CN109507640A - A kind of comprehensive equivalent source identification of sound source method based on solid ball array - Google Patents
A kind of comprehensive equivalent source identification of sound source method based on solid ball array Download PDFInfo
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The comprehensive equivalent source identification of sound source method based on solid ball array that the invention discloses a kind of, it includes step 1, the total acoustic pressure of radiation fields for obtaining medicine ball array measurement；Step 2 calculates equivalent source strength q based on iteration weighting algorithm；Solution formula are as follows:In formula, W is weighting matrix, is the invertible matrix of diagonal element non-zero；λ is regularization parameter；Step 3 rebuilds any position acoustic pressure.The advantages of invention, is: having excellent acoustic source location accuracy and sound field reconstruction performance under middle low frequency and big measurement distance.
Description
Technical field
The invention belongs to sound field identification technology fields, and in particular to a kind of spherical equivalent source identification of sound source of solid ball array
Method.
Background technique
Spherical equivalent source method (Spherical Equivalent Source Method, S- based on solid ball array
It ESM is) that the new omnibearing sound field of one kind is rebuild and identification of sound source algorithm.Traditional S-ESM uses Tikhonov regularization in standard regularization skill
Art solves, however, the limitation and regularization parameter because being limited to Nyquist sampling thheorem and Tikhonov regularization is non-
Stability, reconstruction precision only middle low frequency and it is small measurement apart from when can receive.
The spheric array equivalent source solved based on most rapid decrease iteration (Steepest Descent Iteration, SDI)
(SDI-based S-ESM, abbreviation SDI), realizes preferable medium-high frequency reconstruction performance, has widened S-ESM and has led in identification of sound source
The applicable distance in domain, but be limited to the inherent shortcoming of most rapid decrease iterative solution, SDI in low frequency and big measurement apart from when sound field
It rebuilds and identification of sound source poor performance.
Summary of the invention
SDI technology there are aiming at the problem that, the technical problem to be solved by the invention is to provide one kind be based on medicine ball
The comprehensive equivalent source identification of sound source method of array, it can improve sound field rebuilding and sound source knowledge under low frequency and big measurement distance
Other performance.
The technical problem to be solved by the present invention is in this way technical solution realize, it the following steps are included:
Step 1, the total acoustic pressure of radiation fields for obtaining medicine ball array measurement
The total acoustic pressure expression formula of the radiation fields of any point at medicine ball array surface (a, Ω) are as follows:
In formula, Ω ≡ (θ, φ), θ and φ are respectively the elevation angle and azimuth, and a is array radius；ρ is density, and Q is volume speed
Degree, k are wave number, and n and m are respectively the secondary and rank of spheric harmonic function, r0=(r0,Ω0) be point sound source position, r0Indicate sound source away from
With a distance from array center,Indicate the elevation angle and azimuth of sound source position, hn() indicates first kind ball Hunk
That function, hn' () is hnThe derivative of (),For spheric harmonic function, ()*Indicate complex conjugate；
The total acoustic pressure of measurement radiation fields of ball array surface microphone is write as matrix form:
pt=GNq
In formula, ptFor the rank ball array surface microphone acoustic pressure column vector of L × 1, q is the rank of S × 1 equivalent source intensity column vector,
Each element corresponds respectively to j ω ρ Qs；L is the microphone number of medicine ball array surface, and S is the monopole point sound of equivalent source spherical surface
Source number；GNL × S rank Nuo Yiman Green's function matrix between microphone and equivalent source,
R in formulae=(re,Ωe) indicate equivalent source position, r be any observation point of three-dimensional space at a distance from origin；
Step 2 calculates equivalent source strength based on iteration weighting algorithm
The solution of the matrix form of step 1 are as follows:
In formula, W is weighting matrix, is the invertible matrix of diagonal element non-zero；λ is regularization parameter, | |
||2For l2Norm；
Initialization
In formula, re,sIndicate s-th of equivalent source at a distance from coordinate origin, s=1,2 ... S
Seek the iterative process of equivalent source strength q are as follows:
Step (1) calculates weighting matrix W(i): W(i)=W0Wi,
Step (2) calculates new transfer matrix
It is step (3), rightCarry out singular value decomposition:
Step (4) calculates
Step (5) calculates equivalent source strength q(i):
Step (6) judges termination condition: τ=10log (| | q(i)||2/||q(i+1)||2)≤0.1dB
By the q of step (5)(i)It substitutes into step (1) and acquires Wi+1Into recycling next time, iteration is until step repeatedly
(6) when termination condition meets, equivalent source strength q is obtained；
Step 3 rebuilds any position acoustic pressure
The expression formula of acoustic pressure is rebuild in three-dimensional sound field are as follows:
pr=Grq
In formula, prTo rebuild spherical surface incident sound pressure, GrFor equivalent source and rebuild spherical surface rrLocate the free field lattice between reconstruction point
Woods function, expression formula are as follows:
jn() indicates first kind spheric Bessel function, rr=(rr,Ωr) indicate reconstructed positions, re,sFor s-th of equivalent source
The distance between coordinate origin, Ωe,sIndicate the direction at s-th of equivalent source.
