CN103047946B - A kind of rotational symmetry parameter distribution image rebuilding method based on virtual data - Google Patents

Abstract

The invention provides a kind of rotational symmetry parameter distribution image rebuilding method based on virtual data, comprise the following steps: utilize the single visual angle projection covering measured parameter distribution field, obtain corresponding Cephalometry; Make the visual angle that other is not projected, according to the rotational symmetry characteristic of parameter distribution, obtain corresponding virtual projection measured value equivalently; The system of equations solving parameter value is built according to matrix of coefficients and Cephalometry; Calculate the parameter value in each grid according to arithmetic reconstruction method, and then obtain rotational symmetry parameter distribution image.Effect of the present invention is that system architecture is simple, and reliability is high, and cost is low, is with a wide range of applications.

Description

A kind of rotational symmetry parameter distribution image rebuilding method based on virtual data

Technical field

The present invention relates to a kind of rotational symmetry parameter distribution image rebuilding method based on virtual data, be specifically related to when parameter meets rotational symmetry distribution, can the single visual angle backprojection image reconstruction method based on virtual data of effective simplied system structure.

Background technology

Rotational symmetry parameter distribution characteristic is extensively present in industrial application.Such as, parallel shafting stove is for generation of flame that is stable, even, laminar flow diffusion, and it is widely used in the research field such as flame demarcation, flameholding process, diabatic process, flame velocity and form.Parallel shafting stove in combustion, requires that the flame to it produces accurately controls, to ensure that the temperature of flame, gas component concentrations and flow pattern are in steady state (SS).But, due to the existence in cold boundary layer and the heat interchange of flame and outside air, reduce gradually to flame external temperature from flame kernel, and then cause parallel shafting stove fire flame to present rotational symmetry temperature distributing characteristic.Therefore, for inspection parallel shafting stove produces the stability of flame and the homogeneity of Temperature Distribution, need to carry out on-line monitoring to the Flame Temperature Distribution of parallel shafting stove.And for example, rocket engine wake flame is the jet-flow of high temperature, high speed, and goes out stronger infrared energy to spatial emission.Research shows, the solid in wake flame, liquid particles and gas are everlasting, and nozzle exit is neighbouring produces secondary combustion, and its temperature field and gas component concentrations field also present rotational symmetry distribution character.For optimizing propellant mix proportion scheme, assessment wake flame infrared radiation property, needs to measure rocket engine wake flame Temperature Distribution.

Adopt various visual angles projection can carry out image reconstruction to rotational symmetry parameter distribution.But the structure of design is comparatively complicated like this.For the rotational symmetry distribution character of parameter, in order to reduce the complicacy of system, can only utilize single visual angle to project and obtain projection measurements, the projection angle that the projection at each visual angle is covered be identical, then the virtual projection measured value at other visual angle is identical with real projection measured value.Therefore, the single visual angle projection based on virtual data can be adopted to carry out image reconstruction to rotational symmetry parameter distribution.

Summary of the invention

For the tested region with rotational symmetry parameter distribution characteristic, be further simplied system structure, the invention provides a kind of rotational symmetry parameter distribution image rebuilding method based on virtual data.

The technical solution adopted in the present invention is as follows:

Step one, obtains the projection measurements of single visual angle: utilize single visual angle to project and cover measured parameter distribution field, can be fan beam projections or parallel beam projection, obtain m projection measurements;

Step 2, build virtual measurement data: the projection of total n visual angle covers measured parameter distribution field, n is odd number, one of them visual angle be projected as real projection, other n-1 visual angle be projected as virtual projection, the tested region that the projection at each visual angle covers is identical, and the virtual projection measured value that the virtual projection at n-1 visual angle is obtained is identical with m real projection measured value, the number of overall measurement data is J, J=m × n;

Step 3, builds the system of equations solving parameter value according to matrix of coefficients and Cephalometry: be N number of grid by tested Region dividing, for the projection of jth bundle, and Cephalometry b _jcan be expressed as:

