CN111753419A - Method for detecting rough surface scattering sound pressure based on wavelet matrix method - Google Patents
Method for detecting rough surface scattering sound pressure based on wavelet matrix method Download PDFInfo
- Publication number
- CN111753419A CN111753419A CN202010579344.8A CN202010579344A CN111753419A CN 111753419 A CN111753419 A CN 111753419A CN 202010579344 A CN202010579344 A CN 202010579344A CN 111753419 A CN111753419 A CN 111753419A
- Authority
- CN
- China
- Prior art keywords
- rough surface
- sound pressure
- matrix
- incident
- scattering
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 57
- 239000011159 matrix material Substances 0.000 title claims abstract description 51
- 238000004364 calculation method Methods 0.000 claims abstract description 13
- 230000009466 transformation Effects 0.000 claims abstract description 8
- 239000013598 vector Substances 0.000 claims description 16
- 238000005070 sampling Methods 0.000 claims description 15
- 230000003595 spectral effect Effects 0.000 claims description 7
- 238000004613 tight binding model Methods 0.000 claims description 6
- 230000001419 dependent effect Effects 0.000 claims description 3
- 238000012512 characterization method Methods 0.000 claims description 2
- 230000005428 wave function Effects 0.000 abstract description 4
- 238000004458 analytical method Methods 0.000 description 3
- 238000009795 derivation Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- 238000000354 decomposition reaction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000003745 diagnosis Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000009659 non-destructive testing Methods 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/148—Wavelet transforms
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Data Mining & Analysis (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Software Systems (AREA)
- Databases & Information Systems (AREA)
- Algebra (AREA)
- Computing Systems (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- Operations Research (AREA)
- Investigating Or Analyzing Materials By The Use Of Ultrasonic Waves (AREA)
Abstract
The invention discloses a method for detecting rough surface scattering sound pressure based on a wavelet matrix method, which comprises the following steps: acquiring the statistical characteristics of the roughness of the rough surface, establishing a rough surface model, and discretizing the rough surface model to obtain a function of the plane height along with the change of a coordinate system; then, establishing an incident wave function, and discretizing the incident wave function to obtain discrete data of incident waves changing along with coordinates; obtaining a matrix describing scattering characteristics according to an integral equation and boundary conditions; finally, simplifying the matrix by utilizing the orthogonality of wavelet transformation; and the simplified matrix is used for obtaining the scattering sound pressure of the rough surface. The method combines the advantages of a matrix method and wavelet transformation, greatly reduces the scale of the matrix by utilizing the wavelet transformation on the basis of the original matrix method, overcomes the solving error brought by the original sparse matrix, and has the advantages of simple operation and calculation time saving.
Description
Technical Field
The invention relates to a method for detecting rough surface scattering sound pressure based on a wavelet matrix method, and belongs to the technical field of ultrasonic detection.
Background
The practical application of acoustic scattering is very wide, such as nondestructive testing, medical diagnosis, underwater sound exploration and the like. The sound waves often encounter the ground, sea surface, material surface, etc. in nature during scattering. Both of the above surfaces can be considered as rough surfaces. Therefore, it is very important to study the sound scattering of the rough surface.
The sound scattering research on rough surfaces can be divided into three methods, namely an analytic method, an approximation method and a numerical method. The analytic method is to combine the Helmholtz equation and the boundary condition to directly solve the specific situation, the result is accurate, but the analytic method is only suitable for the sound scattering situation of the boundary condition rule. When the analytic solution does not exist or is very difficult to solve, under certain initial conditions and boundary conditions, an approximate solution or an asymptotic solution of the scattering sound field can be calculated. The common methods comprise a geometric diffraction theory, kirchhoff approximation, Born approximation, perturbation and the like, and can solve the problem that a precise solution cannot be obtained. However, each of these methods has limitations. The numerical method for calculating the sound wave scattering mainly comprises a finite element method, a boundary element method, a time domain finite difference method, a matrix method and the like, and the numerical calculation can provide an approximate solution of the actual problem. The matrix method utilizes an integral equation and a boundary condition to disperse the acoustic scattering problem into a matrix equation for solving, and when the sampling point is large enough, the solved solution can well approach the real solution, but the solution complexity is followed.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects of the prior art and provides a method for detecting the scattering sound pressure of a rough surface based on a wavelet matrix method, which is simple to operate and saves time.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for detecting rough surface scattered sound pressure based on a wavelet matrix method comprises the following steps:
establishing a rough surface model based on the statistical characteristics of the roughness of the rough surface;
obtaining a rough surface height calculation model based on the rough surface model;
establishing a matrix equation related to rough surface and scattering sound pressure based on a calculation model of the height of the rough surface;
simplifying the matrix equation based on Harr wavelet transformation to obtain a simplified equation;
and calculating the scattering sound pressure of the rough surface based on the simplified equation.
