CN107907542B - IVMD and energy estimation combined DSPI phase filtering method - Google Patents
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Abstract
A DSPI phase filtering method combining IVMD and energy estimation, the DSPI phase filtering method comprising the steps of: the method comprises the steps that the number of modes after decomposition is required to be preset in the decomposition process of the VMD method, the number of mode components after decomposition is estimated according to the length and the width of a phase diagram, and the optimal mode number is selected by utilizing an orthogonal index; carrying out variation modal decomposition on the DSPI phase diagram according to the number of the optimal modal quantity to obtain a series of modal function components, namely frequency modulation and amplitude modulation components; calculating the energy of the frequency modulation and amplitude modulation components, and estimating the energy of the noise components by using the energy of the decomposed components; and analyzing a curve change diagram of the energy logarithm value and the modal component number, extracting a noise-free component, and obtaining a filtered DSPI phase diagram. The method avoids the problem of setting the mode number in the VMD decomposition process on the premise of a large amount of noise contained in the speckle phase diagram, and adopts the IVMD to filter the image, remove noise interference and obtain accurate phase measurement information.
Description
Technical Field
The invention relates to the field of laser nondestructive testing and optical image processing, in particular to a DSPI (differential mode decomposition) phase filtering method combining IVMD (improved variable mode decomposition) and energy estimation.
Background
In recent years, with the development of aerospace, various composite materials have been widely used. However, the performance of the components is obviously reduced and the service time is reduced due to the defects of deformation, displacement and the like in the processing, manufacturing and service processes of the composite materials. Therefore, the composite materials need to be detected and evaluated, a scheme is provided for subsequent rush repair, and the healthy operation of aerospace equipment is guaranteed.
Research shows that when the surface of an object irradiated by coherent light is deformed or displaced, the deformation of the object surface is converted into the phase change of speckles on an imaging surface, and the phenomenon is called speckle interference. Digital speckle interference (DSPI) is a non-contact full-field measurement technique that can measure displacement, deformation, surface defects, etc. of composite materials. The acquired speckle phase image is interfered by a large amount of noise, so that the signal-to-noise ratio of the speckle phase image is low, the phase measurement sensitivity is low, and the accurate information of a measurement object cannot be obtained. Therefore, it is necessary to process the speckle phase map to improve the signal-to-noise ratio of the image and remove noise interference.
For DSPI phase noise reduction, scholars at home and abroad propose various noise reduction methods which are mainly classified into a space domain class and a time frequency analysis class. The space domain method mainly comprises a mean filtering method and a median filtering method: the mean filtering method also destroys the detail part of the image while filtering noise, so that the processed image becomes fuzzy, and information with abrupt phase change is lost; the median filtering method can retain the edge information while reducing noise, is simple and easy to implement, and has long calculation time and poor smoothing effect.
The time-frequency analysis denoising method comprises Gabor transformation, wavelet transformation, empirical mode decomposition and the like. Both the Gabor filtering method and the wavelet threshold denoising method filter interference noise by manually setting a threshold, have no self-adaptability and cannot acquire accurate phase information; the empirical mode decomposition method has the defects of mode aliasing, over-enveloping, under-enveloping and the like, and can not effectively process noise.
Disclosure of Invention
The invention provides a DSPI phase filtering method combining IVMD and energy estimation, which aims at a large amount of noise interference in a digital speckle phase diagram, adopts IVMD to process the speckle phase diagram, does not need parameter setting, can decompose the image, removes the noise interference and obtains accurate measurement information, and is described in detail as follows:
a DSPI phase filtering method combining IVMD and energy estimation, the DSPI phase filtering method comprising the steps of:
collecting a DSPI phase diagram, estimating the number of decomposed modal components according to the length and the width of the phase diagram, and extracting the optimal modal quantity by using an orthogonal index;
carrying out variation mode decomposition on the DSPI phase diagram according to the number of the decomposed components to obtain a series of mode function components, namely frequency modulation and amplitude modulation components;
calculating the energy of the frequency modulation and amplitude modulation components, and estimating the energy of the noise components by using the energy of the decomposed components;
and analyzing a curve change diagram of the energy logarithm value and the modal component number, extracting a noise-free component, and obtaining a filtered DSPI phase diagram.
