CN112036234A - PCA-based aircraft conduit vibration signal power frequency noise suppression method - Google Patents
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Abstract
The invention discloses a PCA-based power frequency noise suppression method for an aircraft conduit vibration signal, which comprises the steps of carrying out PCA preprocessing on a vibration signal in a time window to obtain estimated power frequency noise, then obtaining corresponding power frequency noise parameters through the estimated power frequency noise to further obtain constructed power frequency noise, and finally subtracting the constructed power frequency noise from the vibration signal to obtain a vibration signal after noise suppression. The PCA-based power frequency noise suppression method for the aircraft conduit vibration signal can suppress the power frequency noise in the conduit vibration signal, and compared with other power frequency noise suppression methods, the method has the advantages of good noise suppression effect, strong signal protection capability when the signal-noise frequency band is aliased, and capability of effectively improving the signal-to-noise ratio of the vibration signal.
Description
Technical Field
The invention relates to the technical field of airplane conduit vibration signal noise reduction, in particular to a PCA-based airplane conduit vibration signal power frequency noise suppression method.
Background
The sensor arranged on the aircraft guide pipe can acquire a vibration signal after the guide pipe is hammered, but the vibration signal acquired by the aircraft guide pipe in the actual environment has power frequency noise, so that the judgment of the stress state of the aircraft guide pipe is seriously influenced. The method for suppressing the power frequency noise of the vibration signal of the aircraft duct has fewer documents, and the method for suppressing the power frequency noise mainly comprises a frequency domain method and a time domain method at present. In the research of a static monitoring technology and a service life prediction method of a rolling bearing wear area in a doctor thesis, a notch method is used for suppressing power frequency noise, but useful signals are easily damaged when a signal-noise frequency spectrum is aliased; the article 'tilting pad sliding bearing power frequency interference suppression based on harmonic wavelets and SVD' applies harmonic wavelets to extract a power frequency band to carry out singular value decomposition to suppress power frequency noise, but the method neglects the instability of power frequency; the article 'rolling bearing static monitoring signal denoising method based on spectral interpolation and singular value difference spectrum' suppresses power frequency noise by using a spectral interpolation method, but the method is easy to filter partial useful signals during interpolation in a 48-52Hz interval; the article 'elimination of power frequency interference in vibration signals based on independent component analysis' suppresses power frequency noise by using an independent component analysis method, but the noise suppression effect of the method depends on the number of observation signal sources; the article 'power frequency interference elimination method based on singular vector frequency spectrum' applies the frequency spectrum of singular value vectors to suppress power frequency noise, but the method can filter part of useful signals while filtering noise; the method for identifying the fault signal noise reduction reconstruction characteristics of the high-speed wire rod mill, which is disclosed by CN106895985A, provides a method for suppressing power frequency noise based on Fourier transform search characterization power frequency noise singular values, but the method is only suitable for a strong power frequency noise environment; the article 'identification and elimination of single-frequency interference by cosine function self-adaptive method' adopts a function approximation method to eliminate power frequency noise, but the method ignores the instability of power frequency;
the method for automatically identifying and removing the industrial interference based on the two factors disclosed in CN104570118A proposes that the industrial interference is processed by applying a sine and cosine weighted approximation method, but the method is suitable for the conditions of power frequency and stable amplitude; the article 'parallel seismic source power frequency noise suppression based on PCA optimal order' filters power frequency noise by using the relation between principal components and the number of power frequency, but the method also has the problem that useful signals are damaged when signal-to-noise frequency aliasing occurs; therefore, the method can not be completely suitable for suppressing the power frequency noise of the vibration signal of the aircraft conduit, and indicates that the existing research for suppressing the power frequency noise by PCA has the problem of useful signal loss when the signal-noise frequency band is aliased.
Disclosure of Invention
The invention aims to provide a PCA-based aircraft conduit vibration signal power frequency noise suppression method which can effectively protect useful signal details under signal-noise spectrum aliasing and effectively improve the signal-to-noise ratio of a vibration signal.
