A method for locating low-frequency noise sources in substations

Abstract

The present invention relates to a method for locating low-frequency noise sources in a substation, comprising: determining a desired sound source area, simultaneously obtaining sound pressure data of a target sound source measured by an acoustic array and calculating a sound pressure cross-spectral matrix; defining a modal vector related to the phase and amplitude of a real sound source vector, solving the distribution of the real sound source vector in the desired sound source area based on the eigenvalues and eigenvectors of the modal vector and the sound pressure cross-spectral matrix based on a generalized inverse beamforming process, and converting the distribution into an integral form; optimizing and solving the integral form to obtain a weight coefficient vector of the real sound source, and locating the noise source based on the weight coefficient vector of the real sound source. Compared with the existing technology, the present invention has the advantages of accurate low-frequency positioning and strong anti-interference performance.

Description

Technical Field

[0001] The present invention relates to the technical field of transformer substation noise measurement, and in particular to a method for locating a low-frequency noise source in a transformer substation. Background Art

[0002] Due to the complex environment and numerous equipment in substations, transformers, reactors, and transmission and transformation lines all generate varying degrees of noise when working. Therefore, accurately locating the noise source is of great significance for clarifying the substation sound field distribution and then taking corresponding noise reduction measures.

[0003] In recent decades, acoustic array-based beamforming technology has been widely used and developed in the field of noise identification due to its simple principles and accurate positioning. However, since the noise generated by electrical equipment in substations is mostly low-frequency, traditional acoustic array-based beamforming technology is limited by the "Rayleigh criterion". Identifying low-frequency noise sources often requires larger array devices, which undoubtedly increases measurement costs and makes it more difficult to transport, measure, use, and popularize them. Most traditional algorithms suffer from poor low-frequency resolution and poor noise immunity, especially in far-field conditions. Therefore, there is an urgent need for a sound source localization method that can effectively locate low-frequency, far-field noise sources while significantly improving the algorithm's noise immunity. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for accurately identifying and locating the low-frequency noise source of a substation.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A method for locating a low-frequency noise source in a substation, comprising:

[0007] Determine the expected area of the sound source, obtain the sound pressure data of the target sound source measured by the sound array, and calculate the sound pressure cross-spectral matrix;

[0008] Define the modal vector related to the phase and amplitude of the real sound source vector. According to the eigenvalues and eigenvectors of the modal vector and the sound pressure cross-spectral matrix, solve the distribution of the real sound source vector in the expected sound source area based on the generalized inverse beamforming process and convert it into an integral form.

[0009] The integral form is optimized and solved to obtain the weight coefficient vector of the real sound source, and the noise source is located according to the weight coefficient vector of the real sound source.

[0010] In the above process, the modal vector a related to the phase and amplitude of the real sound source vector i The expression is:

[0011]

[0012] Where λ i is the i-th eigenvalue of the sound pressure cross-spectrum matrix, i=1,2,…M h , M h is the number of acoustic array microphones, u i is the i-th column vector of the eigenvector U of the sound pressure cross-spectrum matrix, is the sound pressure cross-spectrum matrix C P The characteristic vector of C P =U∑U H .

[0013] The distribution expression of the real sound source vector in the sound source expected area is:

[0014]

[0015] Where S is the expected area of the sound source, and the expected area of the sound source S is obtained by dividing N s expected area division points; a is M h ×1-order modal vector; G hs M is the distance between the sound array and the desired sound source area S h ×N s The acoustic transfer matrix is of order, and Q is the weight coefficient vector of the real sound source in the target area to be determined.

[0016] The distribution of the real sound source vector in the expected sound source area is converted into an integral form:

[0017] a(r h )=∫ S Q(r s )G hs (r h ,r s )dS

[0018] Where, M between the sound array and the desired sound source area S is h ×N s Acoustic transfer matrix is the imaginary unit, r h =(x h ,y h ,z h ), r s =(x s ,y s ,z s ) are the position vectors of the desired area division points of each sound array and sound source respectively.

[0019] In the method of the present invention, the specific steps of optimizing and solving the integral form include:

[0020] 1) The unknown weight coefficient Q in the distribution of the integral form of the real sound source vector in the expected sound source area is expanded in two directions along the x-axis and y-axis of the expected sound source area S; the x-axis is the axis where the long side of the expected sound source area is located, and the y-axis is the axis where the wide side of the expected sound source area is located. The expanded expression is:

[0021]

[0022] Where A mn is the Fourier expansion coefficient of the unknown weight coefficient Q; m and n are the number of Fourier expansion terms of the y-axis and x-axis respectively; L x 、L y are the length and width of the expected sound source area S respectively.

