CN109916628B - Rolling bearing fault diagnosis method based on improved multi-scale amplitude perception permutation entropy - Google Patents
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Abstract
A rolling bearing fault diagnosis method based on improved multi-scale amplitude perception permutation entropy relates to the field of digital signal processing, and aims to solve the problems of poor characteristic extraction separability, low fault identification accuracy and insufficient fault severity analysis of the existing rolling bearing vibration signal fault diagnosis method, and the method comprises the following steps: acquiring rolling bearing vibration signal sample sets of different fault types and different fault degrees; step two; obtaining the optimal PR component for subsequent feature extraction; step three; acquiring fault characteristic vectors of different fault types and different fault degrees; step four; inputting the feature vectors into a random forest classifier; and step five, obtaining the fault type and the fault severity of the rolling bearing. The feature vector extracted by the invention has good separability and stronger fault description capacity, and the average identification accuracy rate reaches 99.25%. The invention can be widely applied to the field of bearing fault diagnosis.
Description
Technical Field
The invention relates to the field of digital signal processing, in particular to a bearing feature extraction method based on improved multi-scale amplitude perception permutation entropy.
Background
The rolling bearing is one of the most common parts in the rotating machinery, but due to the influence of factors such as abrasion, fatigue, corrosion, overload and the like, the rolling bearing is easy to break down in the working process, and the overall performance of mechanical equipment is influenced. Therefore, fault diagnosis and severity analysis of the rolling bearing have important significance for ensuring the operation reliability of mechanical equipment and formulating corresponding maintenance strategies.
The position and severity of the fault of the rolling bearing cause the impact characteristics of the vibration signal to have obvious difference, so that the fault diagnosis technology based on the vibration signal becomes one of the important research directions for monitoring the abnormal state of the rolling bearing at present. The essence of the fault diagnosis of the rolling bearing is a pattern recognition process which mainly comprises feature extraction and fault classification. However, the vibration signal of the rolling bearing has the characteristics of nonlinearity and non-stationarity, and is easily interfered by various external factors in the operation process, so that the signal-to-noise ratio is low, the fault characteristics of the bearing are difficult to effectively extract, and the accuracy of the fault diagnosis result is influenced.
In view of this, the relevant scholars have conducted a great deal of research work on the diagnosis of the rolling bearing failure and have obtained certain research results. The existing literature describes that self-adaptive decomposition of vibration signals of a rolling bearing is realized by using Ensemble Empirical Mode Decomposition (EEMD), an eigenmode function containing main bearing state information is determined by using a kurtosis value and a correlation coefficient method, singular values of the eigenmode function are used as feature vectors, and multi-fault classification of the rolling bearing is realized by using a hypersphere multi-class support vector machine. However, the EEMD cannot completely solve the modal aliasing problem of the EMD, the kurtosis value combined with the eigen-mode function selection method of the correlation coefficient may lose part of bearing fault information, and the selection and optimization of the kernel parameters of the hypersphere multi-class support vector machine are too complex, increasing the difficulty of practical application. In another document, a Local Mean Decomposition (LMD) algorithm is used for preprocessing a vibration signal of a rolling bearing, a multi-scale entropy (MSE) is used for extracting a fault feature vector, and finally a BP neural network classifier is constructed to realize fault type identification. However, in the course of time-series coarse graining, the sequence length after coarse graining is shortened with the increase of scale factor. When the scale factor is large, the multi-scale entropy has instability, thereby affecting the effectiveness of feature extraction. In another document, the method is described that the multi-scale permutation entropy is used for extracting the fault characteristics in the vibration signals of the rolling bearing, the LaplacianScore algorithm is adopted for characteristic selection, and then the fault type recognition is realized through a Support Vector Machine (SVM). However, the feature extraction based on the permutation entropy ignores the influence of the element amplitude in the time series on the entropy value, so that the extracted feature has greater randomness and influences the fault identification accuracy. Therefore, the existing fault diagnosis method based on the vibration signal of the rolling bearing has the problems of low feature extraction separability, low fault identification accuracy, insufficient fault severity analysis and the like.
Disclosure of Invention
The purpose of the invention is: aiming at the problems of poor characteristic extraction separability, low fault identification accuracy, insufficient fault severity analysis and the like of the conventional fault diagnosis method for the vibration signal of the rolling bearing, the fault diagnosis method for the rolling bearing based on the improved multi-scale amplitude perception permutation entropy is provided.
The invention is realized by adopting the following technical scheme: the rolling bearing fault diagnosis method based on the improved multi-scale amplitude perception permutation entropy comprises the following steps:
the method comprises the following steps: acquiring known rolling bearing vibration signals under different fault types and different fault degrees, and forming rolling bearing vibration signal sample sets under different fault types and different fault degrees;
step two; performing inherent time scale decomposition on each vibration signal in the sample set to obtain a series of inherent rotating PR components, and selecting an optimal PR component from the inherent rotating PR components to perform subsequent feature extraction;
step three; extracting the characteristics of rolling bearing vibration signals contained in the optimal PR component under different time scales by using the improved multi-scale amplitude perception permutation entropy to form fault characteristic vectors under different fault types and different fault degrees, wherein the acquisition step of the improved multi-scale amplitude perception permutation entropy is as follows:
step three, firstly: assume that the time series to be analyzed is { x }1,x2,...,xNCreating a new set of coarse-grained time series using an improved coarse-grained process
Wherein the content of the first and second substances,
step three: for each time scale factor τ and embedding dimension d, a separate calculation is made
The amplitude perceptual permutation entropy of each time series in the sequence is defined, and the average value of the amplitude perceptual permutation entropy is defined as the improved multi-scale amplitude perceptual permutation entropy,
wherein AAPE is amplitude perception permutation entropy;
step four; the rolling bearing vibration signal sample set is subjected to feature extraction to form a rolling bearing vibration signal fault feature set, and the feature vector is input into a random forest classifier.