The invention is realized by the following technical scheme: a PCA-based aircraft conduit vibration signal power frequency noise suppression method comprises the following steps:
(1) collecting a vibration signal x (i) after hammering the airplane guide pipe, wherein the collection time is 1.2 s;
(2) extracting a signal T of which the vibration signal is located in a time windoww；
(3) According to the phase space theory, a signal T of which the vibration signal is positioned in a time window is extractedwConstructing a Hankel matrix;
(4) calculating covariance matrix H of Hankel matrix1；
(5) Calculating covariance matrix H by singular value decomposition1The eigenvalue matrix Λ and the eigenvalue vector matrix V;
(6) calculating the eigenvalue sequence number alpha with the eigenvalue difference of more than 12 times before and after the first appearance according to the eigenvalue arrangement sequence in the eigenvalue matrix Lambda;
(7) performing linear mapping on the Hankel matrix to obtain a principal component matrix F;
(8) respectively reserving the main components of the rows 1 to 2,3 to 4, …, (alpha-1) -alpha of the F in the order of 1 to 2,3 to 4, …, (alpha-1) -alpha, and respectively obtaining the recombined main component F by setting the main components except the reserved main component to zero1～2,F3～4,…,F(α-1)～α；
(9) Respectively for recombinant principal component F1～2,F3～4,…,F(α-1)～αReconstructing to obtain corresponding reconstruction matrix Y1～2,Y3～4,…,Y(α-1)～α；
(10) Respectively reconstructing matrix Y1～2,Y3～4,…,Y(α-1)～αThe first row and the last column are connected end to obtain the estimated power frequency noise y1～2,y3～4,…,y(α-1)～α；
(11) Separately extracting y1～2,y3～4,…,y(α-1)～αThe time corresponding to the 1 st and 3 rd zero points is t1 1～2,t1 3～4,…,t1 (α-1)～α、t3 1～2,t3 3～4,…,t3 (α-1)～αAnd get y1～2,y3～4,…,y(α-1)～αFrequency f of1～2,f3～4,…,f(α-1)～α；
(12) Calculating y1～2,y3～4,…,y(α-1)～αRespectively is
The absolute value of the minimum value is respectively
To obtain y1～2,y3～4,…,y(α-1)～αCorresponding amplitude A1～2,A3～4,…,A(α-1)～α；
(13) Constructive power frequency noise c1～2,c3～4,…,c(α-1)～αRespectively as follows:
(14) suppressing the power frequency noise to obtain a vibration signal x after the power frequency noise is suppressed1(i) And is specifically x1(i)＝x(i)-c1～2-c3～4,…,-c(α-1)～α。
The working principle of the technical scheme is that pre-estimated power frequency noise is obtained by conducting PCA preprocessing on vibration signals in a time window, corresponding power frequency noise parameters are obtained by pre-estimating the power frequency noise so as to obtain constructed power frequency noise, and finally the constructed power frequency noise is subtracted from the vibration signals so as to obtain vibration signals after noise pressing.
In order to better implement the method of the present invention, further, in step (1), an acceleration sensor is used to acquire a vibration signal after hammering the airplane guide pipe.
In order to better implement the method of the present invention, further, in the step (2), the vibration signal is located in the signal T in the time windoww(j), wherein,
j is ROUND (x N), ROUND (x N) +1, …, N, ROUND is rounded in the nearest direction, is a shrinkage coefficient, and has a value range of 9/12 ≦ 11/12.
In order to better implement the method of the present invention, further, in the step (3), the constructed Hankel matrix is as follows:
note that the number of rows in the matrix H is m, the number of columns is N, and if N +1-ROUND (× N) is an even number, m is (N +1-ROUND (× N))/2+1, N is (N +1-ROUND (× N))/2, and if N +1-ROUND (× N) is an odd number, m is (N +2-ROUND (× N))/2.
In order to better implement the method of the present invention, further, in the step (4), the covariance matrix H thereof is calculated by a Hankel matrix1The following formula exists:
wherein HTTranspose the matrix for H, "·" denotes matrix multiplication.
In order to better implement the method of the present invention, further, in the step (5), H is calculated by using a singular value decomposition method1The eigenvalue matrix Λ and the eigenvalue vector matrix V, then a formula exists
H1＝V·Λ·VT
Wherein, Λ is a characteristic value matrix with characteristic values arranged from large to small in a diagonal form, V is a characteristic vector matrix corresponding to each characteristic value, and V is a characteristic vector matrixTIs a transposed matrix of V and satisfies V.VT＝VTV ═ E, E is the identity matrix.
