CN102629243B - End effect suppression method based on neural network ensemble and B-spline empirical mode decomposition (BS-EMD) - Google Patents
End effect suppression method based on neural network ensemble and B-spline empirical mode decomposition (BS-EMD) Download PDFInfo
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Abstract
The invention discloses an end effect suppression method based on the neural network ensemble and B-spline empirical mode decomposition (BS-EMD). The end effect suppression method includes the steps as follows: A, vibration signals are measured and obtained by utilizing a speed sensor; B, the signals are continued leftwards and rightwards by adopting the neural network ensemble; C, a mean curve of the signals is obtained by utilizing a B-spline mean function; and D, empirical mode decomposition (EMD) is conducted, data at the two ends of the mean curve are abandoned, and a plurality of intrinsic mode function (IMF) components corresponding to original signals are obtained; and E, each IMF component is analyzed, and fault feathers are extracted. The end effect suppression method has the advantages that an end effect can be effectively suppressed, and the influence of the end effect on BS-EMD results is avoided.
Description
Technical field
The present invention relates to signal processing technology field, particularly one is based on Artificial neural network ensemble and BS-EMD(B-spline empirical mode decomposition, B-spline empirical mode decomposition) end effect suppressing method.
Background technology
Large rotating machinery is the key equipment of the departments such as modern metallurgy, electric power, oil.By the restriction such as working environment, serviceable life, easily there are some faults in some parts in this plant equipment, thus affect the normal work of whole equipment, even can cause fatal crass, cause heavy economic losses time serious.Vibration signal when rotating machinery breaks down or exception occurs shows as non-linear, non-stationary characteristic more, and these non-stationary signals often include a large amount of fault characteristic informations.Therefore, the fault diagnosis of rotating machinery to avoiding great mechanical accident with monitoring, is promoted economic development and is had great significance.At present, Chinese scholars has achieved certain achievement, but still needs constantly further research and perfect for rotating machinery.
EMD(Empirical Mode Decomposition, empirical mode decomposition) method is a kind of new time series signal analytical approach that development in recent years is got up, the method is a series of IMF(Intrinsic Mode Function the signal decomposition of complexity, intrinsic mode functions) component sum.Because EMD is adaptive, therefore the method is applicable to non-linear and analysis that is non-stationary signal.
But, inventor is when realizing of the present invention, find that prior art exists the problem of end effect, namely in EMD process, when with extreme point be node as spline interpolation to construct envelope time, can not guarantee that data sequence left and right two-end-point is just extreme point, thus make SPL very poor at the interpolation precision at end points place, easy generation " overshoot " or " owing punching " phenomenon, and by loop iteration by this harmful effect progressively " pollution " whole data sequence, finally cause the decomposition result serious distortion of EMD.
Summary of the invention
(1) technical matters that will solve
Problem to be solved by this invention is to provide a kind of end effect suppressing method based on Artificial neural network ensemble and BS-EMD, to overcome the defect that end effect appears in prior art in EMD process.
(2) technical scheme
For achieving the above object, the invention provides a kind of end effect suppressing method based on Artificial neural network ensemble and BS-EMD, said method comprising the steps of:
A, utilize speed pickup measure obtain vibration signal;
B, employing Artificial neural network ensemble carry out left continuation and right continuation to described signal;
C, B-spline mean value function is utilized to obtain the Mean curve of described signal;
D, carry out empirical mode decomposition, abandon two end datas, obtain the some IMF components corresponding with original signal;
E, analyze each IMF component, extract fault signature.
Preferably, described step B specifically comprises:
B1, when only having one deck neural network, described neural network to be learnt, obtaining the determined value of weights and threshold;
B2, according to formula
obtain the output of monolayer neural networks; Wherein,
for single neuronic output,
for weights,
for threshold value,
for input amendment.
B3, employing weighted mean are carried out integrated, adopt
it is integrated right that individual neural network forms
be similar to, the weights of network meet following formula
；
Wherein,
represent from
ndimension space is to the mapping of the one-dimensional space.
B4, according to distribution
randomly draw, obtain training set; Wherein, at network
under, when being input as
time, export and be
;
According to formula
obtain the output of Artificial neural network ensemble;
According to formula
obtain the extensive error of neural network;
According to formula
obtain the extensive error of Artificial neural network ensemble;
According to formula
obtain the weighted mean of each generalization ability of network error;
According to formula
obtain the diversity factor of neural network;
According to formula
obtain integrated diversity factor;
The extensive error of Artificial neural network ensemble can be obtained thus
.
