CN111664932A - Sound source identification method based on Bayesian compressed sensing - Google Patents

Sound source identification method based on Bayesian compressed sensing Download PDF

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CN111664932A
CN111664932A CN202010439202.1A CN202010439202A CN111664932A CN 111664932 A CN111664932 A CN 111664932A CN 202010439202 A CN202010439202 A CN 202010439202A CN 111664932 A CN111664932 A CN 111664932A
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昝鸣
徐中明
张志飞
贺岩松
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Chongqing University
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Abstract

The invention discloses a sound source identification method based on Bayesian compressed sensing, which mainly comprises the following steps: 1) building a sound source identification system based on Bayesian compressed sensing; 2) each microphone respectively monitors time domain analog sound pressure signals of N equivalent sound sources; 3) the multichannel data acquisition unit converts the received time domain analog sound pressure signal into a digital sound pressure signal p; 4) acquiring a transfer matrix A between a sound source and a microphone array sensor; 5) establishing a prior probability distribution function model of a digital sound pressure signal p and a sound source q to be identified; 6) establishing a posterior probability distribution function model of a sound source q to be identified; 7) updating the hyper-parameters of the sound source q to be identified; 8) and the data processor performs iterative calculation on the hyper-parameters of the sound source q to be identified by using a parameter updating formula to obtain an identification result of the sound source q to be identified. The invention effectively overcomes the defect of narrow applicable frequency range of TRESM and WBH methods, and widens the frequency range of sound source identification.

Description

Sound source identification method based on Bayesian compressed sensing
Technical Field
The invention relates to the field of sound source identification, in particular to a sound source identification method based on Bayesian compressed sensing.
Background
The acoustic holography and beam forming technology is two noise source identification methods based on the acoustic array, and has the advantages of high measurement speed, high acoustic imaging efficiency, capability of measuring a moving sound source and the like. The sound field visualization can be realized, and the sound source identification and positioning can be conveniently and intuitively carried out. The acoustic holography technology is a sound source identification method which is rapidly developed in recent years, and the basic principle is that sound pressure data is recorded on a close-distance measuring surface on the surface of a measured sound source object, then a space sound field is reconstructed through a space sound field transformation algorithm, and acoustic quantity of sound transmitted in a three-dimensional space is reconstructed through measuring sound pressure on a measuring surface which is very close to a sound source. Acoustic holography establishes a direct correlation between vibration, acoustic radiation and acoustic energy flow in the surrounding medium. The method has the advantages of flexible dynamic display range, high resolution and the like, so that the method is widely concerned by researchers and practitioners in recent years, the application range of the method is gradually developed and transited from the field of aviation and navigation to the field of automobiles, and meanwhile, various different near-field acoustic holography algorithms, such as statistical optimal near-field acoustic holography and equivalent source method near-field acoustic holography, are derived, and the application range and the field of the method are continuously expanded.
In the prior art, there are two typical equivalent source method near-field acoustic holography methods based on a microphone array, which are a near-field acoustic holography method TRESM based on a Tikhonov regularization method and a broadband near-field acoustic holography WBH. The core idea is to construct a series of imaginary equivalent sources on equivalent source planes close to the sound source plane, and to replace the actual sound source distribution by these equivalent sources. The method comprises the steps of establishing an acoustic transfer equation from an equivalent source surface to a microphone array through a sound source identification theory, solving the transfer equation through a solving algorithm aiming at an inverse problem so as to obtain equivalent source intensity, and reconstructing sound source distribution between the equivalent source surface and the array surface through the equivalent source intensity and based on a sound propagation process. The TRESM method is based on2The norm minimization solving method has poor high-frequency precision. In the WBH method, an iterative filtering process is introduced in the equivalent source solving process, so that the number of equivalent sources is reduced, the sparsity of the equivalent sources is increased, and the convergence efficiency and accuracy of the iterative process are ensured. Due to the introduction of a gradient descent algorithm and a filtering process, the resolution of the traditional equivalent source method in medium-high frequency can be improved. However, the device is not suitable for use in a kitchenHowever, the algorithm has the defects that the reconstruction performance is unstable in a low-frequency range and large errors exist.
Disclosure of Invention
The present invention is directed to solving the problems of the prior art.
