CN109883532A - A kind of identification of sound source and sound field forecasting procedure - Google Patents
A kind of identification of sound source and sound field forecasting procedure Download PDFInfo
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Abstract
The present invention is to provide a kind of identification of sound source and sound field forecasting procedure.Using the sound transmission idea about modeling based on the unit radiation addition method, target Equivalent source face is divided into several and conformal regular piston of object construction；The radiated sound field that Approximate Equivalent source is gone to using the radiated sound field of regular piston, according to the analytical expression of the conformal radiating of circular piston sound field of rule establish equivalent source source strength to radiated sound field acoustic transmission matrix Germ(r,rE)；By array received data and to the equivalent acoustic transmission matrix G to measurement basic matrix strong in a steady streamerm(rH,rE) Regularization is carried out, obtain the distributed intelligence of conformal piston equivalent source source strength W；Utilize the normal direction vibration velocity transfer matrix G in equivalent source source strength W and equivalent face in a steady stream to sound source surfaceerm_v(rS,rE), reconfigured geometry sound source surface normal vibration velocity is distributed vS；Utilize the acoustic pressure transfer matrix G in equivalent source source strength W and equivalent face in a steady stream to radiated sound fielderm_p(rF,rE), vibration velocity transfer matrix Germ_v(rF,rE), the acoustic pressure distribution p of sound source radiation sound field is forecast respectivelyFV is distributed with vibration velocityF.Present invention can apply to Structure Radiant Noise Source Identifications and radiated sound field to forecast.
Description
Technical field
The present invention relates to a kind of identification of sound source and sound field forecasting procedure, specifically a kind of based on conformal piston etc.
The identification of sound source and sound field of the near field acoustic holography algorithm of effect source method are forecast.
Background technique
In order to reduce the radiated noise of submarine navigation device, needs to carry out noise source fixation and recognition and radiated sound field forecast is ground
Study carefully, determine the spatial distribution of Main Noise Sources, finds out contribution of all kinds of noise sources to aircraft radiated noise.Near field acoustic holography
(nearfield acoustic holography, NAH) is exactly that a kind of very effective noise source that developed recently gets up is known
Not, positioning and sound field visualization technique, can provide noise source abundant and sound field information for project planner, for underwater boat
The vibration and noise reducing engineering of row device provides foundation.
The development of near field acoustic holography theory is concentrated mainly near field acoustic holography sound field spatial alternation algorithm, it is near field sound
The key that holography is realized is the tie for contacting measurement data and reconstructed results on holographic facet.Williams and Maynard et al.
(Williams E G,Maynard J D,Skudrzyk E.Sound reconstruction using a microphone
Array [J] .J.Acoust.Soc.Am, 1980,68 (1): 340-344P.) propose the near field based on space Fourier transformation
Acoustic Holography Theory.The basic thought of this method is to measure multiple acoustic pressure on sound source near-field holography face, is become with two-dimensional space Fourier
Changing commanders, it transforms from a spatial domain to wave-number domain, then holographic facet information is transmitted to reconstruction face by transfer operator G, finally with two dimension
Space Fourier inverse transformation obtains the multiple acoustic pressure or particle vibration velocity on reconstruction face.This method is theoretically it can be readily appreciated that algorithm and reality
Test easy to accomplish, calculating speed is fast；But FFT is only applicable to the case where orthogonal coordinate system uniform grid point, it is desirable that holographic facet harmony
Source surface must have well-regulated shape (such as plane, spherical surface, cylinder etc.)；And multiple acoustic pressure is in definite measured hole on holographic facet
Discrete measurement on diameter necessarily brings window effect and wrap around error when carrying out rebuilding calculating with FFT.
In order to random appearance sound source carry out near field acoustic holography analysis, Veronesi et al. (Veronesi W A,
Maynard J D.Digital holography reconstruction of sources with arbitrarily
Shaped surfaces.J.Acoust.Soc.Am, 1989,85 (2): 588-598) propose the near field sound based on boundary element method
It is holographic.The basic thought of this method be using the discrete Helmholtz integral equation of simplest constant unit, establish sound source face and
Vibration acoustic transmission matrix between holographic facet and prediction face determines that the acoustic radiation transitive relation between sound source and sound field, use are unusual
Value decomposes (singular value decomposition, SVD) and inverts to vibration acoustic transmission matrix, to appoint in inverse matrix and near field
The product of multiple acoustic pressure measured on meaning shape holographic facet rebuilds sound source surface vibration velocity, and calculates in sound field sound at arbitrary point with this
Learn parameter.Near field acoustic holography based on boundary element method can be adapted for source face and the holographic facet of arbitrary shape, but boundary element method is deposited
The problems such as nonuniqueness solved at complicated interpolation processing, Treatment of Singular Integration and characteristic waves.Meanwhile it is existing at present
Boundary element method near field acoustic holography is all target to be considered as to the point source being independently distributed, and vibration is calculated using point source spherical surface spread function
Acoustic transmission matrix, and had differences with the acoustic radiation propagation model of this kind of continuously distributed structure sound source of submarine navigation device, it may
Cause identification of sound source result and reality different, and has higher requirements to measuring distance and measurement basic matrix number.
Equivalent source method (equivalent source method, ESM) is the one kind to grow up late 1980s
New calculation of acoustic radiation method (Koopmann G H, Song L, Fahnline J.A method for computing
acoustic field based on the principle of wave superposition.J.Acoust.Soc.Am,
1989,86(6):2433-2438).Its main thought is: vibrating body radiation sound field can by be placed in inside the vibrating body one
The sound field that serial equivalent source generates, which is superimposed, to be replaced, and the source strength of these equivalent sources can be shaken by matching the normal direction on vibrating body surface
Speed obtains.Since the sound field of vibrating body radiation is equivalent to the sound field that its internal equivalent source is radiated, vibrating body boundary has been skipped, because
And the nonuniqueness problem of complexity interpolation arithmetic, Treatment of Singular Integration and solution present in boundary element method is avoided, calculate effect
Rate and precision all greatly improve.The advantage that equivalent source method is calculated by it in adaptability and numerical value, has been widely used in recent years
In the near field acoustic holography research of random appearance sound source.Currently, the equivalent source form according to employed in calculating is different, based on etc.
The near field acoustic holography of effect source method can be divided into the simple source of use as the near field acoustic holography of equivalent source and using spherical wave conduct etc.
The near field acoustic holography in effect source.