Preferably, described step C specifically comprises:
C1, supposition finite interval [
], given division:
,
representation node value, according to formula
calculate
secondary B-spline basis function, wherein,
.Regulation is when the denominator in formula is 0, and the value of this function is 0.The
the local support of individual B-spline function is
；
C2, utilize B-spline, according to formula
obtain the Mean curve of signal.
for the reference mark of B batten, can be obtained by the extreme point running mean of signal,
be
jthe local support of individual B splines.
Preferably, described step D specifically comprises:
D1, supposition original signal
for endless, according to formula
obtain the average of signal
, and according to formula
obtain interpolating function;
D2, according to IMF criterion, if
not an IMF, then will
as
substitute into formula
repeat said process, until
it is an intrinsic mode functions;
Repeat said process, obtain each IMF component and survival function, according to formula
be broken down into
the signal of individual intrinsic mode functions and a trend term
, wherein
be
iindividual intrinsic mode functions,
rfor trend term;
D3, to the IMF process obtained, clip the data of prolongation, obtain the IMF component corresponding with original signal.
Preferably, described step D1 specifically comprises:
D11, find out rotor fault vibration velocity signal
all Local Extremum, to couple together all Local modulus maximas with B-spline curves and form coenvelope line, all local minizing points to be coupled together form lower envelope line with B-spline curves;
The mean value of D12, described coenvelope line, lower envelope line is designated as
, obtain
.
Preferably, described step D2 specifically comprises:
D21, judgement
whether meet the condition of IMF, if so, then
for signal
first component meeting IMF condition;
If not, then will
as raw data, repeat step D11 and D12, recycling B-spline function obtains the mean value of lower envelope
, judge
whether meet IMF condition, repeat said process, until be met IMF condition
; Note
, then
for signal
first component meeting IMF condition;
D22, general
from rate signal
in separate, obtain
;
Will
repeat step D11, D12 and D21 as raw data, obtain
the 2nd meet IMF component condition
; Repetitive cycling
secondary, obtain rate signal
's
the individual component meeting IMF condition
;
When
when becoming monotonic quantity, circulation terminates, and obtains rate signal
.
(3) beneficial effect
1, the present invention adopts Artificial neural network ensemble and BS-EMD methods combining, proposes a kind of new method solving end effect;
2, adopt B-spline interpolation method to ask for the upper lower envelope of signal, solve overshoot that cubic spline enveloping curve method causes and owe the problem of rushing;
3 utilize Artificial neural network ensemble to pass through training by the conjunctival goblet cell of multiple neural network, significantly improve the generalization ability of learning system;
4, the impact of end effect on BS-EMD decomposition result is solved.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of a kind of end effect suppressing method based on Artificial neural network ensemble and BS-EMD of the embodiment of the present invention;
Fig. 2 is the process flow diagram utilizing BS-EMD method to decompose vibration signal of the embodiment of the present invention;
Fig. 3 is the EMD decomposition result schematic diagram of prior art;
Fig. 4 is the decomposition result schematic diagram of the embodiment of the present invention.
Embodiment
Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.Following examples for illustration of the present invention, but are not used for limiting the scope of the invention.
A kind of end effect suppressing method based on Artificial neural network ensemble and BS-EMD of the embodiment of the present invention as shown in Figure 1, comprises the following steps:
Step s101, utilizes speed pickup to measure and obtains vibration signal.
Step s102, adopts Artificial neural network ensemble to carry out left continuation and right continuation to described signal.Utilize Artificial neural network ensemble to carry out continuation to signal, comprise the following steps:
(1) when only having the situation of one deck neural network, utilize neural network to carry out data sequence continuation and be mainly divided into two steps to carry out: study, continuation.The object of neural network learning process is exactly the determined value in order to obtain weights and threshold.
(2) output of monolayer neural networks can be expressed as
（1）
Wherein,
for single neuronic output,
for weights,
for threshold value,
for input amendment.
(3) integrated employing weighted mean, adopts
the collection of individual neural network composition
be similar in pairs, the weights of network meet following formula
（2）
（3）
Wherein,
represent from
ndimension space is to the mapping of the one-dimensional space.
