CN113050038A - Transformer substation sound source positioning method and system based on virtual array extension - Google Patents

Transformer substation sound source positioning method and system based on virtual array extension Download PDF

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CN113050038A
CN113050038A CN202110308374.XA CN202110308374A CN113050038A CN 113050038 A CN113050038 A CN 113050038A CN 202110308374 A CN202110308374 A CN 202110308374A CN 113050038 A CN113050038 A CN 113050038A
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array
sound
representing
sound source
signal
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张瑶
罗林根
盛戈皞
王辉
宋辉
钱勇
江秀臣
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Shanghai Jiaotong University
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Shanghai Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/20—Position of source determined by a plurality of spaced direction-finders

Abstract

The invention discloses a transformer substation sound source positioning method based on virtual array extension, which comprises the following steps: (1) setting a sound sensor uniform plane array to collect K sound signals, wherein the sound sensor uniform plane array is provided with M multiplied by M array elements; (2) expanding the uniform planar array of the sound sensor by adopting a fourth-order cumulant array expansion method; (3) constructing a spatial spectrum function based on the extended array; (4) carrying out maximum value search on the space spectrum function, and obtaining an incidence azimuth angle corresponding to the maximum value based on the maximum value
Figure DDA0002988602560000011
And an estimated value of the incidence pitch angle theta, so as to position the sound source of the substation equipment. In addition, the invention also discloses a system for positioning the partial discharge signal of the transformer substation, and the system can be used for implementing the transformer substation sound source positioning method.

Description

Transformer substation sound source positioning method and system based on virtual array extension
Technical Field
The invention relates to a positioning method and a positioning system, in particular to a transformer substation sound source positioning method and a transformer substation sound source positioning system.
Background
The operation state of the power equipment directly affects the safety and stability of the power grid and the productivity benefit, and a safer and more effective state detection method is urgently needed to ensure the safe production of the power, so as to realize the detection of the operation state of the power equipment.
The existing sound detection technology for the power equipment usually needs to install a sound sensor and a signal conditioning unit on the power equipment, and usually needs to consider the arrangement of a power line and a signal line when the sound detection technology is implemented on site, so that the sound detection technology is tedious and has large workload. In addition, the detection technology cannot realize the positioning of the sound source of the electrical equipment, and if the positioning is to be realized, a sensor needs to be installed on each piece of equipment, so that huge manpower and material resource burden is caused, and the detection cost is extremely high.
In the prior art, some sound source localization methods can perform localization by collecting sound signals using a sound sensor array. The acoustic detection means utilizing the sound sensor array has the advantages of wide measurement range, non-contact measurement, strong fault early warning capability and the like, can realize active positioning of abnormal sound sources of the transformer substation, determine fault sections and prevent further spread of faults. Accordingly, the performance of acoustic source localization techniques based on acoustic sensor arrays is not only related to the processing algorithm, but also depends on the array model of the sensors, and the resolution and localization accuracy of the array can be improved by increasing the number of sensors.
However, it should be noted that such acoustic source localization technology based on acoustic sensor array is affected by hardware cost, and especially for the application of on-line monitoring of acoustic signals, the number of sensors cannot be increased without limit.
Based on this, aiming at the defects and shortcomings of the prior art, the invention is expected to obtain a transformer substation sound source positioning method and system based on virtual array extension, which can perform virtual extension on uniform planar arrays (URAs) to extend the number of sensors without upgrading the sound sensor arrays, thereby effectively inhibiting gaussian noise in transformer substation sound source signals, improving positioning accuracy and realizing accurate positioning of transformer substation equipment sound sources.
Disclosure of Invention
One of the purposes of the invention is to provide a transformer substation sound source positioning method based on virtual array extension, which can virtually extend a sound sensor array to extend the number of sensors without upgrading the sensor array, thereby effectively inhibiting Gaussian noise in a transformer substation sound source signal, improving positioning accuracy and realizing accurate positioning of a transformer substation equipment sound source.