Equivalent source is used as using simple source (monopole, dipole etc.), by the actual measurement acoustic pressure on matching holographic facet, is solved
Meet Source intensity density (weighting coefficient) needed for each simple source when matching condition, is then superimposed each simple source and is generated in target position
Sound field, realize sound field transformation.It as the exemplary process of equivalent source is based on Helmholtz equation minimum two using spherical wave
Multiply (Helmholtz equation-least squares, HELS) near field acoustic holography, since the spherical surface wave source of use has just
The property handed over, is conducive to the determination of equivalent source position and the raising of computational accuracy.But either using simple source or spherical wave come structure
Equivalent source is made, the acoustic radiation propagation model of this kind of continuously distributed structure sound source of submarine navigation device is not all accounted for equally, with reality
Structure acoustic radiation propagation model has differences, and possibly can not accurately identify continuously distributed complicated type sound source；And in reality
It needs to test that basic matrix distance objective sound source is relatively close, site density is higher in, increases the difficulty of engineering construction.
In conclusion target sound source is all considered as the point source being independently distributed by near field acoustic holographies all at present, and use point
Source spherical surface spread function model, has differences with practical structures acoustic radiation propagation model.Therefore above-mentioned algorithm is not all from basic
It is upper to solve the problems, such as to have differences with practical structures acoustic radiation propagation model, due to traditional point source spherical surface spread function and practical mesh
Structure sound source mismatch is marked, the accuracy that will lead to continuously distributed complicated type identification of sound source result reduces；It needs simultaneously to mesh
It marks sound source and carries out close-in measurement and more demanding site density, increase engineer application (particularly with submarine target noise
Identifing source) enforcement difficulty.
Summary of the invention
The purpose of the present invention is to provide a kind of precise positioning that can be realized underwater large scale structure sound source and identifications, improve
The identification of sound source and sound field forecasting procedure of the accuracy of continuously distributed complicated type identification of sound source result.
The object of the present invention is achieved like this:
(1) acoustic transmission matrix is established: using the sound transmission modeling method based on the unit radiation addition method, by target Equivalent source
Face be divided into it is several with the conformal regular piston of object construction (rectangle piston, cylinder piston, spherical crown piston etc.), and with target knot
Structure rule baffle is fitted, and regards each piston as an equivalent source；Using the rule conformal with object construction sound source surface
Then the radiated sound field of piston removes the radiated sound field of approximate target equivalent source, according to the Analytical Expression of the conformal radiating of circular piston sound field of rule
Formula obtains the acoustic transmission matrix G that target Equivalent arrives by force radiated sound field in a steady streamerm(r,rE)。
(2) it obtains the distribution of the conformal piston equivalent source source strength W of object construction: being solved using Tikhonov regularization method close
Ill-posed problem in the acoustical holography algorithm of field；Arrive measurement basic matrix by force in a steady stream by array received data and to target Equivalent
Acoustic transmission matrix Germ(rH,rE) Regularization is carried out, obtain the distributed intelligence of the conformal piston equivalent source source strength W of object construction.
(3) the surface normal vibration velocity reconstruct of object construction sound source is forecast with radiated sound field: sound source surface normal vibration velocity harmony
Source radiation sound field can strong harmony transmission characteristic uniquely determines in a steady stream by target Equivalent.Using obtained target Equivalent in a steady stream strong W and
Normal direction vibration velocity transfer matrix G of the equivalent face in a steady stream to sound source surfaceerm_v(rS,rE), reconfigured geometry sound source surface normal vibration velocity point
Cloth vS；Utilize the obtained target Equivalent acoustic pressure transfer matrix G of strong W and equivalent face in a steady stream to radiated sound field in a steady streamerm_p(rF,rE)、
Vibration velocity transfer matrix Germ_v(rF,rE), the acoustic pressure distribution p of sound source radiation sound field is forecast respectivelyFV is distributed with vibration velocityF。
The present invention may also include:
1. step (1) specifically includes:
(1) using based on unit radiation the addition method sound transmission modeling method, by target Equivalent source face be divided into it is several with
The conformal regular piston of object construction (rectangle piston, cylinder piston, spherical crown piston etc.), and carried out with object construction rule baffle
Fitting regards each piston as an equivalent source, establishes the sound transmission model based on unit radiation method.
(2) spoke of approximate target equivalent source is removed using the radiated sound field of the regular piston conformal with object construction sound source surface
Sound field is penetrated, the conformal piston equivalent source source strength of object construction is obtained to spoke according to the analytical expression of the conformal radiating of circular piston sound field of rule
Penetrate the acoustic transmission matrix of sound field:
[Germ(r,rE)]=[Germ(r,rE1),Germ(r,rE2),···,Germ(r,rEi),···,Germ(r,rEN)]T
In formula, Germ(r,rEi) indicate point rEiThe acoustic pressure that one conformal piston equivalent source at place radiates at point r, it is discrete etc.
Effect source number is N.The acoustic transmission matrix is able to reflect structure wideband acoustic radiation characteristic, describes convenient for quickly calculating and parsing, solution
Certainly continuously distributed, coherent structure noise source propagation model refines characterization problems, and traditional point source spherical surface extension sound is overcome to pass
Broadcast the limitation of model.
2. step (2) specifically includes:
(1) the acoustic transmission matrix G of measurement basic matrix is arrived by force in a steady stream using the target Equivalent obtained based on unit radiation methoderm
(rH,rE), pass through classical Tikhonov regularization expression formula:
Or
Solve the ill-posed problem during Converse solved equivalent source source strength W.In formula, pH=[p (rH1),p
(rH2),···,p(rHM)]TFor the acoustic pressure column vector measured on holographic facet, vH=[v (rH1),v(rH2),···,v(rHM)]TFor
The normal direction vibration velocity column vector measured on holographic facet, M are holographic facet measurement points；Germ_p(rH,rE) and Germ_v(rH,rE) it is M × N
Rank matrix, respectively indicates equivalent source source strength and holographic facet receives acoustic pressure, the transitive relation of normal direction vibration velocity, element are as follows:
[Germ_p(rH,rE)]ji=Germ(rHj,rEi)
In formula, i=1,2, N；J=1,2, M；I is imaginary unit, ρ0For propagation medium density, ω
For angular frequency, rHIndicate the position of measuring point on holographic facet, nH indicates the outer normal direction of holographic facet.Ω (W)=| | LW | |2, Ω (W) title
For discrete smooth norm, L is regularization square matrix.
(2) further, by the reception data of holographic facet array and equivalent source source strength to the acoustic transmission matrix of measurement basic matrix,
It can must solve equivalent source source strength W:
W=L (Germ_p(rH,rE)L)H(Germ_p(rH,rE)L(Germ_p(rH,rE)L)H+λI)-1pH
Or W=L (Germ_v(rH,rE)L)H(Germ_v(rH,rE)L(Germ_v(rH,rE)L)H+λI)-1vH
In formula, the conjugate transposition of H representing matrix, I indicates that diagonal unit matrix, λ indicate regularization parameter.
