Non-synchronous measurement method of cyclic stationary sound source, storage medium and computer device

Abstract

The application provides a non-synchronous measurement method of a cyclostationary sound source, a storage medium and computer equipment. The non-synchronous measurement method of the cyclostationary sound source comprises the following steps: using a microphone array with M channels to measure a to-be-measured sound source at different positions for P times; respectively calculating cross cyclic spectrum matrices of sound signals obtained by the microphone array at different positions; stacking the cross cyclic spectrum matrices according to diagonal lines to obtain a data-missing cross cyclic spectrum matrix with a dimension of MPxMP; constructing a constraint problem based on a 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 application can be widely applied to the technical field of cyclostationary sound source measurement.

Description

Technical Field

[0001] This invention relates to the field of sound source localization technology, and in particular to the field of localization technology for cyclic, stable sound sources. Background Technology

[0002] Mechanical equipment generates noise during operation, and noise is considered a source of environmental pollution. Therefore, people are increasingly concerned about reducing the intensity of noise generated by mechanical equipment, and relevant laws and regulations have been introduced to regulate industrial equipment that may cause noise pollution.

[0003] Noise reduction for mechanical equipment requires identifying the noise source. Currently, microphone array-based acoustic imaging technology is used in industry. The core idea of ​​this technology is to use sound field data measured by a microphone array to infer acoustic physical quantities in the region of interest and obtain an acoustic image. The obtained acoustic image can be used for noise source identification and acoustic-based fault diagnosis. Based on imaging principles, currently accepted 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 signal whose statistics exhibit periodic variations (for rotating machinery, first- and second-order statistics are generally of interest). The cyclostationarity of the radiated acoustic signal from rotating machinery is generated by the rotation and reciprocating motion of multiple mechanical components. Different rotating components correspond to different cyclic frequencies.

[0005] Existing Cyclic Stationary Source Beamforming (CSCBF) methods invert the cyclic spectrum correlation of a sound source (reflecting the cyclic stationarity of the sound source). However, CSCBF is limited by the aperture and microphone density of the microphone array used to acquire the sound signal, resulting in a large main lobe at low frequencies and severe side lobes at high frequencies, which affects the recognition performance of CSCBF sources. Summary of the Invention

[0006] To address the aforementioned problems affecting the identification performance of cyclic steady-state sound sources in existing localization methods, this invention provides an asynchronous measurement method, storage medium, and computer device for cyclic steady-state sound sources.

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

[0008] The asynchronous measurement method for a cyclic steady-state sound source includes the following steps:

[0009] S1. Use a microphone array with M channels to perform P measurements on the sound source under test at different locations.

[0010] S2. Select the cycle frequency α of the sound source to be tested and the spectral frequency f of the imaging;

[0011] S3. Calculate the intercyclic spectrum matrix of the acoustic signals obtained by the microphone array at different positions respectively;

[0012] S4. Stack the P intercyclic spectrum matrices with dimension M×M diagonally to obtain a data missing intercyclic spectrum matrix with dimension MP×MP.

[0013] S5. Based on the completion objective of the missing intercyclic spectrum matrix, construct a constrained problem to complete the matrix completion of the missing intercyclic spectrum matrix and obtain the completed intercyclic spectrum matrix.

[0014] Optionally, the constraints for constructing the constrained problem in step S5 include the weak sparsity of the eigenvalue spectrum of the intercyclic spectral matrix.

[0015] Optionally, the constraints for constructing the constrained problem in step S5 include: the spatial continuity of the cyclic stationary sound field.

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

[0017]

[0018] Where ⊙ represents the Hadamard product; ε represents the truncation error; S PP S is the missing intercyclic spectrum matrix; S is the completed intercyclic spectrum matrix; Ω is the sampling matrix; In frequency The projection basis constructed below is abbreviated as Ψ. L ; In frequency The projection basis constructed below is abbreviated as Ψ. R .

