CN107025446A - A kind of vibration signal combines noise-reduction method - Google Patents
A kind of vibration signal combines noise-reduction method Download PDFInfo
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Abstract
Combine noise-reduction method, its step the present invention relates to a kind of vibration signal：The wavelet modulus maxima of vibration signal is decomposed, the corresponding modulus maxima point of wavelet conversion coefficient on each yardstick and modulus maxima point position is obtained；The out to out J of wavelet decomposition is selected, using the threshold value T that pre-sets as searching threshold on the yardstick, retains the point that wherein modulus maximum is more than T, removes the point that wherein modulus maximum is less than T, obtains modulus maximum point new on yardstick J；New modulus maximum point is searched on yardstick J 1 and falls the sequence of point sets limited on yardstick J in neighborhood；For yardstick J=1, the corresponding extreme point when J=2 exists and retains J=1 on the position of extreme point, and by the extreme point zero setting on remaining position；Using alternating projection method from the modulus maximum on each yardstick and its position reconstruct wavelet coefficient, reconstruction signal then is obtained using inverse transformation to resulting wavelet coefficient；Blind source separating is carried out to signal after noise reduction and vibration signal based on FastICA algorithms, the joint noise reduction process to vibration signal is completed.
Description
Technical field
The present invention relates to a kind of vibration signal noise-reduction method, especially with regard to one kind based on wavelet modulus maxima and solely
The vibration signal joint noise-reduction method of vertical constituent analysis.
Background technology
Due to containing substantial amounts of noise in mechanical equipment vibration signal, the presence of noise to the monitorings of equipment running status,
Fault diagnosis all brings very big interference.ICA in noise-reduction method is had at present to can be only applied to observation signal source number and be no less than
The overdetermination blind source separating of signal number, it is impossible to solve single channel ICA underdetermined problem, but also exist due to inputted vibration signal
It is improper cause inferior separating effect the problem of.
The content of the invention
In view of the above-mentioned problems, combining noise-reduction method it is an object of the invention to provide a kind of vibration signal, this method is based on small
Wave conversion modulus maximum carries out noise reduction with independent component analysis to vibration signal noise, solves single channel ICA underdetermined problem,
Effectively improve ICA separative efficiency.
To achieve the above object, the present invention takes following technical scheme：A kind of vibration signal combines noise-reduction method, its feature
It is to comprise the following steps：1) wavelet modulus maxima decomposition is carried out to the vibration signal x (t) collected, reconstruction signal is obtained
Signal after to noise reduction；1.1) wavelet decomposition is carried out to vibration signal x (t), decomposition scale number is 5；1.2) obtain on each yardstick
The corresponding modulus maximum point of wavelet conversion coefficientAnd obtain modulus maxima point position；Wherein, f (ni) table
Show modulus maximum point function；1.3) the out to out J of wavelet decomposition is selected, using the threshold value T that pre-sets to search on the yardstick
Rope threshold value, retains the point that wherein modulus maximum is more than T, removes the point that wherein modulus maximum is less than T, obtains mould new on yardstick J
Maximum point 1.4) new modulus maximum point is searched on yardstick J-1 and falls to limit neighbour on yardstick J
Sequence of point sets in domain；1.5) for yardstick J=1, the corresponding extreme value when J=2 exists and retains J=1 on the position of extreme point
Point, and by the extreme point zero setting on remaining position；1.6) alternating projection method is used from the modulus maximum on each yardstick and its position
Wavelet coefficient is reconstructed, reconstruction signal v (n then are obtained using inverse transformation to resulting wavelet coefficienti), reconstruction signal v (ni)
Signal as after noise reduction；2) based on FastICA algorithms to signal v (n after noise reductioni) and vibration signal x (ni) carry out blind source point
From obtaining signal source signal and noise signal, complete the joint noise reduction process to vibration signal.
Further, the step 1.4) in, introduce parameter εj, build the restriction neighborhood of different maximum points, modulus maxima
It is worth point search process as follows：Centered on extreme point p position on yardstick J, a neighborhood o (n is constructedj,p,εj), wherein, nj,p
For p-th of extreme point position on yardstick J, εjFor given constant；Only retain to fall very big in the neighborhood on yardstick J-1
Value point.