3. step (3) specifically includes:
(1) sound source surface normal vibration velocity can strong harmony transmission characteristic uniquely determines in a steady stream by target Equivalent, then sound source surface
Normal direction vibration velocity may be expressed as:
vS=Germ_v(rS,rE)W
In formula, vS=[v (rS1),v(rS2),···,v(rSN)]TFor sound source surface normal vibration velocity column vector, Germ_v(rS,
rE) it is N × N rank matrix, element are as follows:
Wherein i=1,2, N；J=1,2, N.Sound source discretization of half-space surface piston number and discrete equivalent source
Number is all N, rSIndicate the position of sound source discretization of half-space surface piston, nSIndicate the outer normal direction on sound source surface.
(2) sound source radiation sound field can strong harmony transmission characteristic uniquely determines in a steady stream by target Equivalent, then the sound of radiated sound field
Pressure distribution may be expressed as:
pF=Germ_p(rF,rE)W
In formula, pF=[p (rF1),p(rF2),···,p(rFN)]TThe sound in face is forecast for object construction sound source radiation sound field
Press column vector, rFIndicate the position in sound field forecast face, site number is N；Germ_p(rF,rE) it is N × N rank matrix, element are as follows:
[Germ_p(rF,rE)]ji=Germ(rFj,rEi)
Wherein i=1,2, N；J=1,2, N.
(3) the vibration velocity distribution of radiated sound field may be expressed as:
vF=Germ_v(rF,rE)W
In formula, vF=[v (rF1),v(rF2),···,v(rFN)]TThe matter in face is forecast for object construction sound source radiation sound field
Point vibration velocity column vector, rFIndicate the position in sound field forecast face, site number is N；Germ_v(rF,rE) it is N × N rank matrix, element
Are as follows:
Wherein i=1,2, N；J=1,2, N.
The present invention proposes to be based on object construction for underwater large-scale object construction identification of sound source and radiated sound field forecasting problem
The near field acoustic holography algorithm of conformal piston equivalent source method.Wherein, water is characterized by the structure propagation model that unit radiation method is established
Transitive relation between lower object construction equivalent source source strength and radiated sound field solves continuously distributed, coherent structure noise source sound
Propagation model fining characterization overcomes the limitation of point source spherical surface extension propagation model in typical near-field acoustical holography；Based on altogether
The near field acoustic holography algorithm of shape piston equivalent source method measures basic matrix to equivalent strong arrive in a steady stream using Tikhonov regularization method
Acoustic transmission matrix Germ(rH,rE) Regularization is carried out, the ill-posed problem during Converse solved equivalent source source strength is solved,
The precision and robustness and measuring distance for further increasing near field acoustic holography algorithm, realize the accurate of underwater large scale structure sound source
Positioning and identification；Meanwhile sound source surface normal vibration velocity and sound source radiation sound field can be by target Equivalent strong harmony transmission characteristics in a steady stream
It uniquely determines.Utilize the obtained target Equivalent normal direction vibration velocity transfer matrix of strong W and equivalent face in a steady stream to sound source surface in a steady stream
Germ_v(rS,rE), reconfigured geometry sound source surface normal vibration velocity is distributed vS；Using obtained target Equivalent in a steady stream strong W and it is equivalent in a steady stream
Acoustic pressure transfer matrix G of the face to radiated sound fielderm_p(rF,rE), vibration velocity transfer matrix Germ_v(rF,rE), sound source radiation is forecast respectively
The acoustic pressure distribution p of sound fieldFV is distributed with vibration velocityF。
The present invention is effectively combined unit radiation method and equivalent source method near field acoustic holography algorithm, in unknown object knot
Structural radiation sound can be carried out again under the premise of structure vibration information, while carrying out object construction noise source Vibration identification pre-
Report.With it is traditional based on the near field acoustic holography method of point source spherical surface spread function model compared with, be able to solve continuously distributed, relevant
The propagation model of Structure Radiant Noise Source refines characterization problems, overcomes using conventional model bring limitation, significantly improves
The accuracy of continuously distributed complicated type identification of sound source result.
The beneficial effects of the present invention are: for underwater large scale structure radiated noise identifing source and radiated sound field forecasting problem,
The propagation model of object construction equivalent source is established using unit radiation method.It is special that the model is able to reflect the acoustic radiation of structure wideband
Property, convenient for quickly calculating and parsing description, solve continuously distributed, coherent structure noise source propagation model fining characterization and ask
Topic overcomes the limitation of traditional point source spherical surface extension propagation model.Under the premise of unknown object structural vibration information, carry out
Structural radiation sound can be forecast again while object construction noise source Vibration identification.In addition, with traditional based on point source
The near field acoustic holography algorithm of spherical surface extended model is compared, the near field of the equivalent source method based on said units radiation method propagation model
Acoustical holography algorithm has higher accuracy and wider array of application range.
Detailed description of the invention
Sound transmission model foundation flow chart of the Fig. 1 based on unit radiation method.
Continuously distributed source radiation schematic diagram in Fig. 2 infinite field.
Fig. 3 equivalent source method theory schematic diagram.
Near field acoustic holography Structure Radiant Noise Source Identification of the Fig. 4 based on conformal piston equivalent source method and acoustic radiation storm rainfall.
Fig. 5 .1 (a) I to Fig. 5 .1 (a) IV be under frequency 200Hz, d=0.05 λ different array received distances based on unit
The freely-supported rectangle of radiation method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Plate surface normal direction vibration velocity simulation result, wherein Fig. 5 .1 (a) I is theoretical distribution；Fig. 5 .1 (a) II is point source Green's function；Figure
5.1 (a) III be unit radiation method；Fig. 5 .1 (a) IV is cutting on the cross line chart.
With 5.1 (b) I to Fig. 5 .1 (b) IV be under frequency 200Hz, d=0.15 λ different array received distances based on unit
The freely-supported rectangle of radiation method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Plate surface normal direction vibration velocity simulation result, wherein Fig. 5 .1 (b) I is theoretical distribution；Fig. 5 .1 (b) II is point source Green's function；Figure
5.1 (b) III be unit radiation method；Fig. 5 .1 (b) IV is cutting on the cross line chart.
Fig. 5 .2 (a) I to Fig. 5 .2 (b) IV be under frequency 200Hz, d=0.05 λ different array received distances based on unit
The freely-supported rectangle of radiation method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Plate sound radiation pressure simulation result, Fig. 5 .2 (a) I are theoretical distribution；Fig. 5 .2 (a) II is point source Green's function；Fig. 5 .2 (a) III is
Unit radiation method；Fig. 5 .2 (a) IV is cutting on the cross line chart.
