CN110161459B - Rapid positioning method for amplitude modulation sound source - Google Patents
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Abstract
The invention discloses a method for quickly positioning an amplitude modulation sound source, which comprises the following steps: (1) sampling sound source radiation signals for T times by using a microphone array formed by Q microphones at a sampling frequency Fs to obtain sampling signals Yn E RQ×T(ii) a (2) Analyzing to obtain a modulation center frequency f to be positioned; (3)obtaining a propagation matrix E and a propagation matrix E obtained after normalization according to the sampling signal Yn and the modulation center frequency f1Obtaining a positioning result BF by using a conventional beam forming method; (4) expanding the positioning result BF into vector form Y according to rows, and according to the propagation matrix E and the normalized propagation matrix E1Obtaining a sensing matrix A; (5) and (4) according to the Y and the sensing matrix A, utilizing a fast reconstruction algorithm to invert the position of the sound source. The method and the device can get rid of the trouble of low computational efficiency of the convex optimization algorithm, give consideration to the positioning precision and the computational efficiency, and accurately and efficiently position the amplitude modulation signal.
Description
Technical Field
The invention belongs to the field of signal processing, and particularly relates to a method for quickly positioning an amplitude modulation sound source.
Background
Sound is a very important source of information for humans, and has irreplaceable effects in both daily life and industrial production. The sound source positioning technology utilizes a microphone array to collect target acoustic signals and inverts the position of sound according to the direction and distance of the collected signals, so that the positioning, identification, tracking and the like of a sound production component are further realized, and the sound source positioning technology has wide application in the fields of mobile communication, industrial monitoring systems, robots, fault identification, diagnosis and the like.
For sound source localization technology, under the condition of specifying a microphone array and a specific measurement environment, the precision of sound source localization mainly depends on a sound source localization inversion algorithm and a signal model of a target sound source.
For an inversion algorithm, related researchers research a plurality of sound source positioning algorithms based on the principle of beam forming, in recent years, the compressed sensing beam forming algorithm based on convex optimization is proposed by being inspired by compressed sensing sparse characteristics and combining sparse characteristics of a sound source with a sound source positioning beam forming technology, but the convex optimization toolkit is high in calculation complexity, the application situation of the compressed sensing beam forming algorithm is seriously hindered by calculation efficiency, and particularly under the condition that a scanning grid is large, the timeliness of the compressed sensing beam forming algorithm is severely limited.
For the signal model, in the actual process industry scenario, most machines belong to rotating and reciprocating machines, such as propellers, pumps, compressors, fans, etc., the aerodynamic noise radiated by such machines belongs to non-stationary signals, and the components thereof include not only axial frequency, blade frequency, integer frequency multiplication, fractional harmonic, complex modulation coupling relationship between various frequencies and between characteristic frequency and environmental noise, but also the modulation frequency can reflect some key information about the operating state of the rotating machine, so that it is necessary to locate the modulation sound source.
In summary, there is a need for a fast and efficient sound source localization method using sound source sparsity as prior information, which performs fast sound source localization on an amplitude modulation signal and improves the universality and timeliness of signal processing.
Disclosure of Invention
The invention provides a rapid positioning method of an amplitude modulation sound source, which can be used for efficiently and accurately positioning a certain frequency range of the amplitude modulation sound source and has strong practicability.
The technical scheme of the invention is as follows;
a method for fast localization of amplitude modulated sound sources, comprising:
(1) sampling sound source radiation signals for T times by using a microphone array formed by Q microphones at a sampling frequency Fs to obtain sampling signals Yn E RQ×T；
(2) Analyzing to obtain a modulation center frequency f to be positioned;
(3) obtaining a propagation matrix E from the sampling signal Yn and the modulation center frequency fAnd a propagation matrix E obtained after normalization1Obtaining a positioning result BF by using a conventional beam forming method;
(4) expanding the positioning result BF into vector form Y according to rows, and according to the propagation matrix E and the normalized propagation matrix E1Obtaining a sensing matrix A;
(5) and (4) according to the Y and the sensing matrix A, utilizing a fast reconstruction algorithm to invert the position of the sound source.
