CN100442030C - A separating method for sound field - Google Patents

Abstract

A method of acoustic field separation is disclosed that characterized in that a detecting surface S<SUB>1</SUB> and a auxiliary detecting surface S<SUB>2</SUB> which is parallel with the detecting surface and spaced with the detecting surface by deltah are set in the acoustic field to be detected; The acoustic pressures of the two surfaces are tested; a void source surface S<SUB>1</SUB><SUP>*</SUP> and S<SUB>2</SUB><SUP>*</SUP> are set, the equivalent sources are spread in the void source surface; the transitive relationship between the equivalent sources and the acoustic pressures of the two surfaces is built; the separation of radiation sound pressure with acoustic sources of the two sides in detecting surface based on the transitive relationship. The measuring surfaces in the invention can be random geometry which contains flat surface, cylindrical surface or spherical surface; the equivalent source method is the sound field separation algorithm, computational stability is well, computational accuracy is high, accomplishment is simple, and the invention can be widely used in the near acoustic field holographic detection of inner acoustic field or in noise environment, the measuring of material reflection coefficient, the separation of scattered acoustic field.

Description

A kind of method for sound field separation

Technical field:

The present invention relates to noise class field method for sound field separation in the Speciality of Physics.

Background technology:

When actual measurement, can run into measurement face both sides usually all has sound source, or a side of the face of measurement exists reflection or scattering.And in the actual engineering, for the sound radiation characteristic of studying actual sound source more exactly or the reflection characteristic of reflecting surface, need and will separate from the radiation sound of the face of measurement both sides.G.V.Frisk etc. proposed in 1980 to adopt space FFT method to realize separating first, the reflection coefficient of indirect Measuring Oceanic bottom surface, and the advantage of this method is intensity and the positional information that does not need to predict sound source.G.Weinreich etc. propose to adopt two to lean on to such an extent that the method for very near measurement planar survey realizes separating of incident wave and radiated wave in 1980.G.V.Frisk has set up the two measurement face sound field separation technique based on space FFT method on the basis of the two-sided measuring method that near field acoustic holography technology that E.G.Williams etc. proposes and G.Weinreich etc. propose.This method is further used and is developed in following period of time subsequently.Masayuki Tamura has set up in detail by two-sided measurement, and the sound field that adopts two-dimensional space FFT method to realize is again separated formula, and tries to achieve the reflection coefficient of reflecting interface by numerical simulation and Success in Experiment.Z.Hu and J.S.Bolton are also to adopting this method measurement plane wave reflection coefficient to carry out further checking.M.T.Cheng etc. have set up the Di Kaer coordinate and have separated formula with the two measurement face sound fields under the cylindrical coordinates, and are used to realize the separation of scattering sound field, have analyzed the susceptibility that this method is separated scattered field.F.Yu etc. successfully adopt this method to separate near field acoustic holography measuring process on the holographic facet noise from dorsad.But this method has its intrinsic defective: restricted to the shape of measuring face on the one hand, and promptly can only be regular shapes such as plane, cylinder or sphere; Be subjected to the influence of fft algorithm on the other hand, the separation error is bigger, and especially when differing big from the face of measurement both sides acoustic pressure, its error is particularly evident.

Summary of the invention:

Technical matters solved by the invention is to avoid above-mentioned existing in prior technology weak point, provides a kind of and realizes conveniently, is applicable to the method for sound field separation of measuring on arbitrary shape measuring face, the employing equivalent source method realization that computational stability is good, computational accuracy is high, the two measurement face.

The technical scheme that technical solution problem of the present invention is adopted is:

The characteristics of the inventive method: carry out as follows:

Acoustic pressure information on a, two faces of measurement

In the tested sound field that constitutes by sound source 1 and sound source 2, between sound source 1 and sound source 2, measurement face S is arranged ₁, at the face of measurement S ₁And be provided with between the sound source 2 one with measure face S ₁Parallel and standoff distance is the subsidiary face S of δ h ₂Be distributed with the measurement net point on two measurement faces respectively, the distance between the neighbor mesh points is less than half wavelength; Measure the sound pressure amplitude at each net point place on two measurement faces and phase information and obtain acoustic pressure on the two measurement faces; Described tested sound field is a steady sound field;

B, measuring face S ₁And set virtual source face S between the sound source 1 ₁ ^*, at subsidiary face S ₂And set virtual source face S between the sound source 2 ₂ ^*, and on two virtual source faces, being distributed with equivalent source respectively, the number of equivalent source is not more than the corresponding veil lattice point number of measuring; Described equivalent source is standard point source, face source or body source;