Fig. 5 .2 (b) I to Fig. 5 .2 (b) IV is frequency 200Hz, different array received distances based on unit under d=0.15 λ
The freely-supported rectangle of radiation method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Plate sound radiation pressure simulation result, wherein Fig. 5 .2 (b) I is theoretical distribution；Fig. 5 .2 (b) II is point source Green's function；Fig. 5 .2 (b)
III is unit radiation method；Fig. 5 .2 (b) IV is cutting on the cross line chart.
Fig. 6 .1 (a) I to Fig. 6 .1 (a) IV is frequency 1250Hz, different array received distances based on list under d=0.05 λ
The freely-supported square of first radiation method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Shape plate surface normal direction vibration velocity simulation result, wherein Fig. 6 .1 (a) I is theoretical distribution；Fig. 6 .1 (a) II is point source Green's function；Figure
6.1 (a) III be unit radiation method；Fig. 6 .1 (a) IV is cutting on the cross line chart.
Fig. 6 .1 (b) I to Fig. 6 .1 (b) IV is frequency 1250Hz, different array received distances based on list under d=0.15 λ
The freely-supported square of first radiation method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Shape plate surface normal direction vibration velocity simulation result, wherein Fig. 6 .1 (b) I is theoretical distribution；Fig. 6 .1 (b) II is point source Green's function；Figure
6.1 (b) III be unit radiation method；Fig. 6 .1 (b) IV is cutting on the cross line chart.
Fig. 6 .2 (a) I to Fig. 6 .2 (a) IV is frequency 1250Hz, different array received distances based on list under d=0.05 λ
The freely-supported square of first radiation method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Shape plate sound radiation pressure simulation result, wherein Fig. 6 .2 (a) I is theoretical distribution；Fig. 6 .2 (a) II is point source Green's function；Fig. 6 .2
(a) III is unit radiation method；Fig. 6 .2 (a) IV is cutting on the cross line chart.
Different array received distances based on (the conformal work of unit radiation method under Fig. 6 .2 (b) frequency 1250Hz, d=0.15 λ
Plug) and based on point source spherical surface extended model (simple source) equivalent source method near field acoustic holography Simply-Supported Rectangular Plates sound radiation pressure emulation
As a result, wherein Fig. 6 .2 (b) I is theoretical distribution；Fig. 6 .2 (b) II is point source Green's function；Fig. 6 .2 (b) III is unit radiation
Method；Fig. 6 .2 (b) IV is cutting on the cross line chart.
Fig. 7 .1 (a) I to Fig. 7 .1 (a) IV is frequency 200Hz, and different array element spacing is radiated based on unit under l=0.05m
The Simply-Supported Rectangular Plates table of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Face normal direction vibration velocity simulation result, wherein Fig. 7 .1 (a) I is theoretical distribution；Fig. 7 .1 (a) II is point source Green's function；Fig. 7 .1 (a)
III is unit radiation method；Fig. 7 .1 (a) IV is cutting on the cross line chart.
Fig. 7 .1 (b) I to Fig. 7 .1 (b) IV is frequency 200Hz, and different array element spacing is radiated based on unit under l=0.10m
The Simply-Supported Rectangular Plates table of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Face normal direction vibration velocity simulation result, wherein Fig. 7 .1 (b) I is theoretical distribution；Fig. 7 .1 (b) II is point source Green's function；Fig. 7 .1 (b)
III is unit radiation method；Fig. 7 .1 (b) IV is cutting on the cross line chart.
Fig. 7 .2 (a) I to Fig. 7 .2 (a) IV is frequency 200Hz, and different array element spacing is radiated based on unit under l=0.05m
The Simply-Supported Rectangular Plates spoke of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Penetrate acoustic pressure simulation result, wherein Fig. 7 .2 (a) I is theoretical distribution；Fig. 7 .2 (a) II is point source Green's function；Fig. 7 .2 (a) III is
Unit radiation method；Fig. 7 .2 (a) IV is cutting on the cross line chart.
Fig. 7 .2 (b) I to Fig. 7 .2 (b) IV is frequency 200Hz, and different array element spacing is radiated based on unit under l=0.10m
The Simply-Supported Rectangular Plates spoke of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Penetrate acoustic pressure simulation result, wherein Fig. 7 .2 (b) I is theoretical distribution；Fig. 7 .2 (b) II is point source Green's function；Fig. 7 .2 (b) III is
Unit radiation method；Fig. 7 .2 (b) IV is cutting on the cross line chart.
Fig. 8 .1 (a) I to Fig. 8 .1 (a) IV is frequency 1250Hz, different array element spacing based on unit spoke under l=0.05m
Penetrate the Simply-Supported Rectangular Plates of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Surface normal vibration velocity simulation result, wherein Fig. 8 .1 (a) I is theoretical distribution；Fig. 8 .1 (a) II is point source Green's function；Fig. 8 .1
(a) III is unit radiation method；Fig. 8 .1 (a) IV is cutting on the cross line chart.
Fig. 8 .1 (b) I to Fig. 7 .1 (b) IV is frequency 1250Hz, different array element spacing based on unit spoke under l=0.10m
Penetrate the Simply-Supported Rectangular Plates of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Surface normal vibration velocity simulation result, wherein Fig. 8 .1 (b) I is theoretical distribution；Fig. 8 .1 (b) II is point source Green's function；Fig. 8 .1
(b) III is unit radiation method；Fig. 8 .1 (b) IV is cutting on the cross line chart.
Fig. 8 .2 (a) I to Fig. 8 .2 (a) IV is frequency 1250Hz, different array element spacing based on unit spoke under l=0.05m
Penetrate the Simply-Supported Rectangular Plates of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Sound radiation pressure simulation result, wherein Fig. 8 .2 (a) I is theoretical distribution；Fig. 8 .2 (a) II is point source Green's function；Fig. 8 .2 (a) III
For unit radiation method；Fig. 8 .2 (a) IV is cutting on the cross line chart.
Fig. 8 .2 (b) I to Fig. 8 .2 (b) IV is frequency 1250Hz, different array element spacing based on unit spoke under l=0.10m
Penetrate the Simply-Supported Rectangular Plates of method (conformal piston) and the equivalent source method near field acoustic holography based on point source spherical surface extended model (simple source)
Sound radiation pressure simulation result, wherein Fig. 8 .2 (b) I is theoretical distribution；Fig. 8 .2 (b) II is point source Green's function；Fig. 8 .2 (b) III
For unit radiation method；Fig. 8 .2 (b) IV is cutting on the cross line chart.