The technical scheme adopted for achieving the aim of the invention is that the sound source identification method based on the Bayesian compressed sensing comprises the following steps:
1) a sound source identification system based on Bayesian compressed sensing is built and comprises a microphone array sensor, a multi-channel data acquisition device and a data processor. The microphone array sensor includes M microphones distributed in a sound source detection space.
2) And each microphone respectively monitors time domain analog sound pressure signals of N equivalent sound sources and simultaneously sends the time domain analog sound pressure signals to a multi-channel data acquisition unit. The N equivalent sound sources are distributed around the sound source.
3) And the multi-channel data acquisition unit converts the received time-domain analog sound pressure signal into a digital sound pressure signal p and sends the digital sound pressure signal p to the data processor.
4) The data processor establishes a sound source identification model and obtains a transfer matrix A between a sound source and a microphone array sensor.
Further, the main steps of establishing a transfer matrix a between the sound source and the microphone array sensors are as follows:
4.1) determining the sound pressure signal p (m) measured by the mth microphone as follows:
Figure BDA0002503447240000021
wherein M is 1,2, …, M.
Figure BDA0002503447240000022
Is a free field green function. k is the number of waves,
Figure BDA0002503447240000023
is the distance of the equivalent source to the measurement face. q. q.snIs the virtual equivalent source sound source intensity. n isAny virtual equivalent source. And N is the number of virtual equivalent sources.
4.2) expressing equation (1) in the form of a vector matrix, i.e.:
p＝Aq。 (2)
in the formula, A is an M multiplied by N dimension sound field transfer matrix. p is an M-dimensional sound pressure vector whose elements are the sound pressure signals of the corresponding sensors. q is an N-dimensional sound source intensity column vector whose element components represent the intensities at corresponding points in the equivalent sound source.
5) And the data processor establishes a prior probability distribution function model of the digital sound pressure signal p and the sound source q to be identified by using a Bayesian algorithm.
The prior probability distribution function model of the sound pressure vector p is as follows:
Figure BDA0002503447240000024
Figure BDA0002503447240000025
in the formula (I), the compound is shown in the specification,
Figure BDA0002503447240000026
is a probability distribution function.
Figure BDA0002503447240000027
Is a gaussian distribution function. s0Is a probability distribution function
Figure BDA0002503447240000028
Is a gamma distribution function α, β are prior parameter values of a prior probability distribution of the sound pressure vector p.
The prior probability distribution function model of the sound source q to be identified is as follows:
Figure BDA0002503447240000031
Figure BDA0002503447240000032
Figure BDA0002503447240000033
in the formula (I), the compound is shown in the specification,
Figure BDA0002503447240000034
a probability distribution function is expressed.
Figure BDA0002503447240000035
Is a gaussian distribution function. siIs a probability distribution function
Figure BDA0002503447240000036
The gaussian variance of (c). And lambda and theta are prior parameter values of prior probability distribution of the sound source q to be identified. i is an arbitrary gaussian distribution; and N is the number of Gaussian distributions.
6) Based on the prior probability distribution function model of the digital sound pressure signal p and the sound source q to be recognized, the data processor establishes a posterior probability distribution function model of the sound source q to be recognized by utilizing a Bayesian algorithm.
The posterior probability distribution function model of the sound source q to be recognized is as follows:
Figure BDA0002503447240000037
wherein the probability distribution function
Figure BDA0002503447240000038
As follows:
Figure BDA0002503447240000039
where μ is the mean equivalent source distribution. Σ is the equivalent source distribution variance.
The equivalent source distribution mean μ and the equivalent source distribution variance Σ are as follows:
Figure BDA00025034472400000310
Figure BDA00025034472400000311
7) and based on the posterior probability distribution function model of the sound source q to be recognized, the data processor updates the hyper-parameters of the sound source q to be recognized. The hyper-parameter comprises a Gaussian variance siGaussian variance s0Prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma, and superparameter giAnd a hyperparameter fi。
The data processor updates the hyper-parameters of the sound source q to be identified, and the main steps are as follows:
7.1) establishing a probability distribution function
Figure BDA00025034472400000312
And
Figure BDA00025034472400000313
the direct ratio of (a) to (b), namely:
Figure BDA00025034472400000314
7.2) establishing a likelihood function that will:
Figure BDA00025034472400000315
where matrix C is decomposed as follows:
Figure BDA00025034472400000316
in the formula, ajIs the jth row vector of the matrix A; i is an identity matrix;
7.3) substituting equation (14) into the likelihood function (13) and taking the logarithm yields:
Figure BDA0002503447240000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002503447240000042
representing a likelihood function.
