CN112345226B - Vibration and sound detection signal reconstruction method and system by utilizing block coordination minimization - Google Patents

Vibration and sound detection signal reconstruction method and system by utilizing block coordination minimization Download PDF

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CN112345226B
CN112345226B CN202011230011.0A CN202011230011A CN112345226B CN 112345226 B CN112345226 B CN 112345226B CN 202011230011 A CN202011230011 A CN 202011230011A CN 112345226 B CN112345226 B CN 112345226B
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翟明岳
罗永春
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North China Electric Power University
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Abstract

The embodiment of the invention discloses a method and a system for reconstructing a vibration and sound detection signal by utilizing block coordination minimization, wherein the method comprises the following steps: step 101, acquiring a signal sequence S acquired according to a time sequence; step 102, calculating the number of blocks; step 103, generating a block signal sequence; step 104, obtaining a coordination matrix; step 105, obtaining a reconstructed block signal sequence; step 106 finds the reconstructed signal sequence.

Description

Vibration and sound detection signal reconstruction method and system by utilizing block coordination minimization
Technical Field
The invention relates to the field of electric power, in particular to a reconstruction method and a reconstruction system of a vibration sound 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.
Disclosure of Invention
As mentioned above, the vibration and sound detection method utilizes the vibration signal emitted by the transformer, which is easily affected by the working environment, resulting in interruption of signal transmission and severe degradation of signal quality, so that the received partial vibration and sound signal cannot be used, and therefore how to effectively reconstruct the vibration and sound signal of the transformer is an important constraint factor for successful application of the method. The existing common method has insufficient attention to the problem, and no effective measure is taken to solve the problem.
The invention aims to provide a vibro-acoustic detection signal reconstruction method and a vibro-acoustic detection signal reconstruction system by utilizing block coordination minimization. The method has better signal reconstruction performance and simpler calculation.
In order to achieve the purpose, the invention provides the following scheme:
a vibro-acoustic detection signal reconstruction method with block coordination minimization, comprising:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102, calculating the number of blocks, specifically: the number of blocks is marked as NBThe formula used is:
Figure GDA0003281277610000021
wherein:
ΔS＝[0，s2-s1，s3-s2，…，sN-sN-1]in order to be able to signal the differential sequence,
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
s3for the 3 rd element of the signal sequence S,
sN-1for the N-1 th element of the signal sequence S,
sNfor the nth element of the signal sequence S,
n is the length of the signal sequence S,
sigma is the mean square error of the signal difference sequence deltas,
σ0is the mean square error of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S,
||*||Frepresents that Frobenius norm is obtained by calculating the sum of the numbers,
Figure GDA0003281277610000022
the expression is given for lower rounding,
denotes any variable;
step 103, generating a block signal sequence, specifically: the ith block signal sequence is denoted xiThe generation formula is as follows:
Figure GDA0003281277610000029
wherein:
Figure GDA0003281277610000023
for a block signal sequence xiThe length of (a) of (b),
Figure GDA0003281277610000024
presentation pair
Figure GDA0003281277610000025
The upper part is taken to be the whole,
Figure GDA0003281277610000026
the | th (i-1) M representing the signal sequence S0The number of +1| N elements,
Figure GDA0003281277610000027
the | th (i-1) M representing the signal sequence S0A number of +2| N elements,
Figure GDA0003281277610000028
represents the | iN of the signal sequence S0|NThe number of the elements is one,
|(i-1)M0+1|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +1,
|(i-1)M0+2|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +2,
