CN112415439B - Vibration and sound detection signal filtering method and system using sparse projection - Google Patents

Vibration and sound detection signal filtering method and system using sparse projection Download PDF

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CN112415439B
CN112415439B CN202011215129.6A CN202011215129A CN112415439B CN 112415439 B CN112415439 B CN 112415439B CN 202011215129 A CN202011215129 A CN 202011215129A CN 112415439 B CN112415439 B CN 112415439B
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signal sequence
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CN112415439A (en
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翟明岳
翁鸿彬
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North China Electric Power University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/72—Testing of electric windings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/62—Testing of transformers

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Abstract

The embodiment of the invention discloses a method and a system for filtering a vibro-acoustic detection signal by utilizing sparse projection, wherein the method comprises the following steps: step 101, acquiring a signal sequence S acquired according to a time sequence; step 102, calculating a projection matrix; step 103, obtaining a sparse matrix; step 104 initializing process parameters; step 105 iteratively updating process parameters; step 106, calculating an iteration error and ending iteration; step 107 is to find the signal sequence after noise filtering.

Description

Vibration and sound detection signal filtering method and system using sparse projection
Technical Field
The invention relates to the field of electric power, in particular to a method and a system for filtering a vibration and sound detection signal of a transformer.
Background
With the high-speed development of the smart grid, the safe and stable operation of the power equipment is particularly important. At present, the detection of the operating state of the power equipment with ultrahigh voltage and above voltage grades, especially the detection of the abnormal state, is increasingly important and urgent. As an important component of an electric power system, a power transformer is one of the most important electrical devices in a substation, and its reliable operation is related to the safety of a power grid. Generally, the abnormal state of the transformer can be divided into core abnormality and winding abnormality. The core abnormality is mainly represented by core saturation, and the winding abnormality generally includes winding deformation, winding looseness and the like.
The basic principle of the transformer abnormal state detection is to extract each characteristic quantity in the operation of the transformer, analyze, identify and track the characteristic quantity so as to monitor the abnormal operation state of the transformer. The detection method can be divided into invasive detection and non-invasive detection according to the contact degree; the detection can be divided into live detection and power failure detection according to whether the shutdown detection is needed or not; the method can be classified into an electrical quantity method, a non-electrical quantity method, and the like according to the type of the detected quantity. In comparison, the non-invasive detection has strong transportability and is more convenient to install; the live detection does not affect the operation of the transformer; the non-electric quantity method is not electrically connected with the power system, so that the method is safer. The current common detection methods for the operation state of the transformer include a pulse current method and an ultrasonic detection method for detecting partial discharge, a frequency response method for detecting winding deformation, a vibration detection method for detecting mechanical and electrical faults, and the like. The detection methods mainly detect the insulation condition and the mechanical structure condition of the transformer, wherein the detection of the vibration signal (vibration sound) of the transformer is the most comprehensive, and the fault and the abnormal state of most transformers can be reflected.
In the running process of the transformer, the magnetostriction of the iron core silicon steel sheets and the vibration caused by the winding electrodynamic force can radiate vibration sound signals with different amplitudes and frequencies to the periphery. When the transformer normally operates, uniform low-frequency noise is emitted outwards; if the sound is not uniform, it is not normal. The transformer can make distinctive sounds in different running states, and the running state of the transformer can be mastered by detecting the sounds made by the transformer. It is worth noting that the detection of the sound emitted by the transformer in different operating states not only can detect a plurality of serious faults causing the change of the electrical quantity, but also can detect a plurality of abnormal states which do not endanger the insulation and do not cause the change of the electrical quantity, such as the loosening of internal and external parts of the transformer, and the like.
Because the vibration sound detection method utilizes the vibration signal sent by the transformer, the vibration sound detection method is easily influenced by environmental noise, and therefore, how to effectively identify the vibration sound and the noise is the key for success of the method.
Disclosure of Invention
Because the vibration sound detection method utilizes the vibration signal sent by the transformer, the vibration sound detection method is easily influenced by environmental noise, and therefore, how to effectively identify the vibration sound and the noise is the key for success of the method.
The invention aims to provide a vibration and sound detection signal filtering method and system by utilizing sparse projection. The method has better robustness and simpler calculation.