Wherein, the hyperparameter fiG, over-parameter giRespectively as follows:
Figure BDA0002503447240000043
Figure BDA0002503447240000044
in the formula, aiIs the ith row vector of matrix a.
7.4) the Gaussian variance s based on equation (15)iGaussian variance s0And the prior parameter lambda is updated, namely:
Figure BDA0002503447240000045
Figure BDA0002503447240000046
Figure BDA0002503447240000047
8) and the data processor performs iterative calculation on the hyper-parameters of the sound source q to be identified by using a parameter updating formula to obtain an identification result of the sound source q to be identified.
The main steps of iterative calculation solution by using an updated formula are as follows:
8.1) parameter initialization, i.e. let the Gaussian variance s00.1var (p), 0 in the matrix S, and 0 in the prior parameter λ. Setting maximum iteration times T and iteration threshold valuemax。
8.2) selecting basis vectors a in matrix AiThe selection mode is as follows:
I) if it is
Figure BDA0002503447240000048
And siIf > 0, the basis vector aiExist, and update the Gaussian variance si。
II) if
Figure BDA0002503447240000049
And siIf 0, the base vector a is added to the matrix aiAnd updating the Gaussian variance si。
III) if
Figure BDA00025034472400000410
The base vector a is deletediAnd let the Gaussian variance si＝0。
8.3) updating prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma and super parameter giAnd a hyperparameter fi。
8.4) if the number of iterations reaches the maximum number of iterations T or the likelihood function
Figure BDA00025034472400000411
Is less than the iteration thresholdmaxThe iteration terminates and step 8.5 is entered. Otherwise, return to step 8.2.
8.5) taking the equivalent source distribution mean value mu as the recognition result of the sound source q to be recognized to obtain an equivalent source intensity vector.
The technical effect of the invention is remarkable. The invention provides a sound source identification method LPBCS with high sound source reconstruction precision, good stability and small error. According to the invention, a transfer matrix is constructed based on a sound source and a microphone array sensor, then the transfer matrix is converted into a Bayes compressed sensing problem, and finally an equivalent source intensity vector is solved through a Bayes sparse prior iterative algorithm. The algorithm applies the sound source sparse prior characteristic, effectively overcomes the defect of narrow applicable frequency range of the TRESM and WBH methods, and widens the frequency range of sound source identification.
Drawings
FIG. 1 is a schematic view of sound source reconstruction;
FIG. 2 is a theoretical sound source reconstruction diagram;
FIG. 3 is a reconstructed image of a conventional TRESM method;
FIG. 4 is a WBH method reconstruction diagram;
FIG. 5 is a reconstructed diagram of an LPBCS method based on Bayesian compressed sensing sound source identification;
fig. 6 is a reconstruction error graph.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1 to 6, a sound source identification method based on bayesian compressed sensing includes the following steps:
1) a sound source identification system based on Bayesian compressed sensing is built and comprises a microphone array sensor, a multi-channel data acquisition device and a data processor. The microphone array sensor includes M microphones distributed in a sound source detection space.
2) And each microphone respectively monitors time domain analog sound pressure signals of N equivalent sound sources and simultaneously sends the time domain analog sound pressure signals to a multi-channel data acquisition unit. The N equivalent sound sources are distributed around the sound source.
3) And the multi-channel data acquisition unit converts the received time-domain analog sound pressure signal into a digital sound pressure signal p and sends the digital sound pressure signal p to the data processor.
4) The data processor establishes a sound source identification model and obtains a transfer matrix A between a sound source and a microphone array sensor.
The main steps of establishing a transfer matrix a between a sound source and a microphone array sensor are as follows:
4.1) determining the sound pressure signal p (m) measured by the mth microphone as follows:
Figure BDA0002503447240000061
wherein M is 1,2, …, M.