|iM0|Nrepresenting the mode pair iM of N0The remainder is taken out,
i＝1，2，…，NBis the serial number of the block;
step 104, obtaining a coordination matrix, specifically: the coordination matrix is marked as A, and the solving formula is as follows:
Figure GDA0003281277610000031
wherein:
v is a matrix
Figure GDA0003281277610000032
The matrix of eigenvalues of (a),
mifor the ith block signal sequence xiThe mean value of (a);
step 105, obtaining the reconstructed block signal sequence, specifically: the ith reconstructed block signal sequence is denoted as biThe formula used is:
Figure GDA0003281277610000033
wherein:
y is an intermediate vector;
step 106, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula used is:
Figure GDA0003281277610000035
a vibro-acoustic detection signal reconstruction system with block-coordination minimization, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 calculates the number of blocks, specifically: the number of blocks is marked as NBThe formula used is:
Figure GDA0003281277610000034
wherein:
ΔS＝[0，s2-s1，s3-s2，…，sN-sN-1]in order to be able to signal the differential sequence,
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
s3for the 3 rd element of the signal sequence S,
sN-1for the N-1 th element of the signal sequence S,
sNfor the nth element of the signal sequence S,
n is the length of the signal sequence S,
sigma is the mean square error of the signal difference sequence deltas,
σ0is the mean square error of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S,
||*||Frepresents that Frobenius norm is obtained by calculating the sum of the numbers,
Figure GDA0003281277610000041
the expression is given for lower rounding,
denotes any variable;
the module 203 generates a block signal sequence, specifically: the ith block signal sequence is denoted xiThe generation formula is as follows:
Figure GDA0003281277610000042
wherein:
Figure GDA0003281277610000043
for a block signal sequence xiThe length of (a) of (b),
Figure GDA0003281277610000044
presentation pair
Figure GDA0003281277610000045
The upper part is taken to be the whole,
Figure GDA0003281277610000046
the | th (i-1) M representing the signal sequence S0+1|NThe number of the elements is one,
Figure GDA0003281277610000047
the | th (i-1) M representing the signal sequence S0+2|NThe number of the elements is one,
Figure GDA0003281277610000048
represents the | iN of the signal sequence S0|NThe number of the elements is one,
|(i-1)M0+1|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +1,
|(i-1)M0+2|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +2,
|iM0|Nrepresenting the mode pair iM of N0The remainder is taken out,
i＝1，2，…，NBis the serial number of the block;
the module 204 calculates a coordination matrix, specifically: the coordination matrix is marked as A, and the solving formula is as follows:
Figure GDA0003281277610000049
wherein:
v is a matrix
Figure GDA00032812776100000410
The matrix of eigenvalues of (a),
mifor the ith block signal sequence xiThe mean value of (a);
the module 205 obtains the reconstructed block signal sequence, specifically: the ith reconstructed block signal sequence is denoted as biThe formula used is:
Figure GDA00032812776100000411
wherein:
y is an intermediate vector;
the module 206 calculates a reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula used is:
Figure GDA0003281277610000052
according to the specific embodiment provided by the invention, the invention discloses the following technical effects:
as mentioned above, the vibration and sound detection method utilizes the vibration signal emitted by the transformer, which is easily affected by the working environment, resulting in interruption of signal transmission and severe degradation of signal quality, so that the received partial vibration and sound signal cannot be used, and therefore how to effectively reconstruct the vibration and sound signal of the transformer is an important constraint factor for successful application of the method. The existing common method has insufficient attention to the problem, and no effective measure is taken to solve the problem.
The invention aims to provide a vibro-acoustic detection signal reconstruction method and a vibro-acoustic detection signal reconstruction system by utilizing block coordination minimization. The method has better signal reconstruction performance and simpler calculation.