The method comprises the following steps of estimating the number of decomposed modal components according to the length and the width of a phase diagram, and extracting the optimal modal quantity by using an orthogonal index:
judging the length and the width of the picture, and calculating the number of modal components by using the length or the width when the length and the width of the picture are equal;
when the two are not equal, firstly, the range of the modal quantity is estimated according to the scale, the orthogonality after decomposition is respectively calculated, and the corresponding component number when the orthogonality is minimum is selected, namely the optimal modal quantity.
Wherein, the orthogonality after the respective calculation and the corresponding component number when the orthogonality is minimum are selected, namely the optimal mode number specifically:
and extracting the optimal modal quantity by utilizing the orthogonality index to obtain a proper modal component.
Further, the step of performing variation modal decomposition on the DSPI phase diagram according to the number of the decomposed components to obtain a series of modal function components specifically includes:
first defining modal components as finite bandwidths with different center frequencies; constructing a constraint variational equation according to the minimum principle of the sum of bandwidths of different modes;
aiming at a constraint variational equation, introducing an augmented Lagrange function to convert the constraint variational equation into a non-constraint variational equation;
calculating a saddle point of the augmented Lagrange function by adopting a multiplicative operator alternating direction method, namely, an optimal solution of a constraint variational equation;
and continuously updating the center frequency and the modal component, stopping updating when the modal component meets the iteration stop condition, and outputting the decomposed modal component.
Further, the step of calculating the fm component energy and estimating the energy of the noise component using the energy of the decomposed component specifically includes:
calculating the energy of the frequency modulation and amplitude modulation component of the DSPI phase diagram after IVMD decomposition;
the energy of the noise component is estimated from the frequency and amplitude modulated energy.
The step of analyzing the curve variation graph of the energy logarithm value and the modal component number, extracting a noise-free component, and obtaining a filtered DSPI phase diagram specifically comprises the following steps:
respectively calculating energy logarithm values of modal components and energy logarithm values of noise components after decomposition of the DSPI phase diagram, and drawing variation conditions of the two energy logarithm values according to the modal quantity K;
the two energy log values are linearly decreased along with the increase of K, the energy log value estimated at a noise-free position is subjected to mutation along with the increase of K, and the frequency modulation and amplitude modulation component after the mutation is a noise-free component;
and reconstructing the noise-free component to obtain a reconstructed DSPI phase diagram, namely a noise-reduced DSPI phase diagram.
The technical scheme provided by the invention has the beneficial effects that:
1. aiming at the characteristic that the modal quantity needs to be set in the VMD decomposition process, the invention provides an improved variational modal decomposition method, which can select the optimal modal quantity in a variational frame and process a speckle phase diagram to obtain the inherent modal component of a DSPI phase diagram;
2. aiming at the fact that the collected speckle phase diagram contains noise components, the invention estimates the noise energy by utilizing the energy of the decomposed modal components, filters the noise components according to the variation curve chart of the energy logarithm value along with the modal quantity K, obtains the filtered DSPI phase diagram, improves the signal-to-noise ratio and further improves the accurate phase information;
3. the IVMD and noise energy estimation combined method can adaptively reduce the noise of the speckle interference phase picture, and avoids the complicated parameter setting of the traditional filtering method.
