A kind of rotary machinery fault diagnosis method based on Fourier decomposition
Technical field
The present invention relates to rotary machinery fault diagnosis field, especially a kind of rotating machinery fault based on Fourier decomposition
Diagnostic method.
Background technology
Time frequency analysis are the powerfuls for processing time-domain signal.Conventional Time-Frequency Analysis Method mainly have Hilbert convert,
Short Time Fourier Transform, Winger-Ville distributions, wavelet transformation, S-transformation and empirical mode decomposition (Empirical Mode
Decomposition, EMD) etc..Because time-frequency characteristics are obtained from the formula of time-frequency distributions, explain comprising many thin
The labyrinth of signal is saved, when the analysis of non-stationary signal, it is difficult to obtain better effects.Hilbert conversion can be very
The good temporal characteristics for providing signal, there is temporal resolution very high, but the BORDER PROCESSING error of signal is larger;In short-term in Fu
Leaf transformation is influenceed by window selection can not be while reach the optimal of temporal resolution and frequency resolution;Winger-Ville points
Though cloth has time frequency resolution very high, for multicomponent data processing, due to the presence of cross term interference, its application is received very
Big limitation;Wavelet transformation can provide preferable time precision, and its low frequency range has resolution ratio very high, but the resolution of high frequency region
Rate is but very weak, and the phase information of part can make it lose physical significance.S-transformation is combined with Short Time Fourier Transform and small echo
Conversion, solves the phase Localization Problems of wavelet transformation, but caused due to implying a window when multifrequency signal is differentiated
Portray inaccurate in the place of frequency discontinuity, and be difficult to accurately portray amplitude.Norden E Huang etc. were carried in 1998
Gone out EMD, the method can carry out adaptive decomposition to non-stationary signal, but the method still suffers from certain defect, such as it
It is a kind of empirical method, still lacks complete theoretical foundation, the orthogonality of resulting modal components still needs after decomposition
Demonstration;It passes through the no science of end criterion that envelope is decomposed, and mould occurs in the signal that may result in decomposition
The problem of state aliasing;Need just to can obtain complete IMF components by successive ignition, time-consuming, computationally intensive.For EMD's
Defect, scholars propose the methods such as set empirical mode decomposition, multiple empirical mode decomposition, compact empirical mode decomposition, this
A little methods overcome the problem that the time scale of EMD methods presence is separate to a certain extent, reduce modal overlap, end points effect
Should, but the problem of EMD can not be fully solved.
The content of the invention
The technical problems to be solved by the invention are, there is provided a kind of rotary machinery fault diagnosis based on Fourier decomposition
Method, can effectively judge the generation of rotating machinery fault, and time frequency resolution is high, in the absence of end effect and modal overlap
Phenomenon.
In order to solve the above technical problems, the present invention provides a kind of rotary machinery fault diagnosis side based on Fourier decomposition
Method, comprises the following steps:
(1) acoustic emission signal is obtained by touching the Experimental on acoustic emission device that rubs;
(2) Fourier decomposition method and the intrinsic frequency band function of Fourier are defined;
(3) in acoustic emission signal Fourier's frequency domain self adaptation search minimum number the intrinsic frequency band function of Fourier;
(4) time-frequency energy spectrum is obtained by parsing the intrinsic frequency band function of Fourier, by the change of signal time-frequency energy spectrum
Carry out the generation of failure judgement.
Preferably, in step (2), it is y to define the intrinsic frequency band function of Fourieri(t)∈C∞[a, b], it meets following bar
Part:
(1) FIBFs is zero-mean function, i.e.,
(2) FIBFs meets orthogonality, i.e.,
(3) instantaneous frequency and instantaneous amplitude of the analytical function AFIBFs of FIBFs be always greater than equal to 0, i.e., Wherein,
Signal decomposition is FIBFs and residual components of minimum number by FDM, is expressed as follows:
Wherein r (t) represents residual error component, yiT () is the M one-component signal of non-stationary, i.e. FIBFs, FIBFs is instantaneous
Frequency has the single group sub-signal of physical significance.
Preferably, in step (3), if signal x (t) is interval [t1,t1+T0] the interior real-valued letter for following dirichlet condition
Number, x (t) is configured to periodic signalI.e.Work as t1≤t≤t+T0When, ω (t)=1;When t≤
t1,t1+T0During≤t, ω (t)=0, thenFourier expansion formula be:
Wherein frequency is
Formula (3-1) can be write as following expression:
Wherein, ck=ak-jbk,ck *=ak+jbk, obtained by formula (3-2):
Analytical function is For
Conjugate complex number,ForReal part, therefore can be byIt is written as:
Following formula can be obtained by formula (3-4) and formula (3-5):
When signal is decomposed, it is thus necessary to determine that maximum NiValue obtains the parsing FIBFs of minimum number;FDM methods
Defined in two kinds of ways of search, i.e., forward search AFIBFs (from low to high search for) and reverse search AFIBFs (from high frequency
To low-frequency acquisition), thus in the presence of two kinds of time-frequency Energy distributions, according to the difference of signal, two kinds of isolations may disclose identical
Or two kinds of different characteristic types, two kinds of algorithms are summarized as follows:
Define to the increased direction search of i to search for AFIBFs forward, i.e., search for (LTH-FS) from low to high;To every
I layers, from (Ni-1+ 1) start, and gradually increase NiTo maximum ∞, i.e. (Ni-1+1)≤Ni≤ ∞ andI is since 1:
It can thus be concluded that,
Wherein, N0=0, NM=∞,
Similar, in the reverse search of AFIBFs (from high frequency to low-frequency acquisition, HTL-FS), formula is limited under (13)
Limit will become from k=NiTo (Ni-1- 1), corresponding N0=∞, NM=1. at this moment from (Ni-1- 1) start to look for, gradually reduce Ni's
Value untill when selecting the FIBFs of minimum number, 1≤Ni≤(Ni- 1), i=1 ..., M;I.e.:
Beneficial effects of the present invention are:The intrinsic frequency band of Fourier of the search minimal amount of self adaptation in Fourier's frequency domain
Non-stationary nonlinear properties are decomposed into the intrinsic frequency band function of several Fourier and a residual components, residual components by function
Almost 0, signal is divided well;The generation of rotating machinery bump-scrape failure can effectively be judged, can determine whether that failure is sent out
Raw time and evolving trend, and time frequency resolution is high, in the absence of end effect and modal overlap phenomenon, is become based on Fourier
Theory is changed, there is solid theoretical foundation and complete Mathematical Modeling.
Brief description of the drawings
Fig. 1 (a) is experiment porch simulation drawing of the invention.
Fig. 1 (b) is experiment porch structural representation of the invention.
Fig. 2 is emulation time domain plethysmographic signal figure of the invention.
Fig. 3 decomposes (LTH) schematic diagram for emulation signal FDM of the invention.
Fig. 4 decomposes (HTL) schematic diagram for emulation signal FDM of the invention.
Fig. 5 is emulation signal EMD decomposing schematic representations of the invention.
Fig. 6 is emulation signal FDM time-frequencies energy spectrum (LTH) schematic diagram of the invention.
Fig. 7 is emulation signal FDM time-frequencies energy spectrum (HTL) schematic diagram of the invention.
Fig. 8 is emulation signal EMD time-frequency energy spectrums of the invention.
Fig. 9 touches the AE time domain plethysmographic signal figures that rub for nothing of the invention.
Figure 10 touches the AE signal spectrum figures that rub for nothing of the invention.
Figure 11 touches AE signal FDM time-frequencies energy spectrum (LTH-FS) schematic diagram that rubs for nothing of the invention.
Figure 12 touches AE signal FDM time-frequencies energy spectrum (HTL-FS) schematic diagram that rubs for nothing of the invention.
Figure 13 touches the AE signal EDM time-frequency energy spectrums that rub for nothing of the invention.
Figure 14 touches the AE time domain plethysmographic signal figures that rub for of the invention.
Figure 15 touches the AE signal spectrum figures that rub for of the invention.
Figure 16 touches AE signal FDM time-frequencies energy spectrum (LTH-FS) schematic diagram that rubs for of the invention.
Figure 17 touches AE signal FDM time-frequencies energy spectrum (HTL-FS) schematic diagram that rubs for of the invention.
Figure 18 touches the AE signal EDM time-frequency energy spectrums that rub for of the invention.
Specific embodiment
As shown in figure 1, touching acoustic emission experiment system of rubbing by rotor rubbing experimental bench, sensor, preamplifier, speed regulator
Constituted with sound emission acquisition system.Rotor rubbing testing stand is flex rotor testing stand, is used to support having for rotor by three
The bearing block of sliding bearing, two touch rub disk and touch mount screw composition.Touching mount screw can be by screw on lid guided wave plate
Spindle central is pointed to, and is in contact with disk side.When rotor is rotated with certain rotating speed, regulation is touched mount screw and touches the disk that rubs
Touch and rub, the bump-scrape acoustic emission signal of generation is received via guided wave plate by acoustic emission sensor.Mount screw is touched by regulation
Screw-in depth is rubbed simulating touching for varying strength, and speed regulator realizes the stepless time adjustment of motor 0-10000r/min scopes.In order to drop
The low acoustic emission waveform caused because medium is discontinuous is distorted, and couplant is filled between contact surface.The material of lid guided wave plate
Expect to be No. 45 steel.
Acoustic emission signal acquisition system is that, by Polar9300e portable industrial pcs, built-in PCI-2 sound emissions capture card is adopted
UT-1000 sensors are used, it is 1MbPS to set AE signal sampling frequencies, and sampled point is 20000, and filtered band is set to 0-
200kHz, gain amplifier is 40db.In order to reduce the aliasing of LAMB ripples and boundary echo, the signal acquisition in experiment is touched and rubbed just
The signal of phase.
A kind of rotary machinery fault diagnosis method based on Fourier decomposition, comprises the following steps:
(1) acoustic emission signal is obtained by touching the Experimental on acoustic emission device that rubs;
(2) Fourier decomposition method and the intrinsic frequency band function of Fourier are defined;
(3) in acoustic emission signal Fourier's frequency domain self adaptation search minimum number the intrinsic frequency band function of Fourier;
(4) time-frequency energy spectrum is obtained by parsing the intrinsic frequency band function of Fourier, by the change of signal time-frequency energy spectrum
Carry out the generation of failure judgement.
In step (2), it is y to define the intrinsic frequency band function of Fourieri(t)∈C∞[a, b], it meets following condition:
(1) FIBFs is zero-mean function, i.e.,
(2) FIBFs meets orthogonality, i.e.,
(3) instantaneous frequency and instantaneous amplitude of the analytical function AFIBFs of FIBFs be always greater than equal to 0, i.e., Wherein,
Signal decomposition is FIBFs and residual components of minimum number by FDM, is expressed as follows:
Wherein r (t) represents residual error component, yiT () is the M one-component signal of non-stationary, i.e. FIBFs, FIBFs is instantaneous
Frequency has the single group sub-signal of physical significance.
In step (3), if signal x (t) is interval [t1,t1+T0] the interior real-valued signal for following dirichlet condition, by x
T () is configured to periodic signalI.e.Work as t1≤t≤t+T0When, ω (t)=1;As t≤t1,t1+
T0During≤t, ω (t)=0, thenFourier expansion formula be:
Wherein frequency is
Formula (3-1) can be write as following expression:
Wherein, ck=ak-jbk,ck *=ak+jbk, obtained by formula (3-2):
Analytical function is For
Conjugate complex number,ForReal part, therefore can be byIt is written as:
Following formula can be obtained by formula (3-4) and formula (3-5):
When signal is decomposed, it is thus necessary to determine that maximum NiValue obtains the parsing FIBFs of minimum number;FDM methods
Defined in two kinds of ways of search, i.e., forward search AFIBFs (from low to high search for) and reverse search AFIBFs (from high frequency
To low-frequency acquisition), thus in the presence of two kinds of time-frequency Energy distributions, according to the difference of signal, two kinds of isolations may disclose identical
Or two kinds of different characteristic types, two kinds of algorithms are summarized as follows:
Define to the increased direction search of i to search for AFIBFs forward, i.e., search for (LTH-FS) from low to high;To every
I layers, from (Ni-1+ 1) start, and gradually increase NiTo maximum ∞, i.e. (Ni-1+1)≤Ni≤ ∞ andI is since 1:
It can thus be concluded that,
Wherein, N0=0, NM=∞,
Similar, in the reverse search of AFIBFs (from high frequency to low-frequency acquisition, HTL-FS), formula is limited under (13)
Limit will become from k=NiTo (Ni-1- 1), corresponding N0=∞, NM=1. at this moment from (Ni-1- 1) start to look for, gradually reduce Ni's
Value untill when selecting the FIBFs of minimum number, 1≤Ni≤(Ni- 1), i=1 ..., M;I.e.:
EMD decomposition is carried out to signal, and carries out Hilbert conversion, obtain time-frequency energy diagram.
Emulation signal x (t) is built, the signal is by a linear FM signal x1(t) and FMAM signal x2(t)
Composition.
x1(t)=cos (400 π t+200 π t2);
x2(t)=cos (100 π t+0.4 π sin (20 π t))+0.1sin (10 π t) cos (100 π t+0.4 π sin (20 π t));
X (t)=x1(t)+x2(t)
Fig. 2 be emulate signal time domain waveform, Fig. 3 be emulate signal through the LTH algorithms of FDM decomposition result, Fig. 4 be through
The decomposition result of the HTL algorithms of FDM, Fig. 5 is to emulate the result that signal is decomposed through EMD.As can be seen that emulation from Fig. 3 and Fig. 4
Signal is effectively decomposed into two FIBFs and residual components, and the two components correspond respectively to linear FM signal
And amplitude-modulation frequency-modulation signal, residual components are zero.From figure 5 it can be seen that emulation signal decomposites 7 rank IMF components and one through EMD
Individual residual error, the natural mode of vibration component for decompositing and emulation signal are not corresponded and there is serious modal overlap and end effect,
It can thus be seen that the effect that EMD is decomposed is undesirable.Fig. 6 is the time-frequency energy spectrum that signal is decomposed by the LTH algorithms of FDM, and Fig. 7 is
The time-frequency energy spectrum that signal is decomposed through the HTL algorithms of FDM, Fig. 8 is the time-frequency energy spectrum that signal is decomposed through EMD.Comparison diagram 6~8
As can be seen that Fig. 6 is that, through two kinds of time-frequency energy spectrums of different searching methods decomposition of FDM, its time frequency resolution is higher with Fig. 7,
LTH algorithms are higher than HTL-FS algorithms in HFS time frequency resolution, and HTL-FS algorithms are higher than in low frequency part time frequency resolution
HTL-FS algorithms.Fig. 8 can be seen that through EMD decompose time-frequency energy spectrum resolution ratio it is relatively low, there is false mode and modal overlap
Phenomenon.Therefore, FDM algorithms overcome the problem of EMD presence to a certain extent.
UT-1000 sensors, AE signals is used to be gathered by the industrial computer of built-in PCI-2 sound emissions capture card in experiment, if
AE signal sampling frequencies are put for 1MbPS, sampled point is 5120, and filtered band is set to 0-200kHz, and gain amplifier is 40db.For
Reduce the aliasing of LAMB ripples and boundary echo, the signal acquisition in experiment touches the signal at the initial stage of rubbing, respectively rubbing without touching and
Touch under the state of rubbing and measure acoustic emission signal.Time domain plethysmographic signal and spectrogram are rubbed without touching as shown in Figure 9 and Figure 10.Figure 11, figure
12 are respectively without the AE signals that rub are touched using FDM-LTH algorithms and the time-frequency energy spectrum of FDMM-HTL algorithms, and Figure 13 is that nothing touches the AE that rubs
Signal is through the time-frequency power spectrum after EMD.Contrast two methods time-frequency energy spectrum, without touch rub AE signals through FDM LTH algorithms and
The time-frequency energy spectrum of HTL algorithms is consistent, and signal is decomposed well, and has time frequency resolution very high.Figure 13
It is evident that time frequency resolution is low, and has modal overlap phenomenon, effect is not so good as Figure 11 and Figure 12.Figure 15 believes to touch the AE that rubs
Number spectrogram, as can be seen from the figure the energy of the AE signals be concentrated mainly within 100kHz.Figure 16, Figure 17 have been respectively
Touch time-frequency energy spectrum of the AE signals using FDM-LTH algorithms and FDM-HTL algorithms that rub, Figure 18 rubs AE signals after EMD to touch
Time-frequency energy spectrum.Time-frequency distributions in Figure 16 and Figure 17 are consistent, and with resolution ratio very high, as can be seen from the figure have
There is the obvious frequency distribution of energy feature, thus can determine whether out faulty generation.The frequency component of fault-signal is can be seen that simultaneously
Energy concentrate on time leading portion, and decay with the time, it can be seen that this is transient state impact-rub malfunction.Figure 18 time frequency resolutions compared with
It is low, it is distributed more disorderly, modal overlap is more, and its frequency distribution can not be corresponding with the spectrogram of Figure 15, hardly results in this and touches and rubs
The time-frequency characteristic of AE signals.FDM can be seen that by above-mentioned experimental analysis bright in terms of the sensitivity that impact-rub malfunction occurs is judged
It is aobvious to be better than EMD methods.
Although the present invention is illustrated and has been described with regard to preferred embodiment, it is understood by those skilled in the art that
Without departing from scope defined by the claims of the present invention, variations and modifications can be carried out to the present invention.