CN112284710A - Vibration and sound detection signal reconstruction method and system by using European optimal approximation - Google Patents

Vibration and sound detection signal reconstruction method and system by using European optimal approximation Download PDF

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CN112284710A
CN112284710A CN202011151359.0A CN202011151359A CN112284710A CN 112284710 A CN112284710 A CN 112284710A CN 202011151359 A CN202011151359 A CN 202011151359A CN 112284710 A CN112284710 A CN 112284710A
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翟明岳
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Guangdong University of Petrochemical Technology
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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 using Euclidean optimal approximation, wherein the method comprises the following steps: step 101, acquiring a signal sequence S acquired according to a time sequence; step 102 of obtaining N2A likelihood probability; step 103 of obtaining N2A joint self-similarity value; 104, obtaining N conditional shannon entropies; step 105, initializing an approximation variable; step 106, solving the value of the (k + 1) th step of the approximation vector; step 107 judges iteration error unionUpdating the bundle iteration; step 108 finds the reconstructed signal sequence.

Description

Vibration and sound detection signal reconstruction method and system by using European optimal approximation
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 vibration and sound detection signal reconstruction method and system by utilizing Euclidean optimal approximation. The method has better signal reconstruction performance and simpler calculation.
In order to achieve the purpose, the invention provides the following scheme:
a vibration and sound detection signal reconstruction method using Euclidean optimal approximation comprises the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102 of obtaining N2The similarity probability is specifically as follows: the similarity probability with sequence number (i, j) is denoted as pj|iThe formula used is:
Figure BDA0002741413930000021
wherein:
σ0is the mean square error of the signal sequence S,
sifor the ith element of the signal sequence S,
sjfor the jth element of the signal sequence S,
szfor the z-th element of the signal sequence S,
z is 1,2, N is the number of the intermediate element,
i is 1,2, N is the first element number,
j is 1,2, N is the second element number,
n is the length of the signal sequence S;
step 103 of obtaining N2The joint self-similarity values are specifically: the joint self-similarity value with sequence number (i, j) is denoted as pijThe calculation formula is as follows:
Figure BDA0002741413930000022
wherein:
pi|jis the likelihood probability of the sequence number (j, i),
pj|iis the self-phase probability of sequence number (i, j);
step 104, calculating N conditional shannon entropies, specifically: the nth conditional Shannon entropy is recorded as HnThe calculation formula used is:
Figure BDA0002741413930000023
wherein: n is 1,2, N is the conditional Shannon entropy sequence number, pinIs a joint self-similarity value of sequence numbers (i, n);
step 105, initializing an approximation variable, specifically: setting the initial value of an iteration control parameter k to be 1; the initial value of the approximation vector b is denoted as b0The nth element thereof is
Figure BDA0002741413930000024
Has a value of
Figure BDA0002741413930000025
The iteration value of step 1 of approximating vector b is recorded as b1The nth element thereof is
Figure BDA0002741413930000026
Has a value of
Figure BDA0002741413930000027
Wherein:
m0is the mean of the signal sequence S;
Figure BDA0002741413930000028
represents a mean value of m0Variance of
Figure BDA0002741413930000029
A gaussian distribution random function of;
step 106, calculating the (k + 1) th step value of the approximation vector, specifically: the step (k + 1) of the approximation vector b is recorded as bk +1The formula used is:
bk+1＝bk+αbk-1
wherein: bkFor the kth step value of the approximation vector b,
bk-1for the value of the (k-1) th step of the approximation vector b,
Figure BDA0002741413930000031
is a Euclidean distance factor;
step 107, judging the iteration error and ending the iteration updating, specifically: the iteration error of the k step is recorded as epsilonkHaving a value of εk＝||bk-bk-1||2(ii) a If epsilonk>0.001σoThen 1 is added to the value of the iterative control parameter k and the process returns to step 106 and step 107 until the iteration error epsilonkIs less than
Figure BDA0002741413930000032
The iteration is ended, and the iteration control parameter K is KoThe value of the approximation vector b is
Figure BDA0002741413930000033
Step 108, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula is
Figure BDA0002741413930000034