In order to achieve the purpose, the invention provides the following scheme:
a vibro-acoustic detection signal filtering method using sparse projection comprises the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102, obtaining a projection matrix, specifically: the projection matrix is recorded as phi, and the ith row and jth column elements are recorded as phiijThe calculation formula is as follows:
Figure BDA0002760103160000021
wherein:
t is the sampling interval of the signal sequence S,
f0is the center frequency of the signal sequence S,
σias a matrix SSTThe ith eigenvalue (eigenvalues are sorted from large to small),
σjas a matrix SSTThe jth eigenvalue (eigenvalues are sorted from large to small),
i is 1,2, N is a row number,
j is 1,2, N is a column number;
step 103, obtaining a sparse matrix, specifically: the sparse matrix is denoted by gamma, and the ith row and jth column elements are denoted by gammaijThe formula used is:
Figure BDA0002760103160000022
wherein:
m0is the mean value of the signal sequence S,
σ0: the mean square error of the signal sequence S,
Figure BDA0002760103160000023
miis a sequence [ s ]1，s2，···，si]The average value of (a) of (b),
mjis a sequence [ s ]1,s2,···,sj]The average value of (a) of (b),
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
sifor the i-th element of the signal sequence S,
sjfor the jth element of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S;
step 104 initializes process parameters, specifically: the process parameters comprise a threshold value tau, a sparse vector d and an iteration control parameter k; the initialization value of the threshold value tau is recorded as tau0The initialized value of the sparse vector d is denoted as d0The initialization formula used is:
d0＝S
τ0＝max||ΓS||
k＝0
step 105 iteratively updates process parameters, specifically: the updated value of the k +1 th step of the threshold value tau is recorded as tauk+1And the (k + 1) th update value of the sparse vector d is recorded as dk+1The update formula used is:
Figure BDA0002760103160000031
Figure BDA0002760103160000032
wherein:
Figure BDA0002760103160000033
as a threshold decision function, the formula used is:
Figure BDA0002760103160000034
sgn (×) represents a sign function with an argument,
the values of the variables are represented by a number,
dkupdating the value for the k-th step of the sparse vector d,
τkrepresents the kth step update value of the threshold value tau,
i is an identity matrix;
step 106, calculating an iteration error and ending iteration, specifically: the iteration error is recorded as epsilon, and the formula used is:
ε＝||dk+1-dk||；
if the iteration error epsilon meets the formula epsilon is more than or equal to 0.001, adding 1 to the value of the iteration control parameter k, and returning to the step 105 and the step 106 to continue the iteration updating process; otherwise, the iterative updating process is ended and the optimal threshold value tau is obtainedOPTHas a value ofOPT＝τkThe best sparse vector dOPTHas a value of dOPT＝dk；
Step 107, obtaining a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as SnewThe formula used is:
Figure BDA0002760103160000035
a vibro-acoustic detection signal filtering system utilizing sparse projection, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 finds a projection matrix, specifically: the projection matrix is recorded as phi, and the ith row and jth column elements are recorded as phiijThe calculation formula is as follows:
Figure BDA0002760103160000036
wherein:
t is the sampling interval of the signal sequence S,
f0is the center frequency of the signal sequence S,
σias a matrix SSTThe ith eigenvalue (eigenvalues are sorted from large to small),
σjas a matrix SSTThe jth eigenvalue (eigenvalues are sorted from large to small),
i is 1,2, N is a row number,
j is 1,2, N is a column number;
the module 203 finds a sparse matrix, specifically: the sparse matrix is denoted by gamma, and the ith row and jth column elements are denoted by gammaijThe formula used is:
Figure BDA0002760103160000041
wherein:
m0is the mean value of the signal sequence S,
σ0: the mean square error of the signal sequence S,
Figure BDA0002760103160000042
miis a sequence [ s ]1,s2,···,si]The average value of (a) of (b),
mjis a sequence [ s ]1,s2,···,sj]The average value of (a) of (b),
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
sifor the i-th element of the signal sequence S,
sjfor the jth element of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S;
the module 204 initializes process parameters, specifically: the process parameters comprise a threshold value tau, a sparse vector d and an iteration control parameter k; the initialization value of the threshold value tau is recorded as tau0The initialized value of the sparse vector d is denoted as d0The initialization formula used is:
