(i,j), according to the position of mesh space, each f(i,j)It is indicated by regularization are as follows:
In formula, δ is regularization factors, when δ is 0, indicates no regularization, when δ is 1, indicates Complete regularization of L fuzzy；
The construction regularization matrix specific steps include: that regularization matrix is expressed as T, and dimension is N × N, wherein N=m ×
N, m, n respectively indicate the direction zone of dispersion x and the direction y lattice number, by the physical quantity f that reconstruction regions represent be rewritten as dimension as
The matrix F of N × 1, the matrix F after regularizationmodifyIt is expressed as
Fmodify=TF；
It is described to specifically include regularization matrix using the expression-form of sparse matrix: comprising more zero in regularization matrix T
Element, so regularization matrix T is rewritten as sparse matrix form, i.e., nonzero element and nonzero element are in square in preservation matrix
Position in battle array, in calculating matrix FmodifyWhen, by eliminating nonzero element, reduces and calculate the time；
It is described to specifically include rarefaction matrix application into 2-d reconstruction algorithm: (1) by regularization matrix (sparse matrix), light
Line projection's value, projection matrix bring gas 2-d reconstruction process into as initial parameter；
(2) algebraic reconstruction algorithm initiation parameter is set, realizes flow field gas temperature and concentration of component using algebraic reconstruction algorithm
2-d reconstruction, wherein algebraic reconstruction algorithm can be expressed as
Wherein k is the number of iterations, and α is relaxation factor, since temperature field and concentration field are positive value, is added in an iterative process non-
Negativity restriction；
In an iterative process, regularization equation is brought into iterative process, is smoothed, it is prominent to weaken reconstruction regions consecutive points
Become response；
(3) reconstructed results are visualized, calculates reconstruction error.
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| CN108627272B (en) * | 2018-03-22 | 2020-04-24 | 北京航空航天大学 | Two-dimensional temperature distribution reconstruction method based on four-angle laser absorption spectrum |
| CN108801496B (en) * | 2018-04-26 | 2020-04-24 | 北京航空航天大学 | Path temperature histogram measurement system and method based on overlapping absorption spectrum |
| CN111157139B (en) * | 2020-02-06 | 2021-09-28 | 北京航空航天大学 | Visual measurement method for temperature distribution of single-connected combustion field |
| CN112304897B (en) * | 2020-09-14 | 2021-09-14 | 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 |
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| CN104081437B (en) * | 2011-09-20 | 2017-02-15 | 西门子公司 | Bayesian approach for gas concentration reconstruction based on tunable diode laser absorption spectroscopy |
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