Figure BDA0002503447240000062
Is a free field green function. k is the number of waves,
Figure BDA0002503447240000063
is the distance of the equivalent source to the measurement face. q. q.snIs the virtual equivalent source sound source intensity. n is any virtual equivalent source; n' is the number of virtual equivalent sources;
4.2) expressing equation (1) in the form of a vector matrix, i.e.:
p＝Aq。 (2)
in the formula, A is an M multiplied by N' dimension sound field transfer matrix. p is an M-dimensional sound pressure vector, and the element of the M-dimensional sound pressure vector is a single beat signal (i.e., beat frequency sound pressure signal) of the corresponding sensor. q is an N' dimensional sound source intensity column vector whose element components represent the intensities at corresponding points in the equivalent sound source.
5) And the data processor establishes a prior probability distribution function model of the digital sound pressure signal p and the sound source q to be identified by using a Bayesian algorithm.
The prior probability distribution function model of the sound pressure vector p is as follows:
Figure BDA0002503447240000064
Figure BDA0002503447240000065
in the formula (I), the compound is shown in the specification,
Figure BDA0002503447240000066
is a probability distribution function.
Figure BDA0002503447240000067
Is a gaussian distribution function. s0Is a probability distribution function
Figure BDA0002503447240000068
Is a gamma distribution function α, β are prior parameter values of a prior probability distribution of the sound pressure vector p.
The prior probability distribution function model of the sound source q to be identified is as follows:
Figure BDA0002503447240000069
Figure BDA00025034472400000610
Figure BDA00025034472400000611
in the formula (I), the compound is shown in the specification,
Figure BDA00025034472400000612
a probability distribution function is expressed.
Figure BDA00025034472400000613
Is a gaussian distribution function. siIs a probability distribution function
Figure BDA00025034472400000614
The gaussian variance of (c). And lambda and theta are prior parameter values of prior probability distribution of the sound source q to be identified.
6) Based on the prior probability distribution function model of the digital sound pressure signal p and the sound source q to be recognized, the data processor establishes a posterior probability distribution function model of the sound source q to be recognized by utilizing a Bayesian algorithm.
The posterior probability distribution function model of the sound source q to be recognized is as follows:
Figure BDA00025034472400000615
wherein the probability distribution function
Figure BDA00025034472400000616
As follows:
Figure BDA0002503447240000071
where μ is the mean equivalent source distribution. Σ is the equivalent source distribution variance.
The equivalent source distribution mean μ and the equivalent source distribution variance Σ are as follows:
Figure BDA0002503447240000072
Figure BDA0002503447240000073
7) and based on the posterior probability distribution function model of the sound source q to be recognized, the data processor updates the hyper-parameters of the sound source q to be recognized. The hyper-parameter comprises a Gaussian variance siGaussian variance s0Prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma, and superparameter giAnd a hyperparameter fi。
The data processor updates the hyper-parameters of the sound source q to be identified, and the main steps are as follows:
7.1) establishing a probability distribution function
Figure BDA0002503447240000074
And
Figure BDA0002503447240000075
the direct ratio of (a) to (b), namely:
Figure BDA0002503447240000076
7.2) establishing a likelihood function that will:
Figure BDA0002503447240000077
where matrix C is decomposed as follows:
Figure BDA0002503447240000078
in the formula, ajIs the jth row vector of the matrix A; i is an identity matrix;
7.3) substituting equation (14) into the likelihood function (13) and taking the logarithm yields:
Figure BDA0002503447240000079
in the formula (I), the compound is shown in the specification,
Figure BDA00025034472400000710
representing a likelihood function.
Wherein, the hyperparameter fiG, over-parameter giRespectively as follows:
Figure BDA00025034472400000711
Figure BDA00025034472400000712
in the formula, aiIs the ith row vector of matrix a.
7.4) the Gaussian variance s based on equation (15)iGaussian variance s0And the prior parameter lambda is updated, namely:
Figure BDA0002503447240000081
Figure BDA0002503447240000082
Figure BDA0002503447240000083
8) and the data processor performs iterative calculation on the hyper-parameters of the sound source q to be identified by using a parameter updating formula to obtain an identification result of the sound source q to be identified.
