CN111751098A - Vibration and sound detection signal reconstruction method and system by using Gaussian prediction model - Google Patents

Vibration and sound detection signal reconstruction method and system by using Gaussian prediction model Download PDF

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CN111751098A
CN111751098A CN202010593737.4A CN202010593737A CN111751098A CN 111751098 A CN111751098 A CN 111751098A CN 202010593737 A CN202010593737 A CN 202010593737A CN 111751098 A CN111751098 A CN 111751098A
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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 vibration and sound detection signal reconstruction method and a system by using a Gaussian prediction model, wherein the method comprises the following steps: step 101, acquiring a signal sequence S acquired according to a time sequence; step 102, generating a signal difference sequence delta S; step 103 finds the desired sequence Sexp(ii) a 104, solving a Lagrangian function matrix K; step 105, calculating Gaussian prediction model parameters; step 106 of solving Lagrangian factor vector aopt(ii) a Step 107, solving a Gaussian prediction matrix G; step 108, obtaining a Gaussian adjustment factor mu; step 109, obtaining the optimal weight matrix W of Gaussopt(ii) a Step 110 finds the reconstructed signal sequence Snew。

Description

Vibration and sound detection signal reconstruction method and system by using Gaussian prediction model
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 using a Gaussian prediction model. 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 a Gaussian prediction model comprises the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102 generates a signal difference sequence Δ S, specifically: the 1 st element in the signal differential sequence delta S is 0, and the ith element in the signal differential sequence delta S is Si-si-1(ii) a i is an element serial number, and the value range of the element serial number i is i-1, 2, ·, N; n is the length of the signal sequence S;
step 103 finds the desired sequence SexpThe method specifically comprises the following steps: the desired sequence SexpIs calculated by the formula Sexp＝U[ΔS+S](ii) a Wherein, U is a left characteristic vector matrix of the correlation matrix B; a characteristic matrix which is the correlation matrix B; the calculation formula of the correlation matrix B is B ═ S delta S]T[SΔS]；
Step 104, solving a lagrangian function matrix K, specifically: the calculation formula of the Lagrange function matrix K is K ═ Delta S-Sexp]T[ΔS-Sexp]；
Step 105, solving parameters of a Gaussian prediction model, specifically: mean value m of the Gaussian prediction modelGIs mG＝||K[K+σI]-1L; mean square error sigma of the Gaussian prediction modelGHas the calculation formula ofG＝||K-[K+σI][ΔSTS]||2(ii) a Wherein I is an identity matrix;
step 106 of solving Lagrangian factor vector aoptThe method specifically comprises the following steps: at all conditions satisfied
Figure BDA0002556760590000021
Is selected so that a isTKa||2+||aTK||2Taking the intermediate vector a of the minimum value as the Lagrangian factor vector aopt. Wherein, ajIs the jth element of the intermediate vector a; j is a sequence number of an intermediate vector element, and the value range of the sequence number j of the intermediate vector element is j ═ 1,2, ·, N;
step 107, solving a gaussian prediction matrix G, specifically: the calculation formula of the Gaussian prediction matrix G is
Figure BDA0002556760590000022
Figure BDA0002556760590000023
Step 108, obtaining a gaussian adjustment factor μ, specifically: the calculation formula of the Gaussian adjustment factor mu is
Figure BDA0002556760590000024
Figure BDA0002556760590000025
Wherein m isSIs the mean of the signal sequence S; lambda [ alpha ]kThe K characteristic value of the Lagrangian matrix K is obtained; k is a characteristic value serial number, and the value range of the characteristic value serial number k is 1,2, ·, N;
step 109, obtaining the optimal weight matrix W of GaussoptThe method specifically comprises the following steps: the Gaussian optimal weight matrix WoptIs calculated by the formula Wopt＝[ΔS-σΔSexp]T[ΔS-σΔSexp]. Wherein σΔIs the mean square error of the signal difference sequence Delta S;
step 110 finds the reconstructed signal sequence SnewThe method specifically comprises the following steps: snew＝[GTG+μWopt]-1[GTG+μWopt]S。