(4) training set is according to distribution
randomly draw, at network
lower to being input as
time, export and be
, the now output of Artificial neural network ensemble is
（4）
The extensive error of neural network
with integrated extensive error
be respectively
（5）
（6）
The weighted mean of each generalization ability of network error is
（7）
The diversity factor of neural network
with integrated diversity factor
be respectively
（8）
（9）
The extensive error of Artificial neural network ensemble is
（10）
In formula (10)
show the degree of correlation of each network of Artificial neural network ensemble, therefore, only have make as far as possible integrated in the error of each network uncorrelated mutually, could the generalization ability of strength neural network.
Step s103, utilizes B-spline mean value function to obtain the Mean curve of described signal:
(1) calculate
secondary B-spline basis function is:
（11）
Wherein,
（12）
Regulation occurs when the denominator in formula (11) is 0
situation time, now defining its value is 0.The
the local support of individual B-spline function is
（13）
(2) B-spline basis function has the character such as recursion, local support and linear independence.The Mean curve utilizing B-spline to calculate signal is
（14）
Step s104, carries out empirical mode decomposition, abandons two end datas, obtains the some IMF components corresponding with original signal.Concrete decomposable process is as follows:
S1041, assuming that original signal
for endless, the average of signal is asked according to formula (14)
, then interpolating function is
（15）
S1042, according to IMF criterion, if
not an IMF, then will
as
substitution formula (15) repeats said process, until
an intrinsic mode functions, until obtain each IMF component and survival function.Now signal
be broken down into
individual intrinsic mode functions and a trend term, namely
（16）
S1043, to the IMF process obtained, clips the data of prolongation, obtains the IMF component corresponding with original signal.
Wherein step s1041 and step s1042 detailed process as follows:
1) rotor fault vibration velocity signal is found out
all Local Extremum, to couple together all Local modulus maximas with B-spline curves and form coenvelope line.All local minizing points to be coupled together with B-spline curves and form lower envelope line, upper and lower envelope should comprise all data points.
2) mean value of upper and lower envelope is designated as
, obtain
（17）
Ideally, if
meet the condition of IMF, so
be exactly
first IMF component.
3) if
do not meet the condition of IMF,
as raw data, repeat step 1) ~ 2), recycling B-spline function obtains the mean value of lower envelope
, then judge
whether meet IMF condition.Note
, then
for signal
first component meeting IMF condition.
4) will
from rate signal
in separate, obtain
（18）
Will
step 1) ~ 3 are repeated as raw data), obtain
the 2nd meet IMF component condition
, repetitive cycling
secondary, obtain vibration acceleration signal
's
each component meeting IMF condition, namely
（19）
When meeting end condition (namely
become monotonic quantity and can not therefrom extract IMF component again) time, circulation terminates.Now rate signal can be expressed as
。（20）
In formula,
the average tendency of representation signal is the residual components of signal.And each IMF component contains the composition of each different frequency section from high to low of signal respectively, the frequency content that each frequency band comprises is different.And each IMF component changes along with the change of vibration signal itself.
Step s105, analyzes each IMF component, extracts fault signature.
BS-EMD of the present invention asks for the upper lower enveloping curve of signal by B-spline interpolating function, and avoid deficient punching and the overshooting problem of signal, B-spline interpolation has good local property, is widely used in function interpolation and matching etc.Artificial neural network ensemble is utilized to carry out left and right continuation to rotor test data, B-spline interpolation curve is utilized to carry out to data the Mean curve that interpolation calculation obtains signal, carry out empirical mode decomposition again, finally abandon the data of two ends continuation, namely obtain the intrinsic mode functions corresponding with original signal.
The present invention is intended to utilize Artificial neural network ensemble to carry out end extending to signal and solves end effect problem, by theoretical research and analysis of experiments, analyzes the rotor unbalance fault-signal of rotating machinery.First, signal is carried out to the continuation of Artificial neural network ensemble, then decompose the characteristic component obtaining signal, by obtaining the frequecy characteristic of signal to each point of quantitative analysis, thus extract the information of this fault.The flow process that the embodiment of the present invention utilizes BS-EMD method to decompose vibration signal as shown in Figure 2.By test signal, the present invention illustrates that the method can suppress end effect problem effectively.
In the present embodiment, rotating machinery fault analog platform is simulated rotor misalignment fault, its fault characteristic frequency, except power frequency, also has two frequencys multiplication.Utilize speed pickup to extract the vibration signal of vertical direction, the rotating speed of axle is 924r/min, and sample frequency is 500Hz, and it is 512 points that collection is counted, and decomposes signal, extracts the eigenwert of signal.