The main steps of iterative calculation solution by using an updated formula are as follows:
8.1) parameter initialization, i.e. let the Gaussian variance s00.1var (p), 0 in the matrix S, and 0 in the prior parameter λ. Setting maximum iteration times T and iteration threshold valuemax. var represents the variance.
8.2) selecting basis vectors a in matrix AiThe selection mode is as follows:
I) if it is
Figure BDA0002503447240000084
And siIf > 0, the basis vector aiExist, and update the Gaussian variance si。
II) if
Figure BDA0002503447240000085
And siIf 0, the base vector a is added to the matrix aiAnd updating the Gaussian variance si。
III) if
Figure BDA0002503447240000086
The base vector a is deletediAnd let the Gaussian variance si＝0。
8.3) updating prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma and super parameter giAnd a hyperparameter fi。
8.4) if the number of iterations reaches the maximum number of iterations T or the likelihood function
Figure BDA0002503447240000087
Is less than the iteration thresholdmaxThe iteration terminates and step 8.5 is entered. Otherwise, return to step 8.2.
8.5) taking the equivalent source distribution mean value mu as the recognition result of the sound source q to be recognized to obtain an equivalent source intensity vector.
Example 2:
a sound source identification method based on Bayesian compressed sensing comprises the following steps:
1) a sound source identification system based on Bayesian compressed sensing is built and comprises a microphone array sensor, a multi-channel data acquisition device and a data processor. The microphone array sensor includes M microphones distributed in a sound source detection space.
2) And each microphone respectively monitors time domain analog sound pressure signals of N equivalent sound sources and simultaneously sends the time domain analog sound pressure signals to a multi-channel data acquisition unit. The N equivalent sound sources are distributed around the sound source.
3) And the multi-channel data acquisition unit converts the received time-domain analog sound pressure signal into a digital sound pressure signal p and sends the digital sound pressure signal p to the data processor.
4) The data processor establishes a sound source identification model and obtains a transfer matrix A between a sound source and a microphone array sensor.
5) And the data processor establishes a prior probability distribution function model of the digital sound pressure signal p and the sound source q to be identified by using a Bayesian algorithm.
6) Based on the prior probability distribution function model of the digital sound pressure signal p and the sound source q to be recognized, the data processor establishes a posterior probability distribution function model of the sound source q to be recognized by utilizing a Bayesian algorithm.
7) And based on the posterior probability distribution function model of the sound source q to be recognized, the data processor updates the hyper-parameters of the sound source q to be recognized. The hyper-parameter comprises a Gaussian variance siGaussian variance s0Prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma, and superparameter giAnd a hyperparameter fi。
8) And the data processor performs iterative calculation on the hyper-parameters of the sound source q to be identified by using a parameter updating formula to obtain an identification result of the sound source q to be identified.
Example 3:
a method for recognizing a sound source based on Bayesian compressed sensing mainly comprises the following steps of embodiment 2, wherein a transfer matrix A between the sound source and a microphone array sensor is established by the following steps:
1) determining the sound pressure signal p (m) measured by the mth microphone as follows:
Figure BDA0002503447240000091
wherein M is 1,2, …, M.
Figure BDA0002503447240000092
Is a free field green function. k is the number of waves,
Figure BDA0002503447240000093
is the distance of the equivalent source to the measurement face. q. q.snIs the virtual equivalent source sound source intensity.
2) Expression of equation (1) in the form of a vector matrix, namely:
p＝Aq。 (2)
in the formula, A is an M multiplied by N dimension sound field transfer matrix. p is an M-dimensional sound pressure vector, the elements of which are the single beat signals of the corresponding sensor. q is an N-dimensional sound source intensity column vector whose element components represent the intensities at corresponding points in the equivalent sound source.
Example 4:
a sound source identification method based on Bayesian compressed sensing mainly comprises the following steps of embodiment 2, wherein a prior probability distribution function model of a sound pressure vector p is as follows:
Figure BDA0002503447240000094
Figure BDA0002503447240000095
in the formula (I), the compound is shown in the specification,
Figure BDA0002503447240000096
is a probability distribution function.
Figure BDA0002503447240000097
Is a gaussian distribution function. s0Is a probability distribution function
Figure BDA0002503447240000098
Is a gamma distribution function α, β are prior parameter values of a prior probability distribution of the sound pressure vector p.