C, set up the transitive relation between equivalent source and the described two measurement faces

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^1={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_1$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_1$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_2$

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_2,$ Wherein

For sound source 1 is being measured face S ₁The acoustic pressure of last institute radiation,

For sound source 2 is being measured face S ₁The acoustic pressure of last institute radiation,

For sound source 1 at subsidiary face S ₂The acoustic pressure of last institute radiation,

For sound source 2 at subsidiary face S ₂The acoustic pressure of last radiation,

W ₁Be virtual source face S ₁ ^*Last equivalent source weight vector, W ₂Be virtual source face S ₂ ^*Last equivalent source weight vector,

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure,

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure,

Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₂Transfer matrix between the last acoustic pressure,

Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure;

D, separate on the two measurement faces acoustic pressure by the both sides sound source radiation

According to the transitive relation that step c is set up, unite and find the solution the acoustic pressure of distinguishing radiation on the two measurement faces of acquisition by sound source 1 and sound source 2:

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}={(I-G_1{G}_2)}^{+}(p_{S_1}-G_1{p}_{S_2})$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={(I-G_2{G}_1)}^{+}(p_{S_2}-G_2{p}_{S_1})$

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}=p_{S_1}-{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}=p_{S_1}-{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}$ Wherein

For measuring face S ₁On record acoustic pressure,

For measuring face S ₂On the acoustic pressure that records,

${\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">G</figure-callout>}}_1={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}\&rsqb;}^{+}$ 、 ${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">G</figure-callout>}}_2={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\left[{\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}\right]}^{+}.$

The characteristics of the inventive method also are:

The sound pressure amplitude on each net point and the measurement of phase information are that the single or multiple microphones of employing are respectively in the once snapshot acquisition on two measurement faces at snapshot on the two measurement faces or the two microphone arrays of employing respectively of scanning on the two measurement faces, employing microphone array.

Measurement face S ₁With subsidiary face S ₂Be plane or curved surface.

Sound source 1 is main sound source, and sound source 2 is noise source, reflection sources or scattering source.

The inventive method is the acoustic pressure on the measurement face that to measure two standoff distances be δ h, adopts equivalent source method to realize on the measurement face separation by both sides sound source radiation acoustic pressure.

Theoretical model:

The basic thought of equivalent source method is to adopt a series of equivalent source weighted stacking that are distributed in sound source inside to be similar to actual sound field, only needs this moment to determine that the source strength of these equivalent source is measurable whole sound field.In actual solution procedure, the source strength of equivalent source can pass through the boundary condition (acoustic pressure or normal direction vibration velocity) of the sound source of measurement and determine.For any measurement face in the sound field, also can be by the radiated sound field that distribution equivalent source on the virtual source face is similar to zone, side in face of this that deviates from the analysis domain at this face.

Referring to Fig. 1, the right side area field point r place acoustics amount of measuring face S can be by being distributed in this left side of face virtual source face S ^*Approximate acquisition of a series of equivalent source.If measure face S and virtual source face S ^*On distributed respectively M measurement point and N equivalent source, the sound radiation pressure on the scene some r place of i equivalent source is p _i ^*(r) and particle rapidity be v _i ^*(r), then the actual emanations acoustic pressure and the particle vibration velocity at field point r place can be expressed as

$p\left(r\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{w}_i{p}_i^{*}\left(r\right)---\left(1\right)$

$v\left(r\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{w}_i{v}_i^{*}\left(r\right)---\left(2\right)$

W in the formula _iBe i the pairing source strength of equivalent source.The source strength of each equivalent source is determined that by the boundary condition of the face of measurement the acoustic pressure that can be measured last M the measurement point of face S by equation (1) can be expressed as

$\begin{array}{cc}{p}_S\left(r_j\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{w}_i{p}_{\mathrm{Si}}^{*}\left(r_j\right)& j=1,2,...,M---\left(3\right)\end{array}$

Formula (3) is write as matrix form

$p_S=p_S^{*}W---\left(4\right)$

In the formula,

$p_S^{*}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^1\left(r_1\right)& {\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^2\left(r_1\right)& ...& p_{\mathrm{SN}}^{*}\left(r_1\right)\\ {\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^1\left(r_2\right)& {\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^2\left(r_2\right)& ...& p_{\mathrm{SN}}^{*}\left(r_2\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ p_{S1}^{*}\left(r_M\right)& {\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^2\left(r_M\right)& ...& p_{\mathrm{SN}}^{*}\left(r_M\right)\end{array}\right]---\left(5\right)$

W＝[w ₁w ₂…w _N](6)

In the formula, p _SAcoustic pressure column vector for M in the sound field measuring point place; W is the shared weight coefficient column vector of a corresponding N equivalent source; P _S ^*Be the M * N rank transfer matrix between N equivalent source and M the measuring point place acoustic pressure.