A vibro-acoustic detection signal reconstruction system using the best euclidean approximation, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
module 202 finds N2The similarity probability is specifically as follows: the similarity probability with sequence number (i, j) is denoted as pj|iThe formula used is:
Figure BDA0002741413930000035
wherein:
σ0is the mean square error of the signal sequence S,
sifor the ith element of the signal sequence S,
sjfor the jth element of the signal sequence S,
szfor the z-th element of the signal sequence S,
z is 1,2, N is the number of the intermediate element,
i is 1,2, N is the first element number,
j is 1,2, N is the second element number,
n is the length of the signal sequence S;
module 203 finds N2The joint self-similarity values are specifically: the joint self-similarity value with sequence number (i, j) is denoted as pijThe calculation formula is as follows:
Figure BDA0002741413930000041
wherein:
pi|jis the likelihood probability of the sequence number (j, i),
pj|iis the self-phase probability of sequence number (i, j);
the module 204 calculates N conditional shannon entropies, specifically: the nth conditional Shannon entropy is recorded as HnThe calculation formula used is:
Figure BDA0002741413930000042
wherein: n is 1,2, N is the conditional Shannon entropy sequence number, pinIs a joint self-similarity value of sequence numbers (i, n);
the module 205 approximates variable initialization, specifically: setting the initial value of an iteration control parameter k to be 1; the initial value of the approximation vector b is denoted as b0The nth element thereof is
Figure BDA0002741413930000043
Has a value of
Figure BDA0002741413930000044
The iteration value of step 1 of approximating vector b is recorded as b1The nth element thereof is
Figure BDA0002741413930000045
Has a value of
Figure BDA0002741413930000046
Wherein:
m0is the mean of the signal sequence S;
Figure BDA0002741413930000047
represents a mean value of m0Variance of
Figure BDA0002741413930000048
A gaussian distribution random function of;
the module 206 calculates the (k + 1) th step of the approximation vector, specifically: the step (k + 1) of the approximation vector b is recorded as bk +1The formula used is:
bk+1＝bk+αbk-1
wherein: bkFor the kth step value of the approximation vector b,
bk-1for the value of the (k-1) th step of the approximation vector b,
Figure BDA0002741413930000049
is a European distanceA factor;
the module 207 determines the iteration error and ends the iteration update, specifically: the iteration error of the k step is recorded as epsilonkHaving a value of εk＝||bk-bk-1||2(ii) a If epsilonk>0.001σoThen the value of the iteration control parameter k is increased by 1 and returns to the block 206 and the block 207 until the iteration error skIs less than
Figure BDA00027414139300000410
The iteration is ended, and the iteration control parameter K is KoThe value of the approximation vector b is
Figure BDA00027414139300000411
The module 208 calculates a reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula is
Figure BDA00027414139300000412
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 vibration and sound detection signal reconstruction method and system by utilizing Euclidean optimal approximation. 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 Euclidean best approximation
Fig. 1 is a schematic flow chart of a method for reconstructing a vibro-acoustic detection signal by using the optimal euclidean approximation according to the present invention. As shown in fig. 1, the method for reconstructing a vibro-acoustic detection signal by using the optimal euclidean approximation specifically includes the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102 of obtaining N2The similarity probability is specifically as follows: the similarity probability with sequence number (i, j) is denoted as pj|iThe formula used is:
Figure BDA0002741413930000051
wherein:
σ0is the mean square error of the signal sequence S,
sifor the ith element of the signal sequence S,
sjfor the jth element of the signal sequence S,
szfor the z-th element of the signal sequence S,
z is 1,2, N is the number of the intermediate element,
i is 1,2, N is the first element number,
j is 1,2, N is the second element number,
n is the length of the signal sequence S;
step 103 of obtaining N2The joint self-similarity values are specifically: the joint self-similarity value with sequence number (i, j) is denoted as pijThe calculation formula is as follows:
Figure BDA0002741413930000061
wherein:
pi|jis the likelihood probability of the sequence number (j, i),
pj|iis the self-phase probability of sequence number (i, j);
step 104, calculating N conditional shannon entropies, specifically: the nth conditional Shannon entropy is recorded as HnThe calculation formula used is:
Figure BDA0002741413930000062