Drawings
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 method for reconstructing a vibro-acoustic detection signal using block coordination minimization
Fig. 1 is a schematic flow chart of a vibro-acoustic detection signal reconstruction method using block coordination minimization according to the present invention. As shown in fig. 1, the method for reconstructing a vibro-acoustic detection signal by block coordination minimization specifically includes the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102, calculating the number of blocks, specifically: the number of blocks is marked as NBThe formula used is:
Figure GDA0003281277610000051
wherein:
ΔS＝[0，s2-s1，s3-s2，…，sN-sN-1]in order to be able to signal the differential sequence,
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
s3for the 3 rd element of the signal sequence S,
sN-1for the N-1 th element of the signal sequence S,
sNfor the nth element of the signal sequence S,
n is the length of the signal sequence S,
sigma is the mean square error of the signal difference sequence deltas,
σ0is the mean square error of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S,
||*||Frepresents that Frobenius norm is obtained by calculating the sum of the numbers,
Figure GDA0003281277610000061
the expression is given for lower rounding,
denotes any variable;
step 103, generating a block signal sequence, specifically: the ith block signal sequence is denoted xiThe generation formula is as follows:
Figure GDA0003281277610000062
wherein:
Figure GDA0003281277610000063
for a block signal sequence xiThe length of (a) of (b),
Figure GDA0003281277610000064
presentation pair
Figure GDA0003281277610000065
The upper part is taken to be the whole,
Figure GDA0003281277610000066
the | th (i-1) M representing the signal sequence S0+1|NThe number of the elements is one,
Figure GDA0003281277610000067
the | th (i-1) M representing the signal sequence S0+2|NThe number of the elements is one,
Figure GDA0003281277610000068
represents the | iN of the signal sequence S0|NThe number of the elements is one,
|(i-1)M0+1|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +1,
|(i-1)M0+2|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +2,
|iM0|Nrepresenting the mode pair iM of N0The remainder is taken out,
i is 1, 2, …, and NB is the block number;
step 104, obtaining a coordination matrix, specifically: the coordination matrix is marked as A, and the solving formula is as follows:
Figure GDA0003281277610000069
wherein:
v is a matrix
Figure GDA00032812776100000610
The matrix of eigenvalues of (a),
mifor the ith block signal sequence xiThe mean value of (a);
step 105, obtaining the reconstructed block signal sequence, specifically: the ith reconstructed block signal sequence is denoted as biThe formula used is:
Figure GDA0003281277610000071
wherein:
y is an intermediate vector;
step 106, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula used is:
Figure GDA0003281277610000072
FIG. 2 structural intent of a vibro-acoustic detection signal reconstruction system using block coordination minimization
Fig. 2 is a schematic structural diagram of a vibro-acoustic detection signal reconstruction system using block coordination minimization according to the present invention. As shown in fig. 2, the vibro-acoustic detection signal reconstruction system using block coordination minimization includes the following structures:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 calculates the number of blocks, specifically: the number of blocks is marked as NBThe formula used is:
Figure GDA0003281277610000073
wherein:
ΔS＝[0，s2-s1，s3-s2，·..，sN-sN-1]in order to be able to signal the differential sequence,
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
s3for the 3 rd element of the signal sequence S,
sN-1for the N-1 th element of the signal sequence S,
sNfor the nth element of the signal sequence S,
n is the length of the signal sequence S,
sigma is the mean square error of the signal difference sequence deltas,
σ0is the mean square error of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S,
||*||Frepresents the calculation of FrobeniuThe number of the s-norm,
Figure GDA0003281277610000074
the expression is given for lower rounding,
denotes any variable;
the module 203 generates a block signal sequence, specifically: the ith block signal sequence is denoted xiThe generation formula is as follows:
Figure GDA0003281277610000081
wherein:
Figure GDA0003281277610000082
for a block signal sequence xiThe length of (a) of (b),
Figure GDA0003281277610000083
presentation pair
Figure GDA0003281277610000084