Drawings
FIG. 1 is a DSPI phase filtering method combining IVMD and energy estimation;
FIG. 2 is a schematic diagram of a digital speckle interferometry system;
FIG. 3 is a diagram of the collected DSPI phase including noise;
fig. 4 is a speckle phase map after IVMD based filtering.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
Example 1
A DSPI phase filtering method combining IVMD and energy estimation, referring to fig. 1, the DSPI phase filtering method includes the following steps:
101: collecting a DSPI phase diagram, estimating the number of decomposed modal components according to the length and the width of the phase diagram, and extracting the optimal modal quantity by using an orthogonal index;
102: carrying out variation mode decomposition on the DSPI phase diagram according to the number of the decomposed components to obtain a series of mode function components, namely frequency modulation and amplitude modulation components;
103: calculating the energy of the frequency modulation and amplitude modulation components, and estimating the energy of the noise components by using the energy of the decomposed components;
104: and analyzing a curve change diagram of the energy logarithm value and the modal component number, extracting a noise-free component, and obtaining a filtered DSPI phase diagram.
Wherein, the step 101 is specifically as follows:
judging the length and the width of the picture, and calculating the number of modal components by using the length or the width when the length and the width of the picture are equal;
when the two are not equal, firstly, the range of the modal quantity is estimated according to the scale, the orthogonality after decomposition is respectively calculated, and the corresponding component number when the orthogonality is minimum is selected, namely the optimal modal quantity.
Wherein, the step 102 specifically includes:
first defining modal components as finite bandwidths with different center frequencies; constructing a constraint variational equation according to the minimum principle of the sum of bandwidths of different modes;
aiming at a constraint variational equation, introducing an augmented Lagrange function to convert the constraint variational equation into a non-constraint variational equation;
calculating a saddle point of the augmented Lagrange function by adopting a multiplicative operator alternating direction method, namely, an optimal solution of a constraint variational equation;
and continuously updating the center frequency and the modal component, stopping updating when the modal component meets the iteration stop condition, and outputting the decomposed modal component.
Further, the step 103 specifically includes:
calculating the energy of the frequency modulation and amplitude modulation component of the DSPI phase diagram after IVMD decomposition;
the energy of the noise component is estimated from the frequency and amplitude modulated energy.
Further, the step 104 specifically includes:
respectively calculating energy logarithm values of modal components and energy logarithm values of noise components after decomposition of the DSPI phase diagram, and drawing variation conditions of the two energy logarithm values according to the modal quantity K;
the two energy log values are linearly decreased along with the increase of K, the energy log value estimated at a noise-free position is subjected to mutation along with the increase of K, and the frequency modulation and amplitude modulation component after the mutation is a noise-free component;
and reconstructing the noise-free component to obtain a reconstructed DSPI phase diagram, namely a noise-reduced DSPI phase diagram.
In summary, in the embodiment of the present invention, through the steps 101 to 104, the DSPI phase diagram can be decomposed on the premise of the phase diagram containing noise, the noise energy is estimated according to the energy of the decomposed components, the energy logarithm change curve diagram is analyzed, the noise components are removed, and accurate measurement information is obtained.
Example 2
The scheme in embodiment 1 is further described below with reference to specific calculation formulas, examples, and fig. 2 to 4, and is described in detail below:
201: a digital speckle interferometry system is built by combining the figure 2, and a CCD camera in the digital speckle interferometry system is used for collecting DSPI phase diagrams before and after deformation of a measured disc;
the detailed operation of the step is as follows:
a digital speckle interferometry system is constructed and comprises a CCD camera, an imaging lens, a laser and the like.
The light path of the measuring system is shown in fig. 2, laser emitted by a laser is divided into two beams by a spectroscope, one beam irradiates the surface of a measured object, the other beam is transmitted along an optical fiber through a coupling lens to be used as object light, diffuse reflected light of the measured object sequentially passes through an optical wave and an imaging lens to form speckle interference with the object light, a DSPI phase diagram is collected by a CCD camera, the material of a measured disc panel is a copper sheet, and the collected DSPI phase diagram is shown in fig. 3.
The embodiment of the invention does not limit the size of the copper sheet and sets the size according to the requirement in practical application.
