CN112200880A - Solid rocket engine combustion surface retreating image reconstruction method - Google Patents
Solid rocket engine combustion surface retreating image reconstruction method Download PDFInfo
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- 238000002485 combustion reaction Methods 0.000 title claims abstract description 62
- 238000000034 method Methods 0.000 title claims abstract description 30
- 239000007787 solid Substances 0.000 title claims abstract description 24
- 239000011159 matrix material Substances 0.000 claims abstract description 24
- 238000013170 computed tomography imaging Methods 0.000 claims abstract description 16
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- 238000013508 migration Methods 0.000 claims abstract description 5
- 238000005070 sampling Methods 0.000 claims description 12
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- 238000002939 conjugate gradient method Methods 0.000 claims description 6
- 238000003325 tomography Methods 0.000 claims description 4
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- 230000005672 electromagnetic field Effects 0.000 claims description 3
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- 239000000446 fuel Substances 0.000 description 1
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Abstract
The invention relates to a dynamic change process of a combustion surface in a solid rocket engine test, in particular to a method for reconstructing a combustion surface migration image of a solid rocket engine. The method comprises the steps of obtaining a magnetic line path of a microwave CT imaging field of the combustion surface of the engine, obtaining microwave projection data of the combustion surface of the engine, reconstructing a retreating image of the combustion surface of the engine, and judging the reconstructed quality. The image reconstruction method provided by the invention mainly determines a projection matrix according to a projection geometric relation, constructs a projection observation model according to a projection physical process, and realizes target reconstruction through optimization solution. The reconstruction method has low requirement on the completeness of projection data, can introduce prior constraint information according to specific imaging conditions, can inhibit noise and finally achieves high reconstruction quality.
Description
Technical Field
The invention relates to a dynamic change process of a combustion surface in a solid rocket engine test, in particular to a method for reconstructing a combustion surface migration image of a solid rocket engine.
Background
The solid rocket engine has become the preferred power device of the strategic and tactical missile weapon system at present due to the advantages of small volume, strong maneuverability, convenient maintenance and use and the like. With the continuous development of the technology of the solid missile weapon system in China, the solid rocket engine of the new generation missile weapon system adopts a propellant with higher fuel value and more sensitivity. However, in the process of developing the novel solid rocket engine, problems such as large combustion speed prediction deviation, erosion combustion, unstable combustion, difficult technical zero-setting positioning and the like occur from the root of combustion, and the important reason for the problems is that the dynamic change process of the combustion surface in the solid rocket engine test is not clear, the relevant key parameters and change rules of the solid rocket engine are difficult to accurately obtain, and the development process of the solid rocket engine in China is seriously hindered. So far, the change of the combustion surface of the explosive column in the solid rocket engine in China can not be detected or can not be accurately detected, and the development level, the performance improvement and the quality zeroing of the solid rocket engine in China are seriously influenced. The research on the combustion surface retrogradation testing technology of the solid rocket engine is urgently needed, and the research on the combustion surface retrogradation image reconstruction method of the solid rocket engine is one of the problems which must be overcome.
The analytic method can obtain better reconstruction quality for complete projection data, has high reconstruction speed, but has higher requirement on the completeness of the data. When projection data are rare and projection angles are missing, high-quality reconstruction effect cannot be obtained. The reconstruction by the analytic method requires complete projection information, and generally data with more than 180 projection angles are reconstructed, so that better reconstruction quality can be obtained for complete projection data.
Disclosure of Invention
Technical problem to be solved
The invention provides a method for reconstructing a combustion surface retreating image of a solid rocket engine, which is used for improving the image edge reconstruction quality; the number of magnetic lines of force of the microwave CT imaging field is increased to increase the imaging information quantity, so that the reconstruction that the error of the retrogradation images of the solid rocket engines with different combustion surface diameters is within 1mm is realized.