A vibro-acoustic detection signal reconstruction system using gaussian prediction models, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 generates a signal difference sequence Δ S, specifically: the 1 st element in the signal differential sequence delta S is 0, and the ith element in the signal differential sequence delta S is Si-si-1(ii) a i is an element serial number, and the value range of the element serial number i is i-1, 2, ·, N; n is the length of the signal sequence S;
module 203 finds the desired sequence SexpThe method specifically comprises the following steps: the desired sequence SexpIs calculated by the formula Sexp＝U[ΔS+S](ii) a Wherein, U is a left characteristic vector matrix of the correlation matrix B; a characteristic matrix which is the correlation matrix B; the calculation formula of the correlation matrix B is B ═ S delta S]T[SΔS]；
The module 204 calculates a lagrangian function matrix K, which specifically includes: the calculation formula of the Lagrange function matrix K is K ═ Delta S-Sexp]T[ΔS-Sexp]；
The module 205 finds gaussian prediction model parameters, specifically: mean value m of the Gaussian prediction modelGIs mG＝||K[K+σI]-1L; mean square error sigma of the Gaussian prediction modelGHas the calculation formula ofG＝||K-[K+σI][ΔSTS]||2(ii) a Wherein I is an identity matrix;
module 206 finds the Lagrangian factor vector aoptThe method specifically comprises the following steps: at all conditions satisfied
Figure BDA0002556760590000035
Is selected so that a isTKa||2+||aTK||2Taking the intermediate vector a of the minimum value as the Lagrangian factor vector aopt. Wherein, ajIs the jth element of the intermediate vector a; j is a sequence number of an intermediate vector element, and the value range of the sequence number j of the intermediate vector element is j ═ 1,2, ·, N;
the module 207 finds a gaussian prediction matrix G, specifically: the calculation formula of the Gaussian prediction matrix G is
Figure BDA0002556760590000031
Figure BDA0002556760590000032
The module 208 obtains a gaussian adjustment factor μ, specifically: the calculation formula of the Gaussian adjustment factor mu is
Figure BDA0002556760590000033
Figure BDA0002556760590000034
Wherein m isSIs the mean of the signal sequence S; lambda [ alpha ]kThe K characteristic value of the Lagrangian matrix K is obtained; k is a characteristic value serial number, and the value range of the characteristic value serial number k is 1,2, ·, N;
module 209 determines the Gaussian optimal weight matrix WoptThe method specifically comprises the following steps: the Gaussian optimal weight matrix WoptIs calculated by the formula Wopt＝[ΔS-σΔSexp]T[ΔS-σΔSexp]. Wherein σΔIs the mean square error of the signal difference sequence Delta S;
the module 210 finds the reconstructed signal sequence SnewThe method specifically comprises the following steps: snew＝[GTG+μWopt]-1[GTG+μWopt]S。
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 using a Gaussian prediction model. The method has better signal reconstruction performance 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 method for reconstructing a vibration-sound detection signal using a Gaussian prediction model
Fig. 1 is a schematic flow chart of a method for reconstructing a vibration-sound detection signal using a gaussian prediction model according to the present invention. As shown in fig. 1, the method for reconstructing a vibro-acoustic detection signal by using a gaussian prediction model specifically includes the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102 generates a signal difference sequence Δ S, specifically: the 1 st element in the signal differential sequence delta S is 0, and the ith element in the signal differential sequence delta S is Si-si-1(ii) a i is an element serial number, and the value range of the element serial number i is i-1, 2, ·, N; n is the length of the signal sequence S;
step 103 finds the desired sequence SexpThe method specifically comprises the following steps: the desired sequence SexpIs calculated by the formula Sexp＝U[ΔS+S](ii) a Wherein, U is a left characteristic vector matrix of the correlation matrix B; a characteristic matrix which is the correlation matrix B; the calculation formula of the correlation matrix B is B ═ S delta S]T[SΔS]；
Step 104, solving a lagrangian function matrix K, specifically: the calculation formula of the Lagrange function matrix K is K ═ Delta S-Sexp]T[ΔS-Sexp]；
Step 105, solving parameters of a Gaussian prediction model, specifically: mean value m of the Gaussian prediction modelGIs mG＝||K[K+σI]-1L; mean square error sigma of the Gaussian prediction modelGHas the calculation formula ofG＝||K-[K+σI][ΔSTS]||2(ii) a Wherein I is an identity matrix;
step 106 of solving Lagrangian factor vector aoptThe method specifically comprises the following steps: at all conditions satisfied
Figure BDA0002556760590000041