In order to better implement the method of the present invention, further, in the step (7), the principal component matrix F is
F＝VT·H。
To better implement the method of the present invention, further, in the step (9), the matrix Y is reconstructed1～2,Y3～4,…,Y(α-1)～αIn particular to
In order to better implement the method of the present invention, further, in the step (11), y1～2,y3～4,…,y(α-1)～αFrequency f of1～2,f3～4,…,f(α-1)～αThe method specifically comprises the following steps:
in order to better implement the method of the present invention, further, in the step (12), y1～2,y3～4,…,y(α-1)～αCorresponding amplitude A1～2,A3～4,…,A(α-1)～αRespectively as follows:
compared with the prior art, the invention has the following advantages and beneficial effects:
according to the PCA-based aircraft conduit vibration signal power frequency noise suppression method provided by the invention, the vibration signal in the time window is subjected to PCA preprocessing to obtain the estimated power frequency noise, then the corresponding power frequency noise parameter is obtained through the estimated power frequency noise to further obtain the constructed power frequency noise, and finally the constructed power frequency noise is subtracted by the vibration signal to obtain the post-noise suppression vibration signal.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a diagram of a vibration signal without suppressing power frequency noise;
FIG. 2 is a graph of a vibration signal when the method of the present invention is used to suppress power frequency noise;
FIG. 3 is a comparison graph of the frequency spectrum of the vibration signal before and after suppressing the power frequency noise.
Detailed Description
The present invention will be described in further detail with reference to the following examples for the purpose of making clear the objects, process conditions and advantages of the present invention, but the embodiments of the present invention are not limited thereto, and various substitutions and modifications can be made according to the common technical knowledge and the conventional means in the art without departing from the technical idea of the present invention described above, and the specific examples described herein are only for explaining the present invention and are not intended to limit the present invention.
Example (b):
in the embodiment, an acceleration sensor is used for acquiring a vibration signal after the airplane guide pipe is hammered, and the recording time is 1.2 s.
Let the vibration signal be x (i), i ═ 1,2, …, N, i is the number of sampling points, N is the number of sampling points, and the sampling frequency is f0In this example, N is 1201, f0＝1000；
(1) Extracting x (i) signals T within a time windoww，Tw＝x(j)，
j is ROUND (x N), ROUND (x N) +1, …, N, ROUND is rounded in the nearest direction, is the shrinkage factor, and has a value in the range of 9/12 ≦ 11/12, in this example 9/12, Tw＝x(j)j＝901,902,…,1201；
(2) According to the phase space theory, let TwThe Hankel matrix is constructed as follows:
taking the number of rows of the matrix H as m and the number of columns as N, if N +1-ROUND (x N) is an even number, then m is (N +1-ROUND (x N))/2+1, N is (N +1-ROUND (x N))/2, if N +1-ROUND (x N) is an odd number, then m is (N) is (N +2-ROUND (x N))/2, in this example m is (N) 151;
(3) computing the covariance matrix H of H1Such as formula
Wherein HTTranspose matrix for H, "·" denotes matrix multiplication;
(4) computing H by singular value decomposition1The eigenvalue matrix Λ and the eigenvalue vector matrix V, then a formula exists
H1＝V·Λ·VT
Wherein Λ is a characteristic value matrix with characteristic values arranged from large to small in a diagonal form, V is a characteristic vector matrix corresponding to each characteristic value, and V is a characteristic vector matrixTIs a transposed matrix of V and satisfies V.VT＝VTV ═ E, E is the identity matrix;
(5) calculating a characteristic value sequence number alpha with characteristic value difference of more than 12 times before and after the first occurrence according to the characteristic value arrangement sequence in the lambda, wherein alpha is 4 in the example;
(6) and H, obtaining a principal component matrix F through linear mapping:
F＝VT·H
(7) respectively reserving the main components of the rows 1 to 2,3 to 4, …, (alpha-1) -alpha of the F in the order of 1 to 2,3 to 4, …, (alpha-1) -alpha, and respectively obtaining the recombined main component F by setting the main components except the reserved main component to zero1～2,F3～4,…,F(α-1)～αIn this example, the main components of the lines 1 to 2,3 to 4 of F are retained, and the main components except the retained main components are set to zero to obtain F1～2，F3～4；