In the invention, the object for sound source localization is amplitude modulation signal, which is a model of non-stationary signal in real scene, and its mathematical model can be expressed as:
wherein alpha isiTo modulate the frequency, AiV (t) is the broadband carrier, typically ambient noise, a for the corresponding amplitude0cos(2πf0t) is a narrowband carrier, the left bracket is modulation information, and the right bracket is carrier information.
In the step (2), for the sound source of the amplitude modulation model, the modulation center frequency alpha is obtained through cyclostationary analysisiThis frequency is the center frequency f to be located.
In the step (3), the propagation matrix E is composed of propagation direction vectors, and the formula is expressed as:
wherein E ∈ RQ×NN is the resolution of the scan grid, E (m, N) represents the propagation response of the mth microphone to the nth grid, r represents the distance between the scanned grid and the array, f represents the modulation center frequency of the sound source location, c represents the sound velocity, and i is an imaginary unit.
The propagation matrix E is obtained after normalization of the propagation matrix E1The normalization process of the propagation matrix E is:
wherein E isiRepresents a certain column of the propagation matrix E, | | | | | | represents a 2-norm.
In the step (3), the process of obtaining the positioning result BF is as follows: obtaining a normalized covariance matrix R from the sampled signal YncovAnd according to the covariance matrix RcovAnd the propagation matrix E after normalization1And obtaining a positioning result BF, wherein the specific formula is as follows:
BF＝E1'RcovE1
wherein E is1' represents E1Yn' denotes the transposition of Yn, a matrix multiplication, Rcov∈RQ×QAnd T is expressed as the number of sample points.
In the step (4), the calculation formula of the sensing matrix A is as follows:
A(i,j)＝(E1(:,i)'*E(:,j))2
wherein A (i, j) represents the ith row and the jth column of the sensing matrix A, E1(i)' represents a matrix E1Ith column vector E of1The transpose of (: i), E (: j) represents the jth column of the propagation matrix E.
In the step (5), the concrete formula for inverting the sound source position X by using the quick reconstruction algorithm is as follows:
where β and μ are fault tolerance constants, viAnd λ is the optimum multiplier, DiX＝ωiRepresenting the discrete gradient of signal x at the ith position, | · | | purpleiThe i norm is expressed, and the sound source X is obtained by iteration. The fast reconstruction algorithm adopts the full variation regularization calculation based on the alternative direction Lagrange methodThe method is carried out.
According to the method, the sparsity of the signals is used as prior information, aiming at the amplitude modulation sound source widely existing in an industrial scene, the position of the sound source is inverted by using a fast algorithm of total variation regularization based on an alternate direction Lagrange method, so that the applicability of the sound source positioning method in the complex industrial scene is enhanced, the calculation complexity is reduced, the calculation efficiency is improved, and an accurate and efficient mode is provided for the positioning of the modulation sound source.
Drawings
Fig. 1 is a schematic flow chart of a method for rapidly positioning an amplitude modulated sound source according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating simulated sound source location distribution according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the distribution of a microphone array in an embodiment of the invention;
FIG. 4 is a sound source localization result obtained by using a convex optimization method according to an embodiment of the present invention;
fig. 5 is a sound source positioning result obtained by applying the fast sound source positioning method in the embodiment of the present invention.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
As shown in fig. 1, a method for fast localization of an amplitude modulated sound source includes the following steps:
s01, setting sound source parameters according to the amplitude modulation sound source model, and sampling sound source radiation signals for T times at the sampling frequency of Fs by using a microphone array formed by Q microphones in a certain arrangement mode; obtaining a sampling signal Yn ∈ RQ×T；
In order to show the advantages of the method in sound source localization, an array composed of 35 microphone sensors Q as shown in fig. 3 is adopted, 14E-shaped amplitude modulation sound sources which are close to each other and are at a distance of 1 meter are sampled at a sampling rate of 10000, the sampling time is 1 second, i.e. Fs is 10000; the amplitude modulated sound source is modeled as follows: (v (t) is Gaussian noise with mean 0 and variance 1)
α1＝2000；α2＝2500；α3＝3500；α4＝4000；f0＝α1；A1＝A2＝A3＝A4＝1；a00.2 to simulate a real industrial scene, 0dB gaussian noise (snr 0dB) is added to the acquired signal, the scan grid spacing is 0.05m, and the modulation frequency α is selected2Locating the centre frequency, i.e. f ═ alpha, for the sound source2The specific sound source location is shown in fig. 2 at 2500 Hz.