By formula (4) as can be known, as transfer matrix P _S ^*Exponent number satisfy M 〉=N, when promptly measure dot number is more than or equal to the equivalent source number, then can pass through the unique definite weight coefficient matrix W of svd, promptly

$W={\left(p_S^{*}\right)}^{+}{p}_S---\left(7\right)$

In the formula, "+" expression generalized inverse.

After trying to achieve the weight coefficient matrix W, just can calculate in the sound field arbitrarily any acoustic pressure and vibration velocity, realize the prediction of sound field by formula (1) and formula (2).

As from the foregoing, the radiated sound field of measurement face one side a series of equivalent source that can distribute by the opposite side at this measurement face are similar in the sound field.If all there is sound source the both sides of the face of measurement, then the acoustic pressure on the measurement face is the combination of both sides sound source radiation acoustic pressure.

Referring to Fig. 2, measure face S ₁On acoustic pressure be

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}={\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}+{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}---\left(8\right)$

In the formula For sound source 1 is being measured face S ₁The acoustic pressure of last institute radiation,

For sound source 2 is being measured face S ₁The acoustic pressure of last institute radiation.With the face of measurement S ₁Identical, measure face S ₂On acoustic pressure can be expressed as

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}={\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}+{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}---\left(9\right)$

In the formula

For sound source 1 is being measured face S ₂The acoustic pressure of last institute radiation,

For sound source 2 is being measured face S ₂The acoustic pressure of last institute radiation.

Because acoustic pressure is a scalar, thereby be difficult to directly the acoustic pressure of both sides sound source radiation on the measurement face be separated.Method of the present invention is to measure on two faces, and then realizes separating by equivalent source method.

As from the foregoing, measure face S ₁And S ₂1 sound radiation pressure of last sound source With

Can pass through at the face of measurement S ₁And the virtual source face S that is provided with between the sound source 1 ₁ ^*The a series of equivalent source of last distribution are similar to.By formula (7) as can be known, the source strength of equivalent source can adopt measurement face S ₁1 sound radiation pressure of last sound source

Determine, promptly

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_1={\&lsqb;{\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}\&rsqb;}^{+}{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^1---\left(10\right)$

Subscript "+" representing matrix generalized inverse in the formula,

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure.

Try to achieve the weight coefficient matrix W ₁After, can predict measurement face S by formula (1) ₂1 sound radiation pressure of last sound source

For

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_1={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}\&rsqb;}^{+}{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}---\left(11\right)$

In the formula

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₂Transfer matrix between the last acoustic pressure.

In like manner can be in the hope of measuring face S ₂Virtual source face S near sound source 2 one sides ₂ ^*The source strength W of a series of equivalent source of last distribution ₂For

${\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_2={\&lsqb;{\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}\&rsqb;}^{+}{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}---\left(12\right)$

In the formula

Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₂Transfer matrix between the last acoustic pressure.

And then can predict measurement face S ₁2 sound radiation pressures of last sound source

For

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_2={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}\&rsqb;}^{+}{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}---\left(13\right)$

In the formula Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure.

With formula (11) and (13) difference substitution formula (9) and (8), can get

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}={\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}+{\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}\&rsqb;}^{+}{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}---\left(14\right)$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}\&rsqb;}^{+}{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}+{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}---\left(15\right)$

Association type (14) and (15) can get

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}={(I-G_1{G}_2)}^{+}(p_{S_1}-G_1{p}_{S_2})---\left(16\right)$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={(I-G_2{G}_1)}^{+}(p_{S_2}-G_2{p}_{S_1})---\left(17\right)$

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}=p_{S_1}-{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}---\left(18\right)$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}=p_{S_1}-{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}---\left(19\right)$

In the formula

${\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">G</figure-callout>}}_1={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}\&rsqb;}^{+}---\left(20\right)$

${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">G</figure-callout>}}_2={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}\&rsqb;}^{+}---\left(21\right)$

By said method, realized the separation of acoustic pressure on the measurement face, can obtain sound radiation pressure from the face of measurement both sides sound source.

