CN111766294B - Sand and stone aggregate nondestructive detection method based on microwave imaging - Google Patents

Sand and stone aggregate nondestructive detection method based on microwave imaging Download PDF

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CN111766294B
CN111766294B CN202010648765.1A CN202010648765A CN111766294B CN 111766294 B CN111766294 B CN 111766294B CN 202010648765 A CN202010648765 A CN 202010648765A CN 111766294 B CN111766294 B CN 111766294B
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CN111766294A (en
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徐魁文
张璐
王忠宾
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Hangzhou Dianzi University
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Abstract

The invention belongs to the field of three-dimensional microwave imaging, and provides a sand aggregate nondestructive testing method based on microwave imaging. The invention adopts the side section to present the limited caliber of the U-shaped to detect the unknown scatterer, thereby more meeting the actual requirement; the design is a model of a production line workbench, so that the detection process is more convenient and automatic; the three-dimensional electromagnetic imaging technology is realized based on the SOM method with the two remarkable advantages of rapid convergence and noise resistance, so that the method can rapidly and accurately obtain a data result.

Description

Sand and stone aggregate nondestructive detection method based on microwave imaging
Technical Field
The invention belongs to the field of three-dimensional microwave imaging, and provides a limited caliber three-dimensional electromagnetic backscatter imaging nondestructive testing method of sandstone aggregate based on microwave imaging, which is suitable for a pipeline workbench mode.
Background
The most important material in construction engineering is concrete, and the sandstone aggregate is the basic constituent of concrete. Therefore, the detection work of the sand aggregate is an important technical part for ensuring the engineering quality, is used for ensuring the concrete quality, and is used for ensuring the building quality. Therefore, the detection work of the sand aggregate is finished, and the method has great practical significance.
Detection of sand aggregates is a typical three-dimensional electromagnetic backscatter imaging problem. For many years, solutions to three-dimensional backscatter problems have received attention for their wide application in the fields of nondestructive evaluation, medical examination, geophysical exploration, etc., and these methods are generally divided into two categories: deterministic methods and stochastic methods. Recently, a deterministic method, the Subspace Optimization Method (SOM), has been proposed for solving the two-dimensional electromagnetic backscatter inversion problem in transverse magnetic wave (TM) scenarios. The method researches the spectral property of mapping from induced current to scattered field, and the SOM algorithm distinguishes the induced current into deterministic current and fuzzy current by utilizing the spectral property. Deterministic currents can be obtained by computation, while fuzzy currents, which are susceptible to noise, are obtained by iterative optimization. Thus, the anti-noise performance of the algorithm is improved, the optimized solving space is reduced, and the stability of the algorithm is improved. Then on the basis of SOM, a double subspace optimization method (TSOM) is proposed to deal with the two-dimensional backscatter problem, which has better stability, good robustness, and anti-noise performance in inversion. Like the conventional contrast source inversion method (CSI), the SOM method also minimizes the objective function by an optimization method, with the biggest difference that the contrast source inversion method is optimized in the whole current space, and the SOM is optimized in the subspace of the current space, and this difference results in different convergence rates of the two algorithms. The SOM algorithm has three main aspects: (1) Through analysis of the current space spectrum, deterministic current can be obtained through a calculation method; (2) The solving object is converted into fuzzy current, and compared with other algorithms, the solving space of the algorithm is greatly compressed; (3) Proper selection of the parameter L can ensure inversion imaging under a high noise background, and the selection space of L is relatively large. These features provide the SOM algorithm with two significant advantages of fast convergence and noise immunity. The SOM method is also successfully applied to the three-dimensional electromagnetic backscatter problem.