[0023] 2) Substitute the result of step 1) into the distribution of the real sound source vector in the integral form in the sound source expected area; obtain:

[0024]

[0025] 3) Divide the coordinates obtained in step 2) into equal parts and perform numerical calculations on the integral, that is, replace the integral interval x in the above formula with s ∈[-L x ,L x ]、y s ∈[-L y ,L y ] is divided into M and N equal parts, and the integral is numerically calculated to obtain:

[0026]

[0027] 4) Truncate the series summation range of the calculation result of step 3) to obtain:

[0028]

[0029] Where m t 、n t represents the number of terms to be summed and truncated; and:

[0030]

[0031] 5) Convert the truncated result in step 4) into a matrix form, the expression is:

[0032]

[0033] Where a represents M h ×1-order modal vector; S represents M h ×M fThe acoustic transfer matrix between the acoustic array measurement surface of order and the unknown weight Fourier expansion coefficient, M f =(2×m t +1)·(2×n t +1) is the total number of terms in Fourier expansion; A mn Indicates M f The weight vector of the Fourier expansion coefficients of order ×1 to be determined.

[0034] 6) For the result converted into matrix form in step 5), the l1 norm minimization in sparse sampling technology is used to solve the Fourier expansion coefficient weight vector. The optimization function used is:

[0035]

[0036] Where A mn is the Fourier expansion coefficient of the unknown weight coefficient Q; m is the number of rows, n is the number of columns; and λ is the Lagrange multiplier. By solving the optimization function of the above equation, the weight coefficient vector of the real sound source can be obtained.

[0037] The method for locating low-frequency noise sources in substations provided by the present invention has at least the following advantages compared to the prior art:

[0038] The method of the present invention is based on conventional generalized inverse beamforming to construct and solve the real noise source vector distribution equation of the target area; secondly, the fast Fourier transform method is used to transform the solution integral so that the noise source weight coefficient vector to be solved has a certain sparsity; finally, the sparse sampling technology is used to construct a new optimization function for solving the noise source weight coefficient vector. By measuring the maximum peak value of the noise source weight coefficient vector, the position and intensity quantization results of the noise source are located, and finally the purpose of noise source positioning is achieved. The method can accurately reconstruct the relevant acoustic quantities of the target sound source, thereby realizing the effective positioning of the sound source, and also has strong anti-interference performance under complex circumstances; in addition, while being based on the high-resolution advantage of generalized inverse beamforming, it also has strong anti-interference performance. The final positioning result not only shows good performance in the medium and high frequency bands, but also maintains good positioning accuracy in the low frequency bands. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the process of locating the low-frequency noise source of a substation according to the present invention;

[0040] Figure 2 Schematic diagram of the positions of the sound source, focus area, and sound array in the embodiment;

[0041] Figure 3Figure 1 is a positioning effect diagram of the method of the present invention and the traditional generalized inverse beamforming method in the embodiment when the test frequency is 300 Hz and the test distance is 1 m, wherein sub-figure (a) is the positioning effect diagram of the method of the present invention, and sub-figure (b) is the positioning effect diagram of the traditional generalized inverse beamforming method;

[0042] Figure 4 Figure 1 is a positioning effect diagram of the method of the present invention and the traditional generalized inverse beamforming method in the embodiment when the test frequency is 1500 Hz and the test distance is 1 m, wherein sub-figure (a) is the positioning effect diagram of the method of the present invention, and sub-figure (b) is the positioning effect diagram of the traditional generalized inverse beamforming method;

[0043] Figure 5 3 is a diagram showing the positioning effects of the method of the present invention and the traditional generalized inverse beamforming method in the embodiment when the test frequency is 300 Hz and the test distance is 2.5 m, wherein sub-figure (a) is a diagram showing the positioning effects of the method of the present invention, and sub-figure (b) is a diagram showing the positioning effects of the traditional generalized inverse beamforming method. DETAILED DESCRIPTION

[0044] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0045] Example

[0046] The present invention provides a method for locating low-frequency noise sources in substations. This method first solves the true noise source vector distribution equation in the target area based on conventional generalized inverse beamforming. Secondly, the fast Fourier transform method is used to transform the integral solution, ensuring that the noise source weight coefficient vector to be solved has a certain degree of sparsity. Finally, sparse sampling technology is used to construct a new optimization function for solving the noise source weight coefficient vector. By measuring the maximum peak value of the noise source weight coefficient vector, the position and intensity of the noise source are quantified, ultimately achieving the purpose of noise source localization. While leveraging the high-resolution advantage of generalized inverse beamforming, this method also has strong anti-interference performance.

[0047] Figure 1 The flow chart of the method of the present invention is shown. The implementation steps of the method of the present invention are divided into two steps to locate the sound source. Figure 1 As shown, the specific implementation steps are as follows:

[0048] Step 1: Conventional generalized inverse beamforming process.