Based on the purpose, the invention provides a transformer substation sound source positioning method based on virtual array extension, which comprises the following steps:
(1) arranging a sound sensor uniform plane array to collect sound signals, wherein the sound sensor uniform plane array is provided with M multiplied by M array elements;
(2) expanding the uniform planar array of the sound sensor by adopting a fourth-order cumulant array expansion method;
(3) constructing a spatial spectrum function based on the extended array;
(4) carrying out maximum value search on the space spectrum function, and obtaining an incidence azimuth angle corresponding to the maximum value based on the maximum value
Figure BDA0002988602540000028
And an estimated value of the incidence pitch angle theta, so as to position the sound source of the substation equipment.
In the above technical solution of the present invention, in the step (2), the present invention provides a Fourth Order Cumulant (FOC) array extension method suitable for uniform planar array (URA), which can effectively expand the number of sound sensors, suppress gaussian noise in signals, and improve positioning accuracy.
Further, in the transformer substation sound source positioning method according to the present invention, the step (2) further includes the steps of:
(a) the uniform planar array of acoustic sensors is expanded using the following formula:
Figure BDA0002988602540000021
Figure BDA0002988602540000022
Figure BDA0002988602540000023
wherein the content of the first and second substances,
Figure BDA0002988602540000024
the array expanded sound signals are directed to a vector matrix,
Figure BDA0002988602540000025
denotes a steering vector of the i-th sound signal after array expansion, and K denotes the number of incident sound signals (i.e., sound source signals), wherein
Figure BDA0002988602540000026
Is the product of kronecker, and is,
Figure BDA0002988602540000027
a steering vector representing an i-th sound signal before the array expansion; csA covariance matrix representing the incident signal after array expansion; e (-) represents the expected value; sHRepresenting the conjugate transpose of S, S representing the incident sound signal,
Figure BDA0002988602540000031
to represent
Figure BDA0002988602540000032
The conjugate transpose of (c).
(b) Covariance matrix R of array extended sound signal4Performing characteristic decomposition to obtain:
Figure BDA0002988602540000033
wherein U ═ US,UN]Σ denotes a diagonal matrix of eigenvalues, USRepresenting a signal subspace, U, consisting of eigenvectors corresponding to the first K larger eigenvalues after eigen decompositionNAnd representing a noise subspace formed by the eigenvectors corresponding to the K +1 th to Mth smaller eigenvalues after the characteristic decomposition, wherein H represents the conjugate transpose.
Further, in the transformer substation sound source positioning method of the present invention, the spatial spectrum function
Figure BDA0002988602540000034
Is configured to:
Figure BDA0002988602540000035
wherein theta represents an incident pitch angle of the sound signal,
Figure BDA0002988602540000036
denotes the sound signal incident azimuth, and H denotes the conjugate transpose.
Further, in the transformer substation sound source positioning method, the value of M is 4.
Accordingly, another object of the present invention is to provide a transformer substation sound source positioning system based on virtual array extension, which can virtually extend a uniform planar array (URA) to extend the number of sensors without upgrading the sensor array, thereby effectively suppressing gaussian noise in a transformer substation sound source signal, improving positioning accuracy, and implementing accurate positioning of a transformer substation equipment sound source.
Based on the above purpose, the present invention further provides a transformer substation sound source positioning system based on virtual array extension, which includes:
the sound sensor uniform plane array is used for collecting sound signals and is provided with M multiplied by M array elements;
control means arranged to perform the steps of:
(1) expanding the uniform planar array of the sound sensor by adopting a fourth-order cumulant array expansion method;
(2) constructing a spatial spectrum function based on the extended array;
(3) carrying out maximum value search on the space spectrum function, and obtaining an incidence azimuth angle corresponding to the maximum value based on the maximum value
Figure BDA0002988602540000037
And an estimated value of the incidence pitch angle theta, so as to position the sound source of the substation equipment.