(8) Are respectively paired with F1～2,F3～4,…,F(α-1)～αReconstructing to obtain corresponding reconstruction matrix Y1～2,Y3～4,…,Y(α-1)～αIs concretely provided with
(9) Respectively adding Y1～2,Y3～4,…,Y(α-1)～αThe first row and the last column are connected end to obtain the estimated power frequency noise y1～2,y3～4,…,y(α-1)～αIn this example, y is obtained1～2,y3～4；
j. Separately extracting y1～2,y3～4,…,y(α-1)～αThe time corresponding to the 1 st and 3 rd zero points is t1 1～2,t1 3～4,…,t1 (α-1)～α、t3 1～2,t3 3～4,…,t3 (α-1)～αAnd get y1～2,y3～4,…,y(α-1)～αFrequency f of1～2,f3～4,…,f(α-1)～αIs composed of
In this example t1 1～2＝0.007,t1 3～4＝0.028,t3 1～2＝0.002，t3 3～4＝0.012，f1～2＝47.6Hz，f3～4＝100Hz；
(10) Calculating y1～2,y3～4,…,y(α-1)～αRespectively is
The absolute value of the minimum value is respectively
To obtain y1～2,y3～4,…,y(α-1)～αCorresponding amplitude A1～2,A3～4,…,A(α-1)～αRespectively as follows:
in this example
A1～2＝0.2964，A3～4＝0.1734；
(11) Constructive power frequency noise c1～2,c3～4,…,c(α-1)～αAre respectively as
Where ". mark" represents multiplication, Δ t is a sampling interval, and Δ t ═ 1/f0In this example,. DELTA.t is 0.001, c1～2＝0.2964*sin(2*47.6*i*0.001)，c3～4＝0.1734*sin(2*100*i*0.001)；
(12) Signal x after suppressing power frequency noise1(i) Is composed of
x1(i)＝x(i)-c1～2-c3～4,…,-c(α-1)～α
In this example x1(i)＝x(i)-c1～2-c3～4。
The vibration signal after the airplane guide pipe is hammered is acquired through the acceleration sensor, the vibration signal when the power frequency noise is suppressed is successively tested by using the vibration signal when the power frequency noise is suppressed by using the method, a signal diagram is drawn, the signal diagram is fitted and then is listed in the same data table for comparison, as shown in figure 1, the power frequency noise runs through the whole acquisition time, as shown in figure 2, the power frequency noise can be effectively suppressed by using the method provided by the invention, and as shown in figure 3, the power frequency noise near 50Hz and 100Hz after the power frequency noise is suppressed by using the method provided by the invention, can be effectively suppressed.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (10)
1. The PCA-based power frequency noise suppression method for the aircraft conduit vibration signal is characterized by comprising the following steps of:
(1) collecting a vibration signal x (i) after hammering the airplane guide pipe, wherein the collection time is 1.2 s;
(2) extracting a signal T of which the vibration signal is located in a time windoww；
(3) According to the phase space theory, a signal T of which the vibration signal is positioned in a time window is extractedwConstructing a Hankel matrix;
(4) calculating covariance matrix H of Hankel matrix1；
(5) Calculating covariance matrix H by singular value decomposition1The eigenvalue matrix Λ and the eigenvalue vector matrix V;
(6) calculating the eigenvalue sequence number alpha with the eigenvalue difference of more than 12 times before and after the first appearance according to the eigenvalue arrangement sequence in the eigenvalue matrix Lambda;
(7) performing linear mapping on the Hankel matrix to obtain a principal component matrix F;
(8) respectively reserving the main components of the rows 1 to 2,3 to 4, …, (alpha-1) -alpha of the F in the order of 1 to 2,3 to 4, …, (alpha-1) -alpha, and respectively obtaining the recombined main component F by setting the main components except the reserved main component to zero1～2,F3～4,…,F(α-1)～α；
(9) Respectively for recombinant principal component F1～2,F3～4,…,F(α-1)～αReconstructing to obtain corresponding reconstruction matrix Y1～2,Y3～4,…,Y(α-1)～α；
(10) Respectively reconstructing matrix Y1～2,Y3～4,…,Y(α-1)～αThe first row and the last column are connected end to obtain the estimated power frequency noise y1～2,y3～4,…,y(α-1)～α；
(11) Separately extracting y1～2,y3～4,…,y(α-1)～αThe time corresponding to the 1 st and 3 rd zero points is t1 1～2,t1 3～4,…,t1 (α-1)～α、t3 1～2,t3 3～4,…,t3 (α-1)～αAnd get y1～2,y3～4,…,y(α-1)～αFrequency f of1～2,f3～4,…,f(α-1)～α；
(12) Calculating y1～2,y3～4,…,y(α-1)～αRespectively is
The absolute value of the minimum value is respectively
To obtain y1～2,y3～4,…,y(α-1)～αCorresponding amplitude A1～2,A3～4,…,A(α-1)～α；
(13) Constructive power frequency noise c1～2,c3～4,…,c(α-1)～αRespectively as follows:
(14) suppressing the power frequency noise to obtain a vibration signal x after the power frequency noise is suppressed1(i) And is specifically x1(i)＝x(i)-c1～2-c3～4,…,-c(α-1)～α。
2. The PCA-based aircraft conduit vibration signal power frequency noise suppression method as claimed in claim 1, wherein in the step (1), an acceleration sensor is used for collecting the vibration signal after the aircraft conduit is hammered.