Further, the step 2) in, the blind source separation method based on FastICA algorithms is as follows：2.1) assume there are m
Separate vibration source sj(t), wherein j=1,2 ..., m, m vibration signal x has been obtained by signal acquisitionj, and m (t)
Vibration signal xj(t) vector form is represented with X '；T represents the time；2.2) to m vibration signal xj(t) in vectorial X ' progress
Heartization processing, even X '-E [X ']=X ", it is 0 to make its average, wherein, E is mathematic expectaion；2.3) according in FastICA algorithms
Albefaction formula to vectorial X " carry out whitening processing, obtain be used for solve approximate signal source yj(t) vectorial X；2.4) basis
Separation matrix W and vector X in FastICA algorithms construct approximate signal source yj(t) vectorial Y=WX so that vectorial Y and original
The independent signal source s comei(t) it is approximate.
Further, the step 2.3) in, whitening processing is as follows：2.3.1 vector X " covariance matrix) is solved first
Cx, Cx=E [X " (X ")T]；T is transposed matrix；2.3.2) according to covariance matrix Cx, obtain with covariance matrix CxUnit model
Number characteristic vector is matrix F=(e of row1…en), wherein, ekFor covariance matrix CxUnit norm characteristic vector, k=1,
2 ..., n, n are natural number；2.3.3) according to covariance matrix Cx, obtain with covariance matrix CxCharacteristic value for diagonal element
Diagonal matrix D=diag (d1…dn), wherein, dyFor covariance matrix CxCharacteristic value, y=1,2 ..., n；2.3.4) by matrix
The albefaction formula that F and diagonal matrix D is substituted into FastICA algorithms, obtains vectorial X：
Further, the step 2.4) in, using the Finland peaceful Hyvarinen of scientist Xu Weili iterative formula to separation
Matrix W carries out convergence calculating, to obtain true and reliable separation matrix W.
Further, separation matrix W convergence method is：2.4.1 random starting values) are assigned to separation matrix W first；
2.4.2) W (k+1) is calculated using Hyvarinen iterative formula：
W (k+1)=E { Xg [W (k)TX]}-E{g[W(k)TX]}W(k)T,
Wherein, E represents to seek mathematic expectaion, and g represents the derivative of non-quadratic function, and k is iterations；2.4.3 W (k+) are utilized
1)←W(k+1)/||W(k+1)||2Standardize W (k+1)；2.4.4) iterate until W convergences, the separation square after being restrained
Battle array W.
The present invention is due to taking above technical scheme, and it has advantages below：1st, the present invention can effectively make up ICA only
Shortcoming of the observation signal source number no less than the overdetermination blind source separating of signal number is can apply to, single channel ICA deficient asking surely is solved
Topic.2nd, the present invention can be solved effectively because input is shaken by original vibration signal after wavelet modulus maxima is handled
The problem of inferior separating effect that dynamic signal is improper to be caused, effectively improve ICA separative efficiency.3rd, signal after noise reduction process of the present invention
Feature it is more obvious, be conducive to the work such as fault diagnosis.
Brief description of the drawings
Fig. 1 is the overall flow schematic diagram of the present invention.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
As shown in figure 1, the present invention provides a kind of vibration signal based on wavelet modulus maxima and independent component analysis
Joint noise-reduction method, this method comprises the following steps：
1) wavelet modulus maxima decomposition is carried out to the vibration signal x (t) collected, reconstruction signal obtains believing after noise reduction
Number, wherein, t represents the time；
Detailed process is as follows：
1.1) wavelet decomposition is carried out to vibration signal x (t).
The characteristics of for vibration signal, decomposition scale number is preferably 5, and the selection of the decomposition scale number has good tight branch
The db3 wavelet basis of support, orthogonality and of a relatively high vanishing moment.
1.2) the corresponding modulus maximum point of wavelet conversion coefficient on each yardstick is obtainedAnd ask
Depanning maximal point position.Wherein, f (ni) represent modulus maximum point function.
1.3) select the out to out J of wavelet decomposition, using the threshold value T that pre-sets as searching threshold on the yardstick, protect
Wherein point of the modulus maximum more than T is stayed, removes the point that wherein modulus maximum is less than T, obtains modulus maximum point new on yardstick J
1.4) new modulus maximum point is searched on yardstick J-1 and falls the sequence of point sets limited on yardstick J in neighborhood.
Introduce parameter εj, the restriction neighborhood of different maximum points is built, modulus maximum point search process is as follows：With yardstick
Centered on the upper extreme point p of J position, a neighborhood o (n is constructedj,p,εj), wherein, nj,pFor p-th of extreme point position on yardstick J
Put, εjFor given constant.Only retain to fall the maximum point in the neighborhood on yardstick J-1.