The upper part is taken to be the whole,
Figure GDA0003281277610000085
the | th (i-1) M representing the signal sequence S0+1|NThe number of the elements is one,
Figure GDA0003281277610000086
the | th (i-1) M representing the signal sequence S0+2|NThe number of the elements is one,
Figure GDA0003281277610000087
represents the | iN of the signal sequence S0L N elements of the number of elements,
|(i-1)M0+1|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +1,
|(i-1)M0+2|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +2,
|iM0|Nrepresenting the mode pair iM of N0The remainder is taken out,
i＝1，2，…，NBis the serial number of the block;
the module 204 calculates a coordination matrix, specifically: the coordination matrix is marked as A, and the solving formula is as follows:
Figure GDA0003281277610000088
wherein:
v is a matrix
Figure GDA0003281277610000089
The matrix of eigenvalues of (a),
mifor the ith block signal sequence xiThe mean value of (a);
the module 205 obtains the reconstructed block signal sequence, specifically: the ith reconstructed block signal sequence is denoted as biThe formula used is:
Figure GDA00032812776100000810
wherein:
y is an intermediate vector;
the module 206 calculates a reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula used is:
Figure GDA00032812776100000811
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, calculating the number of blocks, specifically: the number of blocks is marked as NBThe formula used is:
Figure GDA0003281277610000091
wherein:
ΔS＝[0，s2-s1，s3-s2，…，sN-sN-1]in order to be able to signal the differential sequence,
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
s3for the 3 rd element of the signal sequence S,
sN-1for the N-1 th element of the signal sequence S,
sNfor the nth element of the signal sequence S,
n is the length of the signal sequence S,
sigma is the mean square error of the signal difference sequence deltas,
σ0is the mean square error of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S,
||*||Frepresents that Frobenius norm is obtained by calculating the sum of the numbers,
Figure GDA0003281277610000092
the expression is given for lower rounding,
denotes any variable;
step 303 generates a block signal sequence, specifically: the ith block signal sequence is denoted xiThe generation formula is as follows:
Figure GDA0003281277610000093
wherein:
Figure GDA0003281277610000094
for a block signal sequence xiThe length of (a) of (b),
Figure GDA0003281277610000095
presentation pair
Figure GDA0003281277610000096
The upper part is taken to be the whole,
Figure GDA0003281277610000097
the | th (i-1) M representing the signal sequence S0+1|NThe number of the elements is one,
Figure GDA0003281277610000098
the | th (i-1) M representing the signal sequence S0+2|NThe number of the elements is one,
Figure GDA0003281277610000099
represents the | iN of the signal sequence S0|NThe number of the elements is one,
|(i-1)M0+1|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +1,
|(i-1)M0+2|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +2,
|iM0|Nrepresenting the mode pair iM of N0The remainder is taken out,
i＝1，2，…，NBis the serial number of the block;
step 304, obtaining a coordination matrix, specifically: the coordination matrix is marked as A, and the solving formula is as follows:
Figure GDA0003281277610000101
wherein:
v is a matrix
Figure GDA0003281277610000102
The matrix of eigenvalues of (a),
mifor the ith block signal sequence xiThe mean value of (a);
step 305, obtaining a reconstructed block signal sequence, specifically: the ith reconstructed block signal sequence is denoted as biThe formula used is:
Figure GDA0003281277610000103
wherein:
y is an intermediate vector;
step 306, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula used is:
Figure GDA0003281277610000104
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 reconstruction method using block coordination minimization, comprising:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102, calculating the number of blocks, specifically: the number of blocks is marked as NBThe formula used is:
Figure FDA0003281277600000011
wherein:
ΔS＝[0,s2-s1,s3-s2,…,sN-sN-1]in order to be able to signal the differential sequence,
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
s3for the 3 rd element of the signal sequence S,
sN-1for the N-1 th element of the signal sequence S,
sNfor the nth element of the signal sequence S,
n is the length of the signal sequence S,
sigma is the mean square error of the signal difference sequence deltas,
σ0is the mean square error of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S,