Compared with the prior art, beneficial effect of the present invention:

1, measurement face of the present invention can be the arbitrary shape measuring face, solved the defective that classic method can only be applicable to regular shapes such as plane, cylinder or sphere.

2, the present invention adopts equivalent source method to be used as the sound field separation algorithm, compares with traditional method, and the inventive method has that computational stability is good, the computational accuracy advantages of higher.

3, the inventive method is implemented simply, can be widely used in the near field acoustic holography measurement under internal acoustic field or the noise circumstance, the measurement of material reflection coefficient, the separation of scattering sound field etc.

Description of drawings:

Fig. 1 is a plane sound source equivalent source location map;

Fig. 2 is that two measurement face equivalent source method sound fields are separated synoptic diagram;

When Fig. 3 (a) is 0dB for signal to noise ratio (S/N ratio), measure face S ₁The sound pressure amplitude of last actual measurement distributes;

When Fig. 3 (b) is 0dB for signal to noise ratio (S/N ratio), measure face S ₁The theoretical amplitude distribution of last sound source 1 sound radiation pressure;

When Fig. 3 (c) is 0dB for signal to noise ratio (S/N ratio), the sound source 1 sound radiation pressure amplitude distribution that adopts the inventive method to separate;

When Fig. 3 (d) is 0dB for signal to noise ratio (S/N ratio), the sound source 1 sound radiation pressure amplitude distribution that adopts traditional space FFT method to separate;

When Fig. 3 (e) is 0dB for signal to noise ratio (S/N ratio), measure face S ₁The sound pressure phase of last actual measurement distributes;

When Fig. 3 (f) is 0dB for signal to noise ratio (S/N ratio), measure face S ₁Last sound source 1 sound radiation pressure notional phase distributes;

When Fig. 3 (g) is 0dB for signal to noise ratio (S/N ratio), the sound source 1 sound radiation pressure PHASE DISTRIBUTION that adopts the inventive method to separate;

When Fig. 3 (h) is 0dB for signal to noise ratio (S/N ratio), the sound source 1 sound radiation pressure amplitude distribution that adopts traditional space FFT method to separate;

When Fig. 4 (a) is 0dB for signal to noise ratio (S/N ratio), measure face S ₁Middle row acoustic pressure real part theoretical value and separation value are relatively;

When Fig. 4 (b) is 0dB for signal to noise ratio (S/N ratio), measure face S ₁Middle row acoustic pressure real part theoretical value and separation value are relatively;

Fig. 5 (a) for signal to noise ratio (S/N ratio) be-during 10dB, measure face S ₁The sound pressure amplitude of last actual measurement distributes;

Fig. 5 (b) for signal to noise ratio (S/N ratio) be-during 10dB, measure face S ₁The theoretical amplitude distribution of last sound source 1 sound radiation pressure;

Fig. 5 (c) for signal to noise ratio (S/N ratio) be-during 10dB, the sound source 1 sound radiation pressure amplitude distribution that adopts the inventive method to separate;

Fig. 5 (d) for signal to noise ratio (S/N ratio) be-during 10dB, the sound source 1 sound radiation pressure amplitude distribution that adopts traditional space FFT method to separate;

Fig. 5 (e) for signal to noise ratio (S/N ratio) be-during 10dB, measure face S ₁The sound pressure phase of last actual measurement distributes;

Fig. 5 (f) for signal to noise ratio (S/N ratio) be-during 10dB, measure face S ₁Last sound source 1 sound radiation pressure notional phase distributes;

Fig. 5 (g) for signal to noise ratio (S/N ratio) be-during 10dB, the sound source 1 sound radiation pressure PHASE DISTRIBUTION that adopts the inventive method to separate;

Fig. 5 (h) for signal to noise ratio (S/N ratio) be-during 10dB, the sound source 1 sound radiation pressure amplitude distribution that adopts traditional space FFT method to separate;

Below pass through embodiment, and in conjunction with the accompanying drawings the present invention is further described.