The prior probability distribution function model of the sound source q to be identified is as follows:
Figure BDA0002503447240000101
Figure BDA0002503447240000102
Figure BDA0002503447240000103
in the formula (I), the compound is shown in the specification,
Figure BDA0002503447240000104
a probability distribution function is expressed.
Figure BDA0002503447240000105
Is a gaussian distribution function. siIs a probability distribution function
Figure BDA0002503447240000106
The gaussian variance of (c). And lambda and theta are prior parameter values of prior probability distribution of the sound source q to be identified.
The posterior probability distribution function model of the sound source q to be recognized is as follows:
Figure BDA0002503447240000107
wherein the probability distribution function
Figure BDA0002503447240000108
As follows:
Figure BDA0002503447240000109
where μ is the equivalent source distribution mean μ. Σ is the equivalent source distribution variance.
The equivalent source distribution mean μ and the equivalent source distribution variance Σ are as follows:
Figure BDA00025034472400001010
Figure BDA00025034472400001011
example 5:
a sound source identification method based on Bayesian compressed sensing mainly comprises the following steps of embodiment 2, wherein a data processor updates hyper-parameters of a sound source q to be identified as follows:
1) establishing a probability distribution function
Figure BDA00025034472400001012
And
Figure BDA00025034472400001013
the direct ratio of (a) to (b), namely:
Figure BDA00025034472400001014
2) establishing a likelihood function that will:
Figure BDA00025034472400001015
where matrix C is decomposed as follows:
Figure BDA00025034472400001016
3) substituting equation (14) into the likelihood function (2) and taking the logarithm yields:
Figure BDA00025034472400001017
in the formula (I), the compound is shown in the specification,
Figure BDA0002503447240000111
representing a likelihood function.
Wherein, the hyperparameter fiG, over-parameter giRespectively as follows:
Figure BDA0002503447240000112
Figure BDA0002503447240000113
in the formula, aiIs the ith row vector of matrix a.
4) Based on equation (15) to the Gaussian variance siGaussian variance s0And the prior parameter lambda is updated, namely:
Figure BDA0002503447240000114
Figure BDA0002503447240000115
Figure BDA0002503447240000116
example 6:
a sound source identification method based on Bayesian compressed sensing mainly comprises the following steps of embodiment 2, wherein the updating formula is used for iterative calculation and solving the following steps:
1) parameter initialisation, i.e. ordering the Gaussian variance s00.1var (p), 0 in the matrix S, and 0 in the prior parameter λ. Setting maximum iteration times T and iteration threshold valuemax。
2) Selecting a basis vector a in matrix AiThe selection mode is as follows:
I) if it is
Figure BDA0002503447240000117
And siIf > 0, the basis vector aiExist, and update the Gaussian variance si。
II) if
Figure BDA0002503447240000118
And siIf 0, the base vector a is added to the matrix aiAnd updating the Gaussian variance si。
III) if
Figure BDA0002503447240000119
The base vector a is deletediAnd let the Gaussian variance si＝0。
3) Updating prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma and super parameter giAnd a hyperparameter fi。
4) If the iteration number reaches the maximum iteration number T or the likelihood function
Figure BDA00025034472400001110
Is less than the iteration thresholdmaxThe iteration terminates and step 5 is entered. Otherwise, returning to the step 2.
5) And taking the equivalent source distribution mean value mu as an identification result of the sound source q to be identified to obtain an equivalent source intensity vector.
Example 7:
a sound source identification system based on Bayesian compressed sensing comprises a microphone array sensor, a multi-channel data acquisition unit and a data processor.
The microphone array sensor includes a sound pressure sensor, a microphone stand, and an associated wiring harness. In a microphone array sensor, the distribution of the microphones may be a regularized or pseudo-random spatial distribution of different dimensions, selected according to the actual measurement requirements. The choice of the number of sensors and the choice of the microphone spacing and the size of the array are determined according to the frequency range to be measured.
The multi-channel data acquisition unit is used for measuring time domain analog signals, converting the time domain analog signals into digital signals and transmitting the digital signals to a computer for post-processing. It should include a multi-channel preamplifier and a multi-channel analog/digital converter with high accuracy, and even associated filters, to ensure that the digital signal output to the computer is sufficiently accurate.