The solution have the advantages that:
Present invention employs iteration weighting methods to calculate equivalent source strength q, and compared with SDI, the present invention is in middle low frequency and big survey
Span has superior acoustic source location accuracy and sound field reconstruction performance from lower, is low frequency and big holographic distance in practical application
Omnidirectional sound source identification provides effective technical solution.
Detailed description of the invention
Detailed description of the invention of the invention is as follows:
Fig. 1 is the schematic diagram of the coordinate system of S-ESM；
Fig. 2 is that step 1 calculates the total acoustic pressure distribution map of resulting medicine ball array surface；
It is 1.5a-5a that Fig. 3, which is three sound sources in measurement distance, and frequency is the reconstruction relative error cloud atlas under 200-6000Hz；
Fig. 3 (a) is SDI；Fig. 3 (b) is the present invention；
Fig. 4 is test layout；
The experiment sound field rebuilding acoustic pressure cloud atlas that Fig. 5 is frequency of source when being 200Hz, 1000Hz, 3000Hz and 6000Hz；
Fig. 5 (a)-(d) is SDI；Fig. 5 (e)-(h) is the present invention.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples:
The present invention the following steps are included:
Step 1, the total acoustic pressure of radiation fields for obtaining medicine ball array measurement
S-ESM coordinate system used in the present invention is as shown in Figure 1, set medicine ball array center as coordinate origin, array radius is
a.Any position can be described with r=(r, θ, φ) in three-dimensional space, r indicate any observation point of three-dimensional space and origin away from
From, θ and φ are respectively the elevation angle and azimuth, and value is 0-180 ° and 0-360 ° respectively, for indicating the direction of described position,
And note Ω ≡ (θ, φ).The position of equivalent source is re=(re,Ωe), rebuilding each reconstruction point position on spherical surface is rr=(rr,Ωr),
The position of point sound source is r0=(r0,Ω0), r0Indicate the distance at sound source distance arrays center,Indicate sound source position
The elevation angle and azimuth.
Due to using medicine ball array measurement in three-dimensional sound field, the total acoustic pressure of radiation of the sound source in three-dimensional sound field is incident sound
The sum of pressure and scattering pressure.By taking point sound source as an example, incident sound pressure piIt may be expressed as:
In formula (1), ω is angular frequency, and ρ is density, and Q is volume velocity, and k is wave number, R=| r0- r | for sound source and three-dimensional
The distance between observation point in sound field, G (r, r0) it is free field Green's function.
Under spherical coordinate system, the sound field of any spherical surface can be expressed as the orthonormal basis that one group is known as spheric harmonic function
Linear combination.Therefore, incident sound pressure and free field Green's function can be expressed as spheric harmonic function extension form:
In formula (2) and formula (3),For spheric harmonic function, n and m be respectively spheric harmonic function time and rank, AmnFor incidence system
Number, jn() indicates first kind spheric Bessel function, hn() indicates first kind ball Hankel function, ()*Indicate complex conjugate.
Convolution (1)-(3), it is known that incident coefficient Amn=ρ ck2Q, c indicate the velocity of sound.
Meanwhile scattering pressure can also be expressed as spheric harmonic function extension form, and according to the sound field matter of medicine ball array surface
The boundary condition that point vibration velocity is zero, can be obtained the total acoustic pressure of sound field:
In formula (4), subscript t indicates total acoustic pressure (total), jn' () and hn' () respectively indicate spheric Bessel function and
The derivative of ball Han Er function.Utilize Wronskian relational expression:
jn(ka)hn′(ka)-jn′(ka)hn(ka)=j/ (ka)2 (5)
Then the total acoustic pressure expression formula of radiation fields of any point can be further simplified as at medicine ball array surface (a, Ω)
The total acoustic pressure distribution of medicine ball array surface radiation fields is obtained by formula (6), as shown in Figure 2.
