Asynchronous measurement method of cyclostationary sound source, storage medium and computer equipment

Abstract

The invention provides an asynchronous measurement method for a cyclostationary sound source, a storage medium and computer equipment. The non-synchronous measurement method for the cyclostationary sound source comprises the following steps: measuring a sound source to be measured at different positions for P times by using a microphone array with M channels; respectively calculating a mutual circulation spectrum matrix of the sound signals obtained by the microphone array at different positions; stacking the cross-cyclic spectrum matrixes according to diagonals to obtain a data missing cross-cyclic spectrum matrix with the dimension of MP * MP; and constructing a constraint problem based on the completion target of the data missing cross-cyclic spectrum matrix, completing matrix completion of the data missing cross-cyclic spectrum matrix, and forming a completed cross-cyclic spectrum matrix. The technical scheme of the invention can be widely applied to the technical field of cyclically stationary sound source measurement.

Description

Technical Field

[0001] The present invention relates to the technical field of sound source localization, in particular to the technical field of cyclostationary sound source localization. Background Art

[0002] Mechanical equipment will generate noise during operation, and noise is also considered a source of environmental pollution. Therefore, people are paying more and more attention to reducing the intensity of noise generated by mechanical equipment, and relevant laws and regulations have been introduced to regulate industrial equipment that may generate noise pollution.

[0003] The premise of noise reduction for mechanical equipment is to identify the noise source. At present, acoustic imaging technology based on microphone arrays has been applied in the industrial field. The core idea of ​​this technology is to use the sound field data measured by the microphone array to infer the acoustic physical quantities of the area of ​​interest and obtain an acoustic image. The obtained acoustic image can be used for noise source identification and acoustic-based fault diagnosis. According to the imaging principle, the currently recognized acoustic imaging methods can be divided into two categories: acoustic beamforming and near-field acoustic holography.

[0004] Cyclostationary signals are a special type of non-stationary signals whose statistics show periodic changes (for rotating machinery, first-order and second-order statistics are generally concerned). The cyclostationarity of the acoustic signal radiated by rotating machinery is generated by the rotation and reciprocating motion of multiple mechanical parts. Different rotating parts correspond to different cyclic frequencies.

[0005] The existing cyclostationary sound source beamforming method (CSCBF) inverts the cyclic spectrum correlation of the sound source (reflecting the cyclostationarity of the sound source). The cyclostationary sound source beamforming method is limited by the aperture and microphone density of the microphone array that obtains the sound signal. The main lobe is large at low frequencies and the side lobes are serious at high frequencies, which affects the recognition effect of cyclostationary sound sources. Summary of the invention

[0006] In order to solve the aforementioned problem of affecting the recognition effect of cyclostationary sound sources in the existing cyclostationary sound source localization method, the present invention provides an asynchronous measurement method, storage medium and computer device for cyclostationary sound sources.

[0007] The technical solution of the present invention is as follows:

[0008] The asynchronous measurement method of the cyclostationary sound source comprises the following steps:

[0009] S1, using a microphone array with M channels to perform P measurements on the sound source to be measured at different positions;

[0010] S2, selecting the cycle frequency α of the sound source to be measured and the spectrum frequency f of the imaging;

[0011] S3, respectively calculating the inter-circulation spectrum matrices of the acoustic signals obtained by the microphone array at the different positions;

[0012] S4, stacking the P inter-circular spectral matrices of dimension M×M diagonally to obtain a data-missing inter-circular spectral matrix of dimension MP×MP;

[0013] S5. Construct a constrained problem based on the completion target of the data-missing intercirculant spectral matrix, complete the matrix completion of the data-missing intercirculant spectral matrix, and obtain a completed intercirculant spectral matrix.

[0014] Optionally, the constraint conditions for constructing the constrained problem in step S5 include: weak sparsity of the eigenvalue spectrum of the inter-circulant spectral matrix.

[0015] Optionally, the constraint conditions for constructing the constrained problem in step S5 include: spatial continuity of the cyclostationary sound field.

[0016] Optionally, the expression of the constrained problem in step S5 is:

[0017]

[0018] Where ⊙ represents the Hadamard product; ε represents the truncation error; S PP is the data missing inter-circulation spectrum matrix; S is the completed inter-circulation spectrum matrix; Ω is the sampling matrix; For the frequency The projection basis constructed under L ; For the frequency The projection basis constructed under R .