d0＝S
τ0＝max||ΓS||
k＝0
module 205 iteratively updates the process parameters, specifically: the updated value of the k +1 th step of the threshold value tau is recorded as tauk+1And the (k + 1) th update value of the sparse vector d is recorded as dk+1The update formula used is:
Figure BDA0002760103160000043
Figure BDA0002760103160000044
wherein:
Figure BDA0002760103160000051
as a threshold decision function, the formula used is:
Figure BDA0002760103160000052
sgn (×) represents a sign function with an argument,
the values of the variables are represented by a number,
dkupdating the value for the k-th step of the sparse vector d,
τkrepresents the kth step update value of the threshold value tau,
i is an identity matrix;
module 206 finds the iteration error and ends the iteration, specifically: the iteration error is recorded as epsilon, and the formula used is:
ε＝||dk+1-dk||；
if the iteration error epsilon satisfies the formula epsilon is more than or equal to 0.001, adding 1 to the value of the iteration control parameter k and returning to the module 205 and the module 206 to continue the iteration updating process; otherwise, the iterative updating process is ended and the optimal threshold value tau is obtainedOPTHas a value ofOPT＝τkThe best sparse vector dOPTHas a value of dOPT＝dk；
The module 207 calculates a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as SnewThe formula used is:
Figure BDA0002760103160000053
according to the specific embodiment provided by the invention, the invention discloses the following technical effects:
because the vibration sound detection method utilizes the vibration signal sent by the transformer, the vibration sound detection method is easily influenced by environmental noise, and therefore, how to effectively identify the vibration sound and the noise is the key for success of the method.
The invention aims to provide a vibration and sound detection signal filtering method and system by utilizing sparse projection. The method has better robustness and simpler calculation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments will be briefly described below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic flow chart of the system of the present invention;
FIG. 3 is a flow chart illustrating an embodiment of the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
FIG. 1 is a schematic flow chart of a vibro-acoustic detection signal filtering method using sparse projection
Fig. 1 is a schematic flow chart of a vibro-acoustic detection signal filtering method using sparse projection according to the present invention. As shown in fig. 1, the method for filtering a vibro-acoustic detection signal by using sparse projection specifically includes the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102, obtaining a projection matrix, specifically: the projection matrix is recorded as phi, and the ith row and jth column elements are recorded as phiijThe calculation formula is as follows:
Figure BDA0002760103160000061
wherein:
t is the sampling interval of the signal sequence S,
f0is the center frequency of the signal sequence S,
σias a matrix SSTThe ith eigenvalue (eigenvalues are sorted from large to small),
σjas a matrix SSTThe jth eigenvalue (eigenvalues are sorted from large to small),
i is 1,2, N is a row number,
j is 1,2, N is a column number;
step 103, obtaining a sparse matrix, specifically: the sparse matrix is denoted by gamma, and the ith row and jth column elements are denoted by gammaijThe formula used is:
Figure BDA0002760103160000062
wherein:
m0is the mean value of the signal sequence S,
σ0: the mean square error of the signal sequence S,
Figure BDA0002760103160000063
miis a sequence [ s ]1，s2，···，si]The average value of (a) of (b),
mjis a sequence [ s ]1，s2，···，sj]The average value of (a) of (b),
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
sifor the i-th element of the signal sequence S,
sjfor the jth element of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S;
step 104 initializes process parameters, specifically: the process parameters comprise a threshold value tau, a sparse vector d and an iteration control parameter k; the initialization value of the threshold value tau is recorded as tau0The initialized value of the sparse vector d is denoted as d0The initialization formula used is:
d0＝S
τ0＝max||ΓS||
k＝0
step 105 iteratively updates process parameters, specifically: the updated value of the k +1 th step of the threshold value tau is recorded as tauk+1And the (k + 1) th update value of the sparse vector d is recorded as dk+1The update formula used is:
Figure BDA0002760103160000071
Figure BDA0002760103160000072
wherein:
Figure BDA0002760103160000073
