CN110108489B - Method for acquiring performance degradation trend of rolling bearing - Google Patents
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Abstract
The invention relates to a method for acquiring a performance degradation trend of a rolling bearing, which comprises the steps of firstly acquiring a vibration signal of the rolling bearing, then utilizing an optimal wavelet packet to decompose and extract degradation characteristics of the signal, then fusing all dimensional characteristic vectors to calculate a Mahalanobis distance, and using the Mahalanobis distance as a performance degradation index of the rolling bearing to further acquire the performance degradation trend of the bearing. Compared with the prior art, the method has the advantages of capability of well predicting the performance degradation trend of the bearing, higher precision, obvious prediction effect and the like.
Description
Technical Field
The invention relates to the technical field of rolling bearing performance degradation based on vibration signal analysis, in particular to a rolling bearing performance degradation trend acquisition method.
Background
The rolling bearing is widely applied to industrial departments such as large-scale machinery, production equipment, automobile manufacturing and the like, and the performance degradation of the rolling bearing is a main factor threatening the safety service of the rotary machinery. The rolling bearing is subjected to a series of degradation states from a normal state to a failure, and the current performance degradation trend of the rolling bearing is researched, so that the rolling bearing can be prevented from further degradation and failure. A key technology for researching the performance degradation trend of the rolling bearing is to determine a proper performance degradation index and depict the process of the performance degradation of the bearing.
The vibration analysis analyzes and judges early potential or existing faults by analyzing the characteristics of vibration frequency, vibration amplitude, change of vibration along with time and rotating speed and the like of rotating machinery such as gears, bearings and the like in a transmission system, and has higher accuracy. The traditional FFT spectrum analysis method is based on the stability of the analyzed signal, and has certain limitation in processing the nonlinear and non-stationary vibration signal of the motor rolling bearing.
The wavelet packet decomposition is developed and extended on the basis of the traditional wavelet analysis, and can decompose the signal more finely. Because the method is suitable for the research of actual nonlinear and non-stationary signals, the method is widely applied to the fields of signal denoising, fault diagnosis, trend prediction and the like. However, there are still many problems in the research process, such as: frequency aliasing, determination of the number of wavelet packet decomposition layers, selection of wavelet packet bases, and the like. The selection of wavelet packet basis is a key problem to be solved by wavelet analysis in engineering application, and when the selected wavelet basis functions are different, the effect of extracting the degradation characteristics of the bearing is greatly different. Therefore, when the rolling bearing signals are analyzed by using wavelet packets, it is important to select the optimal wavelet packet basis function. The prior art provides a method for extracting a bearing performance degradation index by combining wavelet packet decomposition with a Gaussian mixture model, and although the bearing degradation trend can be tracked well, the influence of different wavelet basis functions on the degradation trend result is not considered. And when the Gaussian mixture model faces complex bearing data, the interval length of each degradation state is described in an exponential distribution mode, which is often not in accordance with the actual situation, so that the performance degradation trend is not obvious.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for acquiring the performance degradation trend of a rolling bearing.
The purpose of the invention can be realized by the following technical scheme:
a method for acquiring the performance degradation trend of a rolling bearing comprises the following steps:
During bearing degradation, the energy of the vibration signal changes over a frequency band, so the wavelet packet energy can be extracted as a feature vector reflecting the tendency of bearing degradation. The wavelet packet energy is stored in the form of a wavelet packet coefficient, and the expression of the wavelet packet coefficient is as follows:
wj,n(k)＝<x(t),μj,n,k(t)>＝∫x(t)μj,n,k(t)dt
wherein x (t) is a vibration signal; mu.sj,n,k(t) is a wavelet packet function; j is a scale factor; k is a time factor; n is an oscillation factor. When decomposing the signal, the energy of the wavelet packet of the nth node on the jth layer is defined as:
wherein N isjIs the number of wavelet packet coefficients of each node on the jth layer.
When constructing the feature vector, willThe energy of each frequency band on the j layer after j layer decomposition of the bearing signal is 2jThe dimensional feature vector, i.e., the feature vector, is:
and (3) taking the total energy of the signals as E, and carrying out normalization processing on T to obtain a feature vector set T':
preferably, in order to verify the advantage of the preferred wavelet basis function method in the feature extraction of vibration signal analysis, an Approximate Entropy (ApEn) is selected as an evaluation index for measuring the feature extraction effect, because the ApEn can reflect the complexity of a bearing signal, and the larger the Approximate Entropy value obtained by decomposing the same fault signal is, the more obvious the extracted fault feature is.
And 2, selecting the optimal wavelet basis function by utilizing the energy fluctuation change rate.
Considering that the selection of the wavelet basis function has a large influence on the bearing signal feature extraction, the feature extraction part is optimized to obtain the best feature extraction effect.
The vibration signals collected under the bearing health state are decomposed by the wavelet packet, the energy values of all frequency bands are distributed uniformly, and the fluctuation is small. However, once the rolling bearing is out of order, the energy distribution of each frequency band is affected by the change of the signal in the transmission process, and the fluctuation is large. Thereby utilizing the rate of change of energy fluctuation to select the optimal wavelet basis function. First, the percentage of the energy of each frequency band to the overall signal energy is calculated
Wherein n is 1,2, …,2jThen defining an energy fluctuation parameter EfluComprises the following steps:
from the above formula, obtain EfluIs a normalization process, EfluIs taken to be [0, 1 ]]Fluctuates with changes in the signal occurring during transmission. The energy distribution is more uniform in the actual bearing health state, and the energy distribution is unbalanced in the fault state, and the two values may have larger difference. Therefore, in order to make the data in different states have comparability, the energy fluctuation parameter is calculated by the above formula, and the energy fluctuation parameters E corresponding to the vibration signals in the normal state and the fault state of the bearing are respectively calculated according to the above formulanor、EfauAnd then obtaining the energy fluctuation change rate E' between the two through the following formula:
the larger the energy fluctuation change rate E' is, the more the characteristic of the fault signal deviates from the normal signal is shown, and the better the fault characteristic extraction effect is. Maximum energy fluctuation change rate E 'obtained by the method'maxThe corresponding wavelet basis function is the optimal wavelet basis function for decomposing the bearing signal by utilizing the wavelet packet. The optimized optimal wavelet basis function can enable wavelet packet decomposition to have the maximum regularity, and the internal characteristics of bearing vibration signals are mined out, so that a foundation is laid for constructing an effective bearing performance Markov distance degradation index.
Preferably, four wavelet basis functions db3, db8, haar and db4 are selected for the next step of basis function optimization.
And 3, fusing the multi-dimensional characteristic vectors by adopting the Mahalanobis distance to construct an index capable of reflecting the performance degradation process of the bearing, and predicting the state of the bearing.
Considering that the multidimensional feature vectors decomposed and extracted by the optimized wavelet packet method cannot establish a uniform standard, the mahalanobis distance can not be influenced by dimensions, and the scale invariance and the correlation among the features are kept, the invention adopts the mahalanobis distance to fuse the multidimensional feature vectors to construct an index capable of reflecting the performance degradation process of the bearing.
Let Fp×q＝[fab]p×q(a 1,2, …, p, b 1,2, …, q) represents a set of feature vectors for a rolling bearing, where f is the set of feature vectors for the rolling bearingabRepresenting the a-th sample value belonging to the b-th feature; p is the number of samples; q is the number of feature vectors. The mahalanobis distance method is used for eliminating the dimensional relationship among the feature vectors and standardizing the F, and the process is as follows:
wherein m is the number of bearing health sample data; z is a radical ofabIs the data value in F after normalization; assuming C is the normalized covariance matrix, the mahalanobis distance of the feature vector set can be calculated by the following equation:
the performance degradation trend of the rolling bearing is reflected by calculating the MD value of the actual condition, wherein the smaller the MD value (close to 1) indicates that the bearing is closer to the healthy state, and the larger the MD value indicates that the bearing is more biased to the serious fault state.
Compared with the prior art, the invention has the following advantages:
1) on the basis of extracting the energy characteristics of the vibration signals by decomposing the wavelet packet, the Markov distance is used as an index for detecting the degradation process of the bearing to obtain the degradation trend of the bearing, the advantages of the optimized wavelet packet decomposition in the characteristic extraction and the Markov distance in the performance degradation index are fully exerted, the performance degradation trend of the bearing can be well predicted, and the method has high precision and obvious prediction effect;
2) the invention optimizes the wavelet packet decomposition, the optimized optimal wavelet basis function can ensure that the wavelet packet decomposition has the maximum regularity, and the internal characteristics of the bearing vibration signal are mined out, thereby laying a foundation for constructing an effective bearing performance Markov distance degradation index.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of an experimental apparatus and a collection instrument according to an embodiment of the present invention;
fig. 3 is a haar wavelet decomposition energy distribution diagram in an embodiment of the present invention, where fig. 3(a) is a haar wavelet decomposition energy distribution diagram of health data, and fig. 3(b) is a haar wavelet decomposition energy distribution diagram of fault data;
FIG. 4 is a feature set extracted by wavelet packet decomposition according to an embodiment of the present invention;
FIG. 5 is a graph illustrating the result of the Mahalanobis distance degradation indicator of the rolling bearing obtained by the method of the present invention in the embodiment of the present invention;
fig. 6 is a performance index result diagram of wavelet packet decomposition and mahalanobis distance obtained by a conventional empirical method in the embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
As shown in fig. 1, the invention relates to a method for acquiring a performance degradation trend of a rolling bearing, which comprises the following steps:
during bearing degradation, the energy of the vibration signal on a frequency band changes, so that the wavelet packet energy can be extracted as a feature vector reflecting the degradation trend of the bearing.
When decomposing the signal, the energy of the wavelet packet of the nth node on the jth layer is defined as:
wherein N isjIs the number of wavelet packet coefficients of each node on the j-th layer, wj,nIs the wavelet packet coefficient.
When constructing the feature vector, the energy of each frequency band on the j-th layer after j-layer decomposition of the bearing signal is taken as 2jThe dimensional feature vector, i.e., the feature vector, is:
and (3) taking the total energy of the signals as E, and carrying out normalization processing on T to obtain a feature vector set T':
and (II) considering that the selection of the wavelet basis function has great influence on the bearing signal feature extraction, and then optimizing the part to obtain the optimal feature extraction effect.
The vibration signals collected under the bearing health state are decomposed by the wavelet packet, the energy values of all frequency bands are distributed uniformly, and the fluctuation is small. However, once the rolling bearing is out of order, the energy distribution of each frequency band is affected by the change of the signal in the transmission process, and the fluctuation is large. Thereby utilizing the rate of change of energy fluctuation to select the optimal wavelet basis function. First, the percentage of the energy of each frequency band to the overall signal energy is calculated
Wherein n is 1,2, …,2jThen defining an energy fluctuation parameter EfluComprises the following steps:
from the above formula, obtain EfluIs a normalization process, EfluIs taken to be [0, 1 ]]Fluctuates with changes in the signal occurring during transmission. The energy distribution is more uniform in the actual bearing health state, and the energy distribution is unbalanced in the fault state, and the two values may have larger difference. Therefore, in order to make the data in different states have comparability, the energy fluctuation parameter is calculated by the above formula, and the energy fluctuation parameters E corresponding to the vibration signals in the normal state and the fault state of the bearing are respectively calculated according to the above formulanor、EfauAnd then obtaining the energy fluctuation change rate E' between the two through the following formula:
and (III) considering that the multidimensional feature vectors decomposed and extracted by the optimized wavelet packet method cannot establish a uniform standard, the Mahalanobis distance can not be influenced by dimensions, and the scale invariance and the correlation among the features are kept, so that the multidimensional feature vectors are fused by the Mahalanobis distance to construct an index capable of reflecting the performance degradation process of the bearing.
Let Fp×q＝[fab]p×q(a 1,2, …, p, b 1,2, …, q) represents a set of feature vectors for a rolling bearing, where f is the set of feature vectors for the rolling bearingabRepresenting the a-th sample value belonging to the b-th feature; p is the number of samples; q is the number of feature vectors. The mahalanobis distance method is used for eliminating the dimensional relationship among the feature vectors and standardizing the F, and the process is as follows:
wherein the content of the first and second substances,
is the sample mean value of the b-th feature, σbThe variance of the sample of the b-th characteristic is shown, and m is the number of sample data of the bearing health; z is a radical ofabIs the data value in F after normalization; assuming C is the normalized covariance matrix, the mahalanobis distance of the feature vector set can be calculated by the following equation:
the performance degradation trend of the rolling bearing is reflected by calculating the MD value of the actual condition, wherein the smaller the MD value (close to 1) indicates that the bearing is closer to the healthy state, and the larger the MD value indicates that the bearing is more biased to the serious fault state.
In this embodiment, the actual life data SET-2 of the rolling bearing is used to verify the performance degradation trend prediction method provided by the present invention, and the experimental apparatus is shown in fig. 2, and the whole experimental apparatus is provided with 4 double-row roller bearings of type ZA-2115, which are driven by an ac motor and rotate at a constant rotation speed of 2000 r/min. In the experiment, 6000 pounds of radial force is applied to the bearing, a PCB353B33 accelerometer is installed outside each bearing seat, the sampling frequency of the experiment is 20kHz, the sampling interval is 10min, and the sampling length is 20480 points. The bearing was run continuously until failure, and 984 sets of vibration signal data were recorded. In order to eliminate the influence of the bearing break-in period, the first 4 groups of signal data are removed, and the rest 980 groups of signal data are used as monitoring data to carry out experiments.
Based on the determination of the optimal decomposition layer number n of the rolling bearing data to be 3 by an empirical method, four wavelet basis functions of db3, db8, haar and db4 which are commonly used are selected for carrying out the optimization of the next step basis function. The wavelet functions of the db series are close to the measured signal because of the characteristic of the large regular index, while the harr functions are orthogonal wavelets which are both limited support and symmetrical, so that the signals can be accurately reconstructed, the wavelet functions are preferably selected in a wavelet function library, and the two types of wavelet basis functions are also commonly used for comparison in bearing signal characteristic extraction. The preferred algorithm according to the proposed wavelet basis functions, with their respective energy fluctuation parameters and rates of change as shown in table 1.
TABLE 1 energy fluctuation parameters and fluctuation growth rates
Table 1 shows the maximum energy fluctuation change rate E'maxThe corresponding is haar wavelet basis function, so the function is the optimal wavelet basis function of bearing signal decomposition. FIG. 3 shows energy distribution of each node obtained by haar function decomposition, which is consistent with the law that energy distribution is uniform in an actual bearing health state and energy distribution is unbalanced in a fault state, so that the rationality of the decomposition of the optimal wavelet-based haar function of the bearing vibration signal is verified.
The 980 sets of experimental data were decomposed using the preferred wavelet packet to obtain a set of 980 feature vectors, as shown in fig. 4. When the bearing state is good, the fluctuation range of the feature set is small, and the energy fluctuation parameters are stabilized at 0.45 and 0.50. In the process of bearing degradation, the fluctuation of each dimension of feature vector is gradually increased, and when a fault occurs in the later period, the feature value has obvious fluctuation. Therefore, the characteristic set extracted by the optimized wavelet packet method can reflect the process from health to failure of the bearing, and the calculation of the Mahalanobis distance degradation index based on the characteristic set is feasible.
Computing feature set T'980×8The results are shown in FIG. 5. As can be seen, the first 515 samples correspond to the health of the bearing, where the mahalanobis distance change is small. As the bearing gradually moves away from a healthy state, bearing performance begins to degrade, and the mahalanobis distance curve also shows an upward trend. The 800 th to 980 th groups of samples correspond to the process that the bearing is continuously worn, and the Mahalanobis distance continuously reaches a new extreme point in the process. The whole change curve clearly describes the process of gradual degradation to failure of the rolling bearing from the healthy state, andit is sufficient to reflect the early failure of the bearing, so it is reasonable to base the rolling bearing performance degradation indicator on the preferred wavelet packet and mahalanobis distance.
To verify the advantages of the preferred wavelet basis function method in feature extraction for vibration signal analysis. The Approximate Entropy (ApEn) is selected as an evaluation index for measuring the characteristic extraction effect, because ApEn can reflect the complexity of bearing signals, the larger the Approximate Entropy value obtained by decomposing the same fault signal is, the more obvious the extracted fault characteristic is. The approximate entropies of the 8 nodes after 3-layer decomposition of the same fault signal using db3, db8, haar and db4 are shown in table 2.
TABLE 2 approximate entropy values of frequency bands corresponding to four wavelet basis functions
As can be seen from table 2, the approximate entropy values of the frequency bands obtained by the haar decomposition of the preferred wavelet basis functions are all larger than the results of the other wavelet basis functions, wherein the 3 rd, 5 th and 7 th frequency bands are more obvious, and it can be concluded that the preferred wavelet basis functions have the best effect of extracting features and the highest sensitivity to damage.
Then, the accuracy of the method based on the optimized wavelet packet and the Mahalanobis distance as the degradation indexes and the necessity of each link of the whole algorithm are verified, and the method is compared with the performance degradation indexes based on the traditional wavelet packet decomposition (db 3 wavelet basis function determined by an empirical method is subjected to 3-layer decomposition) and the Mahalanobis distance for verification, wherein the performance degradation index curve of the traditional wavelet packet decomposition (db 3 wavelet basis function determined by an empirical method) is shown in FIG. 6. The bearing performance degradation index based on the empirical wavelet packet decomposition and the Mahalanobis distance is noisy, so that the rising trend of the fault is not obvious, the accuracy of trend research is reduced accordingly, and the bearing performance degradation index is not suitable for being used as the performance degradation trend index of the rolling bearing. Therefore, it is important to select a proper wavelet basis function for the vibration signal analysis of the rolling bearing according to practical problems. Based on the performance degradation index obtained by the decomposition of the optimized wavelet basis function, the bearing degradation trend can be well predicted, and the research on the performance degradation trend of the rolling bearing can be accurately carried out.
On the basis of extracting the energy characteristics of the vibration signals by decomposing the wavelet packet, the Mahalanobis distance is used as an index for detecting the degradation process of the bearing to obtain the degradation trend of the bearing, the advantages of the optimized wavelet packet decomposition in the characteristic extraction and the Mahalanobis distance in the performance degradation index are fully exerted, the performance degradation trend of the bearing can be well predicted, and the method has high precision and obvious prediction effect.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and those skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (4)
1. A method for acquiring the performance degradation trend of a rolling bearing is characterized by comprising the following steps:
1) in the bearing degradation period, acquiring a vibration signal of a rolling bearing, and extracting wavelet packet energy as a characteristic vector reflecting the bearing degradation trend;
2) acquiring an energy fluctuation change rate according to the characteristic vector reflecting the bearing degradation trend acquired in the step 1), and selecting an optimal wavelet basis function by using the energy fluctuation change rate;
the energy fluctuation change rate is the change rate between energy fluctuation parameters corresponding to vibration signals under the normal and fault states of the bearing, and the expression is as follows:
in the formula, Enor、EfauEnergy fluctuation parameters corresponding to vibration signals in normal and fault states of the bearing are respectively set;
3) fusing the multi-dimensional feature vectors of the feature vector set of the rolling bearing by adopting the Mahalanobis distance to construct an index reflecting the performance degradation process of the bearing, evaluating the state of the bearing by utilizing the index and finishing the acquisition of the degradation trend;
the concrete content of the step 1) is as follows:
during bearing degradation, wavelet packet energy is extracted as a feature vector reflecting the degradation trend of the bearing, and the expression of wavelet packet coefficients is as follows:
wj,n(k)＝<x(t),μj,n,k(t)>＝∫x(t)μj,n,k(t)dt
in the formula: x (t) is a vibration signal, muj,n,k(t) is a wavelet packet function, j is a scale factor, k is a time factor, n is an oscillation factor, and when a signal is decomposed, the wavelet packet energy of the nth node on the jth layer is defined as:
in the formula: n is a radical ofjThe number of wavelet packet coefficients of each node on the jth layer is shown;
the energy of each frequency band on the j layer after j layer decomposition of the bearing signal is taken as 2jAnd (3) constructing a feature vector according to the following formula:
and (3) taking the total energy of the signals as E, and carrying out normalization processing on T to obtain a feature vector set T':
the step 2) specifically comprises the following steps:
21) calculating the percentage of energy of each frequency band of wavelet packet decomposition to the overall signal energy
Wherein n is 1,2, …,2jDefining energy fluctuationsParameter EfluComprises the following steps:
22) fluctuation parameter E according to energyfluRespectively calculating energy fluctuation parameters E corresponding to vibration signals of the bearing in normal and fault statesnor、EfauAnd obtaining the energy fluctuation change rate E' between the two, wherein the expression is as follows:
the larger the energy fluctuation change rate E ', the more the characteristic of the fault signal deviates from the normal signal, the better the fault feature extraction effect is, and the maximum energy fluctuation change rate E ' obtained by the method 'maxThe corresponding wavelet basis function is the optimal wavelet basis function for decomposing the bearing signal by utilizing the wavelet packet.
2. The method for acquiring the performance degradation trend of the rolling bearing according to claim 1, wherein the specific content in the step 3) is as follows:
let Fp×q＝[fab]p×qIs a set of feature vectors of the rolling bearing, where fabFor the a-th sample value belonging to the b-th feature, a is 1,2, …, p, b is 1,2, …, q, p is the number of samples, q is the number of feature vectors, and F is the pairp×qThe following normalization process was performed:
in the formula, zabTo be standardized Fp×qThe value of the data of (1) is,
is the sample mean value of the b-th feature, σbThe standard deviation of the sample of the b-th characteristic is shown, and m is the number of sample data of the bearing health;
let C be the normalized covariance matrix, then the formula for calculating mahalanobis distance of the feature vector set is:
the performance degradation trend of the rolling bearing is reflected by calculating the MD value of the actual condition, the smaller the MD value is, the closer the bearing is to the healthy state, and the larger the MD value is, the more biased the bearing is to the serious fault state.
3. The method for acquiring the performance degradation trend of the rolling bearing according to claim 1, wherein in the step 22), four wavelet basis functions of db3, db8, haar and db4 are selected for the optimization of the next basis function.
4. The method for acquiring the performance degradation trend of the rolling bearing according to claim 1, wherein ApEn is used as an evaluation index for measuring the feature extraction effect in the step 1).
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