Technical scheme adopted for solving technical problem
The method for reconstructing the combustion surface retreating image of the solid rocket engine comprises the following steps:
1) magnetic line path for acquiring combustion surface microwave CT imaging field
According to the electromagnetic wave attenuation characteristic, battery magnetic wave tomography is simulated, and further through a transmitting device, 29 receiving devices work simultaneously, and firstly, the magnetic line path of a preliminary microwave CT imaging field is obtained. Then according to the propagation rule of the electromagnetic field, respectively adding 2 magnetic lines on two sides of each magnetic line of the preliminarily obtained magnetic line path of the microwave CT imaging field so as to increase the information quantity and obtain the final magnetic line path of the combustion surface microwave CT imaging field;
2) acquiring microwave projection data of combustion surface
Solving a projection matrix according to a magnetic line simulation path equation, wherein a in the projection matrix AijDefining the length of an intersection line of an i-ray and an j-pixel, discretizing a reconstruction region according to a projection matrix, uniformly arranging n transmitting/receiving devices on a circumference which takes the center of a measured object as a circle center, taking one of the n transmitting/receiving devices as a transmitter each time, switching a receiving state, and detecting scattered data together with all other receiving devices, wherein the propagation of microwaves in the measured medium meets the wave equation in a common form:
wherein
Representing the reflectivity of a medium
The scalar function of (a) is selected,
is a vector laplacian operator. Through a series of deformation operations, the formula can be converted into:
wherein
Called objective function，kbRepresents the wave number, mu, of a plane wave in a background mediumrAnd εrRepresenting the relative permeability and relative permittivity relative to the background medium due to the total field
Can be expressed as an incident field
And a scattered field
And incident wave of
Can be defined as:
thus, it is possible to obtain:
with the green's function, the illumination produced by all sources can be found as:
thus obtaining "projection" data a;
3) combustion surface migration image reconstruction
To fully exploit the gradient sparsity of an image, a minimized image can be obtained by a formula, i.e.
Constraint conditions are as follows: subject to y is Ax
Wherein | x | purpleTVIs the TV norm of the image x,
representing an image function, from N image pixels x1，x2，…，xNAnd (4) forming. y is the attenuation of the microwave through the combustion surface and A is the projection matrix.
The formula for the TV norm of image x is as follows,
wherein,
image reconstruction is carried out by taking minimization of TV norm as a target, and an iterative formula is as follows
Wherein p isiFor projecting the measured values,. mu.jFor the attenuation coefficient to be determined, λ is the relaxation factor, aijConstructing an image reconstruction algorithm based on minimization of a TV norm by performing convex set orthogonal projection and TV noise reduction twice correction processing on a calculation result in each step of iterative calculation process for the length of the i microwave intersection j pixels;
4) reconstruction quality discrimination
Comparing the obtained reconstructed values of the combustion surfaces with different diameters with the actual values, finishing iteration when the error between the two values is not more than 1mm, proving that the reconstruction quality of the combustion surfaces meets the requirement, otherwise, continuing the iteration until the error between the two values is not more than 1mm,
δ＝max|fi-fi′|
where δ is the error between the reconstructed value and the actual value, fiIs the true numerical value of the fire face diameter when the image serial number is i, fi' is the reconstructed value of the combustion surface diameter when the image number is i.
Further, the specific algorithm steps of the combustion surface retrogradation image reconstruction are as follows:
1) initial value selection: let S represent a star undersampled matrix, an initial observation set
Fourier transform coefficients representing the original image taken only at the star sample line position (the Fourier-centric slice theorem indicates that sampling along the star sample line in the frequency domain is inherently consistent with the random sampling required by CS theory)
Representing the multiplication of corresponding elements of the matrix. Further, let the iteration initial value x0＝DFT-1(y0)；
2) And (3) iterative calculation: solving and calculating the following iterative formula by using a conjugate gradient method:
wherein λ isnDenotes the iteration step size, dnRepresents the direction of the conjugate gradient;
3) orthogonal projection: orthogonal projection is performed on y as Ax, and calculation is performed first
DFT of (1), preserving the frequency domain information y on the initial sample point0The frequency domain information of the non-sampling point is updated by using the current iteration result without changing, and then the inverse DFT of the frequency domain updating result is calculated, namely
4) Denoising TV: the frequency-domain star sampling causes the iteration result to contain randomly distributed noise, so that the iteration result of the above formula is matched
Carrying out noise reduction treatment by using the following formula to obtain the (n + 1) th step iterationEnd result x ofn+1I.e. by
Wherein for any given two-dimensional image x ═ x (x)ij) The TV noise reduction matrix is TV _ noise (x) ═ tij) And is and
5) and (3) updating the conjugation direction: search direction d of conjugate gradient methodnIs a combination of the direction of the negative gradient of the current iteration and the direction of the last search iteration, i.e.