Fig. 9 is flow chart of the invention.
Specific embodiment
It illustrates below and the present invention is described in more detail.
The first step establishes sound transmission model: using the sound transmission modeling method based on the unit radiation addition method, by target etc.
Effect source face is divided into several and the conformal regular piston of object construction (rectangle piston, cylinder piston, spherical crown piston etc.), and and mesh
Mark tactical rule baffle is fitted, and regards each piston as an equivalent source；Using the radiation of regular baffle surface piston
Sound field removes the radiated sound field of approximate target equivalent source, obtains mesh according to the analytical expression of regular baffle surface piston radiated sound field
Acoustic transmission matrix G of the mark structure equivalent source source strength to radiated sound fielderm(r,rE), sound transmission model foundation flow chart such as Fig. 1 institute
Show.
In the perfect fluid medium of three-dimensional space, three fundamental equations below the communication satisfaction of sound wave:
Formula (1), formula (2) and formula (3) are known respectively as the equation of motion, continuity equation and the equation of state, they are newton
The reflection of second law, mass conservation law and the law of thermodynamics in propagation process of sound wave, wherein formula (1) is otherwise known as
Euler formula.In formula, ρ0For the density of medium；c0For the velocity of sound of medium；V and p respectively indicates particle vibration velocity and acoustic pressure；ρ ' is to be situated between
Matter variable density amount, they are usually the function of room and time.
As shown in Fig. 2, D indicates entire infinite field, S∞Indicate the boundary of D.There are one piece of continuous region E in D, it and
Infinite field D medium having the same.If the medium particle in the E of region carries out amplitude and finely tunes small vibration to generate sound field, determine
Justice:
In formula, q0(r, t) indicates the dielectric in the small size member at point r caused by the medium particle vibration in the E of region
Product is advanced the speed.The continuity equation of acoustic field medium becomes in infinite field D as a result:
By formula (5) and formula (1) and formula (3) simultaneous, the three dimension wave equation in wavelets of sound field in description infinite field D can be obtained:
Fourier transformation is carried out to formula (6), is obtained:
In formula, i is imaginary unit, and ω is angular frequency, q0It (r) is q0The Fourier of (r, t) is converted.It, will to solve formula (7)
Formula (7) both sides are obtained with multiplied by G (r, r'):
In formula, G (r, r') indicates the acoustic pressure that a source at point r' radiates at point r, should meet:
In formula, δ (r, r') is Dirac- δ function.It is all using formula in existing near field acoustic holography Noise Sources Identification algorithm
(9) elementary solution G (r, r')=eikR/ 4 π R (free field Green function) describe acoustic radiation phenomenon, wherein R=| r-r'|.But
For continuously distributed structure sound source, the point source spherical surface extended model and practical structures acoustic radiation propagation model are in the presence of poor
It is different, possibly it can not accurately identify continuously distributed complicated type sound source.The present invention uses the structure-borne sound established by unit radiation method
Propagation model Germ(r, r'), the model are able to reflect structure wideband acoustic radiation characteristic, describe convenient for quickly calculating and parsing, solution
Certainly continuously distributed, coherent structure noise source propagation model refines characterization problems, and traditional point source spherical surface extension sound is overcome to pass
Broadcast the limitation of model.Then formula (8) and formula (9) become:
Formula (11) both sides are obtained with multiplied by p (r):
Formula (10) subtracts formula (12) and can obtain:
According to the r and r ' in sound field reciprocity switch type (13), and utilize GermThe symmetry of (r, r') and δ function can incite somebody to action
Formula (13) becomes:
Formula (14) is integrated in infinite field D, differential element of volume is indicated with d Ω, obtains:
Using the property and equation of δ functionFormula (15) is arranged, is obtained:
Gauss divergence theorem is used to Section 2 on the right of formula (16), is obtained:
According to Sommerfeld radiation conditionSection 2 Line Integral on the right of formula (17)
It is 0, thus:
P (r)=- i ρ0ω∫Dq0(r')Germ(r,r')dΩ(r') (18)
The only q in the E of region in infinite field D0(r) it is not equal to zero, uses r hereEIndicate the point in the E of region, therefore:
P (r)=- i ρ0ω∫Eq(rE)Germ(r,rE)dΩ(rE) (19)
Formula (19) is the equivalent source integral equation based on unit radiation method, it can be seen that sound source region E is in infinite field
Radiated sound field be a series of equivalent source radiated sound fields superposition.
The principle of equivalent source method is continuously distributed equivalent source to be placed in boundary as S0Vibrating body inside, as shown in figure 3,
Make equivalent source face and S0On boundary condition match, it may be assumed that
-iρ0ω∫Eq(rE)Germ(rS,rE)dΩ(rE)=p (rS) (20)
rSIndicate the position on vibrating body boundary, then the external radiation sound field of the vibrating body can be by the equivalent source in portion disposed within
Generated sound field replaces.If equivalent source is distributed in continuous equivalent source face SEOn, rENo longer indicate the position in the E of region, but
SEOn position.Simultaneously to equivalent source integral equation discretization, by SEIt is separated into N sections, each section with SEiIt indicates, if SEiEnough
Small, then formula (19) can approximate representation are as follows:
Formula (21) is the equivalent source integral equation based on unit radiation method of discretization.Equivalent source distribution after discrete is not
It is continuous again, rEiIndicate the position of i-th of equivalent source；W(rEi)=- i ρ0ωq(rEi)SEiFor the source strength of i-th of equivalent source.It is different
Using simple source as the method for equivalent source, the present invention is based on unit radiation method thoughts in existing, if equivalent source face is divided into
Dry and the conformal regular piston of object construction (rectangle piston, cylinder piston, spherical crown piston etc.), regards each piston as one
Equivalent source, then the external radiation sound field of the vibrating body can be regarded as by the superposition of series of rules radiating of circular piston sound field.According to
The particle vibration velocity and normal direction particle vibration velocity of equivalent source radiated sound field can be obtained using identical method in Euler formula:
Wherein, [Germ(r,rE)]=[Germ(r,rE1),Germ(r,rE2),···,Germ(r,rEi),···,Germ
(r,rEN)]TAcoustic transmission matrix for the conformal piston equivalent source source strength of object construction to radiated sound field, Germ(r,rEi) indicate rEiPlace
The acoustic pressure that is radiated at point r of a conformal piston equivalent source.