[0019] Optionally, the method for completing the matrix completion of the missing intercyclic spectrum matrix in step S5 includes the FISTA method, the expression of which is:

[0020]

[0021] Where μ is the step size; λ k Represents the regularization parameter; t k G represents a parameter introduced to accelerate iteration; k It is an intermediate quantity in the iterative process; shrink(G) k ,λ k μ) is the soft threshold shrinkage operator, which is calculated as The `diag` operator is used to extract or construct the diagonal elements of a matrix. Indicates taking 0 and The larger value in G; U is G kThe eigenvector matrix of eigenvalue decomposition; For G k Eigenvalues ​​of eigenvalue decomposition;

[0022] A storage medium storing a computer program, which, when executed by a processor, implements step S5 in the asynchronous measurement method for a cyclic steady sound source as described above.

[0023] A computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the computer program to implement step S5 in the asynchronous measurement method for a cyclic steady sound source as described above.

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

[0025] The asynchronous measurement method for a cyclic steady-state sound source of the present invention measures the sound source at multiple locations by moving the microphone array and merging the measurement results, thereby obtaining the measurement performance of a synthesized microphone array with a larger aperture or higher density. This enhances the sound source identification capability, expands the operating frequency range, solves the aforementioned problems affecting the identification effect of cyclic steady-state sound sources in the prior art, and achieves the objective of the present invention.

[0026] The further effects of the above-mentioned alternative methods will be explained in detail below with reference to specific implementation methods. Attached Figure Description

[0027] Figure 1 This is a flowchart of an embodiment of the asynchronous measurement method for a cyclic steady sound source according to the present invention.

[0028] Figure 2 This is a schematic diagram of an M-channel microphone array and the sound source under test in a simulation experiment.

[0029] Figure 3 This is a schematic diagram of an M×P synthesized array formed based on P measurements and the sound source under test.

[0030] Figure 4 The acoustic image generated by the simulation experiment using the existing cyclic steady beamforming method.

[0031] Figure 5 The acoustic image generated for a simulation experiment using the asynchronous measurement method of the cyclic steady sound source of the present invention. Detailed Implementation

[0032] The technical solution of the present invention will be described below with reference to the accompanying drawings.

[0033] Figure 1The flowchart of an embodiment of the asynchronous measurement method for a cyclic steady sound source of the present invention is shown and described in detail herein.

[0034] S1, Microphone array measuring sound source

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

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

[0037] In this step, the cyclic frequency α of the sound source to be tested and the spectral frequency f of the imaging are selected.

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

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

[0040]

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

[0042] S4. Obtain the data missing intercyclic spectrum matrix.

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

[0044] This step is equivalent to combining the M-channel microphone arrays at each location into a virtual microphone synthesis array with MP channels. The measurement at each location is equivalent to using only a portion of the microphones in the microphone synthesis array; therefore, the inter-loop spectrum matrix obtained in step S3 corresponds to the block diagonal portion of the inter-loop spectrum matrix of the microphone synthesis array. The loss of the remaining portion is due to phase loss between measurements at different locations. The missing inter-loop spectrum matrix S... PP :

[0045]

[0046] S5. Obtain the complete intercyclic spectrum matrix.

[0047] In this step, a constrained problem is constructed based on the completion objective of the missing intercyclic spectrum matrix to complete the matrix completion of the missing intercyclic spectrum matrix, resulting in the completed intercyclic spectrum matrix.

[0048] The objective of the asynchronous measurement method for a cyclic steady-state sound source in this invention is to address the missing data in the intercyclic spectral matrix S. PP The intercyclic spectrum matrix is ​​completed to obtain a complete intercyclic spectral matrix equivalent to that obtained by synchronous measurement from the microphone synthesis array. However, completing the intercyclic spectral matrix is ​​an ill-posed inverse problem, as its known portion (block diagonal elements) is too small relative to the total, thus requiring additional conditions (regularization) to address this issue. The asynchronous measurement method for cyclic stationary sound sources of this invention uses the following two constraints to complete the aforementioned intercyclic spectral matrix: the weak sparsity of the eigenvalue spectrum of the intercyclic spectral matrix; and the spatial continuity of the cyclic stationary sound field. The rank of the intercyclic spectral matrix should theoretically be consistent with the number of incoherent sound sources generating the sound field; the cyclic stationary sound field is spatially continuous, therefore 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 the eigenvalue spectrum of the intercyclic spectral matrix

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

[0051]

[0052] in The m-th row of matrix G is the Green's function g. m .