Is selected so that a isTKa||2+||aTK||2Taking the intermediate vector a of the minimum value as the Lagrangian factor vector aopt. Wherein, ajIs the jth element of the intermediate vector a; j is a sequence number of an intermediate vector element, and the value range of the sequence number j of the intermediate vector element is j ═ 1,2, ·, N;
step 107, solving a gaussian prediction matrix G, specifically: the calculation formula of the Gaussian prediction matrix G is
Figure BDA0002556760590000042
Figure BDA0002556760590000043
Step 108, obtaining a gaussian adjustment factor μ, specifically: the calculation formula of the Gaussian adjustment factor mu is
Figure BDA0002556760590000051
Figure BDA0002556760590000052
Wherein m isSIs the mean of the signal sequence S; lambda [ alpha ]kThe K characteristic value of the Lagrangian matrix K is obtained; k is a characteristic value serial number, and the value range of the characteristic value serial number k is 1,2, ·, N;
step 109, obtaining the optimal weight matrix W of GaussoptThe method specifically comprises the following steps: the Gaussian optimal weight matrix WoptIs calculated by the formula Wopt＝[ΔS-σΔSexp]T[ΔS-σΔSexp]. Wherein σΔIs the mean square error of the signal difference sequence Delta S;
step 110 finds the reconstructed signal sequence SnewThe method specifically comprises the following steps: snew＝[GTG+μWopt]-1[GTG+μWopt]S。
FIG. 2 is a structural view of a vibration and sound detection signal reconstruction system using a Gaussian prediction model
Fig. 2 is a schematic structural diagram of a vibration and sound detection signal reconstruction system using a gaussian prediction model according to the present invention. As shown in fig. 2, the system for reconstructing a vibro-acoustic detection signal by using a gaussian prediction model includes the following structures:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 generates a signal difference sequence Δ S, specifically: the 1 st element in the signal differential sequence delta S is 0, and the ith element in the signal differential sequence delta S is Si-si-1(ii) a i is the element number, saidThe value range of the element serial number i is 1,2, ·, N; n is the length of the signal sequence S;
module 203 finds the desired sequence SexpThe method specifically comprises the following steps: the desired sequence SexpIs calculated by the formula Sexp＝U[ΔS+S](ii) a Wherein, U is a left characteristic vector matrix of the correlation matrix B; a characteristic matrix which is the correlation matrix B; the calculation formula of the correlation matrix B is B ═ S delta S]T[SΔS]；
The module 204 calculates a lagrangian function matrix K, which specifically includes: the calculation formula of the Lagrange function matrix K is K ═ Delta S-Sexp]T[ΔS-Sexp]；
The module 205 finds gaussian prediction model parameters, specifically: mean value m of the Gaussian prediction modelGIs mG＝||K[K+σI]-1L; mean square error sigma of the Gaussian prediction modelGHas the calculation formula ofG＝||K-[K+σI][ΔSTS]||2(ii) a Wherein I is an identity matrix;
module 206 finds the Lagrangian factor vector aoptThe method specifically comprises the following steps: at all conditions satisfied
Figure BDA0002556760590000053
Is selected so that a isTKa||2+||aTK||2Taking the intermediate vector a of the minimum value as the Lagrangian factor vector aopt. Wherein, ajIs the jth element of the intermediate vector a; j is a sequence number of an intermediate vector element, and the value range of the sequence number j of the intermediate vector element is j ═ 1,2, ·, N;
the module 207 finds a gaussian prediction matrix G, specifically: the calculation formula of the Gaussian prediction matrix G is
Figure BDA0002556760590000054
Figure BDA0002556760590000055
The module 208 finds the gaussian adjustment factor mu,the method specifically comprises the following steps: the calculation formula of the Gaussian adjustment factor mu is
Figure BDA0002556760590000056
Figure BDA0002556760590000057
Wherein m isSIs the mean of the signal sequence S; lambda [ alpha ]kThe K characteristic value of the Lagrangian matrix K is obtained; k is a characteristic value serial number, and the value range of the characteristic value serial number k is 1,2, ·, N;
module 209 determines the Gaussian optimal weight matrix WoptThe method specifically comprises the following steps: the Gaussian optimal weight matrix WoptIs calculated by the formula Wopt＝[ΔS-σΔSexp]T[ΔS-σΔSexp]. Wherein σΔIs the mean square error of the signal difference sequence Delta S;
the module 210 finds the reconstructed signal sequence SnewThe method specifically comprises the following steps: snew＝[GTG+μWopt]-1[GTG+μWopt]S。