Further, the rough surface model is established based on the statistical characteristics of the roughness of the rough surface, and the method comprises the following steps:
the statistical characterization of the roughness of the rough surface is carried out using a power spectral density of the gaussian distribution:
wherein W(s) is power spectral density, s is dependent variable, hrmsIs the mean square error of the undulation height of the rough surface, and l is the correlation length of the rough surface.
Further, the obtaining of the calculation model of the rough surface height based on the rough surface model includes:
randomly generating an independent Gauss random number vector α with a mean of 0 and a variance of 1nAnd βn，n＝0,1,2,…,2N；
Generating random complex numbers gamma based on random number vectorsn：
Calculating an expansion coefficient based on the rough surface model:
calculating the asperity height using discrete fourier transform:
wherein z ispThe height of the rough surface at the sampling point p is shown, 2N +1 is the number of sampling points on the truncation length of the rough surface, and L is the truncation length of the rough surface.
Further, the rough surface and scattering sound pressure related matrix equation is established based on the rough surface height calculation model, and the rough surface and scattering sound pressure related matrix equation comprises:
the integral equation of the one-dimensional rough surface is expressed as:
wherein p isinc(x ', z') is an incident wave, (x, z), (x ', z') respectively represents coordinates of a scattering point and an incident point, z (x) represents the height of the rough surface corresponding to the abscissa x of the scattering point, g (x, z; x ', z') is a green function corresponding to (x, z), (x ', z'), ▽ p (x, z) represents scattering sound pressure;
discretizing the integral equation by combining the first type of boundary conditions to obtain a matrix equation:
Am×nQn＝bm，
wherein:
bm＝pinc(xm,zm)；
wherein x ism,xnAbscissa of incidence point and scattering point, respectively, and Δ x is sampling interval, g (x)m,xn) Is xm,xnCorresponding Green function, k is the wave number of incident sound wave, i is the imaginary unit, z' (x)m) Representing the point of incidence xmAt the height of the rough surface, z' (x)n) Represents the scattering point xnThe height of the rough surface is higher than that of the rough surface,
as normal derivative symbols, ▽ p (x)n,zn) Derivative of sound pressure as scattering point, pinc(xm,zm) Representing the incident wave.
Further, the incident wave is a cone wave, and is represented as:
pinc(xp,zp)＝exp[ik(xpcosθi+zpsinθi)-(xp-zpcotθi)2/g2]；
wherein p isinc(xp,zp) Is (x)p,zp) Incident wave of (x)pIs the abscissa, z, of the rough surface sampling point ppP surface height of rough surface sampling point, g is cone wave control parameter, thetaiIs the average angle of incidence of the incident sound field.