Further, in the transformer substation sound source positioning method according to the present invention, the step (1) further includes the steps of:
(a) the uniform planar array of acoustic sensors is expanded using the following formula:
Figure BDA0002988602540000041
Figure BDA0002988602540000042
Figure BDA0002988602540000043
wherein the content of the first and second substances,
Figure BDA0002988602540000044
the array expanded sound signals are directed to a vector matrix,
Figure BDA0002988602540000045
a steering vector representing the ith sound signal after array expansion, and K representing the number of incident sound signals, wherein
Figure BDA0002988602540000046
Is the product of kronecker, and is,
Figure BDA0002988602540000047
a steering vector representing an i-th sound signal before the array expansion; csA covariance matrix representing the virtually extended incident signal; e [. C]Indicates the expected value, SHRepresenting the conjugate transpose of S, S representing the incident sound signal,
Figure BDA0002988602540000048
to represent
Figure BDA0002988602540000049
The conjugate transpose of (c).
(b) Covariance matrix R of array extended sound signal4Performing characteristic decomposition to obtain:
Figure BDA00029886025400000410
wherein U ═ US,UN]Σ denotes a diagonal matrix of eigenvalues, USRepresenting a signal subspace, U, consisting of eigenvectors corresponding to the first K larger eigenvalues after eigen decompositionNAnd representing a noise subspace formed by the eigenvectors corresponding to the K +1 th to Mth smaller eigenvalues after the characteristic decomposition, wherein H represents the conjugate transpose.
Further, in the transformer substation sound source positioning method of the present invention, the spatial spectrum function
Figure BDA00029886025400000411
Is configured to:
Figure BDA00029886025400000412
wherein theta represents an incident pitch angle of the sound signal,
Figure BDA00029886025400000413
denotes the sound signal incident azimuth, and H denotes the conjugate transpose.
Further, in the transformer substation sound source positioning method, the value of M is 4.
Compared with the prior art, the transformer substation sound source positioning method and system based on virtual array extension have the following advantages and beneficial effects:
the transformer substation sound source positioning method based on the virtual array extension overcomes the defects in the prior art, particularly the defects of poor anti-interference performance and low positioning accuracy in the prior art.
In the invention, the transformer substation sound source positioning method based on virtual array extension can virtually extend a uniform planar array (URA) to extend the number of sensors without upgrading the sensor array, thereby effectively inhibiting Gaussian noise in a transformer substation sound source signal, improving positioning accuracy and realizing accurate positioning of a transformer substation equipment sound source.
Accordingly, the transformer substation sound source positioning system based on virtual array extension can be used for implementing the transformer substation sound source positioning method, and has the advantages and beneficial effects.
Drawings
Fig. 1 schematically shows a sound sensor uniform planar array model of a transformer substation sound source positioning system based on virtual array extension according to an embodiment of the present invention.
Fig. 2 schematically shows a system configuration diagram of a transformer substation sound source positioning system based on virtual array extension according to an embodiment of the present invention.
Fig. 3 schematically shows a transformer substation field sound signal diagram acquired by a sound sensor array of the transformer substation equipment abnormal sound source positioning system according to an embodiment of the invention.
Detailed Description
The method and system for positioning a substation sound source based on virtual array extension according to the present invention will be further explained and explained with reference to the drawings and specific embodiments of the specification, but the explanation and explanation do not unduly limit the technical solution of the present invention.
In the invention, the transformer substation sound source positioning method based on virtual array extension can comprise the following steps:
(1) and arranging a sound sensor uniform plane array to collect sound signals, wherein the sound sensor uniform plane array is provided with M multiplied by M array elements.
(2) And expanding the uniform planar array of the sound sensor by adopting a fourth-order cumulant array expansion method.
(3) And constructing a spatial spectrum function based on the extended array.
(4) Carrying out maximum value search on the space spectrum function, and obtaining an incidence azimuth angle corresponding to the maximum value based on the maximum value
Figure BDA0002988602540000051
And an estimated value of the incidence pitch angle theta, so as to position the sound source of the substation equipment.
Fig. 1 schematically shows a sound sensor uniform planar array model of a transformer substation sound source positioning system based on virtual array extension according to an embodiment of the present invention.
In the transformer substation sound source positioning method based on virtual array extension, the sound sensor uniform plane array is provided with M multiplied by M array elements, wherein M represents the number of sensors.