wherein: n is 1,2, N is the conditional Shannon entropy sequence number, pinIs a joint self-similarity value of sequence numbers (i, n);
step 105, initializing an approximation variable, specifically: setting the initial value of an iteration control parameter k to be 1; the initial value of the approximation vector b is denoted as b0N th of itThe element is
Figure BDA0002741413930000063
Has a value of
Figure BDA0002741413930000064
The iteration value of step 1 of approximating vector b is recorded as b1The nth element thereof is
Figure BDA0002741413930000065
Has a value of
Figure BDA0002741413930000066
Wherein:
m0is the mean of the signal sequence S;
Figure BDA0002741413930000067
represents a mean value of m0Variance of
Figure BDA0002741413930000068
A gaussian distribution random function of;
step 106, calculating the (k + 1) th step value of the approximation vector, specifically: the step (k + 1) of the approximation vector b is recorded as bk +1The formula used is:
bk+1＝bk+αbk-1
wherein: bkFor the kth step value of the approximation vector b,
bk-1for the value of the (k-1) th step of the approximation vector b,
Figure BDA0002741413930000069
is a Euclidean distance factor;
step 107, judging the iteration error and ending the iteration updating, specifically: the iteration error of the k step is recorded as epsilonkHaving a value of εk＝||bk-bk-1||2(ii) a If epsilonk>0.001σoThen it is statedAdding 1 to the value of the iteration control parameter k and returning to said step 106 and said step 107 until said iteration error εkIs less than
Figure BDA0002741413930000071
The iteration is ended, and the iteration control parameter K is KoThe value of the approximation vector b is
Figure BDA0002741413930000072
Step 108, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula is
Figure BDA0002741413930000073
FIG. 2 is a structural view of a vibro-acoustic detection signal reconstruction system using Euclidean best approximation
Fig. 2 is a schematic structural diagram of a vibro-acoustic detection signal reconstruction system using the optimal euclidean approximation according to the present invention. As shown in fig. 2, the system for reconstructing a vibro-acoustic detection signal by using the optimal euclidean approximation includes the following structures:
the module 201 acquires a signal sequence S acquired in time sequence;
module 202 finds N2The similarity probability is specifically as follows: the similarity probability with sequence number (i, j) is denoted as pj|iThe formula used is:
Figure BDA0002741413930000074
wherein:
σ0is the mean square error of the signal sequence S,
sifor the ith element of the signal sequence S,
sjfor the jth element of the signal sequence S,
szfor the z-th element of the signal sequence S,
z is 1,2, N is the number of the intermediate element,
i is 1,2, N is the first element number,
j is 1,2, N is the second element number,
n is the length of the signal sequence S;
module 203 finds N2The joint self-similarity values are specifically: the joint self-similarity value with sequence number (i, j) is denoted as pijThe calculation formula is as follows:
Figure BDA0002741413930000075
wherein:
pi|jis the likelihood probability of the sequence number (j, i),
pj|iis the self-phase probability of sequence number (i, j);
the module 204 calculates N conditional shannon entropies, specifically: the nth conditional Shannon entropy is recorded as HnThe calculation formula used is:
Figure BDA0002741413930000081
wherein: n is 1,2, N is the conditional Shannon entropy sequence number,
pinis a joint self-similarity value of sequence numbers (i, n);
the module 205 approximates variable initialization, specifically: setting the initial value of an iteration control parameter k to be 1; the initial value of the approximation vector b is denoted as b0The nth element thereof is
Figure BDA0002741413930000082
Has a value of
Figure BDA0002741413930000083
The iteration value of step 1 of approximating vector b is recorded as b1The nth element thereof is
Figure BDA0002741413930000084
Has a value of
Figure BDA0002741413930000085
Wherein:
m0is the mean of the signal sequence S;
Figure BDA0002741413930000086
represents a mean value of m0Variance of
Figure BDA0002741413930000087
A gaussian distribution random function of;
the module 206 calculates the (k + 1) th step of the approximation vector, specifically: the step (k + 1) of the approximation vector b is recorded as bk +1The formula used is:
bk+1＝bk+αbk-1
wherein: bkFor the kth step value of the approximation vector b,
bk-1for the value of the (k-1) th step of the approximation vector b,
Figure BDA0002741413930000088
is a Euclidean distance factor;
the module 207 determines the iteration error and ends the iteration update, specifically: the iteration error of the k step is recorded as epsilonkHaving a value of εk＝||bk-bk-1||2(ii) a If epsilonk>0.001σoThen the value of the iteration control parameter k is increased by 1 and returns to the block 206 and the block 207 until the iteration error skIs less than