Embodiment:

Referring to Fig. 2, in the present embodiment, measure the face both sides and be distributed with sound source, wherein sound source 1 is main sound source, sound source 2 is noise source or reflection, scattering source, in the tested sound field that is made of sound source 1 and sound source 2, between sound source 1 and sound source 2 measurement face S is arranged ₁, at the face of measurement S ₁And be provided with between the sound source 2 one with measure face S ₁Parallel and standoff distance is the subsidiary face S of δ h ₂Be distributed with the measurement net point on two measurement faces respectively, the distance between the neighbor mesh points is less than half wavelength; δ h value is non-vanishing, and is not more than the minimum interval of measuring net point.

Concrete implementation step is:

A, adopt single or multiple microphones respectively scanning on the two measurement faces, adopt microphone array respectively snapshot on the two measurement faces or adopt two microphone arrays on two measurement faces once snapshot measure two face S ₁And S ₂On acoustic pressure information;

B, measuring face S ₁And set virtual source face S between the sound source 1 ₁ ^*, at subsidiary face S ₂And set virtual source face S between the sound source 2 ₂ ^*, and on two virtual source faces, being distributed with equivalent source respectively, the number of equivalent source is not more than the corresponding torus network of measuring and counts; Described equivalent source is standard point source, face source or body source;

C, set up the transitive relation between equivalent source and the described two measurement faces

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_S^1={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_1$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_1$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_2$

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">W</figure-callout>}}_2,$ Wherein

For sound source 1 is being measured face S ₁The acoustic pressure of last institute radiation,

For sound source 2 is being measured face S ₁The acoustic pressure of last institute radiation,

For sound source 1 at subsidiary face S ₂The acoustic pressure of last institute radiation,

For sound source 2 at subsidiary face S ₂The acoustic pressure of last radiation,

W ₁Be virtual source face S ₁ ^*Last equivalent source weight vector, W ₂Be virtual source face S ₂ ^*Last equivalent source weight vector;

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure,

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₂Transfer matrix between the last acoustic pressure,

Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₂Transfer matrix between the last acoustic pressure,

Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure;

D, separate on the two measurement faces acoustic pressure by the both sides sound source radiation

According to the transitive relation that step c is set up, unite and find the solution the acoustic pressure of distinguishing radiation on the two measurement faces of acquisition by sound source 1 and sound source 2:

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}={(I-G_1{G}_2)}^{+}(p_{S_1}-G_1{p}_{S_2})$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}={(I-G_2{G}_1)}^{+}(p_{S_2}-G_2{p}_{S_1})$

${\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}=p_{S_1}-{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}$

${\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}=p_{S_1}-{\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}$ Wherein

For measuring face S ₁On record acoustic pressure,

Measurement face S ₂On record acoustic pressure,

${\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">G</figure-callout>}}_1={\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}\&rsqb;}^{+}$ 、 ${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">G</figure-callout>}}_2={\left({\mathrm{<figure-callout\; id="2"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_2}\right)}^{*}{\&lsqb;{\left({\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="C20061009701500141.png,C20061009701500151.png"\; state="\{\{state\}\}">p</figure-callout>}}_{S_{}}^{{}_1}\right)}^{*}\&rsqb;}^{+}.$

The check of method:

Measuring face both sides a plurality of pulsation balls that distribute, adopting method for sound field separation of the present invention and traditional space FFT method to realize separating of acoustic pressure on the measurement face respectively, and with its analytic solution relatively.

For single radius is the pulsation ball of a, and the analytic solution of its on the scene some r place acoustic pressure are

$p(r,\mathrm{\&theta;})=-v\&CenterDot;\frac{i2\mathrm{\&pi;f\&rho;}{a}^2}{r(1-\mathrm{ika})}\&CenterDot;\exp \&lsqb;\mathrm{ik}(r-a)\&rsqb;,---\left(22\right)$

In the formula, even radial velocity v=1m/s, atmospheric density is ρ=1.2kg/m ³, the sound source vibration frequency is 400Hz.

Two measure the position relation of face referring to Fig. 2.Measurement face is the plane of 1m * 1m, and the spacing δ h between the measurement face is 0.01m, and 21 * 21 measurement points equably distribute on the measurement face.Sound source 1 is for being positioned at the pulsation ball at (0.6,0,0) m place, and sound source 2 is formed with the pulsation ball that is positioned at (0.6,0.5,0.4) m place for being positioned at (0.6 ,-0.5,0.4) m.Distance delta 1 and σ 2 between pairing virtual source face of two measurement faces and the measurement face are 0.225m.Sound source 1 is main sound source herein, and sound source 2 is a noise source, need be with the face of measurement S ₁Last sound source 1 sound radiation pressure is separated.