Further, the simplifying the matrix equation based on Harr wavelet transform to obtain a simplified equation, including:
constructing a 0-scale space scale function and a 1-scale space scale function:
expanding unknown vector Q by using 0-scale space scale function and 1-scale space scale function respectivelyn：
Wherein,
respectively representing unknown expansion coefficients corresponding to 0 and 1 scale functions, r' is an incident field vector point,
when the index number is discrete n, the 0,1 scale function corresponding to the incident pointNumber, N ═ 1,2, …, N;
and (3) substituting an integral equation of the one-dimensional rough surface to obtain:
wherein r ' and r are vector points of the incident field and the scattered field respectively, g (r, r ') is a green function, and x ' is an abscissa corresponding to the vector points of the incident field;
constructing a weight function:
wherein () is a function, rm,-Δ＝rm-Δx/2，rm,+Δ＝rm+Δx/2，rmIs represented by the formulamCorresponding discrete points; inner products are respectively made by using weight functions:
obtaining:
further, the calculating of the scattering sound pressure of the rough surface based on the simplified equation includes:
constructing a fine solution:
based on simplified equations
Brought into a fine solution to obtain
And
by bringing into the formula to obtain Qn：
The scattering sound pressure p (x) of the rough surface was calculated according to the following formulan,zn)：
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a method for detecting rough surface scattering sound pressure by utilizing wavelet transformation and a matrix method. The method combines the advantages of a matrix method and wavelet transformation, greatly reduces the scale of the matrix by utilizing the wavelet transformation on the basis of the original matrix method, overcomes the solving error brought by the original sparse matrix, and has the advantages of simple operation and calculation time saving.
Drawings
FIG. 1 is a schematic view of rough surface scattering.
Detailed Description
The present invention is further described with reference to the accompanying drawings, and the following examples are only for clearly illustrating the technical solutions of the present invention, and should not be taken as limiting the scope of the present invention.
The invention discloses a method for detecting rough surface scattered sound pressure based on a wavelet matrix method, which combines the matrix method with a Harr wavelet transform method, and is characterized in that a rough plane is expanded along an x-axis direction, z ═ f (x) represents the surface height of the rough surface corresponding to an x point, and a wave beam p is formed by combining a matrix method and a Harr wavelet transform method, as shown in figure 1incEdge of
Direction of incidence, generation
Directionally scattered sound pressure ps. The algorithm specifically comprises the following steps:
1) and acquiring the statistical characteristics of the roughness of the rough surface, establishing a rough surface model, and discretizing the rough surface model to obtain a formula of the surface height changing along with a coordinate system.
Further, the rough surface model is represented by the roughness, which is represented by the statistical characteristics, and the power spectral density of the gaussian distribution is adopted, and the expression is as follows:
wherein W(s) is power spectral density, s is dependent variable, and hrmsIs the mean square error of the relief height of the asperity, and l is the surface correlation length, these two variables affecting the degree of roughness exhibited by the asperity.
After the power spectral density is obtained, a rough surface conforming to the roughness can be randomly generated. The method comprises the following specific steps:
randomly generating an independent Gauss random number vector α with a mean of 0 and a variance of 1nAnd βn(N is 0,1,2, …,2N), 2N +1 is the number of sampling points on the truncation length, and L is the truncation length of the rough surface, then the sampling interval:
and thereby generate a random complex number:
calculating an expansion coefficient:
calculating the rough surface height z using discrete Fourier transformp：
2) And establishing an incident wave function, and discretizing the incident wave function to obtain discrete data of incident waves changing along with coordinates.
The incident wave can be conical wave, the conical wave control parameter g is L/4, and the average incident angle theta of the incident sound field is determined according to the average incident angle thetaiThe wave number k of the incident sound wave is the sampling point (x) of the rough surfacep,zp) The incident cone wave at (a) can be described as:
pinc(xp,zp)＝exp[ik(xpcosθi+zpsinθi)-(xp-zpcotθi)2/g2](6)
xpas coordinates of the rough surface sampling point p, zpThe asperity is sampled at the p surface height.
3) And obtaining a matrix describing scattering characteristics according to an integral equation and boundary conditions.
Using the Green formula, the general form of the helmholtz integral equation can be derived:
wherein,
wherein p (r) is the total sound pressure field, pinc(r') is the incident sound pressure,
for normal derivation notation, ▽ p (r), ▽ g (r, r ') denotes derivation of p (r), green's function g (r, r '), r' and r are vector points of the incident and scattered fields, respectively, D is a scatterer, and s is a rough surface.
The integral equation for a one-dimensional matte can be described as:
wherein, (x, z), (x ', z') respectively represent the coordinates of the scattering point and the incidence point, and z (x) represents the height of the rough surface corresponding to the coordinate x.