as a threshold decision function, the formula used is:
Figure BDA0002760103160000074
sgn (×) represents a sign function with an argument,
the values of the variables are represented by a number,
dkupdating the value for the k-th step of the sparse vector d,
τkrepresents the kth step update value of the threshold value tau,
i is an identity matrix;
step 106, calculating an iteration error and ending iteration, specifically: the iteration error is recorded as epsilon, and the formula used is:
ε＝||dk+1-dk||；
if the iteration error epsilon meets the formula epsilon is more than or equal to 0.001, adding 1 to the value of the iteration control parameter k, and returning to the step 105 and the step 106 to continue the iteration updating process; otherwise, the iterative updating process is ended and the optimal threshold value tau is obtainedOPTHas a value ofOPT＝τkThe best sparse vector dOPTHas a value of dOPT＝dk；
Step 107, obtaining a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as SnewThe formula used is:
Figure BDA0002760103160000081
FIG. 2 is a schematic diagram of a vibro-acoustic detection signal filtering system using sparse projection
Fig. 2 is a schematic structural diagram of a vibro-acoustic detection signal filtering system using sparse projection according to the present invention. As shown in fig. 2, the vibro-acoustic detection signal filtering system using sparse projection includes the following structure:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 finds a projection matrix, specifically: the projection matrix is recorded as phi, and the ith row and jth column elements are recorded as phiijThe calculation formula is as follows:
Figure BDA0002760103160000082
wherein:
t is the sampling interval of the signal sequence S,
f0is the center frequency of the signal sequence S,
σias a matrix SSTThe ith eigenvalue (eigenvalues are sorted from large to small),
σjas a matrix SSTThe jth eigenvalue (eigenvalues are sorted from large to small),
i is 1,2, N is a row number,
j is 1,2, N is a column number;
the module 203 finds a sparse matrix, specifically: the sparse matrix is denoted by gamma, and the ith row and jth column elements are denoted by gammaijThe formula used is:
Figure BDA0002760103160000083
wherein:
m0is the mean value of the signal sequence S,
σ0: the mean square error of the signal sequence S,
Figure BDA0002760103160000084
miis a sequence [ s ]1，s2，···，si]The average value of (a) of (b),
mjis a sequence [ s ]1，s2，···，sj]The average value of (a) of (b),
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
sifor the i-th element of the signal sequence S,
sjfor the jth element of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S;
the module 204 initializes process parameters, specifically: the process parameters comprise a threshold value tau, a sparse vector d and an iteration control parameter k; the initialization value of the threshold value tau is recorded as tau0The initialized value of the sparse vector d is denoted as d0The initialization formula used is:
d0＝S
τ0＝max||ΓS||
k＝0
module 205 iteratively updates the process parameters, specifically: the updated value of the k +1 th step of the threshold value tau is recorded as tauk+1And the (k + 1) th update value of the sparse vector d is recorded as dk+1The update formula used is:
Figure BDA0002760103160000091
Figure BDA0002760103160000092
wherein:
Figure BDA0002760103160000093
as a threshold decision function, the formula used is:
Figure BDA0002760103160000094
sgn (×) represents a sign function with an argument,
the values of the variables are represented by a number,
dkupdating the value for the k-th step of the sparse vector d,
τkrepresents the kth step update value of the threshold value tau,
i is an identity matrix;
module 206 finds the iteration error and ends the iteration, specifically: the iteration error is recorded as epsilon, and the formula used is:
ε＝||dk+1-dk||；
if the iteration error epsilon satisfies the formula epsilon is more than or equal to 0.001, adding 1 to the value of the iteration control parameter k and returning to the module 205 and the module 206 to continue the iteration updating process; otherwise, the iterative updating process is ended and the optimal threshold value tau is obtainedOPTHas a value ofOPT＝τkThe best sparse vector dOPTHas a value of dOPT＝dk；
The module 207 calculates a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as SnewThe formula used is:
Figure BDA0002760103160000095
the following provides an embodiment for further illustrating the invention
FIG. 3 is a flow chart illustrating an embodiment of the present invention. As shown in fig. 3, the method specifically includes the following steps:
step 301, acquiring a signal sequence S acquired according to a time sequence;