Meanwhile formula (6) is further indicated that by Nuo Yiman Green's function are as follows:
pt(a, Ω)=j ω ρ QGN(r|R=a,r0) (7)
In formula (7), GN(r|R=a,r0) Nuo Yiman Green's function between array surface any point and sound source, expression
Formula are as follows:
S-ESM spherical equivalent source method is: a series of equivalent point sound source intensity are obtained based on formula (7) and formula (8), then
Sound field is rebuild using new Green's function.Assuming that medicine ball array surface has L microphone, equivalent source spherical surface has S monopole
Sub- point sound source.The sound source radiation acoustic pressure that each microphone of array surface is received can be equivalent to the point sound source of S discrete distributions
Sound field at this microphone exports superposition.Therefore, first microphone (a, Ω of array surfacel) at the total acoustic pressure of radiation fields
Expression formula is
In formula (9), re,sFor the distance between s-th of equivalent source and coordinate origin, Ωe,sIt indicates at s-th of equivalent source
Direction.When carrying out read group total to above formula, order n can not get ∞, and ∞ is usually substituted with truncation length N, and length N is truncated
The design of value criterion is as follows
In formula (10), [] is indicated the upward rounding of numerical value to nearest integer.Truncation length is determined, then spherical array list
The total acoustic pressure of measurement radiation fields of face microphone can be write as matrix form:
pt=GNq (11)
In formula (11), ptFor the rank ball array surface microphone acoustic pressure column vector of L × 1, GNBetween microphone and equivalent source
L × S rank Nuo Yiman Green's function matrix, q is the rank of S × 1 equivalent source intensity column vector, and each element corresponds respectively to j ω ρ Qs。
ptIt is obtained and (is obtained when test by array measurement) by formula (6), GNIt is obtained by formula (8), q is wait seek equivalent source strength
Spend vector.
In fact, to obtain enough sound field informations, it is desirable that the equivalent source number S of arrangement is much larger than microphone number L, from
And formula (11) is caused to be underdetermined equation, equivalent source strength q's is retrieved as ill posed inverse problem equation solution.It is accurate etc. to obtain
Source strength is imitated, S-ESM uses Tikhonov regularization in standard regularization method, by minimizing secondary remaining norm and solution norm to formula
(11) stablize and solve, then have
In formula (12), p ptShorthand, λ is regularization parameter, can be by L-curve method, GCV method and Bayesian
Regularization Criterion Method determines；||·||2For l2Norm.
Then, it rebuilds sound field and identification sound source is as follows:
Step 2 calculates equivalent source strength based on iteration weighting algorithm
Present method invention is: on the basis of Tikhonov regularization in standard regularization, introducing a penalty term i.e. weighting matrix W
Equivalent source strength is iteratively solved, by the control of penalty term, so that the more and more weights of equivalent source strength concentrate on true sound
Near source, to promote the sparsity of equivalent source strength.Therefore, formula (12) can be further represented as
In formula, weighting matrix W is the invertible matrix of diagonal element non-zero.Solution norm in formula is defined asOn
Formula can be further simplified as
For formula (14), it is iterated and solves q.Initialization
In formula, re,sIndicate distance of s-th of equivalent source apart from origin, s=1,2 ... S.
Seek the iterative process of equivalent source strength q are as follows:
Step (1) calculates weighting matrix W(i):
WiIt is the companion matrix of interative computation, for correcting W(i)；
Step (2) calculates new transfer matrix
It is step (3), rightCarry out singular value decomposition:
WithIt isUnitary matrice after singular value decomposition；S~It isSingular value matrix after singular value decomposition, subscript H representing matrix
Conjugate transposition.
Step (4) calculates I indicates unit matrix.
Step (5) calculates equivalent source strength q(i):
W(i)-1It is the W indicated(i)Inverse matrix.
Step (6) judges termination condition: τ=10log (| | q(i)||2/||q(i+1)||2)≤0.1dB (20)
Based on i-th iteration result qiI+1 time iteration is carried out, i.e., by the q of step (5)(i)It substitutes into step (1) and acquires Wi+1
Into recycling next time, iteration obtains equivalent source strength q when the termination condition of step (6) meets repeatedly.