Second step is obtained the conformal piston equivalent source source strength W distribution of object construction: being solved using Tikhonov regularization method
Ill-posed problem near field acoustic holography algorithm；Arrive measurement basic matrix by force in a steady stream by array received data and to target Equivalent
Acoustic transmission matrix Germ(rH,rE) Regularization is carried out, obtain the distribution letter of the conformal piston equivalent source source strength W of object construction
Breath.
Using the acoustic pressure and normal direction vibration velocity information measured on holographic facet, formula (21) and formula (23) are rewritten into matrix form:
pH=Germ_p(rH,rE)W (24)
vH=Germ_v(rH,rE)W (25)
In formula, pH=[p (rH1),p(rH2),···,p(rHM)]TFor the acoustic pressure column vector measured on holographic facet, vH=[v
(rH1),v(rH2),···,v(rHM)]TFor the normal direction vibration velocity column vector measured on holographic facet, M is the measurement point on holographic facet
Number；Germ_p(rH,rE) and Germ_v(rH,rE) be M × N rank matrix, respectively indicate acoustic pressure on holographic facet and normal direction vibration velocity with it is equivalent
Transitive relation between strong in a steady stream, element are as follows:
[Germ_p(rH,rE)]ji=Germ(rHj,rEi) (26)
In formula, i=1,2, N；J=1,2, M；rHIndicate the point position on holographic facet, nHIndicate complete
The outer normal direction in breath face.
To solve the existing ill-posed problem during formula (24) and the Converse solved equivalent source source strength of formula (25), in conjunction with
Tikhonov regularization method, by equations turned for following form:
In formula, Ω (W)=| | LW | |2, Ω (W) is known as discrete smooth norm, and L is regularization square matrix, and λ indicates regularization ginseng
Number.Further, suitable regularization square matrix and parameter are selected, can must be solved:
W=L (Germ_p(rH,rE)L)H(Germ_p(rH,rE)L(Germ_p(rH,rE)L)H+λI)-1pH (30)
W=LGerm_v(rH,rE)L)H(Germ_v(rH,rE)L(Germ_v(rH,rE)L)H+λI)-1vH (31)
In formula, the conjugate transposition of H representing matrix, I indicates diagonal unit matrix；It, can be by then by formula (30) and formula (31)
The acoustic pressure or normal direction vibration velocity information and equivalent source source strength of array received obtain object construction to the acoustic transmission matrix of measurement basic matrix
The distributed intelligence of conformal piston equivalent source source strength.
Third step, the reconstruct of surface normal vibration velocity and the radiated sound field of object construction sound source are forecast: sound source surface normal vibration velocity
With sound source radiation sound field can strong harmony transmission characteristic uniquely determines in a steady stream by target Equivalent.It is strong in a steady stream using obtained target Equivalent
The normal direction vibration velocity transfer matrix G of W and equivalent face in a steady stream to sound source surfaceerm_v(rS,rE), reconfigured geometry sound source surface normal vibration velocity
It is distributed vS；Utilize the obtained target Equivalent acoustic pressure transfer matrix G of strong W and equivalent face in a steady stream to radiated sound field in a steady streamerm_p(rF,
rE), vibration velocity transfer matrix Germ_v(rF,rE), the acoustic pressure distribution p of sound source radiation sound field is forecast respectivelyFV is distributed with vibration velocityF.It is based on
The near field acoustic holography Structure Radiant Noise Source Identification and acoustic radiation Forecast flow of unit radiation method and equivalent source method are as shown in Figure 4.It can table
It is shown as:
vS=Germ_v(rS,rE)W (32)
pF=Germ_p(rF,rE)W (33)
vF=Germ_v(rF,rE)W (34)
In formula, vS=[v (rS1),v(rS2),···,v(rSN)]TFor sound source surface normal vibration velocity column vector, pF=[p
(rF1),p(rF2),···,p(rFN)]TThe acoustic pressure column vector in face, v are forecast for object construction sound source radiation sound fieldF=[v
(rF1),v(rF2),···,v(rFN)]TThe particle vibration velocity column vector in face is forecast for radiated sound field；rSIndicate sound source discretization of half-space surface
The position of piston, piston number are N；rFIndicate the position in sound field forecast face, site number is N；Germ_v(rS,rE)、Germ_p(rF,
rE) and Germ_v(rF,rE) it is N × N rank matrix, element is respectively as follows:
[Germ_p(rF,rE)]ji=Germ(rFj,rEi)
I=1,2 in formula, N；J=1,2, N, nSIndicate the outer normal direction on sound source surface
The specific embodiment of summary of the invention each section is illustrated above.Below by equivalent based on conformal piston
The near field acoustic holography simulation example of source method is described further present invention specific implementation.
Simulation example:
(1) underwater Simply-Supported Rectangular Plates surface normal vibration velocity and sound radiation pressure emulate: emulation uses the uniform cloth of 21 × 21 array elements
The square matrix put, square matrix aperture 2m × 2m, array element spacing l=0.1m, Simply-Supported Rectangular Plates length and width 0.6m × 0.6m, thick 0.008m are adopted
It is the point exciting force of 1 newton with size.Rectangle baffle is divided into 31 × 31 rectangle pistons, piston size be 0.02m ×
0.02m；Equivalent source face is equally divided into 31 × 31 rectangle pistons etc. by the near field acoustic holography based on conformal piston equivalent source method
The shape size in effect source, source face is consistent with rectangle baffle, carries out pair with using simple source as the near field acoustic holography method of equivalent source
Than.
Fig. 5 .1 (a) I to Fig. 5 .1 (a) IV and Fig. 5 .1 (b) I to Fig. 5 .1 (b) IV is vibrated at frequency f=200Hz
Baffle surface normal vibration velocity, the distance d of receiving array to plate face are respectively 0.05,0.15 times of wavelength.Point source Green is respectively adopted
Function (simple source) and unit radiation method (conformal piston) Lai Jianli propagation model.Fig. 5 .2 (a) I to Fig. 5 .2 (a) IV and 5.2
(b) I to Fig. 5 .2 (b) IV is the baffle sound radiation pressure vibrated at frequency f=200Hz, and the distance d of receiving array to plate face divides
It Wei not 0.05,0.15 times of wavelength.Point source Green's function (simple source) and unit radiation method (conformal piston) Lai Jianli is respectively adopted
Propagation model.