[0019] Optionally, the method for completing the matrix completion of the data-missing inter-circular spectrum matrix in step S5 includes a FISTA method, and the expression of the FISTA method is:

[0020]

[0021] Where μ is the step size; λ k represents the regularization parameter; t k represents a parameter introduced to speed up iteration; G k is the intermediate quantity of the iterative process; shrink(G k ,λ k μ) is the soft threshold shrinkage operator and is calculated as diag is an operator for extracting or constructing matrix diagonal elements. Indicates taking 0 and The larger value of G kEigenvalue decomposition of the eigenvector matrix; G k Eigenvalues ​​of eigenvalue decomposition;

[0022] A storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, step S5 of the asynchronous measurement method for a cyclostationary sound source as described above is implemented.

[0023] A computer device comprises: a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement step S5 in the asynchronous measurement method of a cyclostationary sound source as described above.

[0024] The technical effects of the present invention are as follows:

[0025] The asynchronous measurement method of the cyclostationary sound source of the present invention performs measurements at multiple positions by moving the microphone array and merging the measurement results, thereby obtaining the measurement performance of a synthetic microphone array with a larger aperture or higher density, enhancing the ability of sound source identification, expanding the operating frequency range, solving the aforementioned problems in the prior art that affect the identification effect of the cyclostationary sound source, and achieving the purpose of the present invention.

[0026] The further effects of the above optional manner will be described below in conjunction with the specific implementation manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The present invention is a flowchart of an embodiment of the asynchronous measurement method of a cyclostationary sound source.

[0028] Figure 2 Schematic diagram of the microphone array of M channels and the sound source to be measured in the simulation experiment.

[0029] Figure 3 Schematic diagram of the M×P synthetic array formed based on P measurements and the sound source to be measured.

[0030] Figure 4 An acoustic image generated by a simulation experiment using an existing cyclostationary beamforming method.

[0031] Figure 5 The acoustic image is generated by a simulation experiment using the asynchronous measurement method of the cyclostationary sound source of the present invention. DETAILED DESCRIPTION

[0032] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0033] Figure 1The flow chart of an embodiment of the method for asynchronously measuring a cyclostationary sound source of the present invention is shown and described in detail herein.

[0034] S1. Microphone array measurement sound source

[0035] In this step, a microphone array with M channels is firstly set, and then the microphone array is used to measure the sound source to be measured at P different positions to obtain the sound signal.

[0036] S2. Select the cycle frequency and spectrum frequency

[0037] In this step, the cycle frequency α of the sound source to be measured and the spectrum frequency f of the imaging are selected.

[0038] S3. Calculate the mutual circulation spectrum matrix at different positions

[0039] In this step, the inter-circulation spectrum matrix of the acoustic signal obtained by the microphone array at each position is calculated respectively. The inter-circulation spectrum matrix at the pth position is for:

[0040]

[0041] in, represents the expectation operator, The Fourier transform of the sound pressure with data length L measured at the p-th position.

[0042] S4. Obtaining the data missing inter-circulation spectrum matrix

[0043] In this step, the obtained P inter-circulation spectral matrices of dimension M×M are stacked diagonally to obtain a data-missing inter-circulation spectral matrix of dimension MP×MP.

[0044] This step is equivalent to combining the microphone arrays of M channels at each position into a virtual microphone synthesis array with MP channels. The measurement at each position is equivalent to using only part of the microphones in the microphone synthesis array. Therefore, the inter-circulation spectrum matrix obtained in step S3 is equivalent to the block diagonal part of the inter-circulation spectrum matrix of the microphone synthesis array, and the loss of the remaining part is due to the phase loss between the measurements at each position. The data missing inter-circulation spectrum matrix S PP :

[0045]

[0046] S5. Obtain the completed mutual circulant spectrum matrix

[0047] In this step, a constrained problem is constructed based on the completion target of the data-missing intercirculant spectral matrix, and the matrix completion of the data-missing intercirculant spectral matrix is ​​completed to obtain a completed intercirculant spectral matrix.