Step 3 rebuilds any position acoustic pressure
After equivalent source strength q is determined, the acoustic pressure of any position in sound field can be rebuild.Based on formula (3) free field Green
Function can rebuild incident sound pressure, and can also rebuild total acoustic pressure comprising scattering based on formula (8) Nuo Yiman Green's function.So
The scattering problems as caused by solid ball array can be evaded well in rebuilding acoustic pressure, rebuild acoustic pressure in three-dimensional sound field at this time
Expression formula are as follows:
pr=Grq (21)
In formula (21), prTo rebuild spherical surface incident sound pressure, GrFor equivalent source and rebuild spherical surface rrLocate the freedom between reconstruction point
Field Green's function, expression formula are as follows:
After rebuilding any position acoustic pressure, sound field acoustic pressure cloud atlas is produced, sound source position, the letter of acoustic pressure size are thus obtained
Breath, thus positioning and quantization sound source.
Analogue simulation test
To verify accuracy and the raising for comparing its performance of the invention, identification of sound source analogue simulation is carried out.
Emulation is provided that array center is coordinate origin, sound source i.e. measurement distance (r with a distance from array center0) be
1.5a to 5a；Rebuilding spherical surface is 0.5a at a distance from sound source face, i.e., reconstruction spherical radius is (r0-0.5a)；Rebuild Grid
Point is 37 × 37, i.e., each reconstruction point is with Δ θ=5 °, Δ φ=10 ° equidistantly distributed；Equivalent source is equidistantly evenly arranged in battle array
Column center be the centre of sphere spherical surface on, and its spherical radius be r0+ 0.01m, equivalent source number are 21 × 21.Detailed process are as follows:
1, the point sound source with designated volume speed specific frequency sound wave is assumed in specific position；
2, each microphone reception sound pressure signal is calculated according to formula (6) is positive, here, with the ∞ in 50 substituteds (6)；
3, truncation length is determined according to formula (10)；
4, sound source face is rebuild in setting, and the present invention is to rebuild sound field based on iteration weighting method and be imaged；SDI is under being based on quickly
It drops alternative manner and rebuilds sound field.
Fig. 3 is that three sound sources are located at (r0,90°,90°),(r0, 90 °, 180 °) and (r0, 90 °, 270 °) position when,
Sound field rebuilding knot when measurement distance is 1.5a, 2a, 2.5a, 3a, 3.5a, 4a, 4.5a and 5a and frequency is 200-6000Hz
Fruit relative error RE cloud atlas (pthSound pressure level is discussed to rebuild foliation；preFor weight corresponding on reconstruction face
Build sound pressure level).Fig. 3 (a) is SDI；Fig. 3 (b) is the present invention.
As can be seen from Figure 3, when the present invention is 4000-4500Hz and measures distance greater than 3a in addition to frequency, reconstruction error is abnormal
Increase, far surpasses except 50%, it is higher apart from interior reconstruction precision in entire measurement when frequency is in 4000Hz or less, it rebuilds
Error is lower than 20%.Especially middle low frequency and big measurement apart from when, reconstruction performance is preferable, is effectively improved SDI and rebuilds at this moment
The defect of performance difference；And when SDI can obtain preferable reconstruction precision, reconstructed results of the invention are also preferable.In conclusion this hair
Bright performance is significantly better than SDI.
Verification experimental verification
For the correctness for examining emulation conclusion, verification test is carried out in semianechoic room.
Fig. 4 is test layout, using the loudspeaker of steady-state signal excitation as sound source, using Br ü el&Kjaer company, half
Diameter is 0.0975m, the solid ball array in 36 channels of integrated 4958 type microphones samples sound pressure signal.When measurement, array is each transaudient
The received voice signal of device acquires simultaneously through PULSE 3560D type data collection system and is transferred to PULSE LabShop software
Acoustic pressure cross-spectrum is obtained, sound field rebuilding and identification of sound source are further carried out using the algorithm routine that MATLAB writes.Time domain data note
The record time is 5s, and analysis frequency band is 6.4kHz, sample frequency 16384Hz.Array center surveys with a distance from the measurement of loudspeaker
Span is from r0For 3a, rebuilding distance between spherical surface and sound source face is 0.5a.Test uses three different locations and varying strength
Loudspeaker.
Fig. 5 be SDI and sound field rebuilding of the present invention when frequency is followed successively by 200Hz, 1000Hz, 3000Hz and 6000Hz and
Identification of sound source is as a result, SDI corresponding diagram 5 (a)-(d)；Corresponding diagram 5 (e)-(h) of the present invention.
As can be seen from Figure 5: the present invention can accurately identify in entire frequency range and localization of sound source, reconstructed results can be effective
Reflect that realistic acoustic field is rebuild, especially in 200Hz, resolution ratio is higher.Correspondingly, in 200Hz, SDI rebuilds cloud atlas
Middle sound source merges into each other and resolution ratio is lower.
It tests consistent with simulation result, it was demonstrated that the reliability of simulation result and the practicability of present method invention.
Claims (1)
1. a kind of comprehensive equivalent source identification of sound source method based on solid ball array, comprising the following steps:
Step 1, the total acoustic pressure of radiation fields for obtaining medicine ball array measurement
If medicine ball array center is coordinate origin, any position can be described with r=(r, θ, φ) in three-dimensional space, and r is indicated
Any observation point of three-dimensional space is at a distance from origin, and θ and φ are respectively the elevation angle and azimuth, and remember Ω ≡ (θ, φ), medicine ball
The total acoustic pressure expression formula of the radiation fields of any point at array surface (a, Ω) are as follows:
In formula, a is array radius；C is the velocity of sound, and ρ is density, and Q is volume velocity, and k is wave number, and n and m are respectively spheric harmonic function
Secondary and rank, r0=(r0,Ω0) be point sound source position, hn() indicates first kind ball Hankel function, hn' () is hn(·)
Derivative,For spheric harmonic function, ()*Indicate complex conjugate；
The total acoustic pressure of measurement radiation fields of ball array surface microphone is write as matrix form:
pt=GNq
In formula, ptFor the rank ball array surface microphone acoustic pressure column vector of L × 1, q is the rank of S × 1 equivalent source intensity column vector, each element
Correspond respectively to j ω ρ Qs, ω expression angular frequency；L is the microphone number of medicine ball array surface, and S is the monopole of equivalent source spherical surface
Sub- point sound source number；GNL × S rank Nuo Yiman Green's function matrix between microphone and equivalent source,R in formulae=(re,Ωe) indicate equivalent source position, r tri-
Any observation point of dimension space is at a distance from origin；
It is characterized in that:
Step 2 calculates equivalent source strength based on iteration weighting algorithm；
The solution of the matrix form of step 1 are as follows:
In formula, W is weighting matrix, is the invertible matrix of diagonal element non-zero；λ is regularization parameter, | | | |2For
l2Norm；
Initialization
In formula, re,sIndicate s-th of equivalent source at a distance from coordinate origin, s=1,2 ... S
Seek the iterative process of equivalent source strength q are as follows:
Step (1) calculates weighting matrix W(i): W(i)=W0Wi,
Step (2) calculates new transfer matrix
It is step (3), rightCarry out singular value decomposition:
Step (4) calculates
Step (5) calculates equivalent source strength q(i):
Step (6) judges termination condition: τ=10log (| | q(i)||2/||q(i+1)||2)≤0.1dB
By the q of step (5)(i)It substitutes into step (1) and acquires Wi+1Into recycling next time, iteration is until step (6) repeatedly
When termination condition meets, equivalent source strength q is obtained；
Step 3 rebuilds any position acoustic pressure
The expression formula of acoustic pressure is rebuild in three-dimensional sound field are as follows:
pr=Grq
In formula, prTo rebuild spherical surface incident sound pressure, GrFor equivalent source and rebuild spherical surface rrLocate free field Green's letter between reconstruction point
Number, expression formula are as follows:
In formula, jn() indicates first kind spheric Bessel function, rr=(rr,Ωr) indicate reconstructed positions, Ωe,sIndicate s-th etc.
Direction at effect source.
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| CN113311389A (en) * | 2020-02-27 | 2021-08-27 | 三菱重工业株式会社 | Sound source detection system, sound source detection method thereof, and sound source detection program |
| CN115278449A (en) * | 2022-09-26 | 2022-11-01 | 中国飞行试验研究院 | Method, device and equipment for determining coordinates of microphone array unit and storage medium |
| CN115278449B (en) * | 2022-09-26 | 2023-03-10 | 中国飞行试验研究院 | Method, device and equipment for determining coordinates of microphone array unit and storage medium |
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