$\begin{array}{cc}{b}_j=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{A}_{\mathrm{ji}}{x}_i& (j=\mathrm{1,2},\·\·\·J)---\left(1\right)\end{array}$

Wherein x _ibe the parameter value in i-th pixel, A _jirepresent that jth bundle is projected in the path in i-th grid, then:

b＝Ax (2)

Wherein A is A _jithe dimension formed is the matrix of coefficients of J × N, and x is for forming x _ivector, b for form b _jvector;

Step 4, image reconstruction: solve (2) according to arithmetic reconstruction method, obtains the expression formula of x:

$x^{(k+1)}=x^{\left(k\right)}+\mathrm{\λ}\frac{b_{j_k}-A_{j_k}^T{x}^{\left(k\right)}}{{\left|\right|A_{j_k}\left|\right|}^2}{A}_{j_k}$ (3)

$j_k=[k-\mathrm{Int}\left(\frac{k}{J}\right)J+1]$

Wherein k is iterations, and λ is relaxation factor, and Int representative rounds operator, and the convergence of iteration obtains x by adjacent twice iterative computation ^(k)and x ^(k-1)the mould of difference is relative to x ^(k)the changes delta of mould is monitored, and Δ can be expressed as:

$\mathrm{\Δ}=\frac{|x^{\left(k\right)}-x^{(k-1)}|}{\left|x^{\left(k\right)}\right|}---\left(4\right)$

Iteration is stopped, according to the x tried to achieve when Δ≤0.1% ^(k)the image of rotational symmetry parameter distribution field can be rebuild.

Effect of the present invention: when tested region parameter meets rotational symmetry distribution, rotational symmetry parameter distribution image rebuilding method based on virtual data of the present invention can realize the image reconstruction of rotational symmetry parameter distribution, tested region is scanned without using multiple visual angle, significantly reduce complicacy and the cost of system, and system reliability is high, good stability.

Accompanying drawing explanation

Fig. 1 is the parallel shafting stove in axial direction temperature distributing characteristic recorded by thermopair.

Fig. 2 is the parallel shafting stove in axial direction H calculated by fuel ratio value ₂o Gas concentration distribution characteristic.

Fig. 3 is the temperature distribution measuring system structure principle chart based on tunable diode laser absorption spectrometry technology.

Fig. 4 is that post lens are by collimation laser fanning Shu Jiguang schematic diagram.

Fig. 5 is as n'=5,1 true fan-shaped laser beam and 4 virtual fan-shaped laser beam schematic diagram.

Fig. 6 is the contrast of axisymmetric temperature field distribution and the initial temperature field distribution of being rebuild by method of the present invention.

In Fig. 3: 1-laser controller; 2-semiconductor laser with tunable; 3-2 × 2 optical fiber splitter; 4-optical fiber collimator; 5-post lens; 6-solid etalon; 7-parallel shafting stove; 8-photodetector; 9-photoelectronic detecting array; 10-data collecting card; 11-computing machine.

In Fig. 5: solid line represents true light path, and dotted line represents virtual optical path.

Embodiment

In the present embodiment, produce the flame parameters with rotational symmetry temperature and gas component concentrations distribution for parallel shafting stove, utilize the single visual angle fan beam projections based on laser tunable diode laser absorption spectrometry technology to carry out image reconstruction to rotational symmetry Temperature Distribution.As shown in Figure 1, the in axial direction H2O Gas concentration distribution characteristic calculated by fuel ratio value as shown in Figure 2 for the in axial direction temperature distributing characteristic recorded by thermopair.

Below in conjunction with accompanying drawing, the present invention is further illustrated:

Step one, chooses core frequency and is respectively 7185.6cm ^-1and 7444.4cm ^-1two spectral lines carry out experimental study.

Step 2, the centre wavelength of two distributed feedback semiconductor laser with tunable 1 and 2 is respectively 7185.6cm ^-1and 7444.4cm ^-1, laser controller LDC-3900 by two independently passage temperature and electric current are carried out to two laser instruments, and then realize tuning to two laser frequency;

Step 3, as shown in Figure 3, the two-way laser of two laser instrument outputs passes through the optical fiber splitter of 2 × 2, the road laser that optical fiber splitter exports is collimated by optical fiber collimator and changed into electric signal by a photoelectric detector after solid etalon, electric signal is input to data acquisition module, as the standard signal demarcating frequency displacement; Another road laser is collimated by optical fiber collimator, collimation laser through focal length be the post lens of 0.4cm, as shown in Figure 4, after focus, collimation laser is by fanning Shu Jiguang, and the subtended angle angle that fladellum laser covers is 30 °, ensures that the fladellum laser at this visual angle covers tested region completely.As shown in Figure 5, the radius that definition one comprises tested region is the circumference C of 15cm, the focus of fan-shaped laser beam is made to be positioned on circumference C, fan-shaped laser beam projects to tested region opposite side and is received by the detector array being positioned at the equal photodetector formation in upper 7 intervals of circumference C, the number of photodetector is odd number, make the focus of fan-shaped laser beam and the 4th the tested regional center of the straight-line pass that photodetector is determined, the 7 road electric signal obtained after detector array conversion are input to data acquisition module, as detectable signal;

Step 4, because temperature and gas component concentrations distribution have continuity, the measurement data lacked between adjacent two photodetectors in detector array is obtained by the method for interpolation by the measurement data of these two photodetectors, 20 interpolated datas are increased, if obtain 127(7+20 × 6 altogether after 7 measured data interpolation between two adjacent data for projection) individual data;

Step 5, as shown in Figure 5, circumference C is angularly divided into 5 sections of circular arcs, the mid point of each circular arc is the focus of fan-shaped laser beam with the intersection point of the determined straight line in the center of circle of circumference C on the circumference C relative with this circular arc, 5 fan-shaped laser beam view fields are comprised in circumference C, one of them region comprises a true fan-shaped laser beam, other 4 regions comprise 4 virtual fan-shaped laser beams, the subtended angle angle that each fladellum laser covers is 30 °, the virtual measurement data that virtual fan beam projections obtains to tested region opposite side is identical with 127 true measurement data, the number of overall measurement data is J, J=635,

Step 6, the flame diameter of parallel shafting stove is 10cm, if 10cm × 10cm square region covers the tested region of flame completely, its center overlaps with flame kernel, is 2500(50 × 50 by direction Region dividing) individual grid, resolution is 0.2cm × 0.2cm, because flame profile is circular, have 1876 grids to be in square region center for the center of circle, 5cm is in the circle of radius, for the jth bundle projection that core wavelength is v, absorptivity A _{v, j}can be expressed as:

$\begin{array}{cc}{A}_{v,j}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{L}_{\mathrm{ji}}{a}_{v,i}& (j=\mathrm{1,2},\·\·\·,J)---\left(1\right)\end{array}$

Wherein a _{v, i}centered by frequency be the absorption intensity of spectral line in i-th grid of v, L _jirepresent that jth bundle is projected in the path in i-th grid.General, absorptivity can be represented with vectorial A, then:

A＝La _v(2)

Wherein L is L _jithe dimension formed is the matrix of 635 × 1876, a _vfor forming a _{v, i}vector;

Step 7, solves (2) with algebraic interation method, obtains a _vexpression formula:

$a_v^{(k+1)}=a_v^{\left(k\right)}+\mathrm{\λ}\frac{A_{v,j_k}-L_{j_k}^T{a}_v^{\left(k\right)}}{{\left|\right|L_{j_k}\left|\right|}^2}{L}_{j_k}$ (3)

$j_k=[k-\mathrm{Int}\left(\frac{k}{635}\right)\×635+1]$

Wherein k is iterations, and λ is relaxation factor, and Int representative rounds operator;

Step 8, the convergence of iteration is obtained by adjacent twice iterative computation with difference mould relative to the changes delta of mould is monitored,

Δ can be expressed as:

$\mathrm{\Δ}=\frac{|a_v^{\left(k\right)}-a_v^{(k-1)}|}{\left|a_v^{\left(k\right)}\right|}---\left(4\right)$

Iteration is stopped when Δ≤0.1%;

Step 9, according to the method for accounting temperature in two-wire length scanning temp measuring method, absorbs coordinate (x on path length _l, y _l) the temperature T (x at place _l, y _l) can by two spectral lines at coordinate (x _l, y _l) the absorption intensity ratio at place represents:

$T(x_l,y_l)=\frac{\frac{\mathrm{hc}}{k}(E_2^{\′\′}-E_1^{\′\′})}{1n\frac{a_1(x_l,y_l)}{a_2(x_l,y_l)}+1n\frac{S_2\left(T_0\right)}{S_1\left(T_0\right)}+\frac{\mathrm{hc}}{k}\frac{(E_2^{\′\′}-E_1^{\′\′})}{T_0}}---\left(5\right)$

Wherein a ₁(x _l, y _l) and a ₂(x _l, y _l) represent spectral line 7185.6cm respectively ^-1and 7444.4cm ^-1at coordinate (x _l, y _l) absorption intensity at place.

The axisymmetric temperature field distribution of being rebuild by the method is contrasted as shown in Figure 6 with initial temperature field distribution, left side contour map represents parallel shafting stove initial temperature field distribution situation, and right side contour map represents the result using the image rebuilding method of this invention to rebuild temperature field.Obviously, right figure has reacted the distribution situation of original axisymmetric temperature field without distortion, proves that the method is effective.

Above to the description of the present invention and embodiment thereof, being not limited thereto, is only one of embodiments of the present invention shown in accompanying drawing.When not departing from the invention aim, designing the structure similar with this technical scheme or embodiment without creation, all belonging to scope.

Claims (1)

1., based on a rotational symmetry parameter distribution image rebuilding method for virtual data, the method comprises the following steps:

Step one, obtains the projection measurements of single visual angle: utilize single visual angle to project and cover measured parameter distribution field, obtain m projection measurements;

Step 2, build virtual measurement data: the projection of total n visual angle covers measured parameter distribution field, n is odd number, one of them visual angle be projected as real projection, other n-1 visual angle be projected as virtual projection, the projection angle that the projection at each visual angle covers is identical, and the virtual projection measured value that the virtual projection at n-1 visual angle is obtained is identical with m real projection measured value, the number of overall measurement data is J, J=m × n;

Step 3, builds the system of equations solving parameter value according to matrix of coefficients and Cephalometry: be N number of grid by tested Region dividing, and for the projection of jth bundle, Cephalometry is expressed as:

$b_j=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{A}_{\mathrm{ji}}{x}_i,(j=\mathrm{1,2},...,J)---\left(1\right)$

Wherein x _ibe the parameter value in i-th pixel, A _jirepresent that jth bundle is projected in the path in i-th grid, then:

b＝Ax (2)

Wherein A is A _jithe dimension formed is the matrix of coefficients of J × N, and x is for forming x _ivector, b for form b _jvector;

Step 4, image reconstruction: solve (2) according to arithmetic reconstruction method, obtains the expression formula of x:

$x^{(k+1)}=x^{\left(k\right)}+\mathrm{\λ}\frac{b_{j_k}-A_{j_k}^T{x}^{\left(k\right)}}{{\left|\right|A_{j_k}\left|\right|}^2}{A}_{j_k}---\left(3\right)$

$j_k=[k-\mathrm{Int}\left(\frac{k}{J}\right)J+1]$

Wherein k is iterations, and λ is relaxation factor, and Int representative rounds operator, and the convergence of iteration obtains x by adjacent twice iterative computation ^(k)and x ^(k-1)the mould of difference is relative to x ^(k)the change of mould represents:

$\mathrm{\Δ}=\frac{|x^{\left(k\right)}-x^{(k-1)}|}{\left|x^{\left(k\right)}\right|}---\left(4\right)$

Iteration is stopped, according to the x tried to achieve when Δ≤0.1% ^(k)rebuild the image of rotational symmetry parameter distribution field.