(wherein, Fig. 3 (a) and Fig. 3 (e) are measurement face S referring to Fig. 3 ₁The sound pressure amplitude of last actual measurement and PHASE DISTRIBUTION, Fig. 3 (b) and Fig. 3 (f) are that sound source 1 is at the face of measurement S ₁The sound pressure amplitude of last radiation and PHASE DISTRIBUTION, Fig. 3 (c) and Fig. 3 (g) for the sound source 1 that adopts the inventive method and separate at the face of measurement S ₁The sound pressure amplitude of last radiation and PHASE DISTRIBUTION, Fig. 3 (d) and Fig. 3 (h) for the sound source 1 that adopts traditional space FFT method and separate at the face of measurement S ₁The sound pressure amplitude of last radiation and PHASE DISTRIBUTION), measure face S ₁Differ greatly between the acoustic pressure that the acoustic pressure of last actual measurement and sound source 1 radiation sound produce, can't obtain sound source 1 at the face of measurement S by the acoustic pressure of actual measurement ₁Last radiation information; After adopting the inventive method to implement to separate, can accurately obtain sound source 1 at the face of measurement S ₁Last radiation information, isolated sound pressure amplitude and PHASE DISTRIBUTION and its theoretical value are very identical; After adopting traditional space FFT method to implement to separate, resultant sound source 1 is at the face of measurement S ₁There are apparent in view difference in last sound radiation pressure amplitude and PHASE DISTRIBUTION and its theoretical value.

Referring to Fig. 4 (a) and Fig. 4 (b), that measures face middle row theoretical value and separation value has more clearly illustrated the precision that both separate.

In order to distinguish the separation accuracy of two kinds of methods more quantitatively, ask for the separation error of two kinds of methods below respectively.Definition separates percentage error

$\mathrm{\&eta;}=\sqrt{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left(\right|p_i|-|{\stackrel{\&OverBar;}{p}}_i\left|\right)}^2}/\sqrt{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left|{\stackrel{\&OverBar;}{p}}_i\right|}^2}\&times;100(\%),---\left(23\right)$

In the formula, N is the surperficial node sum of all sound sources, p _iAnd p _iBe respectively corresponding i measurement point that separate with acoustic pressure theory.Calculated and can be got by formula (23), two kinds of methods are separated percentage error and are respectively 0.053% and 12.0397%, obviously adopt the inventive method can obtain accurate more result.

Expressed example in the above-mentioned check for method, sound source 1 is identical with the intensity of sound source 2, and promptly signal to noise ratio (S/N ratio) is 0dB.If the signal to noise ratio (S/N ratio) of sound source 1 and sound source 2 continues to diminish, or even sound source 2 is when being better than sound source 1, and the result that traditional space FFT method is separated will become meaningless, and adopt the inventive method separating resulting equally preferably; If it is big that the signal to noise ratio (S/N ratio) of sound source 1 and sound source 2 becomes,, adopt the inventive method can obtain more high-precision result though the resultant error that adopts traditional space FFT method to separate is also less.

Expressed example in the above-mentioned check for method, sound source 2 is enhanced to signal to noise ratio (S/N ratio) is-10dB, adopt two kinds of separating obtained separation percentage errors of method to be respectively 0.520% and 90.768%, (wherein, Fig. 5 (a) and Fig. 5 (e) are measurement face S to its separating resulting referring to Fig. 5 ₁The sound pressure amplitude of last actual measurement and PHASE DISTRIBUTION, Fig. 5 (b) and Fig. 5 (f) are that sound source 1 is at the face of measurement S ₁The sound pressure amplitude of last radiation and PHASE DISTRIBUTION, Fig. 5 (c) and Fig. 5 (g) for the sound source 1 that adopts the inventive method and separate at the face of measurement S ₁The sound pressure amplitude of last radiation and PHASE DISTRIBUTION, Fig. 5 (d) and Fig. 5 (h) for the sound source 1 that adopts traditional space FFT method and separate at the face of measurement S ₁The sound pressure amplitude of last radiation and PHASE DISTRIBUTION), the result who obviously adopts space FFT method to separate will become meaningless, and adopt the inventive method separating resulting equally preferably; If with sound source 2 weaken to signal to noise ratio (S/N ratio) be 10dB, adopt two kinds of separating obtained separation percentage errors of method to be respectively 0.021% and 7.195%, adopt the inventive method can obtain more accurate result equally.In fact even when sound source 2 is zero, also be so, adopt two kinds of separating obtained separation percentage errors of method to be respectively 0.021% and 7.032% this moment.Hence one can see that, regardless of the signal to noise ratio (S/N ratio) of sound field, adopts the inventive method can both obtain comparatively accurate result, and adopt traditional space FFT rule can not.

Claims (4)

1, a kind of method for sound field separation is characterized in that carrying out as follows:

Acoustic pressure information on a, two faces of measurement

In the tested sound field that constitutes by sound source 1 and sound source 2, between sound source 1 and sound source 2, measurement face S is arranged ₁, at the face of measurement S ₁And be provided with between the sound source 2 one with measure face S ₁Parallel and standoff distance is the subsidiary face S of δ h ₂Be distributed with the measurement net point on two measurement faces respectively, the distance between the neighbor mesh points is less than half wavelength; Measure the sound pressure amplitude at each net point place on two measurement faces and phase information and obtain acoustic pressure on the two measurement faces; Described tested sound field is a steady sound field;

B, measuring face S ₁And set virtual source face S between the sound source 1 ₁ ^*, at subsidiary face S ₂And set virtual source face S between the sound source 2 ₂ ^*, and on two virtual source faces, being distributed with equivalent source respectively, the number of equivalent source is not more than the corresponding veil lattice point number of measuring; Described equivalent source is standard point source, face source or body source;

C, set up the transitive relation between the acoustic pressure on equivalent source and the described two measurement faces

$p_{S1}^1={\left(p_{S_1}^1\right)}^{*}{W}_1$

$p_{S_2}^1={\left(p_{S_2}^1\right)}^{*}{W}_1$

$p_{S_2}^2={\left(p_{S_2}^2\right)}^{*}{W}_2$

$p_{S_1}^2={\left(p_{S_1}^2\right)}^{*}{W}_2,$ Wherein

For sound source 1 is being measured face S ₁The acoustic pressure of last institute radiation,

For sound source 2 is being measured face S ₁The acoustic pressure of last institute radiation,

For sound source 1 at subsidiary face S ₂The acoustic pressure of last institute radiation,

For sound source 2 at subsidiary face S ₂The acoustic pressure of last radiation,

W ₁Be virtual source face s ₁ ^*Last equivalent source weight vector, W ₂Be virtual source face s ₂ ^*Last equivalent source weight vector,

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure,

Be virtual source face S ₁ ^*Last equivalent source and the face of measurement S ₂Transfer matrix between the last acoustic pressure,

Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₂Transfer matrix between the last acoustic pressure,

Be virtual source face S ₂ ^*Last equivalent source and the face of measurement S ₁Transfer matrix between the last acoustic pressure;

D, separate on the two measurement faces acoustic pressure by the both sides sound source radiation

According to the transitive relation that step c is set up, unite and find the solution the acoustic pressure of distinguishing radiation on the two measurement faces of acquisition by sound source 1 and sound source 2:

$p_{S_1}^1={(I-G_1{G}_2)}^{+}(p_{S_1}-G_1{p}_{S_2})$

$p_{S_2}^2={(I-G_2{G}_1)}^{+}(p_{S_2}-G_2{p}_{S_1})$

$p_{S_1}^2=p_{S_1}-p_{S_1}^1$

$p_{S_2}^1=p_{S_1}-p_{S_2}^2$ Wherein

For measuring face S ₁On record acoustic pressure,

For measuring face S ₂On the acoustic pressure that records,

$G_1={\left(p_{S_1}^2\right)}^{*}{\left[{\left(p_{S_2}^2\right)}^{*}\right]}^{+},$ $G_2={\left(p_{S_2}^1\right)}^{*}{\left[{\left(p_{S_1}^1\right)}^{*}\right]}^{+}.$

2, method for sound field separation according to claim 1, the measurement that it is characterized in that sound pressure amplitude on described each net point and phase information be adopt single or multiple microphones respectively scanning on the two measurement faces, adopt microphone array respectively snapshot on the two measurement faces or adopt two microphone arrays on two measurement faces once snapshot obtain.

3, method for sound field separation according to claim 1 is characterized in that described measurement face S ₁With subsidiary face S ₂Be plane or curved surface.

4, method for sound field separation according to claim 1 is characterized in that described sound source 1 is main sound source, and sound source 2 is noise source, reflection sources or scattering source.

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