Figure BDA0002741413930000089
The iteration is ended, and the iteration control parameter K is KoThe value of the approximation vector b is
Figure BDA00027414139300000810
The module 208 calculates a reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula is
Figure BDA00027414139300000811
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 finds N2The similarity probability is specifically as follows: the similarity probability with sequence number (i, j) is denoted as pj|iThe formula used is:
Figure BDA0002741413930000091
wherein:
σ0is the mean square error of the signal sequence S,
sifor the ith element of the signal sequence S,
sjfor the jth element of the signal sequence S,
szfor the z-th element of the signal sequence S,
z is 1,2, N is the number of the intermediate element,
i is 1,2, N is the first element number,
j is 1,2, N is the second element number,
n is the length of the signal sequence S;
step 303 of obtaining N2The joint self-similarity values are specifically: the joint self-similarity value with sequence number (i, j) is denoted as pijThe calculation formula is as follows:
Figure BDA0002741413930000092
wherein:
pi|jis the likelihood probability of the sequence number (j, i),
pj|iis the self-phase probability of sequence number (i, j);
step 304, obtaining N conditional shannon entropies, specifically: the nth conditional Shannon entropy is recorded as HnThe calculation formula used is:
Figure BDA0002741413930000093
wherein: n is 1,2, N is the conditional Shannon entropy sequence number,
pinis a joint self-similarity value of sequence numbers (i, n);
step 305, initializing an approximation variable, specifically: setting the initial value of an iteration control parameter k to be 1; the initial value of the approximation vector b is denoted as b0The nth element thereof is
Figure BDA0002741413930000094
Has a value of
Figure BDA0002741413930000095
The iteration value of step 1 of approximating vector b is recorded as b1The nth element thereof is
Figure BDA0002741413930000096
Has a value of
Figure BDA0002741413930000097
Wherein:
m0is the mean of the signal sequence S;
Figure BDA0002741413930000098
represents a mean value of m0Variance of
Figure BDA0002741413930000099
A gaussian distribution random function of;
step 306, calculating the k +1 th step value of the approximation vector, specifically: the step (k + 1) of the approximation vector b is recorded as bk +1The formula used is:
bk+1＝bk+αbk-1
wherein: bkFor the kth step value of the approximation vector b,
bk-1for the value of the (k-1) th step of the approximation vector b,
Figure BDA0002741413930000101
is a Euclidean distance factor;
step 307, judging an iteration error and ending the iteration updating, specifically: the iteration error of the k step is recorded as epsilonkHaving a value of εk＝||bk-bk-1||2(ii) a If epsilonk>0.001σoThen 1 is added to the value of the iterative control parameter k and the process returns to step 306 and step 307 until the iteration error epsilonkIs less than
Figure BDA0002741413930000102
The iteration is ended, and the iteration control parameter K is KoThe value of the approximation vector b is
Figure BDA0002741413930000103
Step 308, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula is
Figure BDA0002741413930000104
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 vibration and sound detection signal reconstruction method using Euclidean optimal approximation is characterized by comprising the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102 of obtaining N2The similarity probability is specifically as follows: the similarity probability with sequence number (i, j) is denoted as pj|iThe formula used is:
Figure FDA0002741413920000011
wherein:
σ0is the mean square error of the signal sequence S,
sifor the ith element of the signal sequence S,
sjfor the jth element of the signal sequence S,
szfor the z-th element of the signal sequence S,
z is 1,2, N is the number of the intermediate element,
i is 1,2, N is the first element number,
j is 1,2, N is the second element number,
n is the length of the signal sequence S;
step 103 of obtaining N2The joint self-similarity values are specifically: the joint self-similarity value with sequence number (i, j) is denoted as pijThe calculation formula usedComprises the following steps:
Figure FDA0002741413920000012
wherein:
pi|jis the likelihood probability of the sequence number (j, i),
pj|iis the self-phase probability of sequence number (i, j);
step 104, calculating N conditional shannon entropies, specifically: the nth conditional Shannon entropy is recorded as HnThe calculation formula used is:
Figure FDA0002741413920000013
wherein: n is 1,2, N is the conditional Shannon entropy sequence number,
pinis a joint self-similarity value of sequence numbers (i, n);