[0049] 1) First, use the acoustic array to measure the sound pressure data P of the target sound source h, the sound pressure cross-spectrum matrix C is calculated P :

[0050]

[0051] In the formula, the superscript "H" represents conjugation.

[0052] 2) Further, the sound pressure cross spectrum matrix C P Perform eigenvalue decomposition:

[0053] C P =U∑U H (2)

[0054] Where, Represents the eigenvector of the sound pressure cross-spectrum matrix, M h is the number of microphones in the acoustic array, ∑=diag(λ1,λ2…λ M ) is its corresponding eigenvalue.

[0055] 3) Further, define a modal vector a related to the phase and amplitude of the real sound source vector i , modal vector a i for:

[0056]

[0057] Where λ i is the i-th eigenvalue, i=1,2,…M h ,u i is the i-th column vector of the eigenvector U.

[0058] 4) Further, determine the area where the noise source is expected to be identified (expected sound source focus area) S and divide it into N s The expected area division points are then used to solve the distribution of the real sound source vector in the target area S, and we get:

[0059]

[0060] Formula (4) can also be written in the following integral form:

[0061] a(r h )=∫ S Q(r s )G hs (r h ,r s )dS (5)

[0062] Where G hs M is the distance between the sound array and the desired sound source area S h ×N s order acoustic transfer matrix, is the imaginary unit, rh =(x h ,y h ,z h ), r s =(x s ,y s ,z s ) represent the position vectors of each sound array and the sound source expected area division point, and Q represents the weight coefficient vector of the real sound source in the target area to be determined. Figure 2 , L in the figure x 、L y Respectively represent the length and width of the expected area of the sound source.

[0063] Step 2: Optimize and solve the weight coefficient vector Q for solving the real sound source.

[0064] 5) Further, the unknown weight coefficient Q in formula (4) is calculated along the expected sound source area S. Figure 2 The x-axis and y-axis in the figure are expanded in two directions by Fourier series. The x-axis is the axis of the long side of the expected sound source area, and the y-axis is the axis of the wide side of the expected sound source area. We can get:

[0065]

[0066] Where A mn is the Fourier expansion coefficient of the unknown weight coefficient Q, m and n are the number of Fourier expansion terms on the y-axis and x-axis respectively.

[0067] 6) Furthermore, by applying equation (6) back to equation (5) and rearranging it, we can obtain:

[0068]

[0069] 7) Further, the integral interval x in formula (7) is s ∈[-L x ,L x ]、y s ∈[-L y ,L y ] is divided into M and N equal parts respectively, and the integral is numerically calculated to obtain:

[0070]

[0071] 8) Furthermore, by truncating the range of the series summation of formula (8), we can obtain:

[0072]

[0073] Where m t 、n t represents the number of terms to be summed and truncated; and:

[0074]

[0075] 9) Furthermore, formula (9) can be written in matrix form:

[0076]

[0077] Where a represents M h ×1-order modal vector; S represents M h ×M f The acoustic transfer matrix between the acoustic array measurement surface of order and the unknown weight Fourier expansion coefficient, M f =(2×m t +1)·(2×n t +1) is the total number of terms in Fourier expansion; A mn Indicates M f The weight vector of the Fourier expansion coefficients of order ×1 to be determined.

[0078] 10) Further, solve the Fourier expansion coefficient weight vector A mn .

[0079] Sparse sampling is an effective technique for finding the optimal sparse solution to an underdetermined linear system of equations. According to its theory: if the signal itself can be sparsely represented, this technique can obtain all the information of the signal at a sampling frequency far lower than the Nyquist sampling theorem by solving a convex optimization problem. Only a small amount of measurement point information is needed to reconstruct the original signal with a high probability. Sparse sampling technology is applied to the field of array signal processing. The sparse beam pattern shaping method can be used to reduce the sidelobe magnitude while increasing the mainlobe gain level, thereby achieving the purpose of improving the sound source localization effect. This step uses the l1 norm minimization in the sparse sampling technology to solve the Fourier expansion coefficient weight vector A mn :

[0080]

[0081] Where λ is the Lagrange multiplier. By solving the optimization function of equation (11), the weight coefficient vector of the real sound source can be obtained.

[0082] Step 3: By measuring the maximum peak value of the weight coefficient vector of the real sound source obtained in step 2, the estimated position information and intensity quantification result of the noise source are obtained, and the purpose of noise source positioning is finally achieved.

[0083] The proposed method for localizing low-frequency noise sources in substations accurately reconstructs the relevant acoustic parameters of the target sound source, effectively localizing the source and demonstrating strong anti-interference performance even in complex situations. Furthermore, the method demonstrates excellent performance in mid- and high-frequency bands while maintaining good localization accuracy in low-frequency bands.