3. The PCA-based aircraft conduit vibration signal power frequency noise suppression method as claimed in claim 2, wherein in the step (2), the vibration signal is a signal T within a time windowwAnd x (j), wherein j is ROUND (x N), ROUND (x N) +1, …, N, ROUND is rounded in the nearest direction, is a shrinkage coefficient, and has a value range of 9/12 ≦ 11/12.
4. The PCA-based power frequency noise suppression method for the aircraft conduit vibration signal according to claim 3, wherein in the step (3), a Hankel matrix is constructed as follows:
note that the number of rows in the matrix H is m, the number of columns is N, and if N +1-ROUND (× N) is an even number, m is (N +1-ROUND (× N))/2+1, N is (N +1-ROUND (× N))/2, and if N +1-ROUND (× N) is an odd number, m is (N +2-ROUND (× N))/2.
5. The PCA-based power frequency noise suppression method for aircraft conduit vibration signals according to claim 4, wherein in the step (4), the covariance matrix H is calculated through a Hankel matrix1The following formula exists:
wherein HTTranspose the matrix for H, "·" denotes matrix multiplication.
6. The PCA-based power frequency noise suppression method for aircraft conduit vibration signals according to claim 5, wherein in the step (5), H is calculated by using a singular value decomposition method1The eigenvalue matrix Λ and the eigenvalue vector matrix V, then a formula exists
H1＝V·Λ·VT
Wherein, Λ is a characteristic value matrix with characteristic values arranged from large to small in a diagonal form, V is a characteristic vector matrix corresponding to each characteristic value, and V is a characteristic vector matrixTIs a transposed matrix of V and satisfies V.VT＝VTV ═ E, E is the identity matrix.
7. The PCA-based power frequency noise suppression method for aircraft conduit vibration signals according to claim 6, wherein in the step (7), the principal component matrix F is
F＝VT·H。
8. The PCA-based aircraft conduit vibration signal power frequency noise suppression method as claimed in claim 7, wherein in the step (9), the matrix Y is reconstructed1～2,Y3～4,…,Y(α-1)～αIn particular to
9. The PCA-based aircraft conduit vibration signal power frequency noise suppression method as claimed in claim 8, wherein in step (11), y1～2,y3～4,…,y(α-1)～αFrequency f of1～2,f3～4,…,f(α-1)～αThe method specifically comprises the following steps:
10. the PCA-based aircraft duct vibration signal line frequency noise suppression method of claim 9 wherein in step (12), y1～2,y3～4,…,y(α-1)～αCorresponding amplitude A1～2,A3～4,…,A(α-1)～αRespectively as follows:
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| CN114486256B (en) * | 2021-08-22 | 2023-10-31 | 北京燃气绿源达清洁燃料有限公司 | CNG compressor rolling bearing fault feature extraction method |
| CN116975541A (en) * | 2023-09-21 | 2023-10-31 | 深圳市盘古环保科技有限公司 | Automatic screening system for garbage of garbage landfill stock |
| CN116975541B (en) * | 2023-09-21 | 2024-01-09 | 深圳市盘古环保科技有限公司 | Automatic screening system for garbage of garbage landfill stock |
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