In these cases, as shown in Figure 3, the decomposition result schematic diagram of the embodiment of the present invention as shown in Figure 4 for the EMD decomposition result schematic diagram of prior art.
With reference to Fig. 3, the waveform of original signal is " signal ", and directly adopt EMD to decompose, as can be seen from the figure, IMF2, IMF3 occur end effect at end points place.
With reference to Fig. 4, from the IMF2 figure, in IMF3, can find out that the end effect of signal obtains obvious suppression.In the drawings, IMF1 represents two frequency multiplication compositions, and IMF2 represents power frequency composition.IMF3 relatively, finds that rising and falling appears at end points place in the IMF3 using original method to obtain, especially obvious in the fluctuation of left end point place.And the value at the end points place obtained by the embodiment of the present invention is more smooth, frequency content is more concentrated, and energy leakage is fewer.By comparing this two kinds of decomposition methods, that can find out that two kinds of methods successfully can disclose signal misaligns fault, but there is better performance by the signal decomposition of the embodiment of the present invention at end points place, effectively can suppress end effect, make the easier accurate recognition of fault signature.By comparison diagram 3 and Fig. 4, can find out that method that the present invention proposes is a kind of method of highly effective suppression end effect.
The end effect suppressing method based on Artificial neural network ensemble and BS-EMD of the embodiment of the present invention has following beneficial effect:
1, the present invention adopts Artificial neural network ensemble and BS-EMD methods combining, proposes a kind of new method solving end effect;
2, adopt B-spline interpolation method to ask for the upper lower envelope of signal, solve overshoot that cubic spline enveloping curve method causes and owe the problem of rushing;
3 utilize Artificial neural network ensemble to pass through training by the conjunctival goblet cell of multiple neural network, significantly improve the generalization ability of learning system;
4, the impact of end effect on BS-EMD decomposition result is solved.
The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and replacement, these improve and replace and also should be considered as protection scope of the present invention.
Claims (5)
1., based on an end effect suppressing method of Artificial neural network ensemble and BS-EMD, it is characterized in that, said method comprising the steps of:
A, utilize speed pickup measure obtain vibration signal;
B, employing Artificial neural network ensemble carry out left continuation and right continuation to described signal;
C, B-spline mean value function is utilized to obtain the Mean curve of described signal;
D, carry out empirical mode decomposition, abandon two end datas, obtain the some IMF components corresponding with original signal;
E, analyze each IMF component, extract fault signature;
Described step B specifically comprises:
B1, when only having one deck neural network, described neural network to be learnt, obtaining the determined value of weights and threshold;
B2, according to formula a
i=f (ω
i× p
m,i+ b
i) obtain the output of monolayer neural networks; Wherein, a
ifor single neuronic output, ω
ifor weights, b
ifor threshold value, p
m,ifor input amendment;
B3, employing weighted mean are carried out integrated, and what adopt N number of neural network to form is integrated to f:R
n→ R is similar to, the weights ω of network
αmeet following formula
Wherein, f:R
n→ R represents the mapping from n-dimensional space to the one-dimensional space;
B4, to randomly draw according to distribution p (x), obtain training set; Wherein, under network α, when being input as X, export as V
α(X);
According to formula
obtain the output of Artificial neural network ensemble;
According to formula E
α=∫ dxp (x) (f (x)-V
α(x))
2obtain the extensive error of neural network;
According to formula
obtain the extensive error of Artificial neural network ensemble;
According to formula
obtain the weighted mean of each generalization ability of network error;
According to formula
obtain the diversity factor of neural network;
According to formula
obtain integrated diversity factor;
The extensive error of Artificial neural network ensemble can be obtained thus
2. the end effect suppressing method based on Artificial neural network ensemble and BS-EMD according to claim 1, it is characterized in that, described step C specifically comprises:
C1, supposition finite interval [a, b], given division: Δ a=t
0<t
1<...<t
n-1<t
n=b, t
jrepresentation node value, according to formula
Calculate k B-spline basis function, wherein,
regulation is when the denominator in formula is 0, and the value of this function is 0; The local support of a jth B-spline function is
C2, utilize B-spline, according to formula
obtain the Mean curve of signal; ω
jfor the reference mark of B-spline, can be obtained by the extreme point running mean of signal, B
j,kt () is the local support of a jth B-spline function.