step 302, obtaining a projection matrix, specifically: the projection matrix is recorded as phi, and the ith row and jth column elements are recorded as phiijThe calculation formula is as follows:
Figure BDA0002760103160000101
wherein:
t is the sampling interval of the signal sequence S,
f0is the center frequency of the signal sequence S,
σias a matrix SSTThe ith eigenvalue (eigenvalues are sorted from large to small),
σjas a matrix SSTThe jth eigenvalue (eigenvalues are sorted from large to small),
i is 1,2, N is a row number,
j is 1,2, N is a column number;
step 303, obtaining a sparse matrix, specifically: the sparse matrix is denoted by gamma, and the ith row and jth column elements are denoted by gammaijThe formula used is:
Figure BDA0002760103160000102
wherein:
m0is the mean value of the signal sequence S,
σ0: the mean square error of the signal sequence S,
Figure BDA0002760103160000103
miis a sequence [ s ]1,s2,···,si]The average value of (a) of (b),
mjis a sequence [ s ]1,s2,···,sj]The average value of (a) of (b),
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
sifor the i-th element of the signal sequence S,
sjfor the jth element of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S;
step 304 initializes process parameters, in particularComprises the following steps: the process parameters comprise a threshold value tau, a sparse vector d and an iteration control parameter k; the initialization value of the threshold value tau is recorded as tau0The initialized value of the sparse vector d is denoted as d0The initialization formula used is:
d0＝S
τ0＝max||ΓS||
k＝0
step 305 iteratively updates process parameters, specifically: the updated value of the k +1 th step of the threshold value tau is recorded as tauk+1And the (k + 1) th update value of the sparse vector d is recorded as dk+1The update formula used is:
Figure BDA0002760103160000111
Figure BDA0002760103160000112
wherein:
Figure BDA0002760103160000113
as a threshold decision function, the formula used is:
Figure BDA0002760103160000114
sgn (×) represents a sign function with an argument,
the values of the variables are represented by a number,
dkupdating the value for the k-th step of the sparse vector d,
τkrepresents the kth step update value of the threshold value tau,
i is an identity matrix;
step 306, calculating an iteration error and ending the iteration, specifically: the iteration error is recorded as epsilon, and the formula used is:
ε＝||dk+1-dk||；
if the iteration error isIf epsilon satisfies the formula epsilon is more than or equal to 0.001, adding 1 to the value of the iteration control parameter k and returning to the step 305 and the step 306 to continue the iteration updating process; otherwise, the iterative updating process is ended and the optimal threshold value tau is obtainedOPTHas a value ofOPT＝τkThe best sparse vector dOPTHas a value of dOPT＝dk；
Step 307, obtaining a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as SnewThe formula used is:
Figure BDA0002760103160000115
the embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is simple because the system corresponds to the method disclosed by the embodiment, and the relevant part can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (2)

1. A vibro-acoustic detection signal filtering method using sparse projection is characterized by comprising the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102, obtaining a projection matrix, specifically: the projection matrix is recorded as phi, and the ith row and jth column elements are recorded as phiijThe calculation formula is as follows:
Figure FDA0003254118130000011
wherein:
t is the sampling interval of the signal sequence S,
f0is the center frequency of the signal sequence S,
σias a matrix SSTThe ith eigenvalue of (1) is arranged from big to small,
σjas a matrix SSTThe j-th eigenvalue of (2) is arranged from big to small,
i is 1,2, …, N is the row number,
j is 1,2, …, and N is the column number;
step 103, obtaining a sparse matrix, specifically: the sparse matrix is denoted by gamma, and the ith row and jth column elements are denoted by gammaijThe formula used is:
Figure FDA0003254118130000012
wherein:
m0is the mean value of the signal sequence S,
σ0: the mean square error of the signal sequence S,
Figure FDA0003254118130000013
miis a sequence [ s ]1,s2,…,si]The average value of (a) of (b),
mjis a sequence [ s ]1,s2,…,sj]The average value of (a) of (b),
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
sifor the i-th element of the signal sequence S,
sjfor the jth element of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S;
step 104 initializes process parameters, specifically: the process parameters comprise a threshold value tau, a sparse vector d and an iteration control parameter k; the initialization value of the threshold value tau is recorded as tau0The initialized value of the sparse vector d is denoted as d0The initialization formula used is:
d0＝S
τ0＝max||ΓS||
k＝0
step 105 iteratively updates process parameters, specifically: the updated value of the k +1 th step of the threshold value tau is recorded as tauk+1And the (k + 1) th update value of the sparse vector d is recorded as dk+1The update formula used is:
Figure FDA0003254118130000021
Figure FDA0003254118130000022
wherein:
Figure FDA0003254118130000023
as a threshold decision function, the formula used is:
Figure FDA0003254118130000024
sgn (×) represents a sign function with an argument,
the values of the variables are represented by a number,
dkupdating the value for the k-th step of the sparse vector d,
τkrepresents the kth step update value of the threshold value tau,
i is an identity matrix;
step 106, calculating an iteration error and ending iteration, specifically: the iteration error is recorded as epsilon, and the formula used is:
ε＝||dk+1-dk||；
if the iteration error epsilon meets the formula epsilon is more than or equal to 0.001, adding 1 to the value of the iteration control parameter k, and returning to the step 105 and the step 106 to continue the iteration updating process; otherwise, the iterative updating process is ended and the optimal threshold value tau is obtainedOPTHas a value ofOPT＝τkThe best sparse vector dOPTHas a value of dOPT＝dk；
Step 107, obtaining a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as SnewThe formula used is:
Figure FDA0003254118130000025
2. a vibro-acoustic detection signal filtering system using sparse projection, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 finds a projection matrix, specifically: the projection matrix is recorded as phi, and the ith row and jth column elements are recorded as phiijThe calculation formula is as follows:
Figure FDA0003254118130000026
wherein:
t is the sampling interval of the signal sequence S,
f0is the center frequency of the signal sequence S,
σias a matrix SSTThe ith eigenvalue of (1) is arranged from big to small,
σjas a matrix SSTThe j-th eigenvalue of (2) is arranged from big to small,
i is 1,2, …, N is the row number,
j is 1,2, …, and N is the column number;
the module 203 finds a sparse matrix, specifically: the sparse matrix is denoted by gamma, and the ith row and jth column elements are denoted by gammaijThe formula used is:
Figure FDA0003254118130000031
wherein:
m0is the mean value of the signal sequence S,
σ0: the mean square error of the signal sequence S,
Figure FDA0003254118130000032
miis a sequence [ s ]1,s2,…,si]The average value of (a) of (b),
mjis a sequence [ s ]1,s2,…,sj]The average value of (a) of (b),
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
sifor the i-th element of the signal sequence S,
sjfor the jth element of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S;
the module 204 initializes process parameters, specifically: the process parameters comprise a threshold value tau, a sparse vector d and an iteration control parameter k; the initialization value of the threshold value tau is recorded as tau0The initialized value of the sparse vector d is denoted as d0The initialization formula used is:
d0＝S
τ0＝max||ΓS||
k＝0
module 205 iteratively updates the process parameters, specifically: the updated value of the k +1 th step of the threshold value tau is recorded as tauk+1And the (k + 1) th update value of the sparse vector d is recorded as dk+1The update formula used is:
Figure FDA0003254118130000033
Figure FDA0003254118130000034
wherein:
Figure FDA0003254118130000041
as a threshold decision function, the formula used is:
Figure FDA0003254118130000042
sgn (×) represents a sign function with an argument,
the values of the variables are represented by a number,
dkupdating the value for the k-th step of the sparse vector d,
τkrepresents the kth step update value of the threshold value tau,
i is an identity matrix;
module 206 finds the iteration error and ends the iteration, specifically: the iteration error is recorded as epsilon, and the formula used is:
ε＝||dk+1-dk||；
if the iteration error epsilon satisfies the formula epsilon is more than or equal to 0.001, adding 1 to the value of the iteration control parameter k and returning to the module 205 and the module 206 to continue the iteration updating process; otherwise, the iterative updating process is ended and the optimal threshold value tau is obtainedOPTHas a value ofOPT＝τkThe best sparse vector dOPTHas a value of dOPT＝dk；
The module 207 calculates a signal sequence after noise filtering, specifically: filtering noiseThe latter signal sequence is denoted SnewThe formula used is:
Figure FDA0003254118130000043
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