Fig. 6 .1 (a) I to Fig. 6 .1 (a) IV and Fig. 6 .1 (b) I to Fig. 6 .1 (b) IV is vibrated at frequency f=1250Hz
Baffle surface normal vibration velocity, the distance d of receiving array to plate face are respectively 0.05,0.15 times of wavelength.Point source Green is respectively adopted
Function (simple source) and unit radiation method (conformal piston) Lai Jianli propagation model.Fig. 6 .2 (a) I to Fig. 6 .1 (a) IV and figure
6.2 (b) I to Fig. 6 .1 (b) IV be the baffle sound radiation pressure vibrated at frequency f=1250Hz, the distance of receiving array to plate face
D is respectively 0.05,0.15 times of wavelength.Point source Green's function (simple source) and unit radiation method (conformal piston) is respectively adopted to build
Vertical propagation model.
Analogous diagram in the case of comprehensive different frequency, different receiving array distances, can obtain: based on conformal piston equivalent source
The near field acoustic holography of method can effectively improve the accuracy of identification of structure sound source.Equivalent source method based on point source Green's function (simple source)
Near field acoustic holography can only be identified receiving 0.05 times of wavelength of basic matrix distance objective sound source, and precision is limited；And institute of the present invention
The near field acoustic holography based on conformal piston equivalent source method proposed can effectively promote identification distance, especially to the noise of submarine target
For identifing source, engineering construction difficulty can be greatly reduced；And it is able to solve the acoustic propagation of continuously distributed coherent structure noise source
Model refines characterization problems, overcomes using conventional model bring limitation, significantly improves continuously distributed complicated type
The accuracy of identification of sound source result.
Simulation example (1) demonstrates the near field acoustic holography based on conformal piston equivalent source method and is improving precision and promoting identification
Validity apart from aspect, example (2) will be verified in the case where less basic matrix number, and the present invention still has high accuracy.
(2) underwater Simply-Supported Rectangular Plates surface normal vibration velocity and sound radiation pressure emulate: emulation use the aperture of square matrix for 2m ×
2m, the generous size of the length of Simply-Supported Rectangular Plates, the size of exciting force, equivalent source face, plate face piston division all with simulation example (1)
Unanimously；Receiving array to plate face distance d be 0.10 times of wavelength, array element spacing l take respectively 0.05m (array number 41 × 41),
0.10m (array number 21 × 21).
Fig. 7 .1 (a) I to Fig. 7 .1 (a) IV and Fig. 7 .1 (b) I to Fig. 7 .1 (b) IV is vibrated at frequency f=200Hz
Baffle surface normal vibration velocity, array element spacing l take 0.05m, 0.10m respectively.Point source Green's function (simple source) and list is respectively adopted
First radiation method (conformal piston) Lai Jianli propagation model.Fig. 7 .2 (a) I to Fig. 7 .2 (a) IV and Fig. 7 .2 (b) I to Fig. 7 .2 (b)
IV is the baffle sound radiation pressure vibrated at frequency f=200Hz, and array element spacing l takes 0.05m, 0.10m respectively.It is respectively adopted a little
Source Green's function (simple source) and unit radiation method (conformal piston) Lai Jianli propagation model.
Fig. 8 .1 (a) I to Fig. 8 .1 (a) IV and Fig. 8 .1 (b) I to Fig. 8 .1 (b) IV is vibrated at frequency f=1250Hz
Baffle surface normal vibration velocity, array element spacing l take 0.05m, 0.10m respectively.Point source Green's function (simple source) and list is respectively adopted
First radiation method (conformal piston) Lai Jianli propagation model.Fig. 8 .2 (a) I to Fig. 8 .2 (a) IV and Fig. 8 .2 (b) I to Fig. 8 .2 (b)
IV is the baffle sound radiation pressure vibrated at frequency f=1250Hz, and array element spacing l takes 0.05m, 0.10m respectively.It is respectively adopted a little
Source Green's function (simple source) and unit radiation method (conformal piston) Lai Jianli propagation model.
The analogous diagram of comprehensive different frequency, different array element spacing, can obtain: in f=200Hz, based on conformal piston etc.
The near field acoustic holography of effect source method can obtain accurate as a result, and based on point source Green in the case where l=0.05m, 0.10m
The near field acoustic holography of function and equivalent source method is obvious with the increase accuracy decline of array element spacing, and the precision in l=0.05m
Also not as good as the mentioned algorithm of the present invention；In f=1250Hz, the mentioned algorithm of the present invention is same in the case where l=0.05m, 0.10m
It can obtain accurately as a result, and the near field acoustic holography based on point source Green's function and equivalent source method has all failed substantially.For
For the Noise Sources Identification of submarine target, the near field acoustic holography proposed by the present invention based on conformal piston equivalent source method be can reduce
Site density needed for identifying target；And it is able to solve continuously distributed, coherent structure noise source propagation model fining table
Sign problem is overcome and is significantly improved continuously distributed complicated type identification of sound source result using conventional model bring limitation
Accuracy.
Claims (9)
1. a kind of identification of sound source and sound field forecasting procedure, it is characterized in that:
(1) it establishes acoustic transmission matrix: using the sound transmission modeling method based on the unit radiation addition method, target Equivalent source face being drawn
It is divided into several and conformal regular piston of object construction, is fitted with object construction rule baffle, each piston is corresponding
One equivalent source；Using the radiation of the radiated sound field approximate target equivalent source of the regular piston conformal with object construction sound source surface
Sound field obtains the sound transmission that target Equivalent arrives by force radiated sound field in a steady stream according to the analytical expression of the conformal radiating of circular piston sound field of rule
Matrix Germ(r,rE), wherein r indicates the position of radiated sound field, rEIndicate the position of equivalent source；
(2) distribution of the conformal piston equivalent source source strength W of object construction is obtained: by array received data and to target Equivalent source
Acoustic transmission matrix G of the source strength to measurement basic matrixerm(rH,rE) Regularization is carried out, obtain the conformal piston equivalent source of object construction
The distributed intelligence of source strength W, wherein rHIndicate the position of measuring point on holographic facet；
(3) the surface normal vibration velocity reconstruct of object construction sound source is forecast with radiated sound field: sound source surface normal vibration velocity and sound source spoke
Penetrating sound field, strong harmony transmission characteristic uniquely determines in a steady stream by target Equivalent, utilizes obtained target Equivalent strong W and equivalent source in a steady stream
Normal direction vibration velocity transfer matrix G of the source face to sound source surfaceerm_v(rS,rE), reconfigured geometry sound source surface normal vibration velocity is distributed vS,
Middle rSIndicate the position of the conformal piston in structure sound source surface, rEIndicate the position of equivalent source；It is strong in a steady stream using obtained target Equivalent
The acoustic pressure transfer matrix G of W and equivalent face in a steady stream to radiated sound fielderm_p(rF,rE), vibration velocity transfer matrix Germ_v(rF,rE), respectively
Forecast the acoustic pressure distribution p of sound source radiation sound fieldFV is distributed with vibration velocityF, wherein rFIndicate the position in radiated sound field forecast face.