Whether two-dimensional electromagnetic backscatter imaging or three-dimensional electromagnetic backscatter imaging, most existing imaging methods use the measured scattered or total fields at full aperture to reconstruct the dielectric constant of the unknown scatterer. However, the full-caliber imaging method is difficult to realize in practical application, for example, when a wall is detected, 360-degree full-range detection cannot be carried out on the wall in practical situations, and only irradiation and receiving fields on the same face or opposite faces of the wall can be realized. The invention claims a production line workbench for detecting the sand aggregate on the production line, and the full-caliber imaging method is not applicable in the situation. It is important to study two-dimensional or three-dimensional imaging methods at a limited caliber because such an arrangement is more practical.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a method for realizing nondestructive detection of sand aggregate based on microwave imaging under a limited caliber by utilizing a pipeline workbench mode, which comprises the following specific technical scheme:
the method for nondestructive detection of the sand aggregate based on microwave imaging comprises the following steps:
step 1, placing sand and stone aggregate on a workbench type assembly line, and detecting the sand and stone aggregate passing through the detection equipment by adopting detection equipment with a side section of which the shape is U-shaped and under a limited caliber to obtain scattering field data;
and 2, reconstructing the shape and the dielectric constant value of the aggregate of the sand by utilizing the obtained scattered field data and realizing three-dimensional electromagnetic back scattering imaging based on an SOM method.
The specific content of the step 1 comprises:
step 1.1, placing sand and stone aggregates on a workbench type assembly line, and sequentially passing through detection equipment, wherein the detection equipment is provided with three planes with side sections presenting a U shape, each of the three planes faces the sand and stone aggregates, the irradiation angle of each of the three planes is not more than 180 degrees, and detection antennas for transmitting and receiving electric fields are arranged on the planes;
step 1.2. Using a three-dimensional Cartesian coordinate System, 1,2,3 are used to represent the unit vectors for three orientations, respectively
Figure BDA0002572859830000021
And->
Figure BDA0002572859830000022
Coordinates of a point in space are given by x= (x) 1 ，x 2 ，x 3 ) To indicate that there is N i Multiple transmit antennas and N r And is located at point x' n ＝(x′ 1；n ，x′ 2；n ，x′ 3；n )，n＝1，2，...，N r A receiving antenna at the position, which receives electric fields from three directions for each incidence, and measures 3N in total r N i And data of the scattered field.
The specific content of the step 2 comprises:
step 2.1, selecting a certain rectangular domain in the space as an interested domain and dividing the interested domain into M small rectangular domains, wherein the central point coordinate of the small rectangular domains is x m ＝(x 1；m ，x 2；m ，x 3；m )，m＝1，2，...，M；
Step 2.2. Solving three-dimensional electromagnetic backscatter imaging based on SOM method to obtain dielectric constant value, wherein the three-dimensional electromagnetic backscatter imaging consists of data equation and source equation in three-dimensional scene, and for each incidence, the data equation is that
Figure BDA0002572859830000031
Wherein the scattering field->
Figure BDA0002572859830000032
Corresponding to each component therein
Figure BDA0002572859830000033
Inductive current->
Figure BDA0002572859830000034
Corresponding components
Figure BDA0002572859830000035
(l=1, 2, 3), wherein +.>
Figure BDA0002572859830000036
Is 3N in one dimension r X 3M mapping matrix, namely:
Figure BDA0002572859830000037
each of which is +.>
Figure BDA0002572859830000038
Representing the mapping of the induced current v-direction component to the scattered field u-direction component over the measurement region, respectively, the source equation being +.>
Figure BDA0002572859830000039
Wherein the incident field in the region of interest->
Figure BDA00025728598300000310
The corresponding components are +.>
Figure BDA00025728598300000311
And->
Figure BDA00025728598300000312
Having the same structure, it represents the mapping of induced currents to the scattering fields in the region of interest, with dimensions of 3M x 3M,/o>
Figure BDA00025728598300000313
A scattering intensity tensor representing the associated incident field and induced current, expressed as
Figure BDA00025728598300000314
Where n, m=1, 2,..3M, when m+.m, 2M,3M, q=mod (M, M), otherwise q=m, V q Representing the volume size of a small rectangular field, E 0 Dielectric constant value, ε, representing free space background r；q The dielectric constant value corresponding to the q-th small rectangular domain is represented.
The SOM method comprises the following steps: dividing the induced current into deterministic current and ambiguous current, respectively located in mutually orthogonal signal subspace and noise subspace by
Figure BDA00025728598300000315
Singular value decomposition is performed, and deterministic current corresponds to singular value s m m.ltoreq.L, i.e. right singular vectors corresponding to the first L larger singular values +.>
Figure BDA00025728598300000316
The mapped signal subspace; whereas the ambiguity current is defined by the remaining M-L vectors +.>
Figure BDA00025728598300000317
The mapped noise subspace is calculated to obtain deterministic current as follows:
Figure BDA00025728598300000318
wherein the method comprises the steps of
Figure BDA00025728598300000319
Represents the mth left singular vector +.>
Figure BDA00025728598300000320
Represents the conjugate transpose,
Figure BDA00025728598300000321
wherein->
Figure BDA00025728598300000322
m=1, 2, L, by optimizing coefficients->
Figure BDA0002572859830000041
Obtaining the fuzzy current is as follows: />
Figure BDA0002572859830000042
The objective function constructed for optimization by the Conjugate Gradient (CG) method is as follows:
Figure BDA0002572859830000043
wherein the method comprises the steps of
Figure BDA0002572859830000044
Wherein for->
Figure BDA0002572859830000045
The calculation of the composition components is as follows:
Figure BDA0002572859830000046
wherein when u=v, δ (u-v) =1, otherwise equal to 0, k 0 Represents wave number in free space, μ 0 Represents the magnetic permeability of the background, R n，m ＝|x′ n -x m |，n＝1，2，...，N r ，m＝1，2，...，M，g(R n，m )＝exp(ik 0 R n，m )/4πR n，m 。
Figure BDA0002572859830000047
The constituent components are calculated in the same way except that n=1, 2,..m, and when m=n, +.>
Figure BDA0002572859830000048
According to the invention, an unknown scatterer is reconstructed without using a scattered field which is obtained by measurement under a full caliber and is difficult to realize, and the unknown scatterer is detected by adopting a limited caliber with a side section of a U-shaped section, so that the method meets the actual requirement; the design is a model of a production line workbench, so that the detection process is more convenient and automatic; the three-dimensional electromagnetic imaging technology is realized based on the SOM method with two remarkable advantages of rapid convergence and noise resistance, so that whether the aggregate of the sand and stone meets the standard required by a building is detected, and the method can rapidly and accurately obtain a data result.
Drawings
FIG. 1 is a schematic illustration of a sand aggregate detection model of the present invention;
FIG. 2 is a schematic diagram of the experimental measurement device for three-dimensional electromagnetic backscatter imaging under a limited caliber of the invention;
FIGS. 3-5 are schematic diagrams of the results of the present invention for detecting an unknown object using a limited caliber imaging method;
in FIG. 1, a 1-probe device, 2-probe antenna, 3-bench-top pipeline.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings.
The invention relates to a sand aggregate nondestructive testing method based on microwave imaging, which comprises the following steps:
step 1, placing sand and aggregate on a workbench type assembly line 3, and detecting the sand and aggregate passing through the detection equipment 1 with a side section presenting a U-shaped shape under a limited caliber to obtain scattering field data;
and 2, reconstructing the shape and the dielectric constant value of the aggregate of the sand by utilizing the obtained scattered field data and realizing three-dimensional electromagnetic back scattering imaging based on an SOM method.
As shown in fig. 1 and 2, the specific contents of step 1 include:
step 1.1, sand and stone aggregates are placed on a workbench type assembly line 3 and sequentially pass through detection equipment 1, wherein the detection equipment 1 is provided with three planes with inverted U-shaped side sections, each of the three planes faces the sand and stone aggregates, the irradiation angle of each of the three planes is not more than 180 degrees, and detection antennas 2 for transmitting and receiving electric fields are arranged on the planes;
step 1.2. Using a three-dimensional Cartesian coordinate System, 1,2,3 are used to represent the unit vectors for three orientations, respectively
Figure BDA0002572859830000051
And->
Figure BDA0002572859830000052
Coordinates of a point in space are given by x= (x) 1 ，x 2 ，x 3 ) To indicate that there is N i Multiple transmit antennas and N r And is located at point x' n ＝(x′ 1；n ，x′ 2；n ，x′ 3；n )，n＝1，2，...，N r A receiving antenna at the position, which receives electric fields from three directions for each incidence, and measures 3N in total r N i And data of the scattered field.
The specific content of the step 2 comprises:
step 2.1, selecting a certain rectangular domain in the space as an interested domain and dividing the interested domain into M small rectangular domains, wherein the central point coordinate of the small rectangular domains is x m ＝(x 1；m ，x 2；m ，x 3；m )，m＝1，2，...，M；
Step 2.2. Solving three-dimensional electromagnetic backscatter imaging based on SOM method to obtain dielectric constant value, the three-dimensional electromagnetic backscatter imaging is obtained by the number in three-dimensional sceneAccording to the equation and the source equation, for each incidence, the data equation is
Figure BDA0002572859830000053
Wherein the scattering field->
Figure BDA0002572859830000054
Corresponding to each component therein
Figure BDA0002572859830000055
Inductive current->
Figure BDA0002572859830000056
Corresponding components
Figure BDA0002572859830000057
(l=1, 2, 3), wherein +.>
Figure BDA0002572859830000058
Is 3N in one dimension r X 3M mapping matrix, namely:
Figure BDA0002572859830000059
each of which is +.>
Figure BDA00025728598300000510
Representing the mapping of the induced current v-direction component to the scattered field u-direction component over the measurement region, respectively, the source equation being +.>
Figure BDA0002572859830000061
Wherein the incident field in the region of interest->
Figure BDA0002572859830000062
The corresponding components are +.>
Figure BDA0002572859830000063
(l＝1，2，3)，/>
Figure BDA0002572859830000064
And->
Figure BDA0002572859830000065
Having the same structure, it represents the mapping of induced currents to the scattering fields in the region of interest, with dimensions of 3M x 3M,/o>
Figure BDA0002572859830000066
A scattering intensity tensor representing the associated incident field and induced current, expressed as
Figure BDA0002572859830000067
Where n, m=1, 2,..3M, when m+.m, 2M,3M, q=mod (M, M), otherwise q=m, V q Representing the volume size of a small rectangular field, E 0 Dielectric constant value, e, representing free space background r；q The dielectric constant value corresponding to the q-th small rectangular domain is represented.
The SOM method comprises the following steps: dividing the induced current into deterministic current and ambiguous current, respectively located in mutually orthogonal signal subspace and noise subspace by
Figure BDA0002572859830000068
Singular value decomposition is performed, and deterministic current corresponds to singular value s m m.ltoreq.L, i.e. right singular vectors corresponding to the first L larger singular values +.>
Figure BDA0002572859830000069
The mapped signal subspace; whereas the ambiguity current is defined by the remaining M-L vectors +.>
Figure BDA00025728598300000610
The mapped noise subspace is calculated to obtain deterministic current as follows:
Figure BDA00025728598300000611
wherein the method comprises the steps of
Figure BDA00025728598300000612
Represents the mth left singular vector +.>
Figure BDA00025728598300000613
Represents the conjugate transpose,
Figure BDA00025728598300000614
wherein->
Figure BDA00025728598300000615
m=1, 2, L, by optimizing coefficients->
Figure BDA00025728598300000616
Obtaining the fuzzy current is as follows: />
Figure BDA00025728598300000617
The objective function constructed for optimization by the Conjugate Gradient (CG) method is as follows:
Figure BDA00025728598300000618
wherein the method comprises the steps of
Figure BDA00025728598300000619
Wherein for->
Figure BDA00025728598300000620
The calculation of the composition components is as follows:
Figure BDA0002572859830000071
wherein when u=v, δ (u-v) =1, otherwise equal to 0, k 0 Represents wave number in free space, μ 0 Represents the magnetic permeability of the background, R n，m ＝|x′ n -x m |，n＝1，2，...，N r ，m＝1，2，...，M，g(R n，m )＝exp(ik 0 R n，m )/4πR n，m 。
Figure BDA0002572859830000072
The constituent components are calculated in the same manner except that n=1, 2,..m, and when m×n, +.>
Figure BDA0002572859830000073
The invention adopts a limited caliber to detect an unknown target, and is different from full caliber detection, wherein the full caliber detection is used for arranging a detection antenna 2 on three different planes (x-y, y-z, z-x) and carrying out 360-degree full-angle irradiation on the target; the limited caliber detection is to arrange the detection antennas 2 on three planes, namely three planes of x= -lambda, x+lambda and z= +lambda, wherein lambda is wavelength, 16 antennas are arranged on each plane, the detection antennas 2 are orderly arranged in 4 rows and 4 columns, and the interval of each detection antenna 2 is lambda/3, at the moment, for a rectangular area of lambda x lambda, the irradiation angle of each plane to the interested area is not more than 180 degrees, and for x= -lambda and x= +lambda planes, the polarization directions of the set waves are y and z directions respectively, and the polarization direction on the z= +lambda plane is set as x direction.
The sand aggregate is placed on a table-type production line 3, and the sand aggregate passing through the sand aggregate is detected by a detection device 1, and the shape and composition (dielectric constant value) of the sand aggregate are detected.
Selecting size of 0.75X0.75X0.75m 3 Is divided into 30 x 30 small grids when forward computing the scatter field and into 20 x 20 small grids in the inverse problem. The working frequency is 400MHz (lambda=0.75 m), the detecting antenna 2 is arranged on three surfaces of x= -0.75m, x= +0.75m and z+0.75m, 16 antennas are arranged on each surface, the antennas are orderly arranged into 4 rows and 4 columns, the interval between each antenna is 0.25m, three unknown scatterers are selected to verify the effectiveness of a limited caliber detecting scheme, the reconstruction result is shown in fig. 3-5, and the detection of fig. 3 is a sphere with the radius of 0.3lambda and the dielectric constant of 2.0; FIG. 4 is a view of a dielectric with a side length of 0.4λSquare with constant of 2.0; FIG. 5 is a view of a scatterer having an inner side length of 0.2λ, a dielectric constant of 2.0, an outer side length of 0.4λ, and a dielectric constant of 1.5.
The above examples are only illustrative of the method of the present invention and are not limiting, and the present invention is not limited to the above examples, and falls within the scope of the method of the present invention as long as the requirements of the method of the present invention are met.

Claims (2)

1. The method for nondestructive testing of the sand aggregate based on microwave imaging is characterized by comprising the following steps:
step 1, placing sand and stone aggregates on a workbench type assembly line (3), and detecting the sand and stone aggregates passing through the detection equipment by adopting detection equipment (1) with a side section of which the U-shaped section is in a limited caliber to obtain scattering field data;
step 2, reconstructing the shape and the dielectric constant value of the aggregate of the sand by utilizing the obtained scattered field data and realizing three-dimensional electromagnetic back scattering imaging based on an SOM method;
the specific content of the step 1 comprises:
step 1.1, placing sand and stone aggregates on a workbench type assembly line (3) and sequentially passing through detection equipment (1), wherein the detection equipment (1) is provided with three planes with side sections presenting a U shape, and the irradiation angle of each of the three planes facing the sand and stone aggregates is not more than 180 ° The plane is provided with detection antennas (2) for transmitting and receiving electric fields;
step 1.2. Using a three-dimensional Cartesian coordinate System, 1,2,3 are used to represent the unit vectors for three orientations, respectively
Figure FDA0004051223970000011
And
Figure FDA0004051223970000012
coordinates of a point in space are given by x= (x) 1 ,x 2 ,x 3 ) To indicate that there is N i Multiple transmit antennas and N r And is located at point x' n ＝(x′ 1；n ,x′ 2；n ,x′ 3；n ),n＝1,2,…,N r A receiving antenna at the position, which receives electric fields from three directions for each incidence, and measures 3N in total r N i Individual fringe field data;
the specific content of the step 2 comprises:
step 2.1, selecting a certain rectangular domain in the space as an interested domain and dividing the interested domain into M small rectangular domains, wherein the central point coordinate of the small rectangular domains is x m ＝(x 1；m ,x 2；m ,x 3；m ),m＝1,2,…,M；
Step 2.2. Solving three-dimensional electromagnetic backscatter imaging based on SOM method to obtain dielectric constant value, wherein the three-dimensional electromagnetic backscatter imaging consists of data equation and source equation in three-dimensional scene, and for each incidence, the data equation is that
Figure FDA0004051223970000013
Wherein the scattering field->
Figure FDA0004051223970000014
Corresponding to each component therein
Figure FDA0004051223970000015
Inductive current->
Figure FDA0004051223970000016
Corresponding components
Figure FDA0004051223970000017
Wherein->
Figure FDA0004051223970000018
Is 3N in one dimension r X 3M mapping matrix, namely:
Figure FDA0004051223970000019
each of which is +.>
Figure FDA00040512239700000110
Representing the v-direction component of the induced current onto the measurement region as the u-direction of the scattered field
Mapping to components, obtaining a source equation by a discrete Lippmann-Schwinger integral equation
Figure FDA0004051223970000021
Wherein the incident field in the region of interest->
Figure FDA0004051223970000022
The corresponding components are +.>
Figure FDA0004051223970000023
Figure FDA0004051223970000024
And->
Figure FDA0004051223970000025
Having the same structure, it represents the mapping of induced currents to the scattering fields in the region of interest, with dimensions of 3M x 3M,/o>
Figure FDA0004051223970000026
A scattering intensity tensor representing the associated incident field and induced current, expressed as
Figure FDA0004051223970000027
Where n, m=1, 2, …,3M, when m+.m, 2M,3M, q=mod (M, M), otherwise q=m, V q Representing the volume size of a small rectangular field, E 0 Dielectric constant value, e, representing free space background r；q The dielectric constant value corresponding to the q-th small rectangular domain is represented.
2. The method for nondestructive testing of sandstone aggregate based on microwave imaging according to claim 1, wherein the SOM method is as follows: dividing the induced current into determinationsQualitative and ambiguous currents, respectively in mutually orthogonal signal and noise subspaces, by matching
Figure FDA0004051223970000028
Singular value decomposition is performed, and deterministic current corresponds to singular value s m m.ltoreq.L, i.e. right singular vectors corresponding to the first L larger singular values +.>
Figure FDA0004051223970000029
The mapped signal subspace; whereas the ambiguity current is defined by the remaining M-L vectors +.>
Figure FDA00040512239700000210
The mapped noise subspace is calculated to obtain deterministic current as follows:
Figure FDA00040512239700000211
wherein the method comprises the steps of
Figure FDA00040512239700000212
Represents the mth left singular vector +.>
Figure FDA00040512239700000213
Represents the conjugate transpose,
Figure FDA00040512239700000214
wherein->
Figure FDA00040512239700000215
By optimizing coefficients->
Figure FDA00040512239700000216
Obtaining the fuzzy current is as follows: />
Figure FDA00040512239700000217
The objective function constructed for optimization by the Conjugate Gradient (CG) method is as follows:
Figure FDA00040512239700000218
wherein the method comprises the steps of
Figure FDA00040512239700000219
Wherein for->
Figure FDA00040512239700000220
The calculation of the composition components is as follows:
Figure FDA0004051223970000031
wherein when u=v, δ (u-v) =1, otherwise equal to 0, k 0 Represents wave number in free space, μ 0 Represents the magnetic permeability of the background, R n,m ＝|x n ′ -x m |,n＝1,2,…,N r ,m＝1,2,…,M，g(R n,m )＝exp(ik 0 R n,m )/4πR n,m ，
Figure FDA0004051223970000032
And->
Figure FDA0004051223970000033
The constituent components are calculated in the same way, except that n=1, 2, …, M, and when m=n, the term +.>
Figure FDA0004051223970000034
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