[0048] The purpose of the asynchronous measurement method of the cyclostationary sound source of the present invention is to calculate the data missing inter-circular spectrum matrix S PP To complete, a complete inter-circulating spectrum matrix equivalent to that obtained by synchronous measurement of the microphone synthesis array is obtained. However, the completion of the inter-circulating spectrum matrix is ​​an ill-posed inverse problem, and its known part (block diagonal elements) is too small relative to the overall proportion, so additional conditions (regularization) are required to solve this problem. The asynchronous measurement method of the cyclostationary sound source of the present invention uses the following two constraints to complete the completion of the aforementioned inter-circulating spectrum matrix: the weak sparsity of the eigenvalue spectrum of the inter-circulating spectrum matrix; the spatial continuity of the cyclostationary sound field. The rank of the inter-circulating spectrum matrix should theoretically be consistent with the number of incoherent sound sources that generate the sound field; the cyclostationary sound field is continuous in space, so the sound pressure information measured by two adjacent microphones should also be similar. The mathematical expressions of these two constraints are derived below.

[0049] 1. Weak sparsity of eigenvalue spectrum of intercircular spectral matrix

[0050] Assuming that the microphone synthesis array receives a sound pressure signal P generated by K incoherent sound sources, the inter-circular spectrum matrix can be expressed as:

[0051]

[0052] in The mth row of the matrix G is the Green function g m .

[0053] The source strength Q is expressed in a set of basis functions Decompose on:

[0054] Q L (f)=Φ(f)c L , (4)

[0055] Among them, c L is the coefficient of the basis function. Therefore, formula (3) can be expressed as:

[0056]

[0057] in H is a transfer function matrix. Ideally, the signals received by each microphone are independent. Assuming that H is full row rank, we have:

[0058] rank(S PP )=rank(S cc ).

[0059] In asynchronous measurements, K is required to be less than MP, so ideally S will be a low-rank matrix.

[0060] However, in practice, due to noise or other interference, the co-circulant spectral matrix is ​​not strictly low-rank. If the co-circulant spectral matrix is ​​eigenvalue decomposed, it is found to be full rank, but there are only a few dominant eigenvalues ​​representing the source. This is called the weak sparsity assumption of the eigenvalue spectrum, which is more general than the low-rank assumption and provides a global solution that minimizes the nuclear norm. The weak sparsity assumption of the eigenvalue spectrum corresponds to small values ​​of the nuclear norm (the sum of the eigenvalues), so the nuclear norm is used to constrain the co-circulant spectral matrix.

[0061] 2. Spatial continuity of cyclostationary sound field

[0062] The inter-circular spectrum matrix reflects the correlation between different channel data, but it does not contain the position information of the microphone array and does not consider the continuity of the sound field in space. Here, an additional constraint is used to encode the position information of the microphone array into the inter-circular spectrum matrix.

[0063] The received sound pressure signal P is decomposed on the spatial basis Φ: P = Φθ, and its coefficient θ can be expressed as in represents the pseudo-inverse operator. The sound pressure signal after smoothing by this spatial basis can be expressed as:

[0064]

[0065] The smoothed intercirculation spectrum matrix can be expressed as:

[0066]

[0067] in and Respectively, in frequency and The projection basis constructed under L and R , the corresponding space basis and are named as left and right space basis respectively. Equation (7) can be rewritten as This constraint is used to smooth the inter-circular spectral matrix and ensure the spatial continuity of the cyclostationary sound field.

[0068] Based on the above deductions, the asynchronous measurement problem of cyclostationary sound source is finally expressed as the following constrained optimization problem:

[0069]

[0070] where ⊙ represents the Hadamard product, ||·|| * represents the nuclear norm, S represents the complementary intercircular spectrum matrix, S PP represents the data missing intercircular spectrum matrix obtained in step S4, and Ω is a sampling matrix. The above constrained optimization problem can be solved by classical methods such as FISTA.

[0071] The FISTA method has been applied by Yu et al. to the completion of the inter-circulating spectral matrix in traditional asynchronous measurements in the paper “Acoustical source reconstruction from non-synchronous sequential measurements by Fast Iterative Shrinkage Thresholding Algorithm” in the Journal of Sound and Vibration, Vol. 408, pp. 351-367, November 10, 2017. However, the FISTA method needs to be modified for the completion of the inter-circulating spectral matrix in asynchronous measurements of cyclostationary sound sources.