1.5) for yardstick J=1, the corresponding extreme point when J=2 exists and retains J=1 on the position of extreme point, and incite somebody to action
Extreme point zero setting on remaining position.
1.6) using alternating projection method from the modulus maximum on each yardstick and its position reconstruct wavelet coefficient, then to gained
The wavelet coefficient arrived obtains reconstruction signal v (n using inverse transformationi), reconstruction signal v (ni) it is signal after noise reduction.
2) based on FastICA algorithms to signal v (n after noise reductioni) and vibration signal x (ni) blind source separating is carried out, obtain signal
Source signal and noise signal, complete the joint noise reduction process to vibration signal.
Above-mentioned steps 2) in, the blind source separation method based on FastICA algorithms is as follows：
2.1) assume there are m separate vibration source sj(t), wherein j=1,2 ..., m, are obtained by signal acquisition
M vibration signal xj, and m vibration signal x (t)j(t) vector form is represented with X '；T represents time, i.e. sj(t) in
One string sequence is the string number arranged according to time order and function.
2.2) to m vibration signal xj(t) vectorial X ' carry out centralization processing, even X '-E [X ']=X ", makes its equal
It is worth for 0, wherein, E is mathematic expectaion；
2.3) the albefaction formula in FastICA algorithms carries out whitening processing to vectorial X ", obtains being used to solve approximately
Signal source yj(t) vectorial X；Wherein whitening processing is as follows：
2.3.1 vector X " covariance matrix C) is solved firstx, Cx=E [X " (X ")T]；T is transposed matrix.
2.3.2) according to covariance matrix Cx, obtain with covariance matrix CxUnit norm characteristic vector for row matrix F
=(e1…en), wherein, ek(k=1,2 ..., n, n are natural number) is covariance matrix CxUnit norm characteristic vector；
2.3.3) according to covariance matrix Cx, obtain with covariance matrix CxCharacteristic value be diagonal element diagonal matrix D
=diag (d1…dn), wherein, dy(y=1,2 ..., n) are covariance matrix CxCharacteristic value；
2.3.4) by step 2.3.2) and step 2.3.3) in matrix F and diagonal matrix D substitute into FastICA algorithms in
Albefaction formula, obtains vectorial X：
2.4) the separation matrix W in FastICA algorithms and vector X construct approximate signal source yj(t) vectorial Y=
WX so that vectorial Y and original independent signal source si(t) it is approximate；
Because the separation matrix W initial values in FastICA algorithms are random imparting, therefore use initial separation matrix W
To solve vectorial Y, approximate signal source y can be influenceedj(t) with Independent Vibration source sj(t) approximation quality is relatively low, therefore, using Finland
The iterative formula that scientist is permitted Wei Lining (Hyvarinen) carries out convergence calculating to separation matrix W, to obtain true and reliable point
From matrix W, and then improve approximate signal source yj(t) approximation quality.Then separation matrix W convergence method is：
2.4.1 random starting values) are assigned to separation matrix W first；
2.4.2) W (k+1) is calculated using Hyvarinen iterative formula：
W (k+1)=E { Xg [W (k)TX]}-E{g[W(k)TX]}W(k)T,
Wherein, E represents to seek mathematic expectaion, and g represents the derivative of non-quadratic function, and k is iterations；
2.4.3) using W (k+1) ← W (k+1)/| | W (k+1) | |2Standardize W (k+1)；
2.4.4) iterate until W convergences, the separation matrix W after being restrained.
The various embodiments described above are merely to illustrate the present invention, and structure and size, set location and the shape of each part are all can be with
It is varied from, on the basis of technical solution of the present invention, all improvement carried out according to the principle of the invention to individual part and waits
With conversion, it should not exclude outside protection scope of the present invention.
