CN115655719A - Bearing vibration signal staged noise reduction method and bearing fault identification method - Google Patents
Bearing vibration signal staged noise reduction method and bearing fault identification method Download PDFInfo
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Abstract
The invention discloses a method for reducing noise of a bearing vibration signal in stages, which is characterized in that a zero-frequency filter is improved to carry out first-stage filtering noise reduction on the bearing vibration signal, and the frequency response of the zero-frequency filter is adjusted, so that the impact characteristics of vibration pulses of a bearing can be better enhanced while filtering. And during the second-stage denoising, estimating an optimal wavelet decomposition level value according to the sampling frequency and the bearing fault characteristic frequency, then performing optimal wavelet decomposition on the bearing vibration signal filtered by the improved zero-frequency filter, and performing hard threshold denoising on the wavelet decomposition result by using the constructed wavelet denoising self-adaptive threshold function to obtain a final denoising signal. The method can effectively remove noise in the bearing vibration signal, enhance the impact characteristic of the vibration periodic pulse, has better noise reduction effect compared with the prior art, can more clearly present the bearing fault characteristic frequency while better inhibiting the noise, and can be effectively applied to the early detection of the bearing fault of the high-speed train.
Description
Technical Field
The invention relates to the technical field of signal detection, in particular to a bearing vibration signal staged noise reduction method and a bearing fault identification method.
Background
The rolling bearing plays an important role in the operation of a high-speed train, the bearing failure is one of the main reasons of the failure of the rotating machinery of the train, and the operation state of the rolling bearing is directly related to the operation safety of the train. Therefore, the method has important significance for detecting the early bearing fault of the high-speed train.
At present, the bearing fault feature extraction based on vibration signal analysis is an important means for bearing fault detection. Local failure of the high speed train bearings can produce periodic pulses in the vibration signal. However, in the early stage of the failure, the pulse generated by the bearing failure is very weak, and the bearing is in a high-speed heavy-load operation environment for a long time, and is influenced by complex noises such as field equipment and environmental interference. Therefore, it is difficult to detect these weak pulses by directly analyzing the vibration signals, and in order to effectively detect the early bearing failure of the high-speed train, it is necessary to perform noise reduction processing on the collected original bearing vibration signals.
In the noise reduction of the vibration signal of the rolling bearing, commonly used methods include Wavelet Transform (WT), hilbert-Huang transform (HHT), minimum Entropy Deconvolution (MED), singular Value Decomposition (SVD), and the like. The wavelet transformation converts time domain signals into time frequency signals in different translation and proportion through inner products between the signals and mother wavelets, WT has the advantage of multi-resolution analysis and is very suitable for denoising bearing fault signals, but the wavelet transformation has a serious modal chaos phenomenon, the denoising effect is influenced, and the selection of an optimal wavelet basis is a difficult problem.
HHTs are well suited for analysis of nonlinear and non-stationary signals, where the signal is decomposed into a series of eigenmode functions (IMFs) using Empirical Mode Decomposition (EMD), with different IMFs containing information for different frequency bands of the signal. However, the EMD method also has a serious frequency aliasing phenomenon, and is easy to over-decompose to generate more redundancy, which affects the further improvement of the denoising effect.
Minimum Entropy Deconvolution (MED) deconvolves the bearing signal to extract the fault pulse. It searches for a set of filter coefficients that best recovers the carrier signal with respect to minimum entropy and maximum order. However, when the MED computation amount is large and the fault signal is weak, the pulse signal cannot be effectively retained, and the application of the MED computation amount in the denoising of the early fault signal of the bearing is limited.
Singular Value Decomposition (SVD) decomposes a signal into singular components. Usually, the noise corresponds to a smaller singular value, and the original signal is reconstructed by reserving the first K larger singular values, so that the noise can be effectively suppressed. However, in the process of denoising by using SVD, the effective order of the reconstruction matrix is difficult to be accurately determined.
The Zero Frequency Filter (ZFF) has an excellent effect by aiming at the characteristic Frequency extraction caused by periodic pulses, and the vibration signal passes through the resonance Filter with the central Frequency of 0 Hz twice, so that the pulse excitation can be amplified well, and the vibration characteristic caused by pulse impact is enhanced effectively. However, due to the bipolar property of the amplitude modulation signal, false zero crossing is easy to occur under high background noise to generate a false peak value, so that the extraction effect of early fault features is influenced.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a bearing vibration signal staged noise reduction method and a bearing fault identification method, which are used for improving the noise reduction effect on a vehicle bearing fault signal, so that the bearing fault characteristic frequency can be more clearly presented while the noise is better inhibited, and the detection precision of vehicle bearing fault identification is improved.
In order to achieve the above object, in a first aspect, the present invention provides a method for reducing noise of a bearing vibration signal by stages, including:
hilbert transformation is carried out on the bearing vibration signal to obtain a Hilbert envelope curve of the bearing vibration signal;
inputting Hilbert envelope curves of bearing vibration signals into an improved zero-frequency filter to obtain first bearing vibration signals subjected to noise reduction by the improved zero-frequency filter;
calculating an optimal wavelet decomposition level value by using the bearing fault characteristic frequency and the sampling frequency of the bearing vibration signal;
and performing wavelet decomposition on the first bearing vibration signal based on the optimal wavelet decomposition level value, and denoising the wavelet coefficient of the layer corresponding to the optimal wavelet decomposition level value by using a wavelet denoising self-adaptive threshold function to obtain a second bearing vibration signal.
Further, the frequency response expression of the improved zero-frequency filter is as follows:
wherein, the first and the second end of the pipe are connected with each other,Hwhich represents the function of a zero-frequency filter,ωthe frequency is represented by a frequency-dependent variable,Mrepresenting the width of the windowed fourier transform window function,Lwhich is indicative of the length of the signal,kindicating the order of the accumulated frequencies in the fourier transform.
Further, the inputting the Hilbert envelope curve of the bearing vibration signal into the improved zero-frequency filter to obtain the first bearing vibration signal after noise reduction by the improved zero-frequency filter specifically includes:
taking a Hilbert envelope curve of the bearing vibration signal as an input, iterating twice through the improved zero-frequency filter to obtain a third bearing vibration signal;
removing the trend item in the third bearing vibration signal to obtain the first bearing vibration signal.
Further, the formula of iterating the Hilbert envelope curve of the bearing vibration signal as an input and passing through the improved zero-frequency filter twice to obtain the third bearing vibration signal specifically includes:
wherein the content of the first and second substances,s(m) A signal indicative of the vibration of the bearing,mwhich represents the location of the sampling point,b k the coefficients of the filter are represented by,x 1 (m) Representing the signal after the first stage of filtering,x 2 (m) Representing a second stage filtered signal, i.e. the third bearing vibration signal.
Further, the formula for removing the trend term in the third bearing vibration signal to obtain the first bearing vibration signal specifically includes:
wherein, the first and the second end of the pipe are connected with each other,x(n) Representing the first bearing vibration signal.
Further, the formula for calculating the optimal wavelet decomposition level value by using the bearing fault characteristic frequency and the sampling frequency of the bearing vibration signal specifically comprises:
wherein, the first and the second end of the pipe are connected with each other,f s representing the sampling frequency of the bearing vibration signal,C I a characteristic frequency of failure of the bearing is indicated,
which means that the rounding is made up,q opt representing the optimal wavelet decomposition level value.
Further, the expression of the wavelet denoising adaptive threshold function specifically includes:
wherein, the first and the second end of the pipe are connected with each other,
representing the first before denoisingjUnder layer the firstkThe number of the wavelet coefficients is such that,
representing the second after denoisingjUnder layer the firstkThe number of the wavelet coefficients is such that,δrepresenting the denoising threshold.
Further, the denoising threshold value is calculated based on the principle of unbiased likelihood estimation of Steinδ。
Further, the Hilbert transform of the bearing vibration signal to obtain a Hilbert envelope curve specifically includes:
carrying out differential conversion on the bearing vibration signal to remove a direct current component;
and carrying out Hilbert transformation on the differentially transformed bearing vibration signal to obtain a Hilbert envelope line of the bearing vibration signal.
In a second aspect, the invention provides a bearing fault identification method, which performs frequency spectrum analysis based on a second bearing vibration signal obtained by any one of the bearing vibration signal staged noise reduction methods, determines a bearing fault frequency by searching a frequency spectrum peak value, and obtains a bearing fault impact period to realize identification of early bearing faults.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
the invention carries out the first-stage filtering and noise reduction on the bearing vibration signal through the improved zero-frequency filter, and can better enhance the impact characteristic of the bearing vibration pulse while filtering through adjusting the frequency response of the zero-frequency filter. And during the second-stage denoising, estimating an optimal wavelet decomposition level value according to the sampling frequency and the bearing fault characteristic frequency, then performing optimal wavelet decomposition on the bearing vibration signal filtered by the improved zero-frequency filter, and performing hard threshold denoising on the wavelet decomposition result by using the constructed wavelet denoising self-adaptive threshold function to obtain a final denoising signal. The invention can effectively remove the noise in the original bearing vibration signal, enhance the impact characteristic of the vibration periodic pulse, has better noise reduction effect compared with the prior art, can better inhibit the noise and simultaneously more clearly present the bearing fault characteristic frequency, can clearly observe the frequency characteristic of the fault even when the fault is weak, and can be effectively applied to the early detection of the bearing fault of vehicles such as high-speed trains and the like.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a diagram of an optimal horizontal wavelet decomposition spectral bin for simulating a noisy bearing fault signal according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of a method for reducing noise of a bearing vibration signal in stages according to an embodiment of the present invention;
FIG. 3 is a diagram of an IZFF noise reduction spectrum group of an early failure of a bearing outer ring according to an embodiment of the present invention; wherein, (a) in fig. 3 is a bearing vibration signal; FIG. 3 (b) shows the envelope of the bearing vibration signal; fig. 3 (c) is the IZFF noise reduction output;
FIG. 4 is a graph of a comparison spectrum group for WT threshold denoising and IZFF-WT denoising of an outer ring fault provided by an embodiment of the present invention; wherein (a) - (e) in FIG. 4 are WT threshold denoising; FIGS. 4 (f) - (j) illustrate two-stage denoising in IZFF-WT;
FIG. 5 is a diagram of a spectrum analysis group after an IZFF-WT adaptive threshold denoising of a bearing inner race fault provided by an embodiment of the invention; wherein (a) - (e) in fig. 5 are graphs of spectrum analysis group at a sampling frequency of 12000 Hz; FIGS. 5 (f) - (j) are graphs of the spectrum analysis group at a sampling frequency of 48000 Hz;
fig. 6 is a frequency spectrum diagram of a bearing inner race fault signal after noise reduction of the ZFF-LMS algorithm provided by the embodiment of the present invention;
FIG. 7 is a diagram of a spectrum group of a bearing inner race fault signal after noise reduction by the HHT algorithm provided by the embodiment of the invention;
FIG. 8 is a frequency spectrum group diagram of a bearing inner race fault signal after noise reduction of a VMD algorithm provided by an embodiment of the present invention;
fig. 9 is a frequency spectrum diagram of a bearing inner ring fault signal after two-stage denoising in IZFF-WT provided by the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The terms "first," "second," or "third," and the like in the description, claims, or drawings of the present application, are used for distinguishing between different objects and not for describing a particular order. Furthermore, the terms "comprises" or "comprising," as well as any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to only those steps or elements but may alternatively include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Rolling bearings are widely used in high-speed trains, and in order to prevent serious mechanical failure, it is necessary to effectively detect early failure of the bearings. Aiming at the problem that the bearing early fault vibration pulse of the high-speed train is weak and is easy to be annihilated by noise to cause the fault to be difficult to detect, the invention provides a bearing early fault signal two-stage noise reduction method based on Improved Zero Frequency Filter (IZFF) and adaptive threshold wavelet de-noising. In the first stage of noise reduction, an improved zero-frequency filter (short for zero-frequency filter) is used for carrying out noise reduction and enhancement processing on an early bearing fault signal, an envelope curve of the fault signal is enhanced on fault vibration pulses through IZFF, and meanwhile noise and interference signals of other equipment are removed. In the second stage of noise reduction, firstly, estimating an optimal decomposition level according to sampling frequency and bearing fault characteristic frequency, and performing optimal wavelet decomposition on a fault signal subjected to IZFF filtering; and then, constructing an adaptive threshold function, and carrying out hard threshold denoising on the result of the optimal horizontal wavelet decomposition to obtain a final denoising signal. The technical solution of the present invention is further described below with reference to specific examples.
The zero-frequency filter is an infinite impulse response filter with a complex conjugate pole located within a unit circle and a center frequency of 0 Hz. The transfer function of a conventional zero-frequency filter is:
wherein the content of the first and second substances,H(z) Which represents the function of a zero-frequency filter,zrepresenting the zero frequency filter argument. In the detection of early failure of a bearing, the periodic pulse impact characteristics caused by weak failure are key information for failure identification. The traditional zero-frequency filter can also attenuate fault periodic pulses to a certain degree while removing noise interference, and the accuracy of early fault detection is influenced. Therefore, in order to further enhance the periodic pulse peak while eliminating noise, an embodiment of the present invention improves a zero-frequency filter, and provides a 4-order periodic enhancement zero-frequency filtering algorithm, where the frequency response of the improved ZFF is shown in formula (2).
Wherein, the first and the second end of the pipe are connected with each other,Hwhich represents the function of a zero-frequency filter,ωthe frequency is represented by a frequency-dependent variable,Mrepresenting the width of the windowed fourier transform window function,Lwhich is indicative of the length of the signal,kindicating the order of the accumulated frequencies in the fourier transform. In this example toMAnd (2). With the frequency response of the IZFF given in equation (2), the transfer function can be found as:
wherein the content of the first and second substances,b 1 =4, b 2 =﹣6, b 3 =4, b 4 and (c) = -1. Setting the bearing vibration signal ass(m) Will bes(m) The improved zero-frequency filter is passed twice as an input iteration, namely:
wherein the content of the first and second substances,s(m) A signal indicative of the vibration of the bearing is provided,mindicating the location of the sample point,b k the coefficients of the filter are represented by,x 1 (m) Representing the signal after the first stage of filtering,x 2 (m) Representing the second stage filtered signal. The output of the zero-frequency filter is equivalent to two consecutive integrations of the input signal, and the filter output can be implemented as the cumulative sum of the current input sample and the past two output samples. The IZFF has one peak at 0 Hz and the pulse has a flat frequency spectrum, so the IZFF denoises the signal by enhancing the pulse signal and attenuating the noise and sine waves. For periodic pulses, the output of the IZFF has less amplitude fluctuations near the pulse position. To further extract the discontinuity caused by the early fault pulse, the trend term in the filtered signal can be removed by equation (5), which is:
wherein, the first and the second end of the pipe are connected with each other,x(n) Namely, the final output signal after the trend item is removed from the IZFF. The bearing vibration signal is subjected to first-stage filtering noise reduction by improving the zero-frequency filter, and the frequency response of the zero-frequency filter is adjusted, so that the impact characteristic of the bearing vibration pulse can be better enhanced while filtering.
The present embodiment performs a second level of denoising by wavelet transform, to further suppress noise in the fault signal,
highlighting the impact characteristics of the fault cycle pulse. The wavelet transform of a bearing fault signal is defined as:
wherein the content of the first and second substances,W x (a,b) Representing signalsxThe coefficients after the wavelet decomposition are obtained by the wavelet decomposition,x(t) A signal indicative of the vibration of the bearing is provided,ae R + represents a scale parameter,bthe epsilon R represents a time parameter,Ψrepresenting wavelet basis, representing complex conjugate, wavelet transform being signal and wavelet basisΨ(t) The inner product of (2). In the denoising of the bearing vibration signal, the selection of the wavelet decomposition level is crucial, and the denoising effect of the bearing vibration signal is directly influenced. When decomposingWhen the level is appropriate, the pulse period caused by early fault can be observed in the decomposed signal; when the level of decomposition is too low or too high, the pulse period information of the fault will not or not be easily captured in the spectrum of the decomposed signal. Therefore, how to select the optimal decomposition level is the key of performing two-stage de-noising on the bearing signal by using wavelet transform. Therefore, in order to better preserve the period of the fault pulse in the signal while removing noise, the present embodiment derives the optimal decomposition level expression in wavelet decomposition based on the sampling frequency and the bearing fault frequency, so that the fault characteristic frequency can be most clearly represented in the decomposition of this level. Assuming the frequency of a periodic pulse signal in the bearing vibration signalC I Comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,f s is the frequency of the sampling of the samples,mis the number of samples between two pulses. In discrete wavelet transform, the length of the decomposed signal is reduced by half every time the number of decomposed layers is increased by one step, and the frequency band of the corresponding decomposed signal becomes narrower and narrower. Maximum frequency of signal according to Nyquist theoremf max Should be less than or equal to one half of the sampling frequency, i.e.:
thus, in the first level decomposition of the wavelet transform, the upper band limit of the decomposed signal is:
thus, for the secondqAnd (3) level decomposition, wherein the upper band limit of the decomposed signal is as follows:
maximum frequency of the signal is not assumedf max Equal to half the sampling frequency, i.e.
Then, it is shown by the formula (10)
Assume that the frequency of the fault pulse period isC I Then, in order to include the fault pulse in the decomposed signal,f q should be greater thanC I In conjunction with equation (11), it is known that:
after taking the logarithm of equation (12), the number of decomposition stages can be given by:
to pairqRounding to obtain the optimal wavelet decomposition levelq opt I.e. by
In the formula (I), the compound is shown in the specification,
indicating rounding up.
Therefore, in the decomposition of the bearing vibration signal, the optimum decomposition level of the wavelet transform depends on the pulse period and the signal sampling frequency. In the event of a bearing failure, the failure pulse period is the characteristic failure frequency of the bearing, and samples are taken of the analog signal in FIG. 1f s =1000 Hz，Frequency of fault impactC I =20 Hz. From the formulae (13) and (14), it can be seen thatq opt And =4. Fig. 1 shows the peak of the spectrum at the fault frequency which can be seen in each layer of coefficients after wavelet decomposition, and the maximum frequency in the spectrum of the lower layer coefficients is reduced by half compared with the maximum frequency of the upper layer coefficients as the number of the decomposition layers is increased. It can be seen in fig. 1 that the maximum frequency content of the fifth order spectrum is about 14 Hz, while the pulse period is 20 Hz. Therefore, the pulse period cannot be detected at the fifth stage of the decomposition. At the same time it can be seen that,q opt =4 is the optimal level of wavelet decomposition in which the failure signal frequency can be most clearly observed and the interference information is minimal.
In wavelet decomposition denoising, the selection of a threshold function is crucial to the denoising effect, and the traditional threshold function comprises a hard threshold function and a soft threshold function. The hard threshold function is discontinuous, and the denoised signal has oscillation and fuzzy phenomena to a certain degree; although the soft threshold function is continuous, the whole signal is shriveled by a certain proportion, and the distortion of the denoised signal is caused. In order to overcome the disadvantages of the hard and soft threshold functions, the embodiment of the invention provides a continuous wavelet denoising adaptive threshold function at the threshold point, and the function expression of the continuous wavelet denoising adaptive threshold function is as follows:
wherein, the first and the second end of the pipe are connected with each other,
representing first before denoisingjUnder layer the firstkThe number of the wavelet coefficients is such that,
representing the second after denoisingjUnder layer the firstkThe number of the wavelet coefficients is such that,δrepresenting a denoising threshold, the embodiment adopts a Stein-based unbiased likelihood estimation principle to calculate the denoising thresholdδ. It can be shown that the threshold function in equation (15) is continuously derivable at both positive and negative threshold points,and the signal is not scaled down, the threshold function therefore meets all the requirements of the noise reduction threshold function. The embodiment adopts the continuous threshold function and combines the optimal level wavelet decomposition to carry out the second-stage noise reduction on the bearing fault signal.
Aiming at the detection of the early fault signal of the bearing of the high-speed train, the embodiment provides a two-stage denoising algorithm based on improved ZFF filtering and adaptive threshold wavelet denoising, the flow of the algorithm is shown in FIG. 2, and the two-stage denoising algorithm comprises the following specific steps:
(1) And carrying out differential transformation on the collected high-speed train bearing vibration signals to remove direct-current components.
(2) Hilbert transform is performed on the differentially transformed signal, and a Hilbert envelope curve of the differentially transformed signal is calculated.
(3) And inputting the Hilbert envelope curve of the vibration signal into an improved zero-frequency filter to perform first-stage noise reduction.
(4) And searching bearing parameters to determine the characteristic fault frequency and determining the sampling frequency of the bearing fault vibration signal.
(5) Calculating an optimal wavelet decomposition level value using the characteristic failure frequency and the sampling frequency of the vibration dataq opt 。
(6) Subjecting the IZFF denoised signal to wavelet decomposition of an optimal wavelet decomposition level value, and performing threshold function on the second wavelet decomposition level value by using a threshold function in an equation (15)q opt And performing secondary denoising on the layer wavelet coefficients.
The invention also provides a bearing fault identification method, which is used for carrying out frequency spectrum analysis on the bearing vibration signal obtained after the noise reduction by the bearing vibration signal grading noise reduction method according to any one of the above methods and calculating the second threshold value after the noise reductionq opt And determining the fault frequency of the bearing by searching a frequency spectrum peak value of the wavelet coefficient, and acquiring the fault impact period of the bearing so as to realize the identification of the early fault of the bearing.
In order to analyze the effectiveness of the two-stage noise reduction algorithm provided by the invention, the fault vibration signal of the high-speed train bearing is acquired through experiments, and the noise reduction analysis is carried out by using the method provided by the invention. The high-speed train bearing comprehensive experiment platform can replace bearings of different models to carry out experiments, so that fault vibration signals of the bearings of different models are collected. In the experiment, in order to simulate the operation condition of the high-speed train bearing, 90 kN of average radial force is applied to the bearing, and +/-50 kN of maximum axial force is applied to the bearing. The vibration data of the bearing is collected through a sensor, the sampling time of the sensor data is 40 s, and the data of 0.4 s is intercepted to carry out noise reduction experiment analysis.
Firstly, the denoising effect of a vibration signal when the outer ring of the bearing fails in the early stage is analyzed through experiments, wherein in the experiments, the sampling frequency is 12.96 kHz, and the outer ring failure frequency of the bearing is 237 Hz. Periodic vibration caused by fault impact is weak in the early stage of outer ring fault, collected bearing vibration data is shown in a figure 3 (a), and a signal envelope is shown in a figure 3 (b). The signal envelope is first denoised with the improved ZFF, and the output signal of the IZFF denoised is shown in (c) of fig. 3. As can be seen from fig. 3, due to the interference of strong noise, a relatively obvious fault impact characteristic cannot be found directly from the acquired vibration signal, and an obvious fault characteristic spectral line cannot be found in the fourier spectrogram. Calculating the optimal decomposition level value in wavelet decomposition of the outer ring fault signal by adopting the formulas (13) and (14), and obtaining the resultq opt And (5). For comparison, (a) - (e) in fig. 4 show the spectrum after five-level wavelet decomposition when no ZFF is used for first-level filtering denoising, and (f) - (j) in fig. 4 show the spectrum after ZFF filtering denoising and then five-level wavelet decomposition. It can be seen from (e) in fig. 4 that the non-fault frequency amplitude at 168 Hz is the largest, while the fault frequency amplitude at 236 Hz is smaller, becoming a non-dominant peak frequency in the spectrogram. This is mainly due to spectral aliasing of the sampling frequency of the signal during wavelet decomposition and between the failure frequencies, since
Hz, therefore, the non-fault frequency of 168 Hz occupies the main peak in the wavelet decomposed and denoised signal without ZFF filtering processing, whereinC I =237 Hz indicates outer ringThe frequency of the impact of the barrier is,q opt =5 represents the optimum wavelet decomposition level,f s =12960 Hz represents the sampling frequency.
The two-stage noise reduction algorithm provided by the invention is adopted to carry out noise reduction treatment on the bearing fault signal: firstly, filtering and denoising a signal by using an improved zero-frequency filter; and then performing optimal horizontal wavelet decomposition on the filtered signal, and performing hard threshold denoising on the decomposed wavelet coefficients. The frequency spectrums of the subband signals after two-stage noise reduction are shown in (f) - (j) in fig. 4, and it can be seen that after the fault signals are processed by the two-stage noise reduction algorithm, the fault frequency amplitude is the largest in the frequency spectrum of the wavelet coefficient of the 5 th stage, and appears as a main peak, so that the fault characteristic of the bearing can be very clearly identified. Compared with single wavelet denoising, the improved zero-frequency filter can effectively inhibit spectrum aliasing and better reserve fault pulse information. Therefore, the two-stage noise reduction algorithm provided by the invention has a good noise reduction effect on the outer ring early fault vibration signal of the high-speed train bearing, and can better detect the early outer ring fault characteristics.
And carrying out noise reduction test on the fault vibration signal of the bearing inner ring by using the proposed algorithm. The main structural parameters of the bearing are shown in table 1, the inner ring of the bearing has damage with the length of 4 mm, the width of 0.9 mm and the depth of 0.6 mm, and compared with the size of the bearing, the damage size is relatively small, and the bearing belongs to early failure.
Table 1 main parameters of the bearing tested in the experiment
In order to verify the robustness of the method, two sampling frequencies of 12000 Hz and 48000 Hz are adopted to record data respectively in the test process, and the characteristic frequency of the inner ring fault is 163 Hz according to the fault parameters of the bearing.
For the test data set with a sampling frequency of 12000 Hz, the optimal wavelet decomposition level is 5 as shown in equations (13) and (14). Firstly, filtering a fault signal with a sampling frequency of 12000 Hz by a zero-frequency filter; then, performing wavelet decomposition on the filtered signals, and performing hard threshold denoising processing on each layer of coefficients after decomposition; and solving a spectrogram of the signal after two-stage noise reduction, and identifying the bearing fault through characteristic frequency. In order to compare the characteristic frequencies of the optimal decomposition level wavelet coefficients, the ZFF-filtered signal is subjected to 7-level wavelet decomposition.
Fig. 5 (a) - (e) show the frequency spectrums of wavelet coefficients at different levels after the noise reduction processing is performed on the fault signal with the sampling frequency of 12000 Hz by the method. As can be seen from (b) and (c) in fig. 5, an inner ring failure frequency of 162 Hz can be observed in the fourth and fifth stages of the wavelet decomposition. In the frequency spectrum of the fourth-level wavelet coefficient, although the inner-ring fault characteristic frequency can be observed, a strong interference frequency still exists. However, in the frequency spectrum of the fifth-level wavelet coefficient, the inner ring fault frequency is in an obvious main peak position, and the interference frequency amplitude is very weak, so that the effectiveness of the optimal decomposition level calculation method is proved.
In the case of a 48000 Hz sampling frequency, the seventh level is the best level of wavelet decomposition as can be seen from equations (13) and (14). After the zero-frequency filtering and the optimal level wavelet decomposition hard threshold denoising, the spectrogram of the wavelet coefficients at each level is shown as (f) - (j) in fig. 5. As shown in (i) and (j) in fig. 5, an inner ring failure frequency of 162 Hz is observed in the frequency spectrums of the wavelet coefficients of the sixth and seventh levels. But in the frequency spectrum of the sixth-level wavelet coefficient, a strong interference frequency also exists, so that the inner ring fault frequency of 162 Hz does not become the main peak frequency; in the frequency spectrum of the wavelet coefficient of the seventh level, the inner ring fault frequency is at the position of a main peak, and the interference frequency is weaker, so that the wavelet of the seventh level is the best observation level.
In order to compare and analyze the two-stage noise reduction algorithm with other classical noise reduction algorithms, an inner ring fault experiment is carried out on the bearing by using an experiment platform, and vibration data of early inner ring faults are collected. In the experiment, the inner ring fault of the driving end with the diameter of 0.17 mm is considered, data are collected at a sampling rate of 12000 Hz, and the characteristic fault frequency of the inner ring with the load of a 3 horsepower (hp) motor is 156.12 Hz according to the bearing parameters.
The algorithm is compared with a minimum mean square error zero frequency filtering noise reduction algorithm (ZFF-LMS), a HHT noise reduction algorithm (Hilbert-Huang transform, HHT) and a Variational Mode Decomposition (VMD) noise reduction algorithm, and the effectiveness of the algorithm is analyzed.
The ZFF-LMS algorithm iteratively suppresses noise through minimum average error on the basis of zero-frequency filter output, enhances periodic pulse, and the frequency spectrum of a bearing fault signal subjected to noise reduction through the ZFF-LMS method is shown in FIG. 6. As can be seen from fig. 6, after the bearing fault signal is subjected to noise reduction processing by the ZFF-LMS method, a peak corresponding to the fault frequency of the 158.4 Hz inner ring can be observed in the frequency spectrum of the bearing fault signal, but more interference frequencies exist near the peak frequency, and the bearing fault signal has a greater influence on subsequent feature extraction and fault diagnosis.
The Hilbert-Huang transform (HHT) includes two parts of Empirical Mode Decomposition (EMD) and Hilbert Spectral Analysis (HSA). In the HHT noise reduction algorithm, the bearing fault signal is first decomposed into a series of Intrinsic Mode Functions (IMFs); then, respectively carrying out noise reduction treatment on each IMF by using a threshold denoising method; and finally, calculating the frequency spectrum of the IMF subjected to noise reduction by using Hilbert spectrum analysis, and analyzing the fault frequency characteristics. Fig. 7 shows the frequency spectra of the first four IMFs after noise reduction, and it can be seen that an inner ring failure frequency of 158.4 Hz is observed in the spectra of the first 4 IMFs. However, in the vicinity of the failure frequency, there are serious interference frequencies, which result in the failure frequency of the inner ring not being at a significant main peak position, and especially in the spectrogram of the IMF of the fourth layer ((d) in fig. 7), the amplitude of the interference frequency is greater than that of the failure frequency, and the failure frequency of the inner ring is not a main peak in the frequency spectrum. Therefore, the HHT noise reduction algorithm cannot effectively remove noise interference, nor can it accurately extract the fault frequency characteristics.
In VMD decomposition, a signal can be adaptively decomposed into modal functions of different frequencies by calculating the center frequency of the signal and its supporting frequency band. Similar to the HHT noise reduction algorithm, after bearing fault signals are decomposed by VMD, intrinsic mode functions after noise reduction are obtained by carrying out threshold noise reduction processing on each layer of IMF, and then frequency spectrum analysis is carried out on IMF after noise reduction to extract fault frequency characteristics. Fig. 8 is a frequency spectrum diagram of the first four IMFs after noise reduction by using the VMD algorithm, and as can be seen from fig. 8, an inner ring fault frequency of 158.4 Hz can be observed in the frequency spectrums of the four IMFs after noise reduction. Compared with the HHT noise reduction algorithm, after the bearing fault signal is subjected to VMD noise reduction, the detection of the fault frequency is improved to a certain degree, and in the frequency spectrums of the four IMFs, the fault frequency of the inner ring is located at the position of a main peak. However, it can also be seen from fig. 8 that there are still more interference frequencies with larger amplitudes near the failure frequency of the inner ring, and the amplitudes of part of the interference frequencies are very close to the amplitude of the failure frequency, which causes larger interference to the accurate identification of the bearing failure, and affects the extraction of the failure characteristics and the judgment of the failure type.
The frequency spectrum of the fault signal after the noise reduction by the two-stage noise reduction algorithm provided by the invention is shown in fig. 9, and as can be seen from fig. 9, the frequency spectrum of the fault signal after the two-stage noise reduction is very clear, and in a frequency spectrogram, 154.9 Hz inner ring fault characteristic frequency can be observed, and the frequency is at the main peak position and has obvious peak characteristics. In the frequency spectrum of the noise-reduced signal, compared with the amplitude of the main peak, the amplitude of the interference frequency is generally smaller, and the identification of the fault characteristic frequency is basically not interfered. 154.9 The fault frequency of the inner ring of Hz is the only main peak in the frequency spectrum, and an obvious flat sideband exists between the fault characteristic frequency and the interference frequency, so that the fault characteristic can be extracted more accurately, and the identification precision of the fault type is improved. Comparing fig. 6, 7, 8 and 9, it can be seen that the method of the present invention has a better noise reduction effect than ZFF-LMD, HHT and VMD noise reduction algorithms, can better suppress the interference frequency and enhance the impact characteristics of the fault pulse, exhibiting a sharp peak at the fault frequency.
Aiming at the early detection of the weak fault of the high-speed train bearing, the invention provides a two-stage denoising algorithm based on an improved zero-frequency filter and self-adaptive threshold wavelet denoising. The fault signal is subjected to first-stage filtering noise reduction through the improved ZFF, and the impact characteristic of fault pulse can be better enhanced while filtering through adjusting the frequency response of the ZFF. And during the second-stage denoising, estimating an optimal decomposition level according to the sampling frequency and the bearing fault characteristic frequency, then performing optimal level wavelet decomposition on the IZFF filtered fault signal, and performing hard threshold denoising on a wavelet decomposition result by using a constructed threshold function to obtain a final denoising signal. And detecting the fault characteristic frequency and identifying the fault type by performing spectrum analysis on the signal subjected to two-stage noise reduction. Experimental results show that the method can effectively remove noise in the bearing fault signal, enhance the impact characteristic of the fault periodic pulse, clearly observe the frequency characteristic of the fault when the fault is weak, and can be effectively applied to early detection of the bearing fault of the high-speed train. Compared with noise reduction algorithms such as ZFF-LMS, HHT and VMD, the method has better noise reduction effect, can more clearly present the bearing fault frequency characteristics while better inhibiting noise.
It should be noted that the flowchart or block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. It will also be noted that each block of the block diagrams or flowchart illustration, and combinations of blocks in the block diagrams or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
Those skilled in the art will appreciate that various combinations and/or combinations of features recited in the various embodiments and/or claims of the present disclosure can be made, even if such combinations or combinations are not expressly recited in the present disclosure. In particular, various combinations and/or combinations of the features recited in the various embodiments and/or claims of the present disclosure may be made without departing from the spirit and teachings of the disclosure, and all such combinations and/or combinations are intended to fall within the scope of the disclosure.
While the disclosure has been shown and described with reference to certain exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims and their equivalents. Accordingly, the scope of the present disclosure should not be limited to the above-described embodiments, but should be defined not only by the appended claims, but also by equivalents thereof.
Claims (10)
1. A bearing vibration signal staged noise reduction method is characterized by comprising the following steps:
hilbert conversion is carried out on the bearing vibration signal to obtain a Hilbert envelope curve of the bearing vibration signal;
the method comprises the steps that Hilbert envelope lines of bearing vibration signals are input into an improved zero-frequency filter, so that first bearing vibration signals subjected to noise reduction through the improved zero-frequency filter are obtained;
calculating an optimal wavelet decomposition level value by using the bearing fault characteristic frequency and the sampling frequency of the bearing vibration signal;
and performing wavelet decomposition on the first bearing vibration signal based on the optimal wavelet decomposition level value, and denoising the wavelet coefficient of the layer corresponding to the optimal wavelet decomposition level value by using a wavelet denoising self-adaptive threshold function to obtain a second bearing vibration signal.
2. A method for phased noise reduction of a bearing vibration signal as claimed in claim 1, wherein the frequency response of said modified zero frequency filter is expressed as:
wherein the content of the first and second substances,Hwhich represents the function of a zero-frequency filter,ωthe frequency is represented by a frequency-dependent variable,Mrepresenting the width of the windowed fourier transform window function,Lwhich is indicative of the length of the signal,kindicating the order of the accumulated frequencies in the fourier transform.
3. The method for phased noise reduction of a bearing vibration signal according to claim 2, wherein the inputting the Hilbert envelope curve of the bearing vibration signal into the modified zero-frequency filter to obtain the first bearing vibration signal noise-reduced by the modified zero-frequency filter specifically comprises:
taking a Hilbert envelope curve of the bearing vibration signal as an input, iterating twice through the improved zero-frequency filter to obtain a third bearing vibration signal;
removing a trend term in the third bearing vibration signal to obtain the first bearing vibration signal.
4. A method of phased noise reduction of a bearing vibration signal as claimed in claim 3 wherein said iterating the Hilbert envelope of said bearing vibration signal as an input through said modified zero frequency filter twice to obtain a third bearing vibration signal comprises:
wherein the content of the first and second substances,s(m) A signal representative of the vibration of the bearing,mwhich represents the location of the sampling point,b k the coefficients of the filter are represented by,x 1 (m) Representing the signal after the first stage of filtering,x 2 (m) Representing the second stage filtered signal, i.e. the third bearing vibration signal.
5. The method of staged noise reduction for bearing vibration signal as claimed in claim 4, wherein said formula for removing the trend term from the third bearing vibration signal to obtain the first bearing vibration signal specifically comprises:
wherein，x(n) Representing the first bearing vibration signal.
6. The method for phased denoising of a bearing vibration signal according to claim 1, wherein the formula for calculating the optimal wavelet decomposition level value using the bearing fault signature frequency and the sampling frequency of the bearing vibration signal specifically comprises:
wherein the content of the first and second substances,f s representing the sampling frequency of the bearing vibration signal,C I a characteristic frequency of said bearing fault is represented,
which means that the rounding is made up,q opt representing the optimal wavelet decomposition level value.
7. The method for phased denoising of a bearing vibration signal according to claim 6, wherein the expression of the wavelet denoising adaptive threshold function specifically comprises:
wherein the content of the first and second substances,
representing the first before denoisingjUnder layer the firstkThe number of the wavelet coefficients is such that,
representing the second after denoisingjUnder layer the firstkThe number of the wavelet coefficients is such that,δrepresenting the denoising threshold.
8. A method of phased noise reduction of a bearing vibration signal as claimed in claim 7Method, characterized in that the denoising threshold is calculated based on the principle of unbiased likelihood estimation of Steinδ。
9. The method for phased noise reduction of a bearing vibration signal as claimed in claim 1, wherein said Hilbert transforming the bearing vibration signal to obtain a Hilbert envelope thereof specifically comprises:
carrying out differential conversion on the bearing vibration signal to remove a direct current component;
and carrying out Hilbert transformation on the bearing vibration signal after the differential transformation to obtain a Hilbert envelope curve of the bearing vibration signal.
10. A bearing fault identification method is characterized in that the bearing fault identification method is based on a second bearing vibration signal obtained by the bearing vibration signal staged noise reduction method according to any one of claims 1 to 9, frequency spectrum analysis is carried out, the frequency of a bearing fault is determined by searching a frequency spectrum peak value, and the impact cycle of the bearing fault is obtained, so that early fault identification of the bearing is realized.
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