2. identification of sound source according to claim 1 and sound field forecasting procedure, it is characterized in that the acoustic transmission matrix Germ(r,
rE) it is embodied as:
[Germ(r,rE)]=[Germ(r,rE1),Germ(r,rE2),···,Germ(r,rEi),···,Germ(r,rEN)]T
In formula, Germ(r,rEi) indicate point rEiThe acoustic pressure that one conformal piston equivalent source at place radiates at point r, discrete equivalent source
Number is N.
3. identification of sound source according to claim 1 or 2 and sound field forecasting procedure, it is characterized in that the acquisition object construction is total
The distribution of shape piston equivalent source source strength W specifically includes:
(1) the acoustic transmission matrix G of measurement basic matrix is arrived by force in a steady stream using the target Equivalent obtained based on unit radiation methoderm(rH,rE),
Pass through classical Tikhonov regularization expression formula:
Or
In formula, pH=[p (rH1),p(rH2),···,p(rHM)]TFor the acoustic pressure column vector measured on holographic facet, vH=[v
(rH1),v(rH2),···,v(rHM)]TFor the normal direction vibration velocity column vector measured on holographic facet, M is holographic facet measurement points；
Germ_p(rH,rE) and Germ_v(rH,rE) it is M × N rank matrix, it respectively indicates equivalent source source strength and holographic facet receives acoustic pressure, normal direction vibration
The transitive relation of speed, element are as follows:
[Germ_p(rH,rE)]ji=Germ(rHj,rEi)
In formula, i=1,2, N；J=1,2, M；I is imaginary unit, ρ0For propagation medium density, ω is angular frequency
Rate, nHThe outer normal direction of expression holographic facet, Ω (W)=| | LW | |2, Ω (W) is known as discrete smooth norm, and L is regularization square matrix；
(2) equivalent source is solved to the acoustic transmission matrix of measurement basic matrix by the reception data of holographic facet array and equivalent source source strength
Source strength W:
W=L (Germ_p(rH,rE)L)H(Germ_p(rH,rE)L(Germ_p(rH,rE)L)H+λI)-1pH
Or W=L (Germ_v(rH,rE)L)H(Germ_v(rH,rE)L(Germ_v(rH,rE)L)H+λI)-1vH
In formula, the conjugate transposition of H representing matrix, I indicates that diagonal unit matrix, λ indicate regularization parameter.
4. identification of sound source according to claim 1 or 2 and sound field forecasting procedure, it is characterized in that the object construction sound source
The reconstruct of surface normal vibration velocity is specifically included with radiated sound field forecast:
(1) sound source surface normal vibration velocity indicates are as follows:
vS=Germ_v(rS,rE)W
In formula, vS=[v (rS1),v(rS2),···,v(rSN)]TFor sound source surface normal vibration velocity column vector, Germ_v(rS,rE)
For N × N rank matrix, element are as follows:
Wherein i=1,2, N；J=1,2, N, sound source discretization of half-space surface piston number and discrete equivalent source number
It is all N, rSIndicate the position of sound source discretization of half-space surface piston, nSIndicate the outer normal direction on sound source surface；
(2) the acoustic pressure distribution of radiated sound field is expressed as:
pF=Germ_p(rF,rE)W
In formula, pF=[p (rF1),p(rF2),···,p(rFN)]TThe acoustic pressure column in face are forecast for object construction sound source radiation sound field
Vector, rFIndicate the position in sound field forecast face, site number is N；Germ_p(rF,rE) it is N × N rank matrix, element are as follows:
[Germ_p(rF,rE)]ji=Germ(rFj,rEi)
Wherein i=1,2, N；J=1,2, N；
(3) the vibration velocity distribution of radiated sound field is expressed as:
vF=Germ_v(rF,rE)W
In formula, vF=[v (rF1),v(rF2),···,v(rFN)]TThe particle vibration in face is forecast for object construction sound source radiation sound field
Fast column vector, rFIndicate the position in sound field forecast face, site number is N；Germ_v(rF,rE) it is N × N rank matrix, element are as follows:
Wherein i=1,2, N；J=1,2, N.
5. identification of sound source according to claim 3 and sound field forecasting procedure, it is characterized in that the table of the object construction sound source
Normal direction vibration velocity reconstruct in face is specifically included with radiated sound field forecast:
(1) sound source surface normal vibration velocity indicates are as follows:
vS=Germ_v(rS,rE)W
In formula, vS=[v (rS1),v(rS2),···,v(rSN)]TFor sound source surface normal vibration velocity column vector, Germ_v(rS,rE)
For N × N rank matrix, element are as follows:
Wherein i=1,2, N；J=1,2, N, sound source discretization of half-space surface piston number and discrete equivalent source number
It is all N, rSIndicate the position of sound source discretization of half-space surface piston, nSIndicate the outer normal direction on sound source surface；
(2) the acoustic pressure distribution of radiated sound field is expressed as:
pF=Germ_p(rF,rE)W
In formula, pF=[p (rF1),p(rF2),···,p(rFN)]TThe acoustic pressure column in face are forecast for object construction sound source radiation sound field
Vector, rFIndicate the position in sound field forecast face, site number is N；Germ_p(rF,rE) it is N × N rank matrix, element are as follows:
[Germ_p(rF,rE)]ji=Germ(rFj,rEi)
Wherein i=1,2, N；J=1,2, N；
(3) the vibration velocity distribution of radiated sound field is expressed as:
vF=Germ_v(rF,rE)W
In formula, vF=[v (rF1),v(rF2),···,v(rFN)]TThe particle vibration in face is forecast for object construction sound source radiation sound field
Fast column vector, rFIndicate the position in sound field forecast face, site number is N；Germ_v(rF,rE) it is N × N rank matrix, element are as follows:
Wherein i=1,2, N；J=1,2, N.
6. identification of sound source according to claim 1 or 2 and sound field forecasting procedure, it is characterized in that: described and object construction
Conformal regular piston is rectangle piston, cylinder piston or spherical crown piston.
7. identification of sound source according to claim 3 and sound field forecasting procedure, it is characterized in that: described conformal with object construction
Regular piston be rectangle piston, cylinder piston or spherical crown piston.
8. identification of sound source according to claim 4 and sound field forecasting procedure, it is characterized in that: described conformal with object construction
Regular piston be rectangle piston, cylinder piston or spherical crown piston.
9. identification of sound source according to claim 5 and sound field forecasting procedure, it is characterized in that: described conformal with object construction
Regular piston be rectangle piston, cylinder piston or spherical crown piston.
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