dn+1＝dTV(xn+1)+βdn
Wherein d isTV(xn+1) Express | | xn+1||TVIn the direction of the gradient of (a),
is a proportional coefficient, | ·| non-woven phosphorFA Frobenius norm representing a matrix;
6) termination criteria: and stopping iteration when the iteration times reach a certain set value or the iteration result is converged, or returning to the step II to continue the process by iterative computation.
Advantageous effects
The image reconstruction method provided by the invention mainly determines a projection matrix according to the projection geometric relation, constructs a projection observation model according to the projection physical process, and realizes target reconstruction through optimization solution. The reconstruction method has low requirement on the completeness of projection data, can introduce prior constraint information according to specific imaging conditions, can inhibit noise and finally achieves high reconstruction quality.
Drawings
FIG. 1: a three-dimensional reconstruction algorithm flow chart of a combustion surface retreating image of a solid rocket engine;
FIG. 2: a strong electric field simulation result diagram observed at the radiation edge of the antenna;
FIG. 3: a primary magnetic line path simulation graph;
FIG. 4: finally, a magnetic line path simulation graph is obtained;
FIG. 5: microwave tomography projection matrix images;
FIG. 6: microwave projection data of different combustion surface diameters;
FIG. 7: a combustion surface retreating reconstruction algorithm flow chart;
FIG. 8: reconstructing result graphs of different combustion surface diameters;
FIG. 9: comparing the combustion surface diameter results;
FIG. 10: error plots.
Detailed Description
FIG. 1 is a flowchart of a method for reconstructing a combustion surface retrogradation image of a solid rocket engine. The main processes of the invention comprise the steps of obtaining the magnetic line path of the microwave CT imaging field of the combustion surface of the engine, obtaining the microwave projection data of the combustion surface of the engine, reconstructing the retreating image of the combustion surface of the engine and judging the reconstruction quality.
The invention is further described with reference to the accompanying drawings and the detailed description.
As shown in figure 1, the method for reconstructing the combustion surface retrogradation image of the solid rocket engine comprises four parts of obtaining a magnetic line path of a microwave CT imaging field of the combustion surface of the engine, obtaining microwave projection data of the combustion surface of the engine, reconstructing the combustion surface retrogradation image of the engine and judging the reconstruction quality. The method comprises the following specific steps:
1) magnetic line path for acquiring combustion surface microwave CT imaging field
According to the electromagnetic wave attenuation characteristic, battery magnetic wave tomography is simulated, and when the diameter of a grain is 200mm and the number of the loop antenna arrays is 30, the included angle between two adjacent receiving antennas at the left and right of a transmitting antenna (when the antenna is 10mm away from the arc surface of the grain) is about 168 degrees. The simulation result of the strong electric field observed at the radiation edge of the antenna is shown in fig. 2. As can be seen from fig. 2, microstrip antenna radiation ensures that each receiving antenna can receive signals. Further according to the mechanism of 1 transmitting and 29 receiving, the path of magnetic lines of force for primarily acquiring the microwave CT imaging field is shown in fig. 3. Then, according to the propagation rule of the electromagnetic field, 2 magnetic lines are added on two sides of each magnetic line in fig. 2 to increase the information amount, and the final magnetic line path of the combustion surface microwave CT imaging field is obtained, as shown in fig. 4.
2) Acquiring microwave projection data of combustion surface
Solving the projection matrix for the magnetic flux line simulation path equation of fig. 4 is shown in fig. 5. The reconstructed area was discretized using a circular geometry model as shown in fig. 5, and 29 transmitters/receivers were uniformly arranged on a circle centered on the center of the measured object. One of them is used as a transmitter each time, and then the receiving state is switched to detect the scattered data together with all other receivers. In the formula
On the basis of the obtained projection data, the microwave receiving values of 3 magnetic lines in the final magnetic line path of the combustion surface microwave CT imaging field are all set to be the same value, and microwave projection data of the combustion surface 30 × 90 is obtained, as shown in fig. 6.