As shown in fig. 1, the uniform line arrays are uniformly distributed along the x-axis or y-axis, which means that the uniform planar array of the acoustic sensor is a two-dimensional extension of the uniform line arrays on a plane. In the formed uniform planar array of the sound sensor, a plurality of sound signals can be collected, the sound signals are independent from each other, and the direction of an x axis and the direction of a y axis in the uniform planar array of the sound sensor areArray element spacing in direction is dxAnd dy。
It should be noted that, as can be seen with further reference to fig. 1, in the present invention, the collected signals may include an incident sound signal and a noise signal, wherein the incident sound signal exists in an incident direction W, wherein
Figure BDA0002988602540000061
Denotes an incident azimuth angle of the i-th incident sound signal, and i is 1,2, …, K; accordingly, θiDenotes the incident pitch angle of the i-th incident sound signal, and i is 1,2, …, K. Incident azimuth angle
Figure BDA0002988602540000062
Starting from the positive x-axis half shaft and returning to the positive x-axis half shaft in a counterclockwise direction in the range
Figure BDA0002988602540000063
Angle of incidence pitch thetaiStarting from the positive half shaft of the z axis to the positive half shaft of the x axis, and the range is more than or equal to 0 and less than or equal to thetai＜90°。
In the invention, the sound sensor is used for uniformly and flatly acquiring the sound signal Y. Assuming that the vector of the sound signal observed by the uniform planar array of sound sensors is y (t), and t is the sampling point, y (t) can be expressed as:
Y(t)＝AS(t)+N(t) (1)
in the above formula (1), a denotes a steering vector matrix of the sound signal, which is related to the array distribution and the direction of the sound signal; s (t) is an incident sound signal vector, S (t) is [ s ]1(t),s2(t),…sK(t)]T(ii) a N (t) is a noise signal.
Accordingly, in the present invention, the steering vector matrix A of the uniform planar array of acoustic sensors can be similarly decomposed into the x-axis direction and the y-axis direction, respectively, by AxAnd AyRepresents:
Figure BDA0002988602540000064
Figure BDA0002988602540000065
in the above-mentioned formula (2) and formula (3),
Figure BDA0002988602540000066
the direction vector of the 1 st signal in the direction of the x axis;
Figure BDA0002988602540000067
the vector is the guide vector of the 1 st signal in the y-axis direction; by the way of analogy, the method can be used,
Figure BDA0002988602540000068
a guiding vector of the Kth signal in the direction of the x axis;
Figure BDA0002988602540000069
the guiding vector of the K signal in the y-axis direction is shown.
As can be seen from this, it is,
Figure BDA00029886025400000610
and
Figure BDA00029886025400000611
the i-th signal is a guide vector in the x-axis direction and the y-axis direction, and i is 1,2, …, K. Then
Figure BDA00029886025400000612
And
Figure BDA00029886025400000613
can be expressed as:
Figure BDA00029886025400000614
Figure BDA0002988602540000071
in the above-mentioned formula (4) and formula (5),
Figure BDA0002988602540000072
ω represents angular frequency, c represents sound speed; j represents an imaginary part; dxAnd dyRespectively representing the distance between two adjacent sound sensors in the x-axis direction and the y-axis direction; (.)TRepresenting the transpose of the matrix.
It should be noted that the uniform planar array of acoustic sensors can be regarded as a uniform linear array uniformly extending along the x-axis or y-axis, so that the M (M is 1,2, …, M) th row of array elements parallel to the x-axis is a steering vector matrix
Figure BDA0002988602540000073
Can be expressed as:
Figure BDA0002988602540000074
in the above-mentioned formula (6),
Figure BDA0002988602540000075
a guide vector of the No. 1 signal in the m-th row array element parallel to the direction of the x axis; by the way of analogy, the method can be used,
Figure BDA0002988602540000076
the guiding vector of the mth row of array elements of the Kth signal parallel to the direction of the x axis is obtained.