[0084] To verify the superiority of the method of the present invention, this embodiment uses MATLAB software to simulate the method proposed in the present invention. The specific steps are as follows:

[0085] (1) Set two point sound sources with different intensities, with initial coordinates of (-0.1, -0.1, 0) and (0.1, 0.1, 0) respectively; set the size of the desired sound source focus area to 0.5 × 0.5 m, and evenly divide 8 grid nodes on each side; set the array measurement surface size and the number of divided nodes to be consistent with the desired sound source focus area, with a total of 64 microphones, located 1 m above the sound source surface; set the equal fractions M and N of the method of the present invention to be 2 7 , the number of truncation items m t =20, n t =10. In the simulation calculation, this embodiment adds Gaussian white noise with a signal-to-noise ratio of 20dB to the method of the present invention and the traditional generalized inverse beamforming method to simulate the actual environment. The positioning results are tested at frequencies of 300Hz and 1500Hz and at test distances of 1m and 2.5m. The positioning results are shown in Figure 2. Figures 3 to 5 As shown. Figure 3 and Figure 4 It can be seen that as the frequency increases, the positioning accuracy of both methods increases, but the recognition effect of the method of the present invention is always better than that of the traditional method, and it has good positioning accuracy at low frequencies. Figure 3 and Figure 5 It can be seen that as the test distance increases, the positioning accuracy of both methods decreases. The traditional method cannot identify and separate sound sources with irrelevant intensities, while the method of the present invention still has good positioning accuracy and strong anti-interference ability.

[0086] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for locating low-frequency noise sources in a substation, characterized in that: include: Determine the expected area of the sound source, obtain the sound pressure data of the target sound source measured by the sound array, and calculate the sound pressure cross-spectral matrix; Define the modal vector related to the phase and amplitude of the real sound source vector. According to the eigenvalues and eigenvectors of the modal vector and the sound pressure cross-spectral matrix, solve the distribution of the real sound source vector in the expected sound source area based on the generalized inverse beamforming process and convert it into an integral form. Optimize and solve the integral form to obtain the weight coefficient vector of the real sound source, and locate the noise source based on the weight coefficient vector of the real sound source; The specific steps for optimizing the integral form include: 1) Perform a bidirectional Fourier series expansion on the unknown weight coefficient Q of the distribution of the integral form of the real sound source vector in the expected sound source area along the x-axis and y-axis of the expected sound source area S, where the x-axis is the axis of the long side of the expected sound source area and the y-axis is the axis of the wide side of the expected sound source area; 2) Substituting the result of the expansion in step 1) back into the distribution of the real sound source vector in the integral form in the sound source expected area; 3) dividing the coordinates obtained in step 2) into equal parts and performing numerical calculation on the integral; 4) truncating the series summation range of the calculation result of step 3); 5) converting the truncated result in step 4) into a matrix form; 6) For the result converted into matrix form in step 5), the L1 norm minimization in the sparse sampling technology is used to solve the Fourier expansion coefficient weight vector.

2. The method for locating a low-frequency noise source in a substation according to claim 1, wherein: The modal vector a related to the phase and amplitude of the real sound source vector i The expression is: Where λ i is the i-th eigenvalue of the sound pressure cross-spectrum matrix, i=1,2,…M h , M h is the number of acoustic array microphones, u i is the i-th column vector of the eigenvector U of the sound pressure cross-spectrum matrix, is the sound pressure cross-spectrum matrix C P The characteristic vector of C P =U∑U H .

3. The method for locating a low-frequency noise source in a substation according to claim 2, characterized in that: The distribution expression of the real sound source vector in the sound source expected area is: Where S is the expected area of the sound source, and the expected area of the sound source S is obtained by dividing N s expected area division points; a is M h ×1-order modal vector; G hs M is the distance between the sound array and the desired sound source area S h ×N s The acoustic transfer matrix is of order, and Q is the weight coefficient vector of the real sound source in the target area to be determined.

4. The method for locating a low-frequency noise source in a substation according to claim 3, wherein: The distribution of the real sound source vector in the expected sound source area is converted into an integral form: a(r h )=∫ S Q(r s )G hs (r h ,r s )dS Where, M between the sound array and the desired sound source area S is h ×N s Acoustic transfer matrix is the imaginary unit, r h =(x h ,y h ,z h ), r s =(x s ,y s ,z s ) are the position vectors of the desired area division points of each sound array and sound source respectively.

5. The method for locating a low-frequency noise source in a substation according to claim 1, wherein: In step 6), the l1 norm in the sparse sampling technique is used to minimize the Fourier expansion coefficient weight vector A. mn The optimization function used is: Where A mn is the Fourier expansion coefficient of the unknown weight coefficient Q; m and n are the number of Fourier expansion terms on the y-axis and x-axis respectively; λ is the Lagrange multiplier.

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