The computer mainly has the main functions of storing and post-processing the collected sound field signals and can efficiently display the distribution condition of the reconstructed sound field.
Example 8:
an experiment for verifying a Bayesian compressed sensing-based sound source identification method comprises the following steps:
1) referring to fig. 3 to 5, a comparison method is set:
m1: the LBBCS method, i.e. the sound source identification method based on bayesian compressed sensing (i.e. the method disclosed in embodiment 1).
M2: WBH method, broadband acoustic holography method.
M3: the TRESM method, i.e. the sound source identification method based on wave superposition and Tikhonov regularization.
2) Sound sources are identified by methods M1, M2 and M3 respectively.
Referring to fig. 6, the M2 and M3 method errors are advantageous at low and high frequencies, respectively, when the sound source is within the band shown. The M3 method is proved to have better recognition effect under the low-frequency effect than the M2 method, and the M2 method is proved to have better recognition effect under the high-frequency effect than the M3 method. The M1 method errors are all minimal.
When the sound source frequency is 800Hz, the theoretical values show that there are two sound sources (-0.2,0,0) and (0.2,0,0), respectively, neither the M2 method nor the M3 method can effectively identify the two sound sources, but the M1 method effectively identifies the two sound sources. Therefore, the M1 method proves to have a better sound source recognition effect than the M2 method and the M3 method.

Claims (7)

1. A sound source identification method based on Bayesian compressed sensing is characterized by comprising the following steps:
1) building a sound source identification system based on Bayesian compressed sensing, wherein the sound source identification system comprises a microphone array sensor, a multi-channel data acquisition device and a data processor; the microphone array sensor comprises M microphones distributed in a sound source detection space;
2) each microphone respectively monitors time domain analog sound pressure signals of N equivalent sound sources and simultaneously sends the time domain analog sound pressure signals to a multi-channel data acquisition unit; the N equivalent sound sources are distributed around the sound source;
3) the multichannel data acquisition unit converts the received time domain analog sound pressure signal into a digital sound pressure signal p and sends the digital sound pressure signal p to the data processor;
4) the data processor establishes a sound source identification model and obtains a transfer matrix A between a sound source and a microphone array sensor.
5) The data processor establishes a prior probability distribution function model of the digital sound pressure signal p and the sound source q to be identified by using a Bayesian algorithm;
6) based on the prior probability distribution function model of the digital sound pressure signal p and the sound source q to be recognized, the data processor establishes a posterior probability distribution function model of the sound source q to be recognized by utilizing a Bayesian algorithm;
7) based on a posterior probability distribution function model of the sound source q to be recognized, the data processor updates the hyper-parameters of the sound source q to be recognized; the hyper-parameter comprises a Gaussian variance siGaussian variance s0Prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma, and superparameter giAnd a hyperparameter fi；
8) And the data processor performs iterative calculation on the hyper-parameters of the sound source q to be identified by using a parameter updating formula to obtain an identification result of the sound source q to be identified.
2. A sound source identification method based on bayesian compressed sensing according to claim 1 or 2, wherein the main steps of establishing the transfer matrix a between the sound source and the microphone array sensor are as follows:
1) determining the sound pressure signal p (m) measured by the mth microphone as follows:
Figure FDA0002503447230000011
wherein M is 1,2, …, M;
Figure FDA0002503447230000012
is a free field Green function; k is the number of waves,
Figure FDA0002503447230000013
the distance from the equivalent source to the measuring surface; q. q.snThe virtual equivalent source sound source intensity; n is any virtual equivalent source; n is the number of virtual equivalent sources;
2) expression of equation (1) in the form of a vector matrix, namely:
p＝Aq； (2)
in the formula, A is an MxN dimensional sound field transfer matrix; p is an M-dimensional sound pressure vector, and the element of the M-dimensional sound pressure vector is a sound pressure signal of the corresponding sensor; q is an N-dimensional sound source intensity column vector whose element components represent the intensities at corresponding points in the equivalent sound source.