3. the end effect suppressing method based on Artificial neural network ensemble and BS-EMD according to claim 2, it is characterized in that, described step D specifically comprises:
D1, supposition original signal x (t) are endless, according to formula
obtain the average m of signal, and obtain interpolating function according to formula x (t)-m=h;
D2, according to IMF criterion, if h is not an IMF, then using h as x (t) substitute into formula x (t)-m=h repeat said process, until h is an intrinsic mode functions;
Repeat said process, obtain each IMF component and survival function, according to formula
obtain signal x (t) being broken down into n intrinsic mode functions and a trend term, wherein c
it () is i-th intrinsic mode functions, r is trend term;
D3, to the IMF process obtained, clip the data of prolongation, obtain the IMF component corresponding with original signal.
4. the end effect suppressing method based on Artificial neural network ensemble and BS-EMD according to claim 3, it is characterized in that, described step D1 specifically comprises:
D11, find out all Local Extremum of rotor fault vibration velocity signal x (t), with B-spline curves all Local modulus maximas are coupled together and form coenvelope line, with B-spline curves all local minizing points are coupled together and form lower envelope line;
The mean value of D12, described coenvelope line, lower envelope line is designated as m
1, obtain x (t)-m
1=h
1.
5. the end effect suppressing method based on Artificial neural network ensemble and BS-EMD according to claim 4, it is characterized in that, described step D2 specifically comprises:
D21, judge h
1whether meet the condition of IMF, if so, then h
1for first of signal x (t) meets the component of IMF condition;
If not, then by h
1as raw data, repeat step D11 and D12, recycling B-spline function obtains the mean value m of lower envelope
11, judge h
11=h
1-m
11whether meet IMF condition, repeat said process, until be met the h of IMF condition
1k; Note c
1=h
1k, then c
1for first of signal x (t) meets the component of IMF condition;
D22, by c
1separate from rate signal x (t), obtain r
1=x (t)-c
1;
By r
1repeat step D11, D12 and D21 as raw data, obtain the c that the 2nd of x (t) meets IMF component condition
2; Repetitive cycling n time, obtains the individual component meeting IMF condition of n of rate signal x (t)
Work as r
nduring for monotonic quantity, circulation terminates, and obtains rate signal
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| CN104182617B (en) * | 2014-07-30 | 2017-04-12 | 电子科技大学 | End effect suppression method based on intrinsic waveform matching |
| CN104156623A (en) * | 2014-08-27 | 2014-11-19 | 湖南科技大学 | Diagnosis method of mechanical composite faults |
| JP6148316B2 (en) * | 2015-07-31 | 2017-06-14 | ファナック株式会社 | Machine learning method and machine learning device for learning failure conditions, and failure prediction device and failure prediction system provided with the machine learning device |
| DE102016008987B4 (en) | 2015-07-31 | 2021-09-16 | Fanuc Corporation | Machine learning method and machine learning apparatus for learning failure conditions, and failure prediction apparatus and failure prediction system including the machine learning apparatus |
| CN105466710B (en) * | 2015-11-23 | 2017-09-19 | 电子科技大学 | Local mean value based on frequency domain similarity decomposes end effect improved method |
| CN105738107B (en) * | 2016-01-28 | 2019-07-23 | 西安交通大学 | The train wheel Method for Bearing Fault Diagnosis decomposed based on approximate complete changeable mode |
| CN105784364A (en) * | 2016-03-02 | 2016-07-20 | 西安交通大学 | Bearing fault diagnosis method based on total experience mode decomposition and fractal box dimensions |
| CN106503366B (en) * | 2016-10-27 | 2019-12-31 | 石家庄铁道大学 | Method for inhibiting EMD endpoint effect |
| CN108759871B (en) * | 2018-07-03 | 2021-01-05 | 哈尔滨工业大学 | Improved EMD preprocessing algorithm-based strapdown inertial navigation system coarse alignment method |
| CN109520611B (en) * | 2018-11-08 | 2020-09-22 | 温州大学 | Monitoring method for working condition of earthquake simulation vibration table |
| CN113362853B (en) * | 2020-03-03 | 2022-07-01 | 东北大学秦皇岛分校 | EMD endpoint effect suppression method based on LSTM network |
| CN111444613B (en) * | 2020-03-26 | 2023-09-08 | 云南电网有限责任公司电力科学研究院 | Harmonic analysis method, device and storage medium based on improved EMD (electromagnetic radiation) power system |
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