S02, obtaining the modulation center frequency alpha through cyclostationary analysisiThis frequency is the center frequency f to be located.
S03, obtaining a normalized covariance matrix R according to the sampling signal result YncovA propagation matrix E consisting of propagation direction vectors is derived from the sampling conditions and the center frequency, and from the covariance matrix RcovAnd the propagation matrix E after normalization1Obtaining a positioning result BF obtained by using a conventional beam forming method;
the process of obtaining the normalized covariance matrix from the sampling results can be expressed as:
where Yn' represents the transpose of Yn, a matrix multiplication, Rcov∈RQ×Q。
The propagation matrix, which consists of propagation direction vectors, can be represented as:
wherein E ∈ RQ×NN is a scanning gridE (m, n) represents the propagation response of the mth microphone to the nth grid, r represents the distance between the scanned grid and the array, f represents the center frequency of sound source localization, c represents the sound velocity (c in air is 340m/s), and i is an imaginary unit.
The normalization process of the propagation matrix can be expressed as:
wherein E isiRepresents a certain column of the matrix E, | | | |, represents a 1 norm.
Obtaining a space power spectrum by using a conventional beam forming method, and obtaining a positioning result BF according to the distribution of the space power spectrum, wherein the positioning result BF can be expressed as follows:
BF＝E1'RcovE1
s04, spreading the result BF of the conventional beam forming into a vector form Y according to the rows and according to the propagation matrixes E and E1Obtaining a sensing matrix A;
and (4) inverting the position of the sound source by utilizing a quick reconstruction algorithm according to Y and A, and expressing the result as X1The process can be expressed as:
wherein Y, A, X has the same meaning as above, β and μ are fault tolerance constants, viAnd λ is the optimum multiplier, DiX＝ωiRepresenting the discrete gradient of signal x at the ith position, | · | | purpleiRepresenting the i-norm, by iteration X can be found1。
And (4) inverting the position of the sound source by utilizing a convex optimization toolkit algorithm according to Y and A, and expressing the result as X2The process can be expressed as:
argmin||X2||1,subject to:X2＞0,||Y-AX2||2≤δ,δ＞0
according to propagation matrices E and E1Is transmitted toThe process of sensing matrix a can be represented as:
A(i,j)＝(E1(:,i)'*E(:,j))2
wherein A (i, j) represents the ith row and the jth column of the sensing matrix A, and E (: j) represents the jth column of the propagation matrix E;
s05, comparing the inverted sound source position with the actual simulation sound source position, rapidly reconstructing the advantages of the algorithm compared with the convex optimization algorithm through precision and efficiency comparison, and setting the actual position of the simulation sound source as X through 2 norm error comparison precision, then L2The norm error can be expressed as:
the model of the computer processor is Intel (R) core (TM) i7-7700HQ @2.80GHz, and the CPU operation time of the step 4 is calculated and executed by using a CPU time function in MATLAB based on the configuration.