3. The method for recognizing the sound source based on the Bayesian compressed sensing as recited in claim 1, wherein a prior probability distribution function model of the sound pressure vector p is as follows:
Figure FDA0002503447230000021
Figure FDA0002503447230000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002503447230000023
is a probability distribution function;
Figure FDA0002503447230000024
is a Gaussian distribution function; s0Is a probability distribution function
Figure FDA0002503447230000025
Is a gamma distribution function, α, β are prior parameter values of a prior probability distribution of the sound pressure vector p.
4. The Bayesian compressed sensing-based sound source identification method according to claim 1, wherein a prior probability distribution function model of a sound source q to be identified is as follows:
Figure FDA0002503447230000026
Figure FDA0002503447230000027
Figure FDA0002503447230000028
in the formula (I), the compound is shown in the specification,
Figure FDA0002503447230000029
expressing a probability distribution function;
Figure FDA00025034472300000210
is a Gaussian distribution function; siIs a probability distribution function
Figure FDA00025034472300000211
(ii) a gaussian variance of; lambda and theta are prior parameter values of prior probability distribution of a sound source q to be identified; i is an arbitrary gaussian distribution; and N is the number of Gaussian distributions.
5. The sound source identification method based on Bayesian compressed sensing as recited in claim 1, wherein a posterior probability distribution function model of a sound source q to be identified is as follows:
Figure FDA00025034472300000212
wherein the probability distribution function
Figure FDA00025034472300000213
As follows:
Figure FDA00025034472300000214
in the formula, mu is an equivalent source distribution mean value; Σ is the equivalent source distribution variance;
the equivalent source distribution mean μ and the equivalent source distribution variance Σ are as follows:
Figure FDA00025034472300000215
Figure FDA00025034472300000216
wherein S is a Gaussian variance matrix.
6. The method for recognizing the sound source based on the bayesian compressed sensing as recited in claim 1, wherein the data processor updates the hyper-parameters of the sound source q to be recognized by the following steps:
1) establishing a probability distribution function
Figure FDA0002503447230000031
And
Figure FDA0002503447230000032
the direct ratio of (a) to (b), namely:
Figure FDA0002503447230000033
2) establishing a likelihood function that will:
Figure FDA0002503447230000034
where matrix C is decomposed as follows:
Figure FDA0002503447230000035
in the formula, ajIs the jth row vector of the matrix A; i is an identity matrix;
3) substituting the likelihood function (13) with equation (14) and taking the logarithm yields:
Figure FDA0002503447230000036
in the formula (I), the compound is shown in the specification,
Figure FDA0002503447230000037
representing a likelihood function;
wherein, the hyperparameter fiG, over-parameter giRespectively as follows:
Figure FDA0002503447230000038
Figure FDA0002503447230000039
in the formula, aiIs the ith row vector of the matrix A;
4) based on equation (15) to the Gaussian variance siGaussian variance s0And the prior parameter lambda is updated, namely:
Figure FDA00025034472300000310
Figure FDA00025034472300000311
Figure FDA00025034472300000312
7. the Bayesian compressed sensing-based sound source identification method according to claim 1 or 6, wherein the iterative computation solution using the update formula comprises the following main steps:
1) parameter initialisation, i.e. ordering the Gaussian variance s00.1var (p), where S is 0 and λ is 0; setting maximum iteration times T and iteration threshold valuemax；
2) Selecting a basis vector a in matrix AiThe selection mode is as follows:
I) if it is
Figure FDA00025034472300000313
And siIf > 0, the basis vector aiExist, and update the Gaussian variance si；
II) if
Figure FDA0002503447230000041
And siIf 0, the base vector a is added to the matrix aiAnd updating the Gaussian variance si；
III) if
Figure FDA0002503447230000042
The base vector a is deletediAnd let the Gaussian variance si＝0；
3) Updating prior parameter lambda, equivalent source distribution mean mu, equivalent source distribution variance sigma and super parameter giAnd a hyperparameter fi；
4) If the iteration number reaches the maximum iteration number T or the likelihood function
Figure FDA0002503447230000043
Is less than the iteration thresholdmaxThe iteration is terminated, and step 5 is carried out; otherwise, returning to the step 2;
5) and taking the equivalent source distribution mean value mu as an identification result of the sound source q to be identified to obtain an equivalent source intensity vector.
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