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 generates a signal difference sequence Δ S, specifically: the 1 st element in the signal differential sequence delta S is 0, and the ith element in the signal differential sequence delta S is Si-si-1(ii) a i is an element serial number, and the value range of the element serial number i is i-1, 2, ·, N; n is the length of the signal sequence S;
step 303 finds the desired sequence SexpThe method specifically comprises the following steps: the desired sequence SexpIs calculated by the formula Sexp＝U[ΔS+S](ii) a Wherein, U is a left characteristic vector matrix of the correlation matrix B; a characteristic matrix which is the correlation matrix B; the calculation formula of the correlation matrix B is B ═ S delta S]T[SΔS]；
Step 304, solving a lagrangian function matrix K, specifically: the calculation formula of the Lagrange function matrix K is K ═ Delta S-Sexp]T[ΔS-Sexp]；
Step 305, solving gaussian prediction model parameters, specifically: mean value m of the Gaussian prediction modelGIs mG＝||K[K+σI]-1L; mean square error sigma of the Gaussian prediction modelGHas the calculation formula ofG＝||K-[K+σI][ΔSTS]||2(ii) a Wherein I is an identity matrix;
step 306 finds the lagrangian factor vector aoptThe method specifically comprises the following steps: at all conditions satisfied
Figure BDA0002556760590000061
Is selected so that a isTKa||2+||aTK||2Taking the intermediate vector a of the minimum value as the Lagrangian factor vector aopt. Wherein, ajIs the jth element of the intermediate vector a; j is a sequence number of an intermediate vector element, and the value range of the sequence number j of the intermediate vector element is j ═ 1,2, ·, N;
step 307, obtaining a gaussian prediction matrix G, specifically: the calculation formula of the Gaussian prediction matrix G is
Figure BDA0002556760590000062
Figure BDA0002556760590000063
Step 308, obtaining a gaussian adjustment factor μ, specifically: the calculation formula of the Gaussian adjustment factor mu is
Figure BDA0002556760590000064
Figure BDA0002556760590000065
Wherein m isSIs the mean of the signal sequence S; lambda [ alpha ]kIs that it isThe kth eigenvalue of the Lagrangian matrix K; k is a characteristic value serial number, and the value range of the characteristic value serial number k is 1,2, ·, N;
step 309, obtain the optimal weight matrix W of GaussoptThe method specifically comprises the following steps: the Gaussian optimal weight matrix WoptIs calculated by the formula Wopt＝[ΔS-σΔSexp]T[ΔS-σΔSexp]. Wherein σΔIs the mean square error of the signal difference sequence Delta S;
step 310 obtains the reconstructed signal sequence SnewThe method specifically comprises the following steps: snew＝[GTG+μWopt]-1[GTG+μWopt]S。
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 a Gaussian prediction model is characterized by comprising the following steps:
step 101, acquiring a signal sequence S acquired according to a time sequence;
step 102 generates a signal difference sequence Δ S, specifically: the 1 st element in the signal differential sequence delta S is 0, and the ith element in the signal differential sequence delta S is Si-si-1(ii) a i is an element serial number, and the value range of the element serial number i is i-1, 2, ·, N; n is a radical ofIs the length of the signal sequence S;
step 103 finds the desired sequence SexpThe method specifically comprises the following steps: the desired sequence SexpIs calculated by the formula Sexp＝U[ΔS+S](ii) a Wherein, U is a left characteristic vector matrix of the correlation matrix B; a characteristic matrix which is the correlation matrix B; the calculation formula of the correlation matrix B is B ═ S delta S]T[SΔS]；
Step 104, solving a lagrangian function matrix K, specifically: the calculation formula of the Lagrange function matrix K is K ═ Delta S-Sexp]T[ΔS-Sexp]；
Step 105, obtaining parameters of a gaussian prediction model, specifically: mean value m of the Gaussian prediction modelGIs mG＝||K[K+σI]-1L; mean square error sigma of the Gaussian prediction modelGHas the calculation formula ofG＝||K-[K+σI][ΔSTS]||2(ii) a Wherein I is an identity matrix;
step 106 of solving Lagrangian factor vector aoptThe method specifically comprises the following steps: when all the conditions are equal to or less than 0
Figure FDA0002556760580000011
Is selected so that a isTKa||2+||aTK||2Taking the intermediate vector a of the minimum value as the Lagrangian factor vector aopt. Wherein, ajIs the jth element of the intermediate vector a; j is a sequence number of an intermediate vector element, and the value range of the sequence number j of the intermediate vector element is j ═ 1,2, ·, N;