3) Combustion surface migration image reconstruction
As shown in FIG. 7, the reconstruction algorithm includes six parts, namely initial value selection, iterative computation, orthogonal projection, TV noise reduction, conjugate direction update and termination criterion. According to the formula
Minimizing the obtained TV norm as a target according to a formula
The iterative formula of (2) is reconstructed, and the specific steps of the algorithm are as follows:
firstly, selecting an initial value: let S represent a star undersampled matrix, an initial observation set
Fourier transform coefficients representing the original image taken only at the star sample line position (the Fourier center slice theorem indicates that the star sample line is followed in the frequency domainThe sampling is inherently consistent with the random sampling required by Cs theory), where
Representing the multiplication of corresponding elements of the matrix. Further, let the iteration initial value x0＝DFT-1(y0)；
And (2) iterative calculation: solving and calculating the following iterative formula by using a conjugate gradient method:
wherein λ isnDenotes the iteration step size, dnThe conjugate gradient direction is indicated.
③ orthogonal projection: orthogonal projection is performed on y as Ax, and calculation is performed first
DFT of (1), preserving the frequency domain information y on the initial sample point0The frequency domain information of the non-sampling point is updated by using the current iteration result without changing, and then the inverse DFT of the frequency domain updating result is calculated, namely
Fourthly, noise reduction of the TV: the frequency-domain star sampling causes the iteration result to contain randomly distributed noise, so that the iteration result of the above formula is matched
Carrying out noise reduction treatment by using the following formula to obtain a final result x of the (n + 1) th iterationn+1I.e. by
Wherein for any given two-dimensional image x ═ x (x)ij) The TV noise reduction matrix is TV _ noise (x) ═ tij) And is and
conjugate direction updating: search direction d of conjugate gradient methodnIs a combination of the direction of the negative gradient of the current iteration and the direction of the last search iteration, i.e.
dn+1＝dTV(xn+1)+βdn
Wherein d isTV(xn+1) Express | | xn+1||TVIn the direction of the gradient of (a),
is a proportional coefficient, | ·| non-woven phosphorFThe Frobenius norm of the matrix is represented.
Sixthly, termination criterion: and stopping iteration when the iteration times reach a certain set value or the iteration result is converged, or returning to the step II to continue the process by iterative computation.
According to multiple times of calculation, the iteration is performed for 100 times, and the iteration result is converged. The reconstruction result is shown in FIG. 8.
4) Reconstruction quality discrimination
At this time, the reconstructed results of different combustion surface diameters are compared with the actual numerical values, fig. 9 shows that the error curve between the reconstructed numerical values and the actual numerical values of the combustion surfaces with different diameters can be obtained from the error curve, the error between the reconstructed numerical values and the actual numerical values is not more than 1mm, and the reconstructed quality of the combustion surfaces is proved to meet the requirements.
Claims (2)
1. The method for reconstructing the combustion surface retreating image of the solid rocket engine is characterized by comprising the following steps of:
1) magnetic line path for acquiring combustion surface microwave CT imaging field
According to the electromagnetic wave attenuation characteristic, battery magnetic wave tomography is simulated, 29 receiving devices further work simultaneously through one transmitting device, firstly, a magnetic line path of a preliminary microwave CT imaging field is obtained, then, according to the propagation rule of an electromagnetic field, 2 magnetic lines of force are added on two sides of each magnetic line of the magnetic line path of the preliminary obtained microwave CT imaging field respectively, so that the information quantity is increased, and the final magnetic line path of the combustion surface microwave CT imaging field is obtained;
2) acquiring microwave projection data of combustion surface
Solving a projection matrix according to a magnetic line simulation path equation, wherein a in the projection matrix AijDefining the length of an intersection line of i-ray and j-pixel, discretizing a reconstruction region according to a projection matrix, uniformly arranging n transmitting/receiving devices on a circumference taking the center of a measured object as a circle center, taking one of the n transmitting/receiving devices as a transmitter each time, switching a receiving state, and detecting scattered data together with all other receiving devices, wherein at the moment, the propagation of microwaves in a measured medium meets the wave equation in a common form:
wherein
Representing the reflectivity of a medium
The scalar function of (a) is selected,
for the vector laplacian, the formula can be converted into:
wherein
Called the objective function, kbRepresents the wave number, mu, of a plane wave in a background mediumrAnd εrIndicating relative permeability and relative to the background mediumDielectric constant due to total field
Can be expressed as an incident field
And a scattered field
And incident wave of
Can be defined as:
thus, it is possible to obtain:
with the green's function, the illumination produced by all sources can be found as:
thus obtaining "projection" data a;
3) combustion surface migration image reconstruction
To fully exploit the gradient sparsity of an image, a minimized image can be obtained by a formula, i.e.
Constraint conditions are as follows: subject to y is Ax
Wherein | x | purpleTVIs the TV norm of the image x,
representing an image function, from N image pixels x1,x2,L,xNThe composition, y is the attenuation value of the microwave passing through the combustion surface, A is a projection matrix,
the formula for the TV norm of image x is as follows,
wherein,
image reconstruction is carried out by taking minimization of TV norm as a target, and an iterative formula is as follows
Wherein p isiFor projecting the measured values,. mu.jFor the attenuation coefficient to be determined, λ is the relaxation factor, aijConstructing an image reconstruction algorithm based on TV norm minimization by performing convex set orthogonal projection and TV noise reduction twice correction processing on a calculation result in each step of iterative calculation process for the length of i microwave intersection j pixels;
4) reconstruction quality discrimination
Comparing the obtained reconstructed values of the combustion surfaces with different diameters with the actual values, finishing iteration when the error between the two values is not more than 1mm, proving that the reconstruction quality of the combustion surfaces meets the requirement, otherwise, continuing the iteration until the error between the two values is not more than 1mm,
δ＝max|fi-f′i|
where δ is the error between the reconstructed value and the actual value, fiIs a true value of the combustion face diameter f 'of the image number i'iThe numerical value is the reconstructed value of the combustion surface diameter when the image serial number is i.
2. The method for reconstructing a combustion surface retrogradation image of a solid-rocket engine according to claim 1, wherein the algorithm comprises the following steps:
1) initial value selection: let S represent a star undersampled matrix, an initial observation set
Fourier transform coefficients representing the original image taken only at the star sample line position (the Fourier-centric slice theorem indicates that sampling along the star sample line in the frequency domain is inherently consistent with the random sampling required by CS theory)
Multiplying corresponding elements of the representation matrix, and further, making an initial value x of the iteration0＝DFT-1(y0)；
2) And (3) iterative calculation: solving and calculating the following iterative formula by using a conjugate gradient method:
wherein λ isnDenotes the iteration step size, dnRepresents the direction of the conjugate gradient;
3) orthogonal projection: orthogonal projection is performed on y as Ax, and calculation is performed first
DFT of (1), preserving the frequency domain information y on the initial sample point0The frequency domain information of the non-sampling point is updated by using the current iteration result without changing, and then the inverse DFT of the frequency domain updating result is calculated, namely
4) Denoising TV: the frequency-domain star sampling causes the iteration result to contain randomly distributed noise, so that the iteration result of the above formula is matched
Carrying out noise reduction treatment by using the following formula to obtain a final result x of the (n + 1) th iterationn+1I.e. by
Wherein for any given two-dimensional image x ═ x (x)ij) The TV noise reduction matrix is TV _ noise (x) ═ tij) And is and
5) and (3) updating the conjugation direction: search direction d of conjugate gradient methodnIs a combination of the direction of the negative gradient of the current iteration and the direction of the last search iteration, i.e.
dn+1＝dTV(xn+1)+βdn
Wherein d isTV(xn+1) Express | | xn+1||TVIn the direction of the gradient of (a),
as a proportionality coefficient, | g | non-conducting phosphorFA Frobenius norm representing a matrix;
6) termination criteria: and (3) stopping iteration when the iteration times reach a certain set value or the iteration result is converged, or else, returning to 2) iterative computation to continue the process.
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