Fig. 4 is a sound source position obtained by solving the problem solved by the fast reconstruction algorithm in step S04 by using a convex optimization method, fig. 5 is a sound source position obtained by solving the problem by using a fast algorithm, i.e., a total variation regularization algorithm based on an alternating direction lagrange method, according to a positioning result, it can be seen that both algorithms can invert the sound source position, and a reconstruction result is compared with a 2-norm error of an actual sound source, and CPU running time calculated according to a CPU time function of MATLAB is shown in fig. 4 and 5. The 2 norm reconstruction error of the convex optimization algorithm is slightly larger than that of the rapid reconstruction algorithm, and the convex optimization algorithm is about 18 times of the calculation time of the rapid algorithm. When the positions of the sound sources are more complex and the resolution of the scanning grid is higher, the computing efficiency advantage of the fast algorithm is more obvious, and the convex optimization needs to be iterated persistently, so that computing resources are consumed.
The embodiment provides a rapid reconstruction algorithm based on gradient information and sparse information on the basis of amplitude modulation of a sound source, the algorithm can be widely applied to reconstruction algorithms of various compressed sensing beam forming, compared with the traditional convex optimization algorithm, the timeliness of processing is greatly improved on the premise of ensuring the precision, and the method has extremely important significance on sound source detection in an industrial scene.
The embodiments described above are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only specific embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the present invention.
Claims (6)
1. A method for fast localization of amplitude modulated sound sources, comprising:
(1) sampling sound source radiation signals for T times by using a microphone array formed by Q microphones at a sampling frequency Fs to obtain sampling signals Yn E RQ×T；
(2) Analyzing to obtain a modulation center frequency f to be positioned;
(3) obtaining a propagation matrix E and a propagation matrix E obtained after normalization according to the sampling signal Yn and the modulation center frequency f1Obtaining a positioning result BF by using a conventional beam forming method;
(4) expanding the positioning result BF into vector form Y according to rows, and according to the propagation matrix E and the normalized propagation matrix E1Obtaining a sensing matrix A;
(5) according to the Y and the sensing matrix A, the position of the sound source is inverted by using a quick reconstruction algorithm; the specific formula for inverting the position of the sound source by using the rapid reconstruction algorithm is as follows:
where β and μ are fault tolerance constants, viAnd λ is the optimum multiplier, DiX＝ωiRepresenting the discrete gradient of signal x at the ith position, | · | | purpleiExpressing the i norm, and solving a sound source position X through iteration; the fast reconstruction algorithm adopts a total variation regularization algorithm based on an alternating direction Lagrange method.
2. The method for fast localization of an amplitude modulated sound source according to claim 1, wherein in step (2), the modulation center frequency f is obtained by cyclostationary analysis.
3. The method for fast localization of an amplitude modulated sound source according to claim 1, wherein in step (3), the propagation matrix E is composed of propagation direction vectors, and is formulated as:
wherein E ∈ RQ×NN is the resolution of the scan grid, E (m, N) represents the propagation response of the mth microphone to the nth grid, r represents the distance between the scanned grid and the array, f represents the modulation center frequency of the sound source location, c represents the sound velocity, and i is an imaginary unit.
4. The method for fast localization of amplitude modulated sound source according to claim 3, wherein in step (3), the normalization process of the propagation matrix E is:
wherein E isiRepresents a certain column of the propagation matrix E, | | | | | | represents a 2-norm.
5. The method for rapidly positioning an amplitude modulated sound source as claimed in claim 4, wherein in the step (3), the process of obtaining the positioning result BF comprises: obtaining a normalized covariance matrix R from the sampled signal YncovAnd according to the covariance matrix RcovAnd the propagation matrix E after normalization1And obtaining a positioning result BF, wherein the specific formula is as follows:
BF＝E1'RcovE1
wherein E is1' represents E1Yn' denotes the transposition of Yn, a matrix multiplication, Rcov∈RQ×QAnd T is expressed as the number of sample points.
6. The method for rapidly positioning an amplitude modulated sound source according to claim 1, wherein in step (4), the calculation formula of the sensing matrix A is as follows:
A(i,j)＝(E1(:,i)'*E(:,j))2
wherein A (i, j) represents the ith row and the jth column of the sensing matrix A, E1(i)' represents a matrix E1Ith column vector E of1The transpose of (: i), E (: j) represents the jth column of the propagation matrix E.
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