Then
Figure BDA0002988602540000077
And a guide vector of the ith signal in the mth row element parallel to the x-axis direction is represented, and i is 1,2, … and K. Accordingly, the number of the first and second electrodes,
Figure BDA0002988602540000078
can be expressed by the following formula (7):
Figure BDA0002988602540000079
thus, the steering vector matrix a of the uniform planar array of acoustic sensors can be written as:
Figure BDA00029886025400000710
in the above-mentioned formula (8),
Figure BDA00029886025400000711
is an M multiplied by K dimensional matrix;
Figure BDA00029886025400000712
is an M multiplied by K dimensional matrix;
Figure BDA00029886025400000713
is an M multiplied by K dimensional matrix; (.)TRepresenting the transpose of the matrix.
Therefore, the temperature of the molten metal is controlled,
Figure BDA00029886025400000714
is a (M) multiplied by K dimensional matrix,
Figure BDA00029886025400000715
can be expressed as:
Figure BDA00029886025400000716
in the above-mentioned formula (9),
Figure BDA00029886025400000717
a steering vector representing the 1 st signal;
Figure BDA00029886025400000718
a steering vector representing the 2 nd signal;
Figure BDA00029886025400000719
representing the steering vector of the K-th signal. Accordingly, the number of the first and second electrodes,
Figure BDA00029886025400000720
Figure BDA00029886025400000721
a steering vector for the ith signal may be represented, and i ═ 1,2, …, K.
In the transformer substation sound source positioning method, in the step (2), the uniform planar array of the sound sensor can be expanded by adopting a fourth-order cumulant (FOC) array expansion method. With reference to equation (1), since K incident sound signals (i.e., sound source signals) are independent of each other, the fourth-order cumulative quantity (FOC) of incident sound signals collected by the uniform planar array of sound sensors can be expressed as:
Figure BDA0002988602540000081
in the above formula (10), 1. ltoreq. k1,k2,k3,k4≤M*M，k1,k2,k3,k4Random numbers between 1 and M x M; a. thei(k) A K-th element representing an i-th signal steering vector, i ═ 1,2, …, K; gamma ray4,siRepresenting the fourth order accumulation of the ith signal.
In the present invention, k is1,k2,k3,k4In different combinations, C4xIn common (M)2)4A value is taken and placed in the dimension (M)2)2×(M2)2Matrix R of4In (5), the following formula (11) can be obtained:
R4((k1-1)M2+k2,(k3-1)M2+k4)＝C4x(k1,k2,k3,k4) (11)
referring to equation (10) and equation (11) in combination, the matrix R can be expressed as4Written in the form of kronecker product, the following formula (12) is obtained:
Figure BDA0002988602540000082
in the above formula (12), E (·) represents an expectation value; y represents the acquired sound signal;
Figure BDA0002988602540000083
is kronecker product; h represents conjugate transpose;
Figure BDA0002988602540000084
guiding a vector matrix for the sound signals after array expansion; csRepresenting the covariance matrix of the incident signal after array expansion.
In the present invention, the following formula can be used to expand the uniform planar array of acoustic sensors:
Figure BDA0002988602540000085
Figure BDA0002988602540000086
Figure BDA0002988602540000087
wherein the content of the first and second substances,
Figure BDA0002988602540000088
the array expanded sound signals are directed to a vector matrix,
Figure BDA0002988602540000089
a steering vector representing the ith sound signal after array expansion, and K representing the number of incident sound signals, wherein
Figure BDA00029886025400000810
Is the product of kronecker, and is,
Figure BDA00029886025400000811
a steering vector representing an i-th sound signal before the array expansion; csA covariance matrix representing the incident signal after array expansion; e (-) denotes the expected value, SHRepresenting the conjugate transpose of S, S representing the incident sound signal,
Figure BDA00029886025400000812
to represent
Figure BDA00029886025400000813
The conjugate transpose of (c).