step 105, initializing an approximation variable, specifically: setting the initial value of an iteration control parameter k to be 1; the initial value of the approximation vector b is denoted as b0The nth element thereof is
Figure FDA0002741413920000014
Has a value of
Figure FDA0002741413920000015
The iteration value of step 1 of approximating vector b is recorded as b1The nth element thereof is
Figure FDA0002741413920000016
Has a value of
Figure FDA0002741413920000017
Wherein:
m0is the mean of the signal sequence S;
Figure FDA0002741413920000018
represents a mean value of m0Variance of
Figure FDA0002741413920000019
A gaussian distribution random function of;
step 106, calculating the (k + 1) th step value of the approximation vector, specifically: the step (k + 1) of the approximation vector b is recorded as bk+1The formula used is:
bk+1＝bk+αbk-1
wherein: bkFor the kth step value of the approximation vector b,
bk-1for the value of the (k-1) th step of the approximation vector b,
Figure FDA0002741413920000021
is a Euclidean distance factor;
step 107, judging the iteration error and ending the iteration updating, specifically: the iteration error of the k step is recorded as epsilonkHaving a value of εk＝||bk-bk-1||2(ii) a If epsilonk>0.001σoThen 1 is added to the value of the iterative control parameter k and the process returns to step 106 and step 107 until the iteration error epsilonkIs less than
Figure FDA0002741413920000022
The iteration is ended, and the iteration control parameter K is KoThe value of the approximation vector b is
Figure FDA0002741413920000023
Step 108, obtaining the reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula is
Figure FDA0002741413920000024
2. A system for reconstructing a vibro-acoustic detection signal using the best euclidean approximation, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
module 202 finds N2The similarity probability is specifically as follows: the similarity probability with sequence number (i, j) is denoted as pj|iThe formula used is:
Figure FDA0002741413920000025
wherein:
σ0is the mean square error of the signal sequence S,
sifor the ith element of the signal sequence S,
sjfor the jth element of the signal sequence S,
szfor the z-th element of the signal sequence S,
z is 1,2, N is the number of the intermediate element,
i is 1,2, N is the first element number,
j is 1,2, N is the second element number,
n is the length of the signal sequence S;
module 203 finds N2The joint self-similarity values are specifically: the joint self-similarity value with sequence number (i, j) is denoted as pijThe calculation formula is as follows:
Figure FDA0002741413920000026
wherein:
pi|jis the likelihood probability of the sequence number (j, i),
pj|iis the self-phase probability of sequence number (i, j);
the module 204 calculates N conditional shannon entropies, specifically: the nth conditional Shannon entropy is recorded asHnThe calculation formula used is:
Figure FDA0002741413920000031
wherein: n is 1,2, N is the conditional Shannon entropy sequence number,
pinis a joint self-similarity value of sequence numbers (i, n);
the module 205 approximates variable initialization, specifically: setting the initial value of an iteration control parameter k to be 1; the initial value of the approximation vector b is denoted as b0The nth element thereof is
Figure FDA0002741413920000032
Has a value of
Figure FDA0002741413920000033
The iteration value of step 1 of approximating vector b is recorded as b1The nth element thereof is
Figure FDA0002741413920000034
Has a value of
Figure FDA0002741413920000035
Wherein:
m0is the mean of the signal sequence S;
Figure FDA0002741413920000036
represents a mean value of m0Variance of
Figure FDA0002741413920000037
A gaussian distribution random function of;
the module 206 calculates the (k + 1) th step of the approximation vector, specifically: the step (k + 1) of the approximation vector b is recorded as bk+1The formula used is:
bk+1＝bk+αbk-1
wherein: bkFor the kth step value of the approximation vector b,
bk-1for the value of the (k-1) th step of the approximation vector b,
Figure FDA0002741413920000038
is a Euclidean distance factor;
the module 207 determines the iteration error and ends the iteration update, specifically: the iteration error of the k step is recorded as epsilonkHaving a value of εk＝||bk-bk-1||2(ii) a If epsilonk>0.001σoThen the value of the iteration control parameter k is increased by 1 and returns to the block 206 and the block 207 until the iteration error skIs less than
Figure FDA0002741413920000039
The iteration is ended, and the iteration control parameter K is KoThe value of the approximation vector b is
Figure FDA00027414139200000310
The module 208 calculates a reconstructed signal sequence, specifically: the reconstructed signal sequence is denoted SnewThe formula is
Figure FDA00027414139200000311
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