CN103763658A - Method for producing freely curved sound wave beams - Google Patents

Abstract

The invention discloses a method for producing freely curved sound wave beams. By regulating sound source phase distribution at the boundary where z is equal to 0, the sound wave beams broadcasted along a freely curved track is produced in a half space where z is greater than 0. The method has the obvious advantages that a relationship is built between the slope of any one point on the curved track and the intercept, on a coordinate axis, of a tangent line passing through the point through Legendre transformation; a function relationship between the slope of any one point and phase distribution on the boundary is calculated according to the Fermat principle and the geometrical relationship; the two steps are combined, and a function relationship between the sound source phase distribution on the boundary and a space coordinate is obtained through integration; the obtained sound source space phase distribution is used for sound field replaying, the sound wave beams broadcasted along the freely curved track which is set are generated. Compared with a wave beam forming method, the method overcomes the defect that the wave beams only can be broadcasted in the specific direction and can not be curved; compared with a sound contrast control method, the method solves the problem of matrix inversion operation and errors possibly caused by the matrix inversion operation.

Description

A kind of method that produces any flexural acoustic wave bundle

One, technical field

The present invention relates to sound field control technology field.Proposed a kind of regulate and control on border sound source PHASE DISTRIBUTION produce along the method for the beam of sound that serpentine track is propagated arbitrarily.

Two, background technology

The study general of sound field control is at present for two kinds of situations, and a kind of is the noise of eliminating specific region, produces " acoustics dead zone " (Zone of Quite); Another kind is in specific region, to rebuild sound field, produces " acoustics clear zone " (Acoustically BrightZone).For a rear problem, conventional sound field control method adopts wave beam to form (Beamforming) method harmony compared with control (Acoustic Contrast Contro1) method more at present.

It is synthetic that Beamforming Method is used in reference to tropism's sound field, can adopt loudspeaker array to produce the beam of sound of propagating to specific direction.It is the angle direction that produces as required wave beam that conventional wave beam forms optimization method, the source strength of design loudspeaker array distributes (as Daesung Kim, Kihyun Kim, Semyung Wang, Sung Q Lee and Malcolm J.Crocker.Maximization of the Directivity Ratio With the Desired Audible Gain Level for Broadband Design of Near Field Loudspeaker Arrays.[J] .Journal of Sound and Vibration, 2011, 330:5517-5529 and Franz Zotter, Markus Noistemig.Near-and Far-field Beamforming Using Sphericall Loudspeaker Arrays.[C] .Austria, 3 ^rdcongress ofthe Alps Adria Acoustics Association, 2007.).Beamforming Method can only produce the beam of sound of propagating along certain special angle, and cannot make wave beam bend in communication process.

Sound compared with control method is used for making in certain specific region sound field energy compared with large and make another region self-energy less.Conventional method have the acoustic energy of maximization " clear zone " (Bright Zone) and " dark space " (Dark Zone) ratio (as Joung-Woo Choi and Yang-hann Kim.Generation Of an Acoustically Bright Zone With an Illuminated Region Using Multiple Sources.[J] .Journal ofAcoustic Society ofAmerica, 2002, 111 (4): 1695-1700) and maximize acoustic energy poor (as Mincheol Shin of clear zone and dark space, Sung Q.Lee, Filippo M.Fazi, Philip A.Nelson, Daesung Kim, Semyung Wang, Kang Ho Park and Jeongil Seo.Maximization Of Acoustic Energy Difference Between Two Spaces.[J] .Journal of Acoustic Society of America, 2010, 128 (1): 121-131) etc.Sound compared with control method needs matrix inversion operation solving when source strength distributes, and when matrix conditional number is larger, can produce ill-conditioning problem (ill-conditioning Problem), thereby makes the source strength maldistribution that solves true, causes larger error.

Chinese patent CN101251414A (a kind of method and device that utilizes reverse-phase that loudspeaker array is set) in prior art document realizes the optimization of loudspeaker array directive property by adjusting the method for part loudspeaker unit phase place in array, the uniformity coefficient of its directive property is obviously improved.Chinese patent CN102711015A (based on loudspeaker array sound field control method and the device of quadratic residue sequence combination) proposes to utilize quadratic residue subsequence to design optimum array phase delay vector, according to optimum phase delay vector control loudspeaker array, improved the uniformity coefficient of array manifold radiated sound field.Above method can improve the uniformity coefficient of array directive property, but cannot produce the beam of sound of propagating along serpentine track.In further retrieving, not yet find the bibliographical information identical or similar with theme of the present invention.