The covariance matrix of the array-extended sound signal is R4Because there is no correlation between the incident sound signal and the ambient noise, the subspace can be decomposed into a signal subspace and a noise subspace. Thus, for the covariance matrix R4Decomposition is carried out, the following formula (16) is obtained:
Figure BDA0002988602540000091
where U denotes a subspace, Σ denotes a diagonal matrix composed of eigenvalues, and U ═ US,UN]；USRepresenting a signal subspace, U, consisting of eigenvectors corresponding to the first K larger eigenvalues after eigen decompositionNAnd representing a noise subspace formed by eigenvectors corresponding to the K +1 th to Mth smaller eigenvalues after the characteristic decomposition, wherein H represents the conjugate transpose of the matrix.
Then Σ can be expressed as:
Figure BDA0002988602540000092
in the above formula (6), λiPerforming eigen decomposition on the covariance matrix, and arranging the ith eigenvalue (i is 1,2, … …, M) after the eigenvalues are arranged from large to smallSIs a signal subspace, U, composed of eigenvectors corresponding to the first K larger eigenvaluesNThe noise subspace is formed by eigenvectors corresponding to the K +1 th to Mth small eigenvalues.
In the invention, a new spatial spectrum function can be obtained by utilizing the orthogonal characteristic of two subspaces
Figure BDA0002988602540000093
The spatial spectrum function
Figure BDA0002988602540000094
Is configured to:
Figure BDA0002988602540000095
in the above equation (18), θ represents the incident pitch angle of the sound signal,
Figure BDA0002988602540000096
denotes the sound signal incident azimuth, and H denotes the conjugate transpose.
Correspondingly, a maximum value search is carried out on the spatial spectrum function, and the incidence azimuth angle corresponding to the maximum value is obtained based on the maximum value
Figure BDA0002988602540000097
And the sound source of the substation equipment can be positioned by the estimated value of the incident pitch angle theta.
Fig. 2 schematically shows a system configuration diagram of a transformer substation sound source positioning system based on virtual array extension according to an embodiment of the present invention.
In order to better illustrate the effectiveness of the transformer substation sound source positioning method based on virtual array extension, the invention collects sound signals of a certain transformer substation through field test for further explanation.
As shown in fig. 2, in the present embodiment, the transformer substation sound source localization method according to the present invention is implemented by using a transformer substation sound source localization system based on virtual array extension. In this embodiment, the substation sound source localization system may include: a uniform planar array of acoustic sensors and a control device. The control device can comprise a preprocessing unit, a 16-channel synchronous acquisition unit and a computer.
In the present embodiment, the uniform planar array of the sound sensor in the system is a 4 × 4 uniform planar array with an array element pitch of 7cm, which can collect sound signals of the substation; the control device can adopt a fourth-order cumulant array expansion method to expand the uniform planar array of the sound sensor, construct a space spectrum function based on the expanded array, then search the maximum value of the space spectrum function, and obtain the incident azimuth angle corresponding to the maximum value based on the maximum value
Figure BDA0002988602540000101
And an estimated value of the incidence pitch angle theta, so as to position the sound source of the substation equipment.
Accordingly, in the present embodiment, the tester can use the handheld electrostatic gun to discharge for testing, and the sound signal generated by the discharge of the handheld electrostatic gun is as shown in fig. 3.
Fig. 3 schematically shows a transformer substation field sound signal diagram acquired by a uniform planar array of sound sensors in an embodiment of the transformer substation equipment abnormal sound source positioning system according to the present invention.
As shown in fig. 3, fig. 3 shows 16 sound signals received by a uniform planar array of sound sensors in the abnormal sound source localization system of substation equipment according to the present invention. Accordingly, each signal is normalized, and CH1 to CH16 shown in fig. 3 represent 16-way sound sensors, respectively.
As can be seen by further referring to fig. 3, in the sound signals shown in fig. 3, the signals of [1.5s,2s ], [2.5s,3s ] and [3.2s,6.2s ] are incident sound signals of electrostatic gun discharge, and the signals at the rest of the time are noise signals existing in the substation.