Discretizing the integral equation by combining the first type of boundary conditions to obtain a matrix equation:
Am×nQn＝bm，
in the formula:
matrix:
unknown variables:
the known incident wave variation: bm＝pinc(xm,zm)；
Wherein x ism,xnRespectively represent the abscissa of the incident point, the abscissa of the scattering point, g (x)m,xn) Is xm,xnCorresponding Green's function, i in imaginary units, ▽ p (x)n,zn) The sound pressure derivative of the scattering point.
4) And simplifying the matrix by utilizing the orthogonality of the Harr wavelet transform to obtain a fine solution.
Firstly, a 0-scale space scale function and a 1-scale space scale function are constructed:
expanding the unknown vector Q by using 0,1 scale function respectivelyn，
Wherein,
respectively represent the unknown expansion coefficients corresponding to the 0,1 scale functions,
for a discrete index N, the incident point r' corresponds to a 0,1 scale function, where N is 1,2, …, N.
And substituting into integral equation (8):
wherein x' represents the incident point coordinates.
Constructing a weight function:
wherein () is a function, rm,-Δ＝rm-Δx/2，rm,+Δ＝rm+Δx/2，rmIs represented by the formulamCorresponding discrete points.
Inner products are made for equation (14) using weight functions (15) and (16), respectively:
from the above system of equations, it can be derived:
constructing a fine solution:
substituting the 0-scale expansion coefficient obtained from equation (21) into the following equation:
can obtain an unknown vector Qn。
That is, in the actual calculation process, it is only necessary to obtain the values from the equation sets (19) and (20)
A finer solution is obtained from a coarser approximation solution, the size of the matrix equation being reduced from N x N to two N/2 x N/2.
5) And calculating the scattering sound pressure of the rough surface.
From the new matrix Q obtained in step 4)nSubstituting the following formula:
then p (x) can be obtainedn,zn) I.e. the scattering sound pressure of the rough surface.
Based on the shape inflexibility of a matrix method and the advantages of decomposition and reconstruction of a wavelet transform method, the invention greatly reduces the scale of the matrix, overcomes the solving error brought by the original sparse matrix, and has the advantages of simple operation and calculation time saving.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A method for detecting rough surface scattering sound pressure based on a wavelet matrix method is characterized by comprising the following steps:
establishing a rough surface model based on the statistical characteristics of the roughness of the rough surface;
obtaining a rough surface height calculation model based on the rough surface model;
establishing a matrix equation related to rough surface and scattering sound pressure based on a calculation model of the height of the rough surface;
simplifying the matrix equation based on Harr wavelet transformation to obtain a simplified equation;
and calculating the scattering sound pressure of the rough surface based on the simplified equation.
2. The method for detecting the scattered sound pressure of the rough surface based on the wavelet matrix method as claimed in claim 1, wherein the rough surface model is established based on the statistical characteristics of the roughness of the rough surface, and the method comprises the following steps:
the statistical characterization of the roughness of the rough surface is carried out using a power spectral density of the gaussian distribution:
wherein W(s) is power spectral density, s is dependent variable, hrmsIs the mean square error of the undulation height of the rough surface, and l is the correlation length of the rough surface.
3. The method for detecting the scattered sound pressure of the rough surface based on the wavelet matrix method as claimed in claim 2, wherein the obtaining of the calculation model of the height of the rough surface based on the rough surface model comprises:
randomly generating an independent Gauss random number vector α with a mean of 0 and a variance of 1nAnd βn，n＝0,1,2,…,2N；
Generating random complex numbers gamma based on random number vectorsn：
Calculating an expansion coefficient based on the rough surface model:
calculating the asperity height using discrete fourier transform:
wherein z ispThe height of the rough surface at the sampling point p is shown, 2N +1 is the number of sampling points on the truncation length of the rough surface, and L is the truncation length of the rough surface.