Distinguishing feature of the present invention is to propose a kind of new algorithm, by any bending acoustic beam track conversion, obtaining being positioned at the borderline sound source space phase in z=0 place distributes, by the borderline sound source PHASE DISTRIBUTION in regulation and control z=0 place, at half space z > 0 place, produce along the beam of sound that serpentine track is propagated arbitrarily.

Three, summary of the invention

1, goal of the invention: propose a kind of new algorithm, by the acoustic beam track conversion of any bending, obtaining borderline sound source space phase distributes, by the borderline sound source initial phase in regulation and control z=0 place, distribute, at half space z > 0 place, produce along the beam of sound that serpentine track is propagated arbitrarily.

2, technical scheme: for achieving the above object, as shown in Figure 1, algorithm basic calculating flow process as shown in Figure 2 for any bending acoustic beam track and coordinate relation described in algorithm proposed by the invention.Sound source of the present invention is arranged in the represented straight line of plane z=0 place (being x axle) as shown in Figure 1, and any flexural acoustic wave bundle producing is arranged in plane z > 0 part as shown in Figure 1.The present invention specifically comprises the following steps:

The first step: according to any bending acoustic beam track x=f (z) setting, by the functional relation (as shown in Figure 1) of any point slope t (z)=df (z)/dz and tangent line intercept x on transverse axis on Legendre transformation (Legendre Transform) calculating track.Introduce calculation process below: first, can obtain its inverse function z=z (t) by t=t (z); Secondly, by Legendre transformation defined function g (z)=tz-f (z); Then, bring z=z (t) into function g (z), and obtain function x=g (t) by the geometric meaning of Legendre transformation; Finally, the inverse function of computing function x=-g (t) obtains functional relation:

t(x)＝g ^-1(-x)＝h(x) (1)

Second step: in conjunction with geometrical relationship and Fermat's principle (Fermat ' s Principle), the functional relation of sound source space phase distribution phi (x) and transverse axis coordinate x on computation bound.Introduce calculation process below: according to setting any serpentine track x=f (z), can obtaining any point slope on track by geometrical relationship, be:

$t\left(z\right)=\frac{\mathrm{df}\left(z\right)}{\mathrm{dz}}=-\tan \mathrm{\θ}---\left(2\right)$

In formula, df (z)/dz is the first derivative of f (z).

On the other hand, according to Fermat's principle, can obtain sound source space phase distribute derivative and the pass of acoustic propagation angle be:

$\frac{\mathrm{d\φ}\left(x\right)}{\mathrm{dx}}=-k\sin \mathrm{\θ}---\left(3\right)$

In formula, k is wave number, φ (x) be on border sound source phase place with the distribution of space coordinates x.

There is following trigonometric function relation in SIN function and tan:

$\sin \mathrm{\θ}=\frac{\tan \mathrm{\θ}}{\sqrt{1+{\tan }^2\mathrm{\θ}}}---\left(4\right)$

Convolution (2), formula (3) and formula (4), the functional relation of the derivative of sound source PHASE DISTRIBUTION on the slope t (z) that can obtain any point in serpentine track and border:

$\frac{\mathrm{d\φ}\left(x\right)}{\mathrm{dx}}=\frac{\mathrm{kt}\left(z\right)}{\sqrt{1+t{\left(z\right)}^2}}---\left(5\right)$

Bring formula (1) into formula (5) and can obtain derivative that sound source space phase on border distributes and the functional relation of transverse axis coordinate x:

$\frac{\mathrm{d\φ}\left(x\right)}{\mathrm{dx}}=\frac{\mathrm{kh}\left(x\right)}{\sqrt{1+h{\left(x\right)}^2}}---\left(6\right)$

Formula (6) is carried out to integration and can obtain any point x on border ₀sound source phase (the x of place ₀), shown in (7):

$\mathrm{\φ}\left(x_0\right)={\∫}_0^{x_0}\frac{\mathrm{kh}\left(x\right)}{\sqrt{1+h{\left(x\right)}^2}}\mathrm{dx}---\left(7\right)$

The 3rd step: utilize second step to convert sound source PHASE DISTRIBUTION φ (x) playback sound field on the border obtaining, produce the beam of sound of propagating along any serpentine track of setting.Concrete calculation process is as follows: sound source PHASE DISTRIBUTION on border is carried out to discretization, and note sampled point is x _n(n=1,2 ..., N; N is point source number), discretization PHASE DISTRIBUTION is φ (n)=φ (x _n).Each sampled point is approximate with the point-source model to semi-free space radiation on infinitely great baffle, and the source strength of each point source is expressed as q _n=e ^{j φ (n)}, j is imaginary unit.Space any point acoustic pressure can be calculated by following formula:

$p=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{q}_n\frac{e^{-\mathrm{<figure-callout\; id="2"\; label="jk\; R\; n"\; filenames="HSA0000100993230000012.png,HSA0000100993230000021.png"\; state="\{\{state\}\}">jk</figure-callout>}{R}_n{}_{}}}{2\mathrm{\&pi;}{R}_n}=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&phi;}\left(n\right)}\frac{e^{-\mathrm{<figure-callout\; id="2"\; label="jk\; R\; n"\; filenames="HSA0000100993230000012.png,HSA0000100993230000021.png"\; state="\{\{state\}\}">jk</figure-callout>}{R}_n{}_{}}}{2\mathrm{\&pi;}{R}_n}---\left(8\right)$

In formula, k is wave number, R _nbe the distance of n point source and calculated field point, p is calculated field point sound pressure level.

3, beneficial effect: remarkable advantage of the present invention is: propose a kind of initial phase by regulation and control z=0 place, border sound source and distribute, produce along the beam of sound that serpentine track is propagated arbitrarily at half space z > 0 place.Overcome Beamforming Method and can only produce along the shortcoming of certain direction straightline propagation beam of sound, and avoided the ill-conditioning problem of matrix inversion in sound compared with control method.

Four, accompanying drawing explanation

Fig. 1 is any serpentine track and coordinate system schematic diagram.

Fig. 2 obtains PHASE DISTRIBUTION algorithm principle block diagram on border by any serpentine track conversion.

Fig. 3 is logarithm track flexural acoustic wave bundle simulation result, and in figure, (a) is space PHASE DISTRIBUTION on the acoustics border calculating; Sound pressure level (dB) distribution map that in figure, (b) obtains for simulation calculation, in figure (b), white dashed line is the logarithmic function propagation trajectories of setting.

Fig. 4 is semicircle track flexural acoustic wave bundle simulation result, and in figure, (a) is space PHASE DISTRIBUTION on the acoustics border calculating; Sound pressure level (dB) distribution map that in figure, (b) obtains for simulation calculation, in figure (b), white dashed line is the semicircle propagation trajectories of setting.

Five, embodiment

Algorithm characteristics proposed by the invention is: the space phase that any bending acoustic beam track is transformed to sound source on border distributes, and by regulating and controlling borderline sound source initial phase, distributes, and produces along the beam of sound that serpentine track is propagated arbitrarily.Take logarithmic function track and semicircle track as embodiment, introduce in detail its implementation procedure respectively below.The present embodiment is implemented under take technical solution of the present invention as prerequisite, has provided detailed implementation process, and protection scope of the present invention includes but not limited to following embodiment.

Embodiment mono-: produce the beam of sound of propagating along logarithmic function track x=f (z)=aln (bz) (a and b are constant):

The 1st step: according to logarithmic function track x=f (the z)=aln (bz) setting, calculate the functional relation of any point slope t (z)=df (z)/dz=a/z and tangent line intercept x on transverse axis on track by Legendre transformation.Introduce calculation process below: first, can obtain its inverse function z=z (t)=a/t by t=t (z)=a/z; Secondly, by Legendre transformation defined function g (z)=tz-f (z); Then, bring z=z (t) into function g (z) and obtain g (t)=a-a ln (ab/t)=a[1-1n (ab/t)], and obtain function x=-g (t)=a[ln (ab/t)-1 by the geometric meaning of Legendre transformation]; Finally, the inverse function of computing function x=-g (t) obtains functional relation t (x)=h (x)=abe ^(1-x/a).

The 2nd step: according to geometrical relationship and Fermat's principle, the functional relation of sound source space phase distribution phi (x) and transverse axis coordinate x on computation bound.Bring the 1st step result of calculation into formula (6) and obtain d φ (x)/dx=kh (x)/[1+h (x) ²] ^1/2=kabe ^(1-x/a)/ [1+a ²b ²e ^(2-2x/a)] ^1/2, by formula (7), carry out integration and obtain φ (x)=-ka asinh (abe ^-1-x/a)(omitted integral constant item, asinh () represents asinh function).

The 3rd step: bring the 2nd step result of calculation into formula (8) computer memory any point sound field and distribute.Frequency is 5kHz, point source spacing 0.01m, and point source number is 401, constant a=1, simulation result during b=0.5 is as shown in Figure 3.

Embodiment bis-: produce along semicircle track x=f (z)=[a ²-(z-a) ²] ^1/2(a is radius, the beam of sound that propagate the center of circle (0, a)):

The 1st step: according to semicircle track x=f (z)=[a setting ²(z-a) ²] ^1/2, by Legendre transformation, calculate any point slope t (z)=df (z)/dz=--(z-a)/[a on track ²-(z-a) ²] ^1/2functional relation with tangent line intercept x on transverse axis.Introduce calculation process below: first, can be by t=t (z)=(z-a)/[a ²-(z-a) ²] ^1/2obtain its inverse function z=z (t)=a-at/ (1+t ²) ^1/2; Secondly, by Legendre transformation defined function g (z)=tz-f (z); Then, z=z (t) is brought into function g (z) and obtain g (t)=at-a (1+t ²) ^1/2, and obtain function x=-g (t)=at-a (1+t by the geometric meaning of Legendre transformation ²) ^1/2; Finally, the inverse function of computing function x=-g (t) obtains functional relation t (x)=h (x)=(a ²-x ²)/2ax.

The 2nd step: according to geometrical relationship and Fermat's principle, the functional relation of sound source space phase distribution phi (x) and transverse axis coordinate x on computation bound.Bring the 1st step result of calculation into formula (6) and obtain d φ (x)/dx=kh (x)/[1+h (x) ²] ^1/2=k (a ²-x ²)/{ x ²+ a ²), by formula (7), carry out integration and obtain φ (x)=2aatan (x/a)-x (atan () represents arctan function).

The 3rd step: bring the 2nd step result of calculation into formula (8) computer memory any point sound field and distribute.Frequency is 5kHz, point source spacing 0.01m, and point source number is 601, simulation result during radius a=2 is as shown in Figure 4.

Claims (4)

1. produce a method for any flexural acoustic wave bundle, by regulation and control z=0 place, border sound source PHASE DISTRIBUTION, at half space z > 0 place, produce along the beam of sound that serpentine track is propagated arbitrarily.It is characterized in that comprising following three steps: the first step, according to any serpentine track x=f (z) setting, by Legendre transformation (Legendre Transform), calculate the functional relation of any point slope t (z)=df (z)/dz and tangent line intercept x on transverse axis on track; Second step, according to geometrical relationship and Fermat's principle (Fermat ' s Principle), the functional relation of sound source PHASE DISTRIBUTION φ (x) and transverse axis coordinate x on computation bound; The 3rd step, utilize second step to convert sound source PHASE DISTRIBUTION φ (x) playback sound field on the border obtaining, produce the beam of sound of propagating along any serpentine track of setting.

2. the method for any flexural acoustic wave bundle of generation as claimed in claim 1, it is characterized in that: the functional relation of any point slope t (z)=df (z)/dz and tangent line intercept x on transverse axis in serpentine track arbitrarily, calculation process is as follows: first, by t=t (z), obtain its inverse function z=z (t); Secondly, by Legendre transformation defined function g (z)=tz-f (z); Then, bring z=z (t) into function g (z), and obtain function x=-g (t) by the geometric meaning of Legendre transformation; Finally, the inverse function of computing function x=-g (t) obtains functional relation t (x)=g ^-1(-x)=h (x).

3. the method for any flexural acoustic wave bundle of generation as claimed in claim 1, is characterized in that: any point x on border ₀sound source phase (the x of place ₀) by formula (1), calculate:

$\mathrm{\&phi;}\left(x_0\right)={\&Integral;}_0^{x_0}\frac{\mathrm{kh}\left(x\right)}{\sqrt{1+h{\left(x\right)}^2}}\mathrm{dx}---\left(1\right)$

In formula, k is wave number.

4. the method for any flexural acoustic wave bundle of generation as claimed in claim 1, it is characterized in that: utilize sound source PHASE DISTRIBUTION φ (x) playback sound field on the border that second step calculates, calculation process is as follows: borderline sound source PHASE DISTRIBUTION is carried out to discretization, note sampled point is for surveying (n=1,2 ..., N, N is point source number), discretization PHASE DISTRIBUTION is φ (n)=φ (x _n).Each sampled point is approximate with the point-source model to semi-free space radiation on infinitely great baffle, and the source strength of each point source is expressed as q _n=e ^{j φ (n)}, j is imaginary unit.Space any point sound pressing type (2) calculates:

$p=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{q}_n\frac{e^{-\mathrm{jk}{R}_n}}{2\mathrm{\&pi;}{R}_n}=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&phi;}\left(n\right)}\frac{e^{-\mathrm{jk}{R}_n}}{2\mathrm{\&pi;}{R}_n}---\left(2\right)$

In formula, k is wave number, R _nbe the distance of n point source and calculated field point, p is calculated field point sound pressure level.

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