||*||Frepresents that Frobenius norm is obtained by calculating the sum of the numbers,
Figure FDA0003281277600000012
the expression is given for lower rounding,
denotes any variable;
step 103, generating a block signal sequence, specifically: the ith block signal sequence is denoted xiThe generation formula is as follows:
Figure FDA0003281277600000016
wherein:
Figure FDA0003281277600000013
for a block signal sequence xiThe length of (a) of (b),
Figure FDA0003281277600000014
presentation pair
Figure FDA0003281277600000015
The upper part is taken to be the whole,
Figure FDA0003281277600000017
the | th (i-1) M representing the signal sequence S0+1|NThe number of the elements is one,
Figure FDA0003281277600000018
the | th (i-1) M representing the signal sequence S0+2|NThe number of the elements is one,
Figure FDA0003281277600000019
represents the | iN of the signal sequence S0|NThe number of the elements is one,
|(i-1)M0+1|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +1,
|(i-1)M0+2|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +2,
|iM0|Nrepresenting the mode pair iM of N0The remainder is taken out,
i＝1,2,…,NBis the serial number of the block;
step 104, obtaining a coordination matrix, specifically: the coordination matrix is marked as A, and the solving formula is as follows:
Figure FDA0003281277600000021
wherein:
v is a matrix
Figure FDA0003281277600000022
The matrix of eigenvalues of (a),
mifor the ith block signal sequence xiThe mean value of (a);
step 105, obtaining the reconstructed block signal sequence, specifically: the ith reconstructed block signal sequence is denoted as biThe formula used is:
Figure FDA0003281277600000023
wherein:
y is an intermediate vector;
step 106, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula used is:
Figure FDA0003281277600000024
2. a vibro-acoustic detection signal reconstruction system utilizing block-coordination minimization, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 calculates the number of blocks, specifically: the number of blocks is marked as NBThe formula used is:
Figure FDA0003281277600000025
wherein:
ΔS＝[0,s2-s1,s3-s2,…,sN-sN-1]in order to be able to signal the differential sequence,
s1for the 1 st element of the signal sequence S,
s2for the 2 nd element of the signal sequence S,
s3for the 3 rd element of the signal sequence S,
sN-1for the N-1 th element of the signal sequence S,
sNfor the nth element of the signal sequence S,
n is the length of the signal sequence S,
sigma is the mean square error of the signal difference sequence deltas,
σ0is the mean square error of the signal sequence S,
the SNR is the signal-to-noise ratio of the signal sequence S,
||*||Frepresents that Frobenius norm is obtained by calculating the sum of the numbers,
Figure FDA0003281277600000026
the expression is given for lower rounding,
denotes any variable;
the module 203 generates a block signal sequence, specifically: the ith block signal sequence is denoted xiThe generation formula is as follows:
Figure FDA0003281277600000038
wherein:
Figure FDA0003281277600000031
for a block signal sequence xiLength of (2)，
Figure FDA0003281277600000032
Presentation pair
Figure FDA0003281277600000033
The upper part is taken to be the whole,
Figure FDA0003281277600000039
the | th (i-1) M representing the signal sequence S0+1|NThe number of the elements is one,
Figure FDA00032812776000000310
the | th (i-1) M representing the signal sequence S0+2|NThe number of the elements is one,
Figure FDA00032812776000000311
represents the | iN of the signal sequence S0|NThe number of the elements is one,
|(i-1)M0+1|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +1,
|(i-1)M0+2|Nrepresents that N is a modulus pair (i-1) M0The remainder is taken from +2,
|iM0|Nrepresenting the mode pair iM of N0The remainder is taken out,
i＝1,2,…,NBis the serial number of the block;
the module 204 calculates a coordination matrix, specifically: the coordination matrix is marked as A, and the solving formula is as follows:
Figure FDA0003281277600000034
wherein:
v is a matrix
Figure FDA0003281277600000035
The matrix of eigenvalues of (a),
mifor the ith block signal sequence xiThe mean value of (a);
the module 205 obtains the reconstructed block signal sequence, specifically: the ith reconstructed block signal sequence is denoted as biThe formula used is:
Figure FDA0003281277600000036
wherein:
y is an intermediate vector;
the module 206 calculates a reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula used is:
Figure FDA0003281277600000037
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