[0072] First, we briefly introduce the FISTA method. A general constrained optimization problem can be expressed as:

[0073]

[0074] Where λ represents the regularization parameter, is a non-empty closed convex set, f(x) and g(x) represent smooth and possibly non-smooth convex functions respectively, and its iterative solution is:

[0075]

[0076] in Representing to a collection The projection of μ represents the step size, prox λμ represents the proximal operator associated with parameters λ and μ, and its definition is related to g(x), represents the gradient of f(x). When the proximal operator prox λμ is calculated as the contraction operator, i.e. When , the algorithm is called the Fast Iterative Shrinkage Thresholding Algorithm (FISTA).

[0077] For the inter-circular spectral matrix completion problem of equation (8), the specific process of the FISTA method is as follows. First, equation (8) is rewritten as:

[0078]

[0079] in Represents a set, defined as λ represents the regularization parameter. is a convex function, λ||S|| * are non-smooth convex functions, which can be regarded as f(x) and g(x) in the general constrained optimization problem. For the constrained optimization problem of equation (11), the FISTA method can be expressed as:

[0080]

[0081] Where μ is the step size, shrink(G k ,λ k μ) is the soft threshold shrinkage operator, which is calculated here as diag is an operator for extracting or constructing matrix diagonal elements. Indicates taking 0 and For large values ​​of U and Respectively represent G k The eigenvector matrix and eigenvalues ​​of eigenvalue decomposition. In actual use, the initial value of the iteration can be set to t1=1, G at convergence k+1 This is the complete mutual circulant spectral matrix S obtained.

[0082] S6. Calculate cyclostationary beamforming output

[0083] In this step, the left and right steering vectors are constructed based on the M×P synthetic array formed by the P measurements, and the cyclic spectrum correlation of each scanning point on the sound source plane is calculated in combination with the completed inter-cyclic spectrum matrix.

[0084] After obtaining the completed inter-circular spectrum matrix, the cyclostationary sound source with a specific cyclic frequency is identified by the cyclostationary beamforming method. Cyclostationary beamforming uses steering vectors for focusing, but the inter-circular spectrum matrix is ​​not a Hermitian matrix, so there are two steering vectors in cyclostationary beamforming: left steering vector and right steering vector (Assume that the source plane is divided into N grids), the elements of which are defined as follows:

[0085]

[0086] where r m and r n represents the position of the mth microphone (a total of MP microphones) and the nth grid point, respectively. f and α can be determined by spectrum analysis and cyclic spectrum analysis, respectively. and Focus ((·) T represents transpose), the cyclostationary beamforming output of the nth grid point can be obtained:

[0087]

[0088] in(·) * represents the conjugate transpose, and S is the completed intercircular spectral matrix.

[0089] S7. Generate sonogram

[0090] According to the B obtained in step S6 n Assign corresponding colors to each grid point in the image to generate the final sonogram.

[0091] Figure 1 Steps S6 and S7 are corresponding steps of the cyclostationary beamforming method. In other embodiments, Figure 1 Steps S6 and S7 can be implemented using other existing technologies, such as the high-resolution cyclostationary sound source identification method based on iterative Bayesian focusing proposed by Zhang et al. in the article "Localization of cyclostationary acoustic sources via cyclostationary beamforming and its high spatial resolution implementation" in the journal "Mechanical Systems and Signal Processing" Volume 204 on December 1, 2023.

[0092] The computer program stored on the storage medium of the embodiment of the present invention and the computer program executed by the computer device of the embodiment of the present invention can be executed as follows: Figure 1 The step S5 in the embodiment of the method for asynchronously measuring a cyclostationary sound source of the present invention is shown.

[0093] The effect of the asynchronous measurement method of the cyclostationary sound source of the present invention is verified by simulation experiments as follows.

[0094] like Figure 2 and Figure 3 As shown, the experimental settings are described below.

[0095] Four different sound sources are set on the sound source surface, namely:

[0096] ●Two incoherent broadband cyclostationary sound sources, with position coordinates of (-0.2, 0.2)m and (-0.2, 0.2)m respectively

[0097] m, the cycle frequency is 100Hz;

[0098] ●A broadband cyclostationary sound source with a cycle frequency of 160 Hz and a position coordinate of (-0.2, -0.2) m;

[0099] Gaussian white noise source, with the location coordinates at (0.2, -0.2) m.