202: the number of the modal components after decomposition is set according to the size of the digital speckle interference phase diagram, and the detailed operation of the step is as follows:
1) decomposing any one-dimensional signal, wherein the number of the modal components after decomposition is as follows:
D＝log2L-1
wherein, L is the length of the one-dimensional signal, and D is the number of the modal components after decomposition.
2) Assuming that the size of the DSPI phase diagram is M multiplied by N, and the number of the components after VMD decomposition is K;
and extracting the optimal modal quantity by utilizing the orthogonality index to obtain a proper modal component.
203: carrying out variation mode decomposition on the digital speckle interference phase diagram by using the number K of modal components to obtain a series of modal function components, namely frequency modulation and amplitude modulation components, wherein the detailed operation of the step is as follows:
the VMD method determines the frequency center and the bandwidth of the decomposed component by iteratively searching the optimal solution of the variation model in a variation frame, thereby being capable of decomposing the digital speckle phase diagram in a self-adaptive manner.
1) Initialization
And n ← 0, constructing a variation problem, and correspondingly constraining variation equations as follows:
wherein f (x) is a DSPI phase diagram, uk(x) Obtaining a 2D analytic signal u of a single-side frequency spectrum for a component after 2D signal decomposition, namely an intrinsic mode function, by using Hilbert transformAS,k(x) Its mathematical expression is as follows:
wherein, ω iskα as center frequencykIs a penalty parameter; x is a vector of the picture; k is the number after decomposition; u. ofkAs decomposed components; δ (d)<x,ωk>Is a dirac function; δ (d)<x,ωk,⊥>) Is omegakInverse Fourier transform under frequency band ⊥ inverse Fourier transform, pi<x,ωk>Are parameters.
2) Aiming at the problem of constrained variation, introducing an augmented Lagrange function to convert the problem of constrained variation into the problem of unconstrained variation, wherein the mathematical expression of the augmented Lagrange function is as follows:
wherein the penalty parameter is αkLagrange function multiplier is lambda, lambda (x) is a multiplier function, ▽ is a calculation norm;<.>is a convolution.
3) In order to solve the problem of the optimal solution, a multiplication operator alternating direction method is adopted to calculate the saddle point of the augmented Lagrange function, namely the optimal solution of the constraint variation equation. The alternate update obtains modal components and center frequency mathematical expressions as follows:
wherein i is a parameter and the value range is 1 to k.
4) Updating Lagrange function multiplier lambda.
Wherein the content of the first and second substances,
a frequency domain function that is a multiplier; τ is a coefficient;
is a function of the frequency domain of f (x),
is composed of
Is measured.
5) If it is not
And ending the circulation, and outputting the modal components, otherwise, continuing the circulation.
Wherein the content of the first and second substances,
for the decomposed modal components, ε is an infinitesimally small positive number.
204: calculating the energy value of the component of the DSPI phase diagram after VMD decomposition, estimating the energy of the noise component according to the energy value, analyzing two curve change diagrams according to the relation between the energy logarithm and the decomposed quantity K, and extracting the noise-free component;
1) calculating the energy value of the decomposed component, wherein the modal component after decomposition is uk(i, j) having an energy value of:
wherein E iskFor the energy of the decomposed modal components, M and N are the length and width of the DSPI phase picture, respectively.
2) Estimating the energy of the noise component in the picture by using the energy of the decomposed modal component:
wherein E is1The energy value of the first frequency modulation and amplitude modulation component after IVMD decomposition is obtained, and the parameters gamma and rho are respectively 0.719 and 2.01 after repeated experiments.
3) Calculating the logarithm value of the decomposed component by using the energy and the noise energy of the decomposed component:
F＝log2Ek
wherein, F is the logarithm value of the modal component of DSPI after VMD decomposition, and H is the logarithm value of the estimated noise component.