step 107, obtaining a gaussian prediction matrix G, specifically: the calculation formula of the Gaussian prediction matrix G is
Figure FDA0002556760580000012
Step 108, obtaining a gaussian adjustment factor μ, specifically: the calculation formula of the Gaussian adjustment factor mu is
Figure FDA0002556760580000013
Wherein m isSIs the mean of the signal sequence S; lambda [ alpha ]kThe K characteristic value of the Lagrangian matrix K is obtained; k is a characteristic value serial number, and the value range of the characteristic value serial number k is 1,2, ·, N;
step 109, obtaining the optimal weight matrix W of GaussoptThe method specifically comprises the following steps: the Gaussian optimal weight matrix WoptIs calculated by the formula Wopt＝[ΔS-σΔSexp]T[ΔS-σΔSexp]. Wherein σΔIs the mean square error of the signal difference sequence Delta S;
step 110 finds the reconstructed signal sequence SnewThe method specifically comprises the following steps: snew＝[GTG+μWopt]-1[GTG+μWopt]S。
2. A system for reconstructing vibro-acoustic detection signals using gaussian predictive models, comprising:
the module 201 acquires a signal sequence S acquired in time sequence;
the module 202 generates a signal difference sequence Δ S, specifically: the 1 st element in the signal differential sequence delta S is 0, and the ith element in the signal differential sequence delta S is Si-si-1(ii) a i is an element serial number, and the value range of the element serial number i is i-1, 2, ·, N; n is the length of the signal sequence S;
module 203 finds the desired sequence SexpThe method specifically comprises the following steps: the desired sequence SexpIs calculated by the formula Sexp＝U[ΔS+S](ii) a Wherein, U is a left characteristic vector matrix of the correlation matrix B; a characteristic matrix which is the correlation matrix B; the calculation formula of the correlation matrix B is B ═ S delta S]T[SΔS]；
The module 204 calculates a lagrangian function matrix K, which specifically includes: the calculation formula of the Lagrange function matrix K is K ═ Delta S-Sexp]T[ΔS-Sexp]；
The module 205 calculates gaussian prediction model parameters, specifically: mean value m of the Gaussian prediction modelGMeter (2)The formula is mG＝||K[K+σI]-1L; mean square error sigma of the Gaussian prediction modelGHas the calculation formula ofG＝||K-[K+σI][ΔSTS]||2(ii) a Wherein I is an identity matrix;
module 206 finds the Lagrangian factor vector aoptThe method specifically comprises the following steps: when all the conditions are equal to or less than 0
Figure FDA0002556760580000023
Is selected so that a isTKa||2+||aTK||2Taking the intermediate vector a of the minimum value as the Lagrangian factor vector aopt. Wherein, ajIs the jth element of the intermediate vector a; j is a sequence number of an intermediate vector element, and the value range of the sequence number j of the intermediate vector element is j ═ 1,2, ·, N;
the module 207 calculates a gaussian prediction matrix G, specifically: the calculation formula of the Gaussian prediction matrix G is
Figure FDA0002556760580000021
The module 208 obtains a gaussian adjustment factor μ, specifically: the calculation formula of the Gaussian adjustment factor mu is
Figure FDA0002556760580000022
Wherein m isSIs the mean of the signal sequence S; lambda [ alpha ]kThe K characteristic value of the Lagrangian matrix K is obtained; k is a characteristic value serial number, and the value range of the characteristic value serial number k is 1,2, ·, N;
module 209 determines the Gaussian optimal weight matrix WoptThe method specifically comprises the following steps: the Gaussian optimal weight matrix WoptIs calculated by the formula Wopt＝[ΔS-σΔSexp]T[ΔS-σΔSexp]. Wherein σΔIs the mean square error of the signal difference sequence Delta S;
the module 210 finds the reconstructed signal sequence SnewThe method specifically comprises the following steps: snew＝[GTG+μWopt]-1[GTG+μWopt]S。
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CN112284520A (en) * 2020-10-25 2021-01-29 广东石油化工学院 Vibration and sound detection signal reconstruction method and system by using optimal rank approximation

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112284520A (en) * 2020-10-25 2021-01-29 广东石油化工学院 Vibration and sound detection signal reconstruction method and system by using optimal rank approximation
CN112284520B (en) * 2020-10-25 2022-06-24 广东石油化工学院 Vibration and sound detection signal reconstruction method and system by using optimal rank approximation

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