[0100] The microphone array is a uniform rectangular array consisting of 25 microphones (M=25), with a spacing of 0.06m between adjacent microphones. The microphone array moves uniformly 9 times on the plane, with each movement distance of 0.1m. The microphone array plane is 0.9m away from the sound source plane. The speed of sound is 343m / s. Figure 2 and Figure 3 The black hollow circles indicate the microphones, the red asterisks indicate the sound sources, and the red solid circles indicate the locations to which the microphone array is moved.

[0101] The parameters of the FSITA algorithm are set as follows: each regularization parameter is iterated 3 times, and the initial regularization parameter is λ0 = || S PP ||2, the final regularization parameter is λ d =10 -6 λ0, the proportional coefficient used to adjust the regularization parameter, is 0.7, and the step size is 1.2. The maximum number of iterations is set to 50, and the stopping criterion is set to 10 -4 .

[0102] Figure 4 and Figure 5 The cycle frequency is set to 100Hz, the spectrum frequency is set to 2500Hz, and the target sound source is the sound image of the two sound sources above the figure. Figure 4 is the imaging result of the existing cyclostationary beamforming method (CSCBF), Figure 5 This is the imaging result of the asynchronous measurement method of the cyclostationary sound source of the present invention.

[0103] from Figure 4 It can be seen that although the cyclostationary beamforming method can realize the localization of cyclostationary sound sources with a specific cyclic frequency, it is unable to distinguish two adjacent cyclostationary sound sources at 2500 Hz due to the small aperture of the microphone array and insufficient resolution. The asynchronous measurement method of the cyclostationary sound source of the present invention achieves a higher resolution by measuring with a moving microphone array, and the generated acoustic image can clearly distinguish two cyclostationary sound sources with a cyclic frequency of 100 Hz.

[0104] It is worth noting that the above description is only a preferred embodiment of the present invention, and does not limit the scope of patent protection of the present invention. The present invention can also be replaced by equivalent technologies. Therefore, any equivalent changes made by using the description and illustrations of the present invention, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims

1. Asynchronous measurement method for cyclostationary sound source, characterized by: The steps include: S1, using a microphone array with M channels to perform P measurements on the sound source to be measured at different positions; S2, selecting the cycle frequency α of the sound source to be measured and the spectrum frequency f of the imaging; S3, respectively calculating the inter-circulation spectrum matrices of the acoustic signals obtained by the microphone array at the different positions; S4, stacking the P inter-circular spectral matrices of dimension M×M diagonally to obtain a data-missing inter-circular spectral matrix of dimension MP×MP; S5. Construct a constrained problem based on the completion target of the data-missing intercirculant spectral matrix, complete the matrix completion of the data-missing intercirculant spectral matrix, and obtain a completed intercirculant spectral matrix.

2. The asynchronous measurement method of a cyclostationary sound source according to claim 1, characterized in that: The constraint conditions for constructing the constrained problem in step S5 include: weak sparsity of the eigenvalue spectrum of the inter-circulant spectral matrix.

3. The asynchronous measurement method of cyclostationary sound source according to claim 2, characterized in that: The constraint conditions for constructing the constrained problem in step S5 include: spatial continuity of the cyclostationary sound field.

4. The asynchronous measurement method of a cyclostationary sound source according to claim 3, characterized in that: The expression of the constrained problem in step S5 is: Where ⊙ represents the Hadamard product, S PP is the data missing inter-circulation spectrum matrix; S is the completed inter-circulation spectrum matrix; Ω is the sampling matrix; For the frequency The projection basis constructed under L ; For the frequency The projection basis constructed under R .

5. The asynchronous measurement method of cyclostationary sound source according to claim 4, characterized in that: The method for completing the matrix completion of the data-missing inter-circular spectrum matrix in step S5 includes the FISTA method, and the expression of the FISTA method is: Where μ is the step size; t k represents a parameter introduced to speed up iteration; G k is the intermediate quantity of the iterative process; shrink(G k ,λ k μ) is the soft threshold shrinkage operator and is calculated as diag is an operator for extracting or constructing matrix diagonal elements. Indicates taking 0 and The larger value of G k Eigenvalue decomposition of the eigenvector matrix; G k Eigenvalues ​​of eigenvalue decomposition; 6. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, step S5 of the asynchronous measurement method for a cyclostationary sound source according to any one of claims 1 to 5 is implemented.

7. Computer equipment, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement step S5 in the asynchronous measurement method for a cyclostationary sound source according to any one of claims 1 to 5.

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