4) And analyzing the change curve graphs of the two energy logarithm values along with the K, extracting a noise-free modal component according to the K value corresponding to the mutation position of the two curves, and reconstructing the noise-free modal component to obtain a filtered DSPI phase diagram.
In summary, in the embodiment of the present invention, through the steps 201 to 204, on the premise that the DSPI phase diagram containing a large amount of noise does not need to set parameters, the IVMD is adopted to perform adaptive decomposition on the DSPI phase diagram, so as to reduce noise according to energy, improve the signal-to-noise ratio of the phase diagram, and reduce the phase error.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (4)
1. A DSPI phase filtering method combining IVMD and energy estimation is characterized by comprising the following steps:
collecting a DSPI phase diagram, estimating the number of decomposed modal components according to the length and the width of the phase diagram, and extracting the optimal modal quantity by using an orthogonal index;
carrying out variation modal decomposition on the DSPI phase diagram according to the optimal modal quantity to obtain a series of modal function components, namely frequency modulation and amplitude modulation components;
calculating the energy of the frequency modulation and amplitude modulation components, and estimating the energy of the noise components by using the energy of the decomposed components;
analyzing a curve variation graph of the energy logarithm value and the modal component number, extracting a noise-free component, and obtaining a filtered DSPI phase diagram;
the step of estimating the number of the decomposed modal components according to the length and the width of the phase diagram and extracting the optimal modal quantity by using the orthogonal index specifically comprises the following steps:
judging the length M and the width N of the picture, and calculating the number of modal components by using the length or the width when the length M and the width N are equal;
when the two are not equal, firstly, estimating the range of the modal quantity according to the scale, respectively calculating the orthogonality after decomposition, and selecting the corresponding component number when the orthogonality is minimum, namely the optimal modal quantity;
and extracting the optimal modal quantity by utilizing the orthogonality index to obtain a proper modal component.
2. The method according to claim 1, wherein the step of obtaining a series of modal function components by performing a variational modal decomposition on the DSPI phase diagram according to the number of decomposed components comprises:
first defining modal components as finite bandwidths with different center frequencies; constructing a constraint variational equation according to the minimum principle of the sum of bandwidths of different modes;
aiming at a constraint variational equation, introducing an augmented Lagrange function to convert the constraint variational equation into a non-constraint variational equation;
calculating a saddle point of the augmented Lagrange function by adopting a multiplicative operator alternating direction method, namely, an optimal solution of a constraint variational equation;
and continuously updating the center frequency and the modal component, stopping updating when the modal component meets the iteration stop condition, and outputting the decomposed modal component.
3. The combination of IVMD and energy estimation DSPI phase filtering method of claim 1, wherein said step of computing FM component energy and estimating noise component energy using decomposed component energy comprises:
calculating the energy of the frequency modulation and amplitude modulation component of the DSPI phase diagram after IVMD decomposition;
the energy of the noise component is estimated from the frequency and amplitude modulated energy.
4. The method of claim 1, wherein the step of analyzing a curve variation graph of log values of energy and number of modal components, extracting a noise-free component, and obtaining a filtered DSPI phase diagram specifically comprises:
respectively calculating energy logarithm values of modal components and energy logarithm values of noise components after decomposition of the DSPI phase diagram, and drawing variation conditions of the two energy logarithm values according to the modal quantity K;
the two energy log values are linearly decreased along with the increase of K, the energy log value estimated at a noise-free position is subjected to mutation along with the increase of K, and the frequency modulation and amplitude modulation component after the mutation is a noise-free component;
and reconstructing the noise-free component to obtain a reconstructed DSPI phase diagram, namely a noise-reduced DSPI phase diagram.
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| CN105674065A (en) * | 2016-01-18 | 2016-06-15 | 南京信息职业技术学院 | Variational mode decomposition-based method for locating leakage point of pipeline by acoustic emission |
| CN205561775U (en) * | 2016-04-26 | 2016-09-07 | 盐城工学院 | Three dimension word speckle interference synchronous measurement devices |
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