Correspondingly, after the sound signals of the transformer substation are collected, the uniform planar array (URA) of the sound sensor can be expanded based on a four-order cumulant (FOC) array expansion method, a spatial spectrum function is constructed based on the expanded array, and then a conventional multiple signal classification Method (MUSIC) is adopted to perform maximum value search on the spatial spectrum function so as to position the sound source of the transformer substation equipment.
In order to prove the superiority of the URA-FOC-MUSIC method for positioning the sound source, in the invention, a tester can use a handheld electrostatic gun to discharge in the direction with the incident azimuth angle of 135 degrees and the incident pitch angle of 30 degrees, and based on sound signals collected by a sound sensor uniform plane array consisting of 16 sound sensors, the sound source can be positioned by respectively adopting two completely different methods, namely the URA-FOC-MUSIC method (the method of the invention) and a multiple signal classification Method (MUSIC), so as to obtain the corresponding test data result. The results of the relevant test data can be shown in table 1 below.
Table 1 shows the results of on-site sound source localization using the URA-FOC-MUSIC method and the MUSIC method, respectively.
Table 1.
Figure BDA0002988602540000111
Analysis table 1 shows that the mean square error of locating a live sound source using the conventional MUSIC method is 1.6340 °. By adopting the URA-FOC-MUSIC method, the uniform planar array (URA) of the sound sensor is expanded by utilizing a fourth-order cumulant (FOC) array expansion method, a spatial spectrum function is constructed based on the expansion array, and the maximum value search is carried out on the spatial spectrum function, so that the mean square error can be reduced to 0.3874 degrees from 1.6340 degrees by the positioning method for positioning the sound source of the transformer substation equipment.
The invention adds Fourth Order Cumulant (FOC) to make uniform planar array (URA) of sound sensor virtually expand, which is equivalent to increase the number of arrays and improve the resolution of arrays; meanwhile, the high-order cumulant only contains information of non-Gaussian components, so that the method has better Gaussian noise resistance.
In conclusion, the transformer substation sound source positioning method based on virtual array expansion can virtually expand the sensor array to expand the number of sensors without upgrading the sensor array, thereby effectively inhibiting Gaussian noise in a transformer substation sound source signal, improving positioning accuracy and realizing accurate positioning of a transformer substation equipment sound source.
Accordingly, the transformer substation sound source positioning system based on virtual array extension can be used for implementing the transformer substation sound source positioning method, and has the advantages and beneficial effects.
It should be noted that the prior art in the protection scope of the present invention is not limited to the examples given in the present application, and all the prior art which is not inconsistent with the technical scheme of the present invention, including but not limited to the prior patent documents, the prior publications and the like, can be included in the protection scope of the present invention.
In addition, the combination of the features in the present application is not limited to the combination described in the claims of the present application or the combination described in the embodiments, and all the features described in the present application may be freely combined or combined in any manner unless contradictory to each other.
It should also be noted that the above-mentioned embodiments are only specific embodiments of the present invention. It is apparent that the present invention is not limited to the above embodiments and similar changes or modifications can be easily made by those skilled in the art from the disclosure of the present invention and shall fall within the scope of the present invention.

Claims (8)

1. A transformer substation sound source positioning method based on virtual array extension is characterized by comprising the following steps:
(1) arranging a sound sensor uniform plane array to collect sound signals, wherein the sound sensor uniform plane array is provided with M multiplied by M array elements;
(2) expanding the uniform planar array of the sound sensor by adopting a fourth-order cumulant array expansion method;
(3) constructing a spatial spectrum function based on the extended array;
(4) carrying out maximum value search on the space spectrum function, and obtaining an incidence azimuth angle corresponding to the maximum value based on the maximum value
Figure FDA0002988602530000011
And an estimated value of the incidence pitch angle theta, so as to position the sound source of the substation equipment.