4. The method for detecting scattered sound pressure of a rough surface based on the wavelet matrix method as claimed in claim 3, wherein the rough surface and scattered sound pressure related matrix equation is established based on the calculation model of the height of the rough surface, and comprises:
the integral equation of the one-dimensional rough surface is expressed as:
wherein p isinc(x ', z') is an incident wave, (x, z), (x ', z') respectively represents coordinates of the scattering point and the incident point, z (x) represents the height of the rough surface corresponding to the abscissa x of the scattering point, g (x, z; x ', z') is a Green function corresponding to (x, z), (x ', z'),
represents a scattered sound pressure;
discretizing the integral equation by combining the first type of boundary conditions to obtain a matrix equation:
Am×nQn＝bm，
wherein:
bm＝pinc(xm,zm)；
wherein x ism,xnAbscissa of incidence point and scattering point, respectively, and Δ x is sampling interval, g (x)m,xn) Is xm,xnCorresponding Green function, k is the wave number of incident sound wave, i is the imaginary unit, z' (x)m) Representing the point of incidence xmAt the height of the rough surface, z' (x)n) Represents the scattering point xnThe height of the rough surface is higher than that of the rough surface,
in order to derive the sign in the normal direction,
derivative of sound pressure as scattering point, pinc(xm,zm) Representing the incident wave.
5. The method for detecting rough surface scattered sound pressure based on the wavelet matrix method as claimed in claim 4, wherein the incident wave is a cone wave represented by:
pinc(xp,zp)＝exp[ik(xpcosθi+zpsinθi)-(xp-zpcotθi)2/g2]；
wherein p isinc(xp,zp) Is (x)p,zp) Incident wave of (x)pIs the abscissa, z, of the rough surface sampling point ppP surface height of rough surface sampling point, g is cone wave control parameter, thetaiIs the average angle of incidence of the incident sound field.
6. The method for detecting rough surface scattered sound pressure based on the wavelet matrix method as claimed in claim 4, wherein the simplifying the matrix equation based on Harr wavelet transform to obtain a simplified equation comprises:
constructing a 0-scale space scale function and a 1-scale space scale function:
expanding unknown vector Q by using 0-scale space scale function and 1-scale space scale function respectivelyn：
Wherein,
respectively representing unknown expansion coefficients corresponding to 0 and 1 scale functions, r' is an incident field vector point,
ψ1,n(r') is a discrete index N, the incident point corresponds to a 0,1 scale function, and N is 1,2, …, N;
and (3) substituting an integral equation of the one-dimensional rough surface to obtain:
wherein r ' and r are vector points of the incident field and the scattered field respectively, g (r, r ') is a green function, and x ' is an abscissa corresponding to the vector points of the incident field;
constructing a weight function:
wherein () is a function, rm,-Δ＝rm-Δx/2，rm,+Δ＝rm+Δx/2，rmIs represented by the formulamCorresponding discrete points;
inner products are respectively made by using weight functions:
obtaining:
7. the method for detecting the scattered sound pressure of the rough surface based on the wavelet matrix method as claimed in claim 6, wherein the calculating the scattered sound pressure of the rough surface based on the simplified equation comprises:
constructing a fine solution:
based on simplified equations
Brought into a fine solution to obtain
And
by bringing into the formula to obtain Qn：
The scattering sound pressure p (x) of the rough surface was calculated according to the following formulan,zn)：
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010579344.8A CN111753419B (en) | 2020-06-23 | 2020-06-23 | Method for detecting rough surface scattering sound pressure based on wavelet matrix method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010579344.8A CN111753419B (en) | 2020-06-23 | 2020-06-23 | Method for detecting rough surface scattering sound pressure based on wavelet matrix method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111753419A true CN111753419A (en) | 2020-10-09 |
| CN111753419B CN111753419B (en) | 2023-03-31 |
Family
ID=72676558
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010579344.8A Active CN111753419B (en) | 2020-06-23 | 2020-06-23 | Method for detecting rough surface scattering sound pressure based on wavelet matrix method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111753419B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113124999A (en) * | 2021-04-13 | 2021-07-16 | 常州工学院 | Method and device for acquiring scattering sound pressure based on three-dimensional scanning and Fourier transform |