[0053] Source strength Q is based on a set of basis functions. Decompose the above:

[0054] Q L (f)=Φ(f)c L (4)

[0055] Among them, c L These are the coefficients of the basis functions. Therefore, equation (3) can be expressed as:

[0056]

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

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

[0059] In asynchronous measurements, K << MP is required, so ideally S would be a low-rank matrix.

[0060] However, in practice, due to noise or other interference, the intercyclic spectrum matrix is ​​not strictly low-rank. If we perform eigenvalue decomposition on the intercyclic spectrum matrix, we find that it is full-rank, but only a few of the dominant eigenvalues ​​representing the sources are present. 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 a small value of the nuclear norm (the sum of eigenvalues), thus constraining the intercyclic spectrum matrix using the nuclear norm.

[0061] 2. Spatial continuity of a circulating, stable sound field

[0062] The inter-circular spectrum matrix reflects the correlation between data from different channels, but it does not include the positional information of the microphone array and does not consider the spatial continuity of the sound field. Here, an additional constraint is used to encode the positional 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 This represents the pseudo-inverse operator. The sound pressure signal smoothed by this space basis can be expressed as:

[0064]

[0065] The smoothed intercyclic spectrum matrix can be represented as:

[0066]

[0067] in and They represent the frequencies respectively. and The projective bases constructed below are abbreviated as Ψ. L and Ψ R The corresponding space basis and They are named as left and right space bases, respectively. Equation (7) can be rewritten as This constraint is used to smooth the intercyclic spectral matrix and ensure the spatial continuity of the cyclic, stationary sound field.

[0068] Based on the above deductions, the asynchronous measurement problem of a cyclic stationary sound source can be finally formulated as the following constrained optimization problem:

[0069]

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

[0071] The FISTA method has been applied by Yu et al. to complete the intercyclic spectral matrix in traditional asynchronous measurements in the paper "Acoustical source reconstruction from non-synchronous sequential measurements by Fast Iterative Shrinkage Thresholding Algorithm" published in the Journal of Sound and Vibration, November 10, 2017, Volume 408, pp. 351-367. However, the FISTA method needs to be modified for the problem of completing the intercyclic spectral matrix in asynchronous measurements of cyclic stationary sound sources.

[0072] First, a brief introduction to the FISTA method will be given. A general constrained optimization problem can be expressed as:

[0073]

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

[0075]

[0076] in Represents a set The projection, μ represents the step size, prox λμ This represents the proximal operator related to the parameters λ and μ, and its definition is related to g(x). Let f(x) represent the gradient of f(x). When the proximal operator prox... λμ Calculated as a contraction operator When this algorithm is used, it is called the Fast Iterative Shrinkage Thresholding Algorithm (FISTA).

[0077] For the problem of completing the intercyclic spectral matrix in equation (8), the specific process of the FISTA method is as follows. First, equation (8) is rewritten as:

[0078]

[0079] in Denote a set as defined λ represents the regularization parameter. In equation (11) It is a convex function, λ||S|| * These are non-smooth convex functions, which can be considered as f(x) and g(x) in a general constrained optimization problem, respectively. 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 The `diag` operator is used to extract or construct the diagonal elements of a matrix. Indicates taking 0 and The largest value in the middle, U and G k The eigenvector matrix and eigenvalues ​​of eigenvalue decomposition. In practical applications, the initial values ​​for iteration can be set to... t1=1, G at convergence k+1 This is the obtained complete intercyclic spectrum matrix S.

[0082] S6. Calculate the output of the cyclically stable beamforming.

[0083] In this step, 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 surface is calculated in combination with the completed intercyclic spectrum matrix.

[0084] After obtaining the complete intercyclic spectral matrix, cyclic stationary sound sources with specific cyclic frequencies are identified using cyclic stationary beamforming. Cyclic stationary beamforming uses steering vectors for focusing, but since the intercyclic spectral matrix is ​​not a Hermitian matrix, there are two steering vectors in cyclic stationary beamforming: a left steering vector and a right steering vector. and right guide vector (Assuming the source plane is divided into N grids), the elements are defined as follows:

[0085]

[0086] Where r m and r n Let f and α represent the positions of the m-th microphone (out of a total of MP microphones) and the n-th grid point, respectively. f and α can be determined through spectral analysis and cyclic spectrum analysis, respectively. This is achieved using left and right steering vectors. and Focusing (·) T (Indicates transpose), then the cyclically stationary beamforming output of the nth grid point can be obtained:

[0087]

[0088] in(·) * Let S denote the conjugate transpose, and S be the complete intercyclic spectrum matrix.

[0089] S7. Generate audio-visual image

[0090] Based on B obtained in step S6 n The corresponding color is assigned to each grid point in the image to generate the final audio-visual image.

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

[0092] The computer program stored on the storage medium of the present invention and the computer program executed in the computer device of the present invention can both execute the following: Figure 1 Step S5 in an embodiment of the asynchronous measurement method for the cyclic steady sound source of the present invention is shown.

[0093] The following simulation experiment verifies the effectiveness of the asynchronous measurement method of the cyclic steady sound source of the present invention.

[0094] like Figure 2 and Figure 3 As shown, the experimental setup is explained below.

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

[0096] ● Two incoherent broadband cyclic stationary sound sources, located at coordinates (-0.2, 0.2) m and (-0.2, 0.2) m respectively.

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

[0098] ●A broadband, cyclic, stable sound source with a cyclic frequency of 160Hz, located at coordinates (-0.2, -0.2)m;

[0099] • Gaussian white noise source, located at coordinates (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 a plane, with each movement covering a distance of 0.1m. The plane of the microphone array is 0.9m above the plane of the sound source. The speed of sound is 343m / s. Figure 2 and Figure 3 The black hollow circle represents a microphone, the red asterisk represents a sound source, and the red solid circle represents the position where the microphone array has 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 is used to adjust the scaling factor of the regularization parameter, which 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 To set the cycle frequency to 100Hz, the spectral frequency to 2500Hz, and the target sound source to the acoustic images of the two sound sources at the top of the diagram, the following settings are used. Figure 4 The imaging results are based on existing Cyclic Steady Beamforming (CSCBF) methods. Figure 5 The image shows the imaging results of the asynchronous measurement method for the cyclic steady sound source of the present invention.

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

[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, all equivalent changes made based on the description and figures of the present invention, or direct or indirect applications to other related technical fields, are included within the scope of the present invention.

Claims

1. An asynchronous measurement method for a cyclic steady-state sound source, characterized in that: Includes the following steps: S1. Use a microphone array with M channels to perform P measurements on the sound source under test at different locations. S2. Select the cycle frequency of the sound source to be tested. With the spectral frequency of imaging ; S3. Calculate the intercyclic spectrum matrix of the acoustic signals obtained by the microphone array at different positions respectively; S4. Stack the P intercyclic spectrum matrices with dimension M×M diagonally to obtain a data missing intercyclic spectrum matrix with dimension MP×MP. S5. Based on the completion objective of the missing data intercyclic spectrum matrix, construct a constrained problem to complete the matrix completion of the missing data intercyclic spectrum matrix and obtain the completed intercyclic spectrum matrix. The constraints for constructing the constrained problem in step S5 include: the weak sparsity of the eigenvalue spectrum of the intercyclic spectral matrix; The constraints for constructing the constrained problem in step S5 include: the spatial continuity of the cyclic stationary sound field; The expression for the constrained problem described in step S5: ， in, It represents the Hadamah accumulation. The missing intercyclic spectrum matrix of the data; This is the completed intercyclic spectrum matrix; The sampling matrix; In frequency The projection basis constructed below is abbreviated as ; In frequency The projection basis constructed below is abbreviated as .

2. The asynchronous measurement method for a cyclic steady-state sound source according to claim 1, characterized in that: The method for completing the matrix imputation of the missing intercyclic spectrum matrix in step S5 includes the FISTA method, the expression of which is: ， in, It is the step size; This represents a parameter introduced to accelerate iteration; It is an intermediate quantity in the iterative process; It is the soft threshold shrinkage operator, which is calculated as `diag` is an operator for extracting or constructing diagonal elements of a matrix. Indicates taking 0 and The larger value in; for The eigenvector matrix of eigenvalue decomposition; for Eigenvalues ​​of eigenvalue decomposition.

3. A storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements step S5 in the asynchronous measurement method of any one of claims 1 to 2 for a cyclic steady sound source.

4. A computer device, characterized in that: include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the computer program to implement step S5 in the asynchronous measurement method of any one of claims 1 to 2 for a cyclic steady sound source.

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