2. The substation sound source localization method of claim 1, wherein the step (2) further comprises the steps of:
(a) the uniform planar array of acoustic sensors is expanded using the following formula:
Figure FDA0002988602530000012
Figure FDA0002988602530000013
Figure FDA0002988602530000014
wherein the content of the first and second substances,
Figure FDA0002988602530000015
the array expanded sound signals are directed to a vector matrix,
Figure FDA0002988602530000016
a steering vector representing the ith sound signal after array expansion, and K representing the number of incident sound signals, wherein
Figure FDA0002988602530000017
Is the product of kronecker, and is,
Figure FDA0002988602530000018
a steering vector representing an i-th sound signal before the array expansion; csA covariance matrix representing the incident signal after array expansion; e (-) denotes the expected value, SHRepresenting the conjugate transpose of S, S representing the incident sound signal,
Figure FDA0002988602530000019
to represent
Figure FDA00029886025300000110
The conjugate transpose of (c).
(b) Covariance matrix R of array extended sound signal4Performing characteristic decomposition to obtain:
Figure FDA00029886025300000111
wherein U ═ US,UN]Σ denotes a diagonal matrix of eigenvalues, USRepresenting a signal subspace, U, consisting of eigenvectors corresponding to the first K larger eigenvalues after eigen decompositionNAnd representing a noise subspace formed by the eigenvectors corresponding to the K +1 th to Mth smaller eigenvalues after the characteristic decomposition, wherein H represents the conjugate transpose.
3. The substation sound source localization method of claim 2, wherein the spatial spectral function
Figure FDA00029886025300000112
Is configured to:
Figure FDA0002988602530000021
wherein theta represents an incident pitch angle of the sound signal,
Figure FDA0002988602530000022
denotes the sound signal incident azimuth, and H denotes the conjugate transpose.
4. The substation sound source positioning method of claim 1, wherein M takes the value of 4.
5. A transformer substation sound source positioning system based on virtual array extension is characterized by comprising:
the sound sensor uniform plane array is used for collecting sound signals and is provided with M multiplied by M array elements;
control means arranged to perform the steps of:
(1) expanding the uniform planar array of the sound sensor by adopting a fourth-order cumulant array expansion method;
(2) constructing a spatial spectrum function based on the extended array;
(3) carrying out maximum value search on the space spectrum function, and obtaining an incidence azimuth angle corresponding to the maximum value based on the maximum value
Figure FDA0002988602530000023
And an estimated value of the incidence pitch angle theta, so as to position the sound source of the substation equipment.
6. The substation sound source localization system of claim 5, wherein the step (1) further comprises the steps of:
(a) the uniform planar array of acoustic sensors is expanded using the following formula:
Figure FDA0002988602530000024
Figure FDA0002988602530000025
Figure FDA0002988602530000026
wherein the content of the first and second substances,
Figure FDA0002988602530000027
the array expanded sound signals are directed to a vector matrix,
Figure FDA0002988602530000028
a steering vector representing the ith sound signal after array expansion, and K representing the number of incident sound signals, wherein
Figure FDA0002988602530000029
Is the product of kronecker, and is,
Figure FDA00029886025300000210
a steering vector representing an i-th sound signal before the array expansion; csA covariance matrix representing the incident signal after array expansion; e (-) denotes the expected value, SHRepresenting the conjugate transpose of S, S representing the incident sound signal,
Figure FDA00029886025300000211
to represent
Figure FDA00029886025300000212
The conjugate transpose of (c).
(b) Covariance matrix R of array extended sound signal4Performing characteristic decomposition to obtain:
Figure FDA00029886025300000213
wherein U ═ US,UN]Σ denotes a diagonal matrix of eigenvalues, USRepresenting a signal subspace, U, consisting of eigenvectors corresponding to the first K larger eigenvalues after eigen decompositionNAfter representing the feature decomposition byAnd H represents conjugate transpose.
7. The substation sound source localization system of claim 6, wherein the spatial spectral function
Figure FDA0002988602530000031
Is configured to:
Figure FDA0002988602530000032
wherein theta represents an incident pitch angle of the sound signal,
Figure FDA0002988602530000033
denotes the sound signal incident azimuth, and H denotes the conjugate transpose.
8. The substation sound source positioning system of claim 5, wherein M takes the value 4.
CN202110308374.XA 2021-03-23 2021-03-23 Transformer substation sound source positioning method and system based on virtual array extension Pending CN113050038A (en)

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