Claims (6)
1. a kind of vibration signal combines noise-reduction method, it is characterised in that comprise the following steps：
1) wavelet modulus maxima decomposition is carried out to the vibration signal x (t) collected, reconstruction signal obtains signal after noise reduction；
1.1) wavelet decomposition is carried out to vibration signal x (t), decomposition scale number is 5；
1.2) the corresponding modulus maximum point of wavelet conversion coefficient on each yardstick is obtainedJ=1 ... 5, and obtain mould pole
A little bigger position；Wherein, f (ni) represent modulus maximum point function；
1.3) the out to out J of wavelet decomposition is selected, using the threshold value T that pre-sets as searching threshold on the yardstick, retains it
Middle modulus maximum is more than T point, removes the point that wherein modulus maximum is less than T, obtains modulus maximum point new on yardstick JJ=1 ... 5；
1.4) new modulus maximum point is searched on yardstick J-1 and falls the sequence of point sets limited on yardstick J in neighborhood；
1.5) for yardstick J=1, J=2 exist on the position of extreme point retain J=1 when corresponding extreme point, and by remaining
Extreme point zero setting on position；
1.6) using alternating projection method from the modulus maximum on each yardstick and its position reconstruct wavelet coefficient, then to resulting
Wavelet coefficient obtains reconstruction signal v (n using inverse transformationi), reconstruction signal v (ni) it is signal after noise reduction；
2) based on FastICA algorithms to signal v (n after noise reductioni) and vibration signal x (ni) blind source separating is carried out, obtain signal source letter
Number and noise signal, complete to the joint noise reduction process of vibration signal.
2. a kind of vibration signal joint noise-reduction method as claimed in claim 1, it is characterised in that：The step 1.4) in, draw
Enter parameter εj, the restriction neighborhood of different maximum points is built, modulus maximum point search process is as follows：With extreme point p on yardstick J
Position centered on, construct a neighborhood o (nj,p,εj), wherein, nj,pFor p-th of extreme point position on yardstick J, εjIt is given
Constant；Only retain to fall the maximum point in the neighborhood on yardstick J-1.
3. a kind of vibration signal joint noise-reduction method as claimed in claim 1, it is characterised in that：The step 2) in, it is based on
The blind source separation method of FastICA algorithms is as follows：
2.1) assume there are m separate vibration source sj(t), wherein j=1,2 ..., m, m have been obtained by signal acquisition
Vibration signal xj, and m vibration signal x (t)j(t) vector form is represented with X '；T represents the time；
2.2) to m vibration signal xj(t) vectorial X ' carry out centralization processing, even X '-E [X ']=X ", it is 0 to make its average,
Wherein, E is mathematic expectaion；
2.3) the albefaction formula in FastICA algorithms carries out whitening processing to vectorial X ", obtains being used to solve approximate signal
Source yj(t) vectorial X；
2.4) the separation matrix W in FastICA algorithms and vector X construct approximate signal source yj(t) vectorial Y=WX, makes
Obtain vectorial Y and original independent signal source si(t) it is approximate.
4. a kind of vibration signal joint noise-reduction method as claimed in claim 3, it is characterised in that：The step 2.3) in, in vain
Change processing as follows：
2.3.1 vector X " covariance matrix C) is solved firstx,T is transposed matrix；
2.3.2) according to covariance matrix Cx, obtain with covariance matrix CxUnit norm characteristic vector for row matrix F=
(e1…en), wherein, ekFor covariance matrix CxUnit norm characteristic vector, k=1,2 ..., n, n is natural number；
2.3.3) according to covariance matrix Cx, obtain with covariance matrix CxCharacteristic value be diagonal element diagonal matrix D=
diag(d1…dn), wherein, dyFor covariance matrix CxCharacteristic value, y=1,2 ..., n；
2.3.4) the albefaction formula for substituting into matrix F and diagonal matrix D in FastICA algorithms, obtains vectorial X：
5. a kind of vibration signal joint noise-reduction method as claimed in claim 3, it is characterised in that：The step 2.4) in, adopt
Convergence calculating is carried out to separation matrix W with the Finland peaceful Hyvarinen of scientist Xu Weili iterative formula, it is true and reliable to obtain
Separation matrix W.
6. a kind of vibration signal joint noise-reduction method as claimed in claim 5, it is characterised in that：Separation matrix W convergence side
Method is：
2.4.1 random starting values) are assigned to separation matrix W first；
2.4.2) W (k+1) is calculated using Hyvarinen iterative formula：
Wherein, E represents to seek mathematic expectaion, and g represents the derivative of non-quadratic function, and k is iterations；
2.4.3) using W (k+1) ← W (k+1)/| | W (k+1) |2Standardize W (k+1)；
2.4.4) iterate until W convergences, the separation matrix W after being restrained.
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| CN110081967A (en) * | 2019-05-30 | 2019-08-02 | 重庆大学 | Mechanical oscillation signal Threshold Noise Reduction Methods based on spectrogram wavelet transformation |
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