| CN114757074A (en) * | 2022-04-18 | 2022-07-15 | 天津大学 | Rusted steel simulation method based on surface random roughness |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106326579A (en) * | 2016-08-27 | 2017-01-11 | 安徽大学 | Method for generating visualizing of land and sea environment based on electromagnetic scattering technique |
| CN109100692A (en) * | 2018-06-19 | 2018-12-28 | 西安电子科技大学 | Rough surface and multiple target combination scattering emulation modes based on iterative physical optics |
-
2020
- 2020-06-23 CN CN202010579344.8A patent/CN111753419B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106326579A (en) * | 2016-08-27 | 2017-01-11 | 安徽大学 | Method for generating visualizing of land and sea environment based on electromagnetic scattering technique |
| CN109100692A (en) * | 2018-06-19 | 2018-12-28 | 西安电子科技大学 | Rough surface and multiple target combination scattering emulation modes based on iterative physical optics |
Non-Patent Citations (1)
| Title |
|---|
| 郭立新等: "一维随机粗糙面电磁散射的小波矩量解", 《西安电子科技大学学报(自然科学版)》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113124999A (en) * | 2021-04-13 | 2021-07-16 | 常州工学院 | Method and device for acquiring scattering sound pressure based on three-dimensional scanning and Fourier transform |
| CN113124999B (en) * | 2021-04-13 | 2023-09-22 | 常州工学院 | Method and device for acquiring scattering sound pressure based on three-dimensional scanning and Fourier transformation |
| CN114757074A (en) * | 2022-04-18 | 2022-07-15 | 天津大学 | Rusted steel simulation method based on surface random roughness |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111753419B (en) | 2023-03-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111753419B (en) | Method for detecting rough surface scattering sound pressure based on wavelet matrix method | |
| Haltmeier et al. | Thermoacoustic computed tomography with large planar receivers | |
| Yang et al. | Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence | |
| Xiong et al. | The time-singularity multifractal spectrum distribution | |
| Higgins et al. | Alignment trends of velocity gradients and subgrid-scale fluxes in the turbulent atmospheric boundary layer | |
| Carpio et al. | Bayesian approach to inverse scattering with topological priors | |
| CN111999712B (en) | Parameter estimation method for scattering center point of three-dimensional GTD scattering center model | |
| CN109241556B (en) | Random asperity object modeling method and storage medium | |
| Zangerl et al. | Photoacoustic tomography with direction dependent data: an exact series reconstruction approach | |
| Franceschetti et al. | An electromagnetic fractal-based model for the study of fading | |
| Florindo et al. | Enhancing multiscale fractal descriptors using functional data analysis | |
| Valdivia et al. | Krylov subspace iterative methods for boundary element method based near-field acoustic holography | |
| CN113487724B (en) | Modeling method for terahertz device mounting material forming interface morphology characteristics | |
| CN117709235A (en) | Method for analyzing association of pulse flow field and sound source of underwater vehicle | |
| CN111272274B (en) | Closed space low-frequency sound field reproduction method based on microphone random sampling | |
| CN117274096A (en) | X-ray coherent diffraction image recovery method for generating binarization airspace constraint | |
| Dong et al. | Accelerated nonlinear multichannel ultrasonic tomographic imaging using target sparseness | |
| Bendjoya et al. | Wavelet analysis and applications to some dynamical systems | |
| Gavrilieva et al. | Numerical homogenization for wave propagation in fractured media | |
| Chen et al. | Texture Feature Extraction Method for Ground Nephogram Based on Contourlet and the Power Spectrum Analysis Algorithm. | |
| Haynes et al. | Inverse Scattering under the Born Approximation using an Object T-matrix and Full Bistatic Spherical Sampling Geometry | |
| Feng et al. | An Equivalent Source Method Based on Sound Pressure Differential Filter for Particle Velocity Reconstruction | |
| Ali et al. | 2-D Slicewise Waveform Inversion of Sound Speed and Acoustic Attenuation for Ring Array Ultrasound Tomography Based on a Block LU Solver | |
| Guo | A meshless regularized local boundary integral equation method and the selection of weight function and geometrical parameters | |
| Klyuchinskiy et al. | Quantity of the inverse problem data for the system of conservation laws |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |