CN117349615B - Self-adaptive enhancement envelope spectrum method for fault diagnosis of rolling bearing under strong noise condition - Google Patents
Self-adaptive enhancement envelope spectrum method for fault diagnosis of rolling bearing under strong noise condition Download PDFInfo
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Abstract
The invention discloses a self-adaptive enhancement envelope spectrum method for rolling bearing fault diagnosis under a strong noise condition, which comprises the following steps: generating a series of IMF components by utilizing the VMD, normalizing the mutual information and the time domain fuzzy entropy based on the envelope spectrum of the IMF, and jointly selecting two IMFs with the most abundant fault information content by combining the time domain and the frequency domain to reconstruct a signal; post-processing a reconstructed signal through a self-adaptive MED filter, optimizing the length of the filter through a variable step search method based on unbiased autocorrelation analysis, and filtering the reconstructed signal to obtain a final filtered signal; and carrying out envelope spectrum analysis on the filtered signal, and diagnosing the health condition of the bearing by checking the characteristic frequency information on the envelope spectrum. When the health state of the rolling bearing is diagnosed under the condition of strong noise, the invention can accurately extract the corresponding characteristic frequency, thereby effectively identifying the health state of the rolling bearing.
Description
Technical Field
The invention belongs to the technical field of fault diagnosis and signal processing analysis, and particularly relates to a self-adaptive enhancement envelope spectrum method for rolling bearing fault diagnosis under a strong noise condition.
Background
Rolling bearings are one of the components widely used in rotary machines. In the actual operation process, the rolling bearing is easy to damage due to the reasons of complex working conditions, overload, poor installation precision, poor lubrication and the like, thereby affecting the operation safety and reliability of the whole mechanical system. Therefore, a reliable bearing fault diagnosis method is important to avoid potential problems such as mechanical performance reduction, faults, casualties and the like. The bearing fault diagnosis can be implemented on the basis of different information carriers, such as current information, temperature data, acoustic signals, vibration signals, etc. Among them, vibration signals are widely used because of their easy measurement and high signal-to-noise ratio, and the method of the invention also uses vibration signals as information carriers.
Due to the complex structure of the rotary machine, vibration signals generated by the excitation sources are mutually coupled and attenuated on the transmission path, so that impact characteristics caused by the faults of the rolling bearing are difficult to identify. Sliding occurs between the bearing components, making the bearing system a nonlinear system. If a defect occurs on the rotating race or rolling body, the characteristics associated with the defect may be further modulated to non-stationary characteristics. Furthermore, the vibration signal measured under actual operating conditions typically contains a strong background noise, which makes it more difficult to extract fault-related features from the bearing vibration signal. Therefore, it remains a challenging task to perform fault diagnosis on rolling bearings under strongly noisy and non-stationary conditions.
Since the vibration signal obtained from the sensor contains a large amount of redundant information and disturbances, it is necessary to remove noise and extract features related to faults using signal processing techniques. There are many signal processing techniques for bearing fault diagnosis, mainly including time domain, frequency domain and time-frequency domain techniques. Common time domain techniques typically rely on analysis of the probability density distribution characteristics of the vibration signal, such as skewness, kurtosis, effective value, and crest factor, which are susceptible to noise and are quite sensitive to load and speed variations. In the frequency domain analysis, the most common bearing fault diagnosis method is the fourier transform-based spectrum analysis. However, direct fourier transform analysis cannot handle non-stationary fault signals, such as those generated when bearing defects occur on the rotating raceways or rolling bodies. Envelope spectrum analysis is one of the accepted bearing failure detection techniques that is implemented by demodulating the dither signal generated by the damaged bearing area striking other bearing components. The health of the bearing is diagnosed by examining the characteristic frequencies associated with bearing defects on the envelope spectrum. The key to envelope spectrum analysis is how to select the appropriate frequency band, which is a challenging task in many applications. On the other hand, random sliding between bearing components can also affect the results of the envelope spectrum analysis.
Common time-frequency analysis methods include Short-time Fourier transform (Short-Time Fourier Transform, STFT), wigner-Vill distribution (Wigner-Ville Distrubution, WVD), wavelet transform (Wavelet Transform, WT), modal decomposition methods, etc., which can be used to process non-stationary signals. The variational modal decomposition (Variational Mode Decomposition, VMD) is used as a new variational modal decomposition method, unlike STFT, WVD and WT which need to rely on predefined basis functions, is widely applied to bearing fault diagnosis, and can avoid modal confusion and end-point effect problems in empirical modal decomposition. For example, some people use VMDs to process bearing vibration signals for fault diagnosis, but wherein the decomposition parameters are selected by trial and error; still others use envelope entropy as an objective function for VMD parameter optimization, but the fault features are manually extracted; some have used improved VMD and resonance demodulation for fault detection of locomotive bearings; however, the choice of the mode, i.e. the eigenmode function (INTRINSIC MODE FUNCTION, IMF), is based on the principle of maximum kurtosis, the effectiveness of which in the presence of interfering components is affected. Many people have made many efforts in the selection of IMFs and the reconstruction of signals. For example, some people use correlation analysis to select IMFs; some people select IMFs by examining their spectra; some people propose a correlation metric based on normalized correlation coefficients and mutual information loss for IMF analysis; some people apply envelope correlation spectrum analysis to select the most unique IMF for fault feature extraction; some people introduce a normalization test method for IMF selection and integration; still others use indices based on kurtosis, instantaneous energy, and approximate entropy products to select IMFs. However, the above methods of analyzing and selecting IMFs have two main disadvantages: (1) The above-described methods focus only on analyzing IMFs within a single domain (time or frequency domain) and therefore may limit their robustness in bearing failure detection, especially when the vibration signal is severely nonlinear, non-stationary and contains strong noise; (2) The method of selecting IMFs by means of correlation measures has the problem that IMFs are selected because they are highly correlated with interfering components in the original signal.
On the other hand, under strong noise or complex system conditions, the original signal may not be able to be decomposed into relatively clean IMF components. If only signal decomposition and reconstruction are performed, the interference component in the IMF component may still be present, resulting in that the extraction of fault-related features is still not ideal or even fails. Therefore, it is necessary to use additional denoising techniques on the reconstructed signal, thereby further highlighting the inherent fault-related features. The blind deconvolution method provides a new idea for denoising the vibration signal. When the vibration source, transmission channel characteristics and noise intensity are unknown, it can adaptively design an inverse filter to recover the original pulse signal. The parameters of the anti-filter may be determined by minimizing the entropy of the signal or maximizing the kurtosis of the signal using minimum entropy deconvolution (Minimum Entropy Deconvolution, MED), maximum correlation kurtosis deconvolution (Maximum Correlation Kurtosis Deconvolution, MCKD), multi-point optimal minimum entropy deconvolution adjustment (Multipoint Optimal Minimum Entropy Deconvolution Adjustment, MOMEDA), and the like. The MCKD and MOMEDA methods require prior knowledge of the frequency of the fault-related features and even strict knowledge of the location of each fault pulse. Therefore, they are greatly limited in practical applications in the engineering field. As for the MED method, one of the most important parameters, i.e., the filter length, is usually implemented by trial and error. Furthermore, classical MED filter length selection methods based on the kurtosis value of the output signal are susceptible to noise components (e.g. strong impulse disturbances) and tend to recover single or small strong impulses rather than periodic impulses related to faults, which would affect their use under strong noise conditions.
In summary, in order to solve the problem of difficulty in diagnosis of a rolling bearing fault under strong noise and non-stationary conditions, many people have made some attempts in selection of signal modes and blind deconvolution, but robustness under strong noise and non-stationary conditions based on correlation measures and a mode selection method limited to a single domain is not ideal, and researches on adaptive denoising using blind deconvolution still have many disadvantages of being susceptible to noise components and limited ability to highlight periodic pulses related to faults. Therefore, how to realize stable mode selection, signal reconstruction and effective adaptive denoising under the conditions of strong noise and non-stability, so as to improve the accuracy of the fault diagnosis of the rolling bearing is a technical problem to be solved by the technicians in the field.
Disclosure of Invention
The invention aims to provide a self-adaptive enhancement envelope spectrum method for fault diagnosis of a rolling bearing under a strong noise condition, aiming at the defects of the prior art.
The aim of the invention is realized by the following technical scheme: an adaptive enhancement envelope spectrum method for rolling bearing fault diagnosis under a strong noise condition comprises the following steps:
(1) Analyzing based on the envelope spectrum normalized mutual information and the time domain fuzzy entropy to obtain a selected reserved eigenmode function, and reconstructing the finally reserved eigenmode function into a new signal to be analyzed;
(1.1) acquiring an original vibration signal y (t) of the rolling bearing through an acceleration sensor;
(1.2) decomposing the acquired original vibration signal by using a variation modal decomposition method to obtain k eigenmode function components u i (t), i=1, 2, …, k;
(1.3) calculating an envelope spectrum function of the original vibration signal and each eigenmode function component by hilbert transformation;
(1.4) respectively calculating normalized mutual information values between the envelope spectrum function of the original vibration signal and the envelope spectrum function of each eigenmode function component;
(1.5) calculating the average value of the normalized mutual information values, and selecting and reserving the eigen mode function corresponding to the normalized mutual information value larger than the average value of the normalized mutual information values;
(1.6) calculating the time domain fuzzy entropy value of the eigenmode function reserved in the step (1.5);
(1.7) selecting and reserving two eigenvalue functions with the maximum time domain fuzzy entropy value, and reconstructing the two finally reserved eigenvalue functions into a new signal S (t) to be analyzed;
(2) Performing post-processing on the signal to be analyzed obtained in the step (1) by using a self-adaptive minimum entropy deconvolution filter, optimizing the filter length by using a variable step length search method based on unbiased autocorrelation analysis, and filtering the signal to be analyzed by using the optimal filter length to obtain a final filtered signal;
(2.1) initializing a minimum entropy deconvolution filter length search range of [ L min,Lmax ], searching for a large step size of S 1, and searching for a small step size of S 2;
(2.2) filtering the signal S (t) to be analyzed by using a minimum entropy deconvolution filter with the filter length L of L min,Lmin+S1,…,Lmax respectively to obtain a filtered signal x L (t) corresponding to the filter length L;
(2.3) performing unbiased autocorrelation transformation on each of the filtered signals x L (t) to obtain And interceptThe second half of the data points of the first 2% and the last 10% are removed to obtain the signals/>, after the data points are intercepted
(2.4) Calculating the result of the step (2.3)Kurtosis value Ku (L);
(2.5) determining a large-step optimal L according to the kurtosis value Ku (L), namely a filter length L 1 corresponding to the peak value of the group of Ku (L);
(2.6) setting a new filter length search range to [ L 1-S1,L1+S1 ];
(2.7) filtering the signal S (t) to be analyzed by using a minimum entropy deconvolution filter with the filter length L of L 1-S1,L1-S1+S2,…,L1+S1 respectively to obtain a filtered signal x L (t) corresponding to the filter length L of the group;
(2.8) repeating said step (2.3) -said step (2.4), resulting in a filter length L corresponding to the set Kurtosis value Ku (L);
(2.9) repeating the step (2.5), and determining a small step length optimal L according to the kurtosis value Ku (L), namely, determining the filter length L 2,L2 corresponding to the peak value of the group of Ku (L), namely, the optimal filter length at the moment;
(2.10) filtering the signal S (t) to be analyzed by using a minimum entropy deconvolution filter with a filtering length of L 2 to obtain a final filtered signal
(3) Calculating and mapping the filtered signal obtained in the step (2)Is a envelope spectrum of (2); and carrying out qualitative diagnosis on the health condition of the bearing by checking the characteristic frequency information on the envelope spectrum.
Further, the calculation formula of the envelope spectrum function is as follows:
Wherein V (t) is the calculated envelope spectrum function, s (t) represents the input signal, i.e. the signal of the envelope spectrum to be calculated, and HT represents the Hilbert transform.
Further, the calculation formula of the normalized mutual information value is:
Wherein NMI (X, Z) is a normalized mutual information value between two input signals X, Z, H (·) represents shannon entropy, p (·) represents a probability distribution function, X a、zb is a discrete value in the two input signals X, Z, respectively, and I (X, Z) represents a mutual information value of the two input signals.
Further, in the step (1.6), calculating the time domain fuzzy entropy value of the eigenmode function reserved in the step (1.5), specifically including:
Firstly, the eigenmode function reserved in the step (1.5) is a time sequence, the time sequence corresponding to the eigenmode function is composed of N sampling points and is expressed as { c (z): 1 is less than or equal to z is less than or equal to N }, and m-dimensional vectors are constructed for the eigenmode function in sequence and expressed as:
Wherein c 0 (z) is the average value of m consecutive c (z), and the calculation formula is:
Wherein r represents a number traversing 0 to m-1;
Then, at the determined z value, a vector is calculated Sum vectorInter chebyshev distance
Wherein z+.z', o is a number traversing 0 to m-1, c (z+o) represents the (o+1) th sampling point of the m-dimensional vector; second, by a blurring functionCalculate vectorVectorSimilarity between
Wherein,For the exponential function, η and γ are the width and gradient of the exponential function boundary, respectively;
Then, define a function The method comprises the following steps:
when the dimension increase 1 becomes m+1, it is calculated according to the formula (6) -the formula (10):
The fuzzy entropy is defined as:
When N is a finite value, equation (12) is converted to:
FuzzyEn (m, eta, gamma, N) is a time domain fuzzy entropy value;
Finally, calculating the time domain fuzzy entropy value of the eigenmode function reserved in the step (1.5) according to the formula (13).
Further, in the step (2.2), the minimum entropy deconvolution filter filters the signal S (t) to be analyzed, specifically including:
For an input signal S (t) of the minimum entropy deconvolution filter, x (t) is a filtered signal output by the minimum entropy deconvolution filter;
The minimum entropy deconvolution filter f (t) is modeled as a filter length as an FIR filter with L coefficients according to the filter length L:
the optimal filter coefficients are determined by maximizing the kurtosis of the filtered signal x (t):
wherein O (f) represents the optimal filter coefficient of the minimum entropy deconvolution filter f;
The filtered signal x (t) under the optimal filter coefficient is the filtered signal x L (t) under the filter length L.
Further, in the step (2.3), the filtered signal x L (t) is subjected to unbiased autocorrelation transformationThe expression of (2) is:
Where τ=q/f s is the delay factor, f s is the sampling frequency of the signal, q=0, 1, …, N-1, N is the length of the signal x L (t), Representing the similarity between the filtered signal x L (t) and the filtered signal x L (t- τ) after a delay τ;
In the step (2.3), the signals after the data points are intercepted The expression of (2) is:
wherein, U 1＝1.02N+1;U2 =1.9n_1; n is a signal Is a length of (c).
Further, in the step (2.4), the step (2.3) is performedCalculating the/>, corresponding to different filter lengths L, through a formula (18)Kurtosis value Ku (L):
wherein N 1 is a signal Is a length of (c).
Further, in the step (2.5), the expression of the large-step optimal L is:
O(L)＝arg(L)max{Ku(L)} (19)
where O (L) represents the optimal value of the filter length L.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the invention, an original signal is decomposed into a group of IMFs by using VMD, then time domain and frequency domain measures (namely envelope spectrum normalization mutual information and time domain fuzzy entropy) are combined, and the most representative IMFs are jointly selected from the time domain and the frequency domain to reconstruct the signal, wherein the envelope spectrum information directly corresponds to the characteristic frequency related to the defect, and the normalization mutual information can well quantize the linear and nonlinear correlations between time sequences on the basis of being insensitive to noise or outlier data without making any assumption or requirement on the distribution of the normalization mutual information, so that the IMFs which are more related to the original signal can be robustly selected through the analysis of the envelope spectrum normalization mutual information; the fuzzy entropy can effectively characterize the regularity and complexity of nonlinear and non-stationary time series when the data set is shorter and the noise is larger, and the fuzzy entropy value of the periodic pulses is higher compared with the random pulses, so the fuzzy entropy analysis can effectively select IMFs containing more periodic impact information related to faults. Compared with the existing IMF selection method which is focused on analyzing the representative IMF in a single domain (time domain or frequency domain), the novel IMF selection and integration strategy provided by the invention can improve the robustness of the most representative IMF selection under the non-stationary and strong noise conditions, and avoid the problem that the IMF is selected due to the high correlation between the IMF and the interference component in the original signal by the method of selecting the IMF through the correlation measure.
(2) The invention utilizes the self-adaptive MED filter to carry out post-processing on the reconstruction signal, reduces the noise brought to the reconstruction signal by the selected IMF, and highlights the pulse information related to the defect; the length of the MED filter is adaptively selected by using a proposed variable step search method based on unbiased autocorrelation transformation; the unbiased autocorrelation transformation is introduced before the kurtosis of the MED output signal is calculated, gaussian noise and aperiodic strong pulse components in the signal can be attenuated, and periodic pulse components are reserved, so that the interference caused by the noise components received by the filter length selection operation is reduced and focused on the periodic pulses related to faults, the problem that the classical MED filter length selection method based on the kurtosis value of the output signal is easily influenced by the noise components and tends to recover single or small amount of strong pulses instead of the periodic pulses related to the faults is solved, and the use effect of the classical MED filter length selection method under the condition of strong noise is improved; finally, through envelope spectrum analysis of the processed signals, rolling bearing fault diagnosis under the condition of strong noise is realized. The invention can accurately extract the corresponding characteristic frequency, thereby effectively identifying the health state of the rolling bearing and diagnosing the fault of the rolling bearing under the condition of strong noise.
Drawings
FIG. 1 is a flow chart of an adaptive boost envelope spectrum method for rolling bearing fault diagnosis under strong noise conditions of the present invention;
FIG. 2 is a diagram of a system for simulating a fault of a rolling bearing in an embodiment of the present invention;
FIG. 3 is a time domain diagram of vibration signals of a healthy bearing, an outer ring fault bearing, an inner ring fault bearing and a rolling body fault bearing under the influence of strong noise in an embodiment of the present invention;
FIG. 4 is a graph of vibration signals of a healthy bearing, an outer ring fault bearing, an inner ring fault bearing, and a rolling body fault bearing under the influence of strong noise in an embodiment of the present invention;
FIG. 5 is an envelope spectrum of VMD modal components of an inner race fault bearing vibration signal in an embodiment of the present invention;
FIG. 6 is a match diagram of the envelope spectrum normalized mutual information value and the time domain fuzzy entropy value calculation result of the VMD modal component of the vibration signal of the inner ring fault bearing in the embodiment of the present invention;
FIG. 7 is an envelope spectrum of reconstructed signals to be analyzed of a healthy bearing, an outer ring fault bearing, an inner ring fault bearing and a rolling body fault bearing under a strong noise condition in an embodiment of the present invention;
FIG. 8 is a schematic diagram of an MED filter implementation process of the present invention;
Fig. 9 is an envelope spectrum of vibration signals of a healthy bearing, an outer ring fault bearing, an inner ring fault bearing and a rolling body fault bearing under a strong noise condition treated by the method according to the embodiment of the invention.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples do not represent all implementations consistent with the application. Rather, they are merely examples of apparatus and methods consistent with aspects of the application as detailed in the accompanying claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application as claimed.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.
It should be understood that although the terms first, second, third, etc. may be used herein to describe various information, these information should not be limited by these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the application. The word "if" as used herein may be interpreted as "at … …" or "at … …" or "in response to a determination" depending on the context. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
As shown in fig. 2, a system structure diagram of a rolling bearing fault simulation test is provided, and the self-adaptive enhancement envelope spectrum method for diagnosing the rolling bearing fault under the strong noise condition is based on the system for testing and collecting vibration data. In fig. 2, ① is a frequency converter for controlling the rotation speed of the motor, ② is a three-phase asynchronous motor of the driving system, ③ is a data acquisition system for acquiring vibration signals of the rolling bearing and sending the vibration signals to a computer end for analysis, ④ is a flexible coupler for inhibiting high-frequency vibration generated by the motor and adjusting misalignment errors of the assembly, ⑤ is an optical sensor for measuring the rotation speed of the shaft, ⑥ is an acceleration sensor for measuring vibration signals, ⑦ is the rolling bearing for testing, and ⑧ is a weight plate for applying additional radial load.
In this embodiment, the bearing model is selected to be SKF F6004-2RS1, and specific parameters thereof are shown in table 1. The selected health state types of the rolling bearing are respectively as follows: a healthy bearing, an outer ring failure bearing with failure dimensions of 0.3mm 2 x 0.4mm (area x depth), an inner ring failure bearing with failure dimensions of 0.3mm 2 x 0.4mm (area x depth) and a rolling element failure bearing with failure dimensions of 0.3mm 2 x 0.5mm (area x depth).
Table 1 structural parameters of the bearing
| Parameter name | Parameter value |
| Inner diameter (mm) | 20 |
| Outer diameter (mm) | 42 |
| Thickness (mm) | 12 |
| Pitch diameter (mm) | 31.06 |
| Rolling element diameter (mm) | 6.36 |
| Number of rolling elements | 9 |
| Contact angle (°) | 0 |
In this embodiment, the collected shaft rotation frequency is 20Hz, and the sampling frequency is 25600Hz. The theoretical characteristic frequency of the health state of each corresponding bearing is as follows: 20Hz (healthy bearing), 72Hz (outer ring failure bearing), 108Hz (inner ring failure bearing) and 94Hz (rolling element failure bearing). The acquired bearing vibration signal contains only part of the interference noise, so that some extra noise needs to be added to simulate a strong noise environment. Because noise in the vibration signal of the rolling bearing is mainly noise similar to Gaussian noise, and in the application scene of bearing fault diagnosis, the signal to noise ratio of the signal is below 5dB, namely belongs to a stronger noise background, the signal to noise ratio of the whole signal is changed between 1dB and 3dB by adding extra Gaussian white noise into data so as to simulate a strong noise condition.
The invention relates to a self-adaptive enhancement envelope spectrum method for rolling bearing fault diagnosis under the condition of strong noise, which is shown in figure 1 and specifically comprises the following steps:
(1) And carrying out analysis based on the envelope spectrum normalized mutual information and the time domain fuzzy entropy to obtain the IMF which is selected to be reserved, and reconstructing the IMF which is finally reserved into a new signal to be analyzed.
(1.1) Acquiring an original vibration signal y (t) of the rolling bearing by using the acceleration sensor and the data acquisition system mounted on the left bearing seat in fig. 2, wherein the acquired vibration signals are shown in fig. 3 and 4, and (a), (b), (c) and (d) in fig. 3 are time domain diagrams of vibration signals of the healthy bearing, the outer ring fault bearing, the inner ring fault bearing and the rolling body fault bearing under the influence of strong noise respectively; fig. 4 (a), (b), (c) and (d) are frequency spectra of vibration signals of the healthy bearing, the outer ring fault bearing, the inner ring fault bearing and the rolling body fault bearing under the influence of strong noise, respectively, wherein arrows point to characteristic frequencies corresponding to health conditions. As can be seen from fig. 3 and 4, under the influence of strong noise, a large number of interference components exist in the time domain and the spectrogram, and the health state of the bearing cannot be effectively identified.
Taking an inner ring fault bearing vibration signal as an example, the VMD method is used for decomposing the collected original vibration signal y (t) to obtain k IMF components u i (t), i=1, 2, …, k. For example, in this embodiment, k=10, i.e., 10 IMF components are obtained after decomposition. Each IMF component u i (t) has a different center frequency and the sum of the estimated bandwidths of the resulting IMF components is minimal.
(1.3) Respectively calculating envelope spectrums of the original vibration signal and each IMF component, wherein an envelope spectrum calculation formula is as follows:
Wherein V (t) is the calculated envelope spectrum function, s (t) represents the input signal, i.e. the signal of the envelope spectrum to be calculated, and HT represents the Hilbert transform.
(1.4) Respectively calculating normalized mutual information values between the envelope spectrum function of the original vibration signal and the envelope spectrum function of each IMF component, wherein the calculation formula is as follows:
Wherein NMI (X, Z) is a normalized mutual information value between two input signals X, Z, H (·) represents shannon entropy, p (·) represents a probability distribution function, X a、zb is a discrete value in the two input signals X, Z, respectively, and I (X, Z) represents a mutual information value of the two input signals.
It should be understood that X represents the envelope spectrum function of the original vibration signal, Z represents the envelope spectrum function of the IMF component, and the normalized mutual information value between the envelope spectrum function of the original vibration signal and the envelope spectrum function of each IMF component, that is, a plurality of normalized mutual information values, is calculated according to the method of formula (2) -formula (5).
(1.5) Calculating the average value of the normalized mutual information values, and selecting and retaining IMFs corresponding to the normalized mutual information values larger than the average value of the normalized mutual information values, wherein the IMFs are considered to be more relevant to the original vibration signal and are retained.
(1.6) Calculating the time domain fuzzy entropy value of the IMF retained in step (1.5).
In this embodiment, calculating the time domain fuzzy entropy value of the IMF reserved in step (1.5) specifically includes:
first, the IMF reserved in the step (1.5) is a time sequence, the time sequence corresponding to the IMF is composed of N sampling points, which are expressed as { c (z): 1 ∈z ∈N }, and m-dimensional vectors are constructed for the IMF in sequence, which are expressed as:
Wherein c 0 (z) is the average value of m consecutive c (z), and the calculation formula is:
Where r is represented as a number traversing 0 to m-1.
Then, at the determined z value, a vector is calculatedSum vectorInter chebyshev distance
Where z+.z', o is a number traversing 0 to m-1, c (z+o) represents the (o+1) th sampling point of the m-dimensional vector.
It should be understood that the vectorSum vectorInter chebyshev distanceAs the maximum absolute difference of the corresponding scalar component, this equation (8) can be understood as: at a certain z value, for a certain z', traversing the corresponding scalar in the two m-dimensional vectors, calculating chebyshev distance
Second, by a blurring functionCalculate vectorVectorSimilarity between
Wherein,For an exponential function, η and γ are the width and gradient of the exponential function boundary, respectively.
Then, define a functionThe method comprises the following steps:
When the dimension increase 1 becomes m+1, the calculation according to the formula (6) -the formula (10) can be obtained:
The fuzzy entropy is defined as:
When N is a finite value, equation (12) is converted to:
Wherein FuzzyEn (m, η, γ, N) is the time domain fuzzy entropy value.
Finally, calculating the time domain fuzzy entropy value of the IMF reserved in the step (1.5) according to the formula (13).
(1.7) Selecting and retaining two IMFs with the largest time-domain fuzzy entropy values, wherein the IMFs are considered to contain more information related to fault characteristics; and reconstructing the two finally reserved IMFs into a new signal S (t) to be analyzed for subsequent processing, wherein the two IMFs are linearly added to obtain the new signal S (t) to be analyzed.
It should be understood that through envelope spectrum normalization mutual information and time domain fuzzy entropy analysis, modes with higher correlation degree with the original signal and more fault related information are jointly selected in the time domain and the frequency domain to reconstruct the signal to be analyzed.
In this embodiment, the envelope spectrum of ten IMFs obtained by VMD-decomposing the vibration signal of the bearing with the inner ring fault is shown in fig. 5, and according to the theoretical characteristic frequency of 108Hz at this time, it can be seen that the IMFs with the most obvious characteristic frequency and harmonic components thereof and relatively lower noise components are the first IMF and the fourth IMF corresponding to (a) and (d) in fig. 5. The envelope spectrum normalized mutual information values and the time domain fuzzy entropy values corresponding to the ten IMFs are calculated by adopting the methods in the step (1.4) and the step (1.6), as shown in fig. 6, as can be seen from the normalized mutual information value result in the step (a) in fig. 6: the normalized mutual information values corresponding to the first, second, fourth, fifth and seventh IMFs are selected because the normalized mutual information values are larger than the average value of all IMFs; and as can be seen from the time-domain fuzzy entropy value calculation result in (b) of fig. 6: of the IMFs retained in fig. 6 (a), the first and fourth IMFs are finally selected to reconstruct the signal to be analyzed for subsequent processing due to having the largest time-domain fuzzy entropy value. According to the envelope spectrum of each IMF shown in fig. 5, the result shown in fig. 6 may illustrate that the analysis based on the envelope spectrum normalized mutual information and the time domain fuzzy entropy in the step (1) of the present invention can effectively select the IMF with more obvious characteristic frequency and harmonic thereof and lower noise level under the condition of strong noise by using the obtained IMF selection and integration strategy.
After the original vibration signals are decomposed and reconstructed in the step (1), the obtained reconstructed signal envelope spectra to be analyzed of the healthy bearing, the outer ring fault bearing, the inner ring fault bearing and the rolling body fault bearing under the strong noise condition are respectively shown as (a), (b), (c) and (d) in fig. 7, wherein the arrows point to the characteristic frequencies and the harmonics thereof corresponding to the health conditions (wherein the characteristic frequency of the healthy bearing is 20Hz, the characteristic frequency of the outer ring fault bearing is 72Hz, the characteristic frequency of the inner ring fault bearing is 108Hz, and the characteristic frequency of the rolling body fault bearing is 94 Hz). It can be seen that the characteristic frequencies and their harmonics of the bearing for each state of health have been extracted at this time and that the interfering frequency components have been removed to some extent. However, in the envelope spectrum of the healthy axis bearing component signal shown in fig. 7 (a), the second harmonic dominates the spectrum, which may mislead the diagnosis as a rotor misalignment fault characterized by the dominant second harmonic of the rotating frequency; in addition, in the envelope spectrum of the bearing-structure signal of the outer ring fault bearing and the rolling body fault shaft shown in fig. 7 (b) and (d), the noise component is still more obvious, and the higher harmonic extraction effect of the characteristic frequency is not very ideal, because under the condition of strong noise, only through signal decomposition and reconstruction, the interference component existing in the IMF still exists in the reconstructed signal, which reduces the reliability of fault diagnosis. It is therefore necessary to post-process the reconstructed signal to be analyzed in order to further de-noise and highlight the inherent fault-related features.
(2) And (3) performing post-processing on the signal to be analyzed obtained in the step (1) by using an adaptive MED filter, so that the influence of interference components in the IMF can be reduced, the pulse related to faults is enhanced, the filter length is optimized by using a variable step search method based on unbiased autocorrelation analysis, and the signal to be analyzed is filtered by using the optimal filter length, so that a final filtered signal is obtained.
(2.1) Initializing MED filter length search range to be [ L min,Lmax ], searching large step to be S 1, and searching small step to be S 2.
Specifically, taking the inner ring fault signal analyzed in the step (1) as an example, according to the signal S (t) to be analyzed obtained in the step (1), the filter length search range [ L min,Lmax ] is set to be [1, 300], the large step S 1 is 20, and the small step S 2 is 5.
And (2.2) filtering the signal S (t) to be analyzed by using MED filters with the filter length L min,Lmin+S1,…,Lmax respectively to obtain a filtered signal x L (t) corresponding to the filter length L.
In this embodiment, the implementation method for filtering the signal S (t) by the MED filter is specifically as follows:
For the input signal S (t) of the MED filter, x (t) is the filtered signal output by the MED filter. The implementation process is shown in fig. 8, wherein S (t) is the signal to be analyzed obtained in step (1). The signal S (t) mainly contains three components: the original periodic pulse component I P, random noise component N r, and strong impulse interference components I I,P1、P2 and P 3 are the transfer functions of the three components in the system, respectively. The basic idea of MED filters is to iteratively construct an inverse filter that maximizes the kurtosis of the signal or minimizes noise (i.e., entropy) to highlight the original pulses in the mixed signal. The MED filter f (t) can be modeled as a FIR filter with a filter length of L coefficients (i.e., a filter length of L):
the optimal filter coefficients are determined by maximizing the kurtosis of the filtered signal x (t):
Where O (f) represents the optimal filter coefficient of the MED filter f.
The filtered signal x (t) under the optimal filter coefficient is the filtered signal x L (t) under the filter length L.
(2.3) Performing unbiased autocorrelation transformation on each of the filtered signals x L (t) to obtainAnd interceptThe second half of the data points of the first 2% and the last 10% are removed to obtain the signals/>, after the data points are intercepted
It will be appreciated that the unbiased autocorrelation transformation is used to attenuate gaussian noise and non-periodic strong impulse components in the filtered signal output by the MED filter, so that noise components and interference from strong impulses experienced by subsequent filter length selection operations are reduced, and so that subsequent search processes can effectively select the filter length that best recovers periodic impulse performance associated with the fault.
Further, the unbiased autocorrelation of the filtered signal x L (t) output by the MED filter is transformed into:
Where τ=q/f s is the delay factor, f s is the sampling frequency of the signal, q=0, 1, …, N-1, N is the length of the signal x L (t), The similarity between the filtered signal x L (t) and the filtered signal x L (t- τ) after its delay τ is described. As can be seen from equation (16), the unbiased autocorrelation transformation can be used to attenuate the magnitude of the non-periodic components in the signal to thereby emphasize the periodic components.
Further, the number of signal points after unbiased autocorrelation transformation is twice that before transformation and is symmetrical in front and back in time domain, in addition, the non-periodic component (Gaussian noise and strong impact interference) in the signal can have larger amplitude in the middle of the transformed signal, and the tail end can have abnormal amplitude due to the reduction of samples, so after unbiased autocorrelation transformation is carried out on the signal, the second half of the signal is taken, the data points of the first 2% and the data points of the second 10% are removed, and the signal after the data points are intercepted is usedThe expression is that:
wherein, U 1＝1.02N+1;U2 =1.9n_1; n is a signal Is a length of (c).
(2.4) Calculating the result of step (2.3)Kurtosis value Ku (L).
Specifically, for the unbiased autocorrelation signal after the truncated data points obtained in step (2.3)Calculating the/>, corresponding to different filter lengths L, through a formula (18)Kurtosis value Ku (L):
wherein N 1 is a signal Is a length of (c).
(2.5) Determining the large step optimal L according to the kurtosis value Ku (L), namely the filter length L 1 corresponding to the peak value of the group of Ku (L).
Specifically, a large step optimal L can be obtained according to formula (19):
O(L)＝arg(L)max{Ku(L)} (19)
Wherein O (L) represents an optimal value of L.
(2.6) Setting a new filter length search range to [ L 1-S1,L1+S1 ].
And (2.7) filtering the signal S (t) to be analyzed by using MED filters with the filter length L 1-S1,L1-S1+S2,…,L1+S1 respectively to obtain a filtered signal x L (t) corresponding to the filter length L of the group, wherein the filtering process of the MED filters is the same as that described in the step (2.2).
(2.8) Repeating the steps (2.3) - (2.4) to obtain the filter length L corresponding to the groupKurtosis value Ku (L).
(2.9) Repeating the step (2.5), and determining the small step length optimal L according to the kurtosis value Ku (L) through a formula (19), namely determining the filter length L 2,L2 corresponding to the peak value of the group of Ku (L), namely determining the optimal filter length for the time.
And (2.10) filtering the signal S (t) to be analyzed by using an MED filter with a filtering length of L 2 to obtain a final filtered signal x L2 (t), wherein the filtering process of the MED filter is the same as that described in the step (2.2).
It should be noted that the unbiased autocorrelation transformation serves to attenuate noise components in the signal and preserve periodic pulse components, so that the filter length selection operation is more prone to select lengths that are more effective for the periodic pulse components associated with faults; the variable step search method is used to adaptively select the filter length.
The MED filter length is optimized through a variable step length search method based on unbiased autocorrelation analysis, so that the MED filter adaptively carries out post-processing on the reconstructed signal to be analyzed obtained in the step (1) to further remove noise and highlight information related to defects. The complete algorithm of the adaptive MED filter post-processing procedure is shown in table 2.
In summary, the steps (2.1) - (2.2) are used for filtering respectively by using the initialized filter length to obtain a plurality of filtered signals, then the steps (2.3) - (2.5) are used for selecting a large step length optimal according to the plurality of filtered signals, then the steps (2.6) - (2.7) are used for setting a new filter length searching range according to the large step length optimal, filtering is performed respectively by using the newly set filter length, then the steps (2.8) - (2.9) are used for selecting a small step length optimal according to the signals filtered by the steps (2.7), finally the step (2.10) is used for filtering the signal to be analyzed S (t) obtained after the reconstruction of the step (1) by using the finally determined filter length (namely the small step length optimal), and a final filtering signal is obtained, wherein the filtering signal is the filter signal with the optimal filter length.
Table 2 adaptive MED filter post-processing algorithm
(3) Calculating and mapping the filtered signal obtained in step (2)Is a envelope spectrum of (2); and carrying out qualitative diagnosis on the health condition of the bearing by checking the characteristic frequency information on the envelope spectrum.
After the original vibration signals are processed by the method, the obtained envelope spectrums of the signals of the healthy bearing, the outer ring fault bearing, the inner ring fault bearing and the rolling body fault bearing under the strong noise condition are respectively shown as (a), (b), (c) and (d) in fig. 9, wherein the arrows point to the characteristic frequencies and the harmonic waves thereof corresponding to the health conditions (wherein the characteristic frequency of the healthy bearing is 20Hz, the characteristic frequency of the outer ring fault bearing is 72Hz, the characteristic frequency of the inner ring fault bearing is 108Hz and the characteristic frequency of the rolling body fault bearing is 94 Hz). It can be seen that, compared with the signal which is not post-processed by the adaptive MED filter in fig. 7, the characteristic frequency component in the signal is obviously enhanced, the higher harmonics are effectively highlighted, and the noise component is effectively attenuated. According to the theoretical characteristic frequencies of the healthy bearing, the outer ring fault bearing, the inner ring fault bearing and the rolling body fault bearing, the health state of the rolling bearing can be effectively diagnosed by checking the characteristic frequency components in (a), (b), (c) and (d) in fig. 9. Therefore, when the method disclosed by the invention is applied to the diagnosis of the health states of the healthy bearing, the outer ring fault bearing, the inner ring fault bearing and the rolling body fault bearing under the strong noise condition, the corresponding characteristic frequency can be accurately extracted, so that the health state of the rolling bearing can be effectively identified, and the diagnosis of the rolling bearing fault under the strong noise condition can be effectively realized.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. The self-adaptive enhancement envelope spectrum method for the fault diagnosis of the rolling bearing under the condition of strong noise is characterized by comprising the following steps of:
(1) Analyzing based on the envelope spectrum normalized mutual information and the time domain fuzzy entropy to obtain a selected reserved eigenmode function, and reconstructing the finally reserved eigenmode function into a new signal to be analyzed;
(1.1) acquiring an original vibration signal y (t) of the rolling bearing through an acceleration sensor;
(1.2) decomposing the acquired original vibration signal by using a variation modal decomposition method to obtain k eigenmode function components u i (t), i=1, 2, …, k;
(1.3) calculating an envelope spectrum function of the original vibration signal and each eigenmode function component by hilbert transformation;
(1.4) respectively calculating normalized mutual information values between the envelope spectrum function of the original vibration signal and the envelope spectrum function of each eigenmode function component;
(1.5) calculating the average value of the normalized mutual information values, and selecting and reserving the eigen mode function corresponding to the normalized mutual information value larger than the average value of the normalized mutual information values;
(1.6) calculating the time domain fuzzy entropy value of the eigenmode function reserved in the step (1.5);
in the step (1.6), calculating the time domain fuzzy entropy value of the eigenmode function reserved in the step (1.5), which specifically includes:
Firstly, the eigenmode function reserved in the step (1.5) is a time sequence, the time sequence corresponding to the eigenmode function is composed of N sampling points and is expressed as { c (z): 1 is less than or equal to z is less than or equal to N }, and m-dimensional vectors are constructed for the eigenmode function in sequence and expressed as:
Wherein c 0 (z) is the average value of m consecutive c (z), and the calculation formula is:
wherein r is a number traversing 0 to m-1;
Then, at the determined z value, a vector is calculated Sum vectorInter chebyshev distance
Wherein z+.z', o is a number traversing 0 to m-1, c (z+o) represents the (o+1) th sampling point of the m-dimensional vector;
Second, by a blurring function Calculate vectorVectorSimilarity between
Wherein,For the exponential function, η and γ are the width and gradient of the exponential function boundary, respectively;
Then, define a function The method comprises the following steps:
when the dimension increase 1 becomes m+1, it is calculated according to the formula (6) -the formula (10):
The fuzzy entropy is defined as:
When N is a finite value, equation (12) is converted to:
FuzzyEn (m, eta, gamma, N) is a time domain fuzzy entropy value;
Finally, calculating the time domain fuzzy entropy value of the eigenmode function reserved in the step (1.5) according to the formula (13);
(1.7) selecting and reserving two eigenvalue functions with the maximum time domain fuzzy entropy value, and reconstructing the two finally reserved eigenvalue functions into a new signal S (t) to be analyzed;
(2) Performing post-processing on the signal to be analyzed obtained in the step (1) by using a self-adaptive minimum entropy deconvolution filter, optimizing the filter length by using a variable step length search method based on unbiased autocorrelation analysis, and filtering the signal to be analyzed by using the optimal filter length to obtain a final filtered signal;
(2.1) initializing a minimum entropy deconvolution filter length search range of [ L min,Lmax ], searching for a large step size of S 1, and searching for a small step size of S 2;
(2.2) filtering the signal S (t) to be analyzed by using a minimum entropy deconvolution filter with the filter length L of L min,Lmin+S1,…,Lmax respectively to obtain a filtered signal x L (t) corresponding to the filter length L;
(2.3) performing unbiased autocorrelation transformation on each of the filtered signals x L (t) to obtain And interceptThe second half of the data points of the first 2% and the last 10% are removed to obtain the signals/>, after the data points are intercepted
In the step (2.3), the filtered signal x L (t) is subjected to unbiased autocorrelation transformationThe expression of (2) is:
Where τ=q/f s is the delay factor, f s is the sampling frequency of the signal, q=0, 1, …, N-1, N is the length of the signal x L (t), Representing the similarity between the filtered signal x L (t) and the filtered signal x L (t- τ) after a delay τ;
In the step (2.3), the signals after the data points are intercepted The expression of (2) is:
wherein, U 1＝1.02N+1;U2 =1.9n_1; n is a signal Is a length of (2);
(2.4) calculating the result of the step (2.3) Kurtosis value Ku (L);
In the step (2.4), the method obtained in the step (2.3) Calculating the/>, corresponding to different filter lengths L, through a formula (18)Kurtosis value Ku (L):
wherein N 1 is a signal Is a length of (2);
(2.5) determining a large-step optimal L according to the kurtosis value Ku (L), namely a filter length L 1 corresponding to the peak value of the group of Ku (L);
in the step (2.5), the expression of the large-step optimal L is as follows:
O(L)＝arg(L)max{Ku(L)} (19)
wherein O (L) represents an optimal value of the filter length L;
(2.6) setting a new filter length search range to [ L 1-S1,L1+S1 ];
(2.7) filtering the signal S (t) to be analyzed by using a minimum entropy deconvolution filter with the filter length L of L 1-S1,L1-S1+S2,…,L1+S1 respectively to obtain a filtered signal x L (t) corresponding to the filter length L of the group;
(2.8) repeating said step (2.3) -said step (2.4), resulting in a filter length L corresponding to the set Kurtosis value Ku (L);
(2.9) repeating the step (2.5), and determining a small step length optimal L according to the kurtosis value Ku (L), namely, determining the filter length L 2,L2 corresponding to the peak value of the group of Ku (L), namely, the optimal filter length at the moment;
(2.10) filtering the signal S (t) to be analyzed by using a minimum entropy deconvolution filter with a filtering length of L 2 to obtain a final filtered signal
(3) Calculating and mapping the filtered signal obtained in the step (2)Is a envelope spectrum of (2); and carrying out qualitative diagnosis on the health condition of the bearing by checking the characteristic frequency information on the envelope spectrum.
2. The method for adaptively enhancing envelope spectrum of rolling bearing fault diagnosis under strong noise condition according to claim 1, wherein the calculation formula of the envelope spectrum function is:
Wherein V (t) is the calculated envelope spectrum function, s (t) represents the input signal, i.e. the signal of the envelope spectrum to be calculated, and HT represents the Hilbert transform.
3. The method for adaptively enhancing envelope spectrum of rolling bearing fault diagnosis under strong noise condition according to claim 1, wherein the calculation formula of the normalized mutual information value is:
Wherein NMI (X, Z) is a normalized mutual information value between two input signals X, Z, H (·) represents shannon entropy, p (·) represents a probability distribution function, X a、zb is a discrete value in the two input signals X, Z, respectively, and I (X, Z) represents a mutual information value of the two input signals.
4. The method of adaptively enhancing envelope spectrum for fault diagnosis of rolling bearing under strong noise condition according to claim 1, wherein in the step (2.2), the minimum entropy deconvolution filter filters the signal S (t) to be analyzed, specifically comprising:
For an input signal S (t) of the minimum entropy deconvolution filter, x (t) is a filtered signal output by the minimum entropy deconvolution filter;
The minimum entropy deconvolution filter f (t) is modeled as a filter length as an FIR filter with L coefficients according to the filter length L:
the optimal filter coefficients are determined by maximizing the kurtosis of the filtered signal x (t):
wherein O (f) represents the optimal filter coefficient of the minimum entropy deconvolution filter f;
The filtered signal x (t) under the optimal filter coefficient is the filtered signal x L (t) under the filter length L.
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