Step five: and inputting the test set into a random forest classifier to obtain the fault type and the fault severity of the rolling bearing of the test set.
The invention has the following beneficial effects: the improved multi-scale amplitude perception permutation entropy fault feature extraction method has good fault severity description capacity, and the extracted feature vectors have good separability;
the coarse graining process in multi-scale analysis is improved by improving the multi-scale amplitude perception permutation entropy, and AAPE values under different time scales are calculated and form feature vectors by utilizing the characteristic that the amplitude perception permutation entropy is sensitive to signal amplitude and frequency change, so that the fault description capability is strong;
the rolling bearing fault diagnosis method for improving the multi-scale amplitude perception permutation entropy and the RF can further analyze the fault severity on the basis of accurately identifying the fault type, and under the condition that the fault severity is relatively complex, the average identification accuracy rate reaches 99.25%.
Drawings
Fig. 1 is a flow chart of fault identification and fault severity analysis.
Fig. 2 is a graph of vibration signatures for rolling bearings of varying severity of failure under 0 load.
Fig. 3 is a graph of vibration signatures for rolling bearings of varying severity of failure under 0 load.
Fig. 4 is a graph of rolling bearing vibration signatures for different severity of failure at 0 load.
FIG. 5 is a graph of improved multi-scale amplitude-aware permutation entropy signature clusters for different fault types under 0 load.
FIG. 6 is a graph of clusters of improved multi-scale amplitude-aware permutation entropy features for different fault severity under 0 load.
Detailed Description
The first embodiment is as follows: the present embodiment will be specifically described below with reference to fig. 1. The rolling bearing fault diagnosis method based on the improved multi-scale amplitude perception permutation entropy comprises the following steps:
the method comprises the following steps: acquiring known rolling bearing vibration signals under different fault types and different fault degrees, and forming rolling bearing vibration signal sample sets under different fault types and different fault degrees;
step two; performing inherent time scale decomposition on each vibration signal in the sample set to obtain a series of inherent rotating PR components, and selecting an optimal PR component from the inherent rotating PR components to perform subsequent feature extraction;
step three; extracting the characteristics of rolling bearing vibration signals contained in the optimal PR component under different time scales by using the improved multi-scale amplitude perception permutation entropy to form fault characteristic vectors under different fault types and different fault degrees, wherein the acquisition step of the improved multi-scale amplitude perception permutation entropy is as follows:
step three, firstly: assume that the time series to be analyzed is { x }1,x2,...,xNCreating a new set of coarse-grained time series using an improved coarse-grained process
Wherein the content of the first and second substances,
j represents yi,1、 y i,21, 2;
step three: for each time scale factor τ and embedding dimension d, a separate calculation is made
The amplitude perceptual permutation entropy of each time series in the sequence is defined, and the average value of the amplitude perceptual permutation entropy is defined as the improved multi-scale amplitude perceptual permutation entropy,
wherein AAPE is amplitude perception permutation entropy;
step four; the rolling bearing vibration signal sample set is subjected to feature extraction to form a rolling bearing vibration signal fault feature set, and the feature vector is input into a random forest classifier.
Step five: and inputting the test set into a random forest classifier to obtain the fault type and the fault severity of the rolling bearing of the test set.
Firstly, the invention extracts the best inherent rotation component of the vibration signal of the rolling bearing by an inherent time scale decomposition (ITD) method, and highlights the characteristics of different fault signals; secondly, by utilizing the characteristic that the improved multi-scale amplitude perception permutation entropy (IMAAPE) is sensitive to the amplitude and frequency change of the fault signal, the amplitude perception permutation entropy under different time scales is calculated to be used as a feature vector, meanwhile, the coarse graining process in multi-scale analysis is improved, and the stability of fault feature extraction is improved; and finally, a random forest multi-classifier is constructed by utilizing the fault feature set, the identification and severity analysis of different fault types of the rolling bearing can be realized through simple parameter selection, and the method has strong generalization capability.
The fault diagnosis method provided by the invention can realize fault identification and fault severity analysis of the inner ring, the outer ring and the balls of the rolling bearing, and the fault identification and fault severity analysis process of the method is shown in figure 1.
The improved coarse granulation process described herein is prior art and is taught by Azami H, approximate multiscale property analysis for biological Signal analysis, Interpretation and application to electronic particle recording [ J ]. biological Signal Processing and Control,2016,23: 28-41.
Example (b):
according to the invention, a rolling bearing fault data set provided by a bearing data center of American western university of storage is selected to carry out experimental verification on the provided fault diagnosis method. In the experiment, an SKF bearing is taken as a research object, a data set collects bearing vibration signals under four states of Normal (NM), inner ring fault (IR), outer ring fault (OR) and ball fault (B) through an acceleration sensor, and the sampling frequency is 12 KHz; and for the three fault types, three different fault severity degrees with the fault diameters of 7mils, 14mils and 21mils are respectively selected for data acquisition. Time domain waveforms of rolling bearing vibration signals of different fault severity under 0 load are shown in fig. 2 and 3, and it can be seen that the variation of the fault type and the fault severity is related to the variation of the amplitude and frequency of the vibration signal. Table 1 shows the composition of the type and severity of failure in the experimental samples, which included a total of 10 different rolling bearing health states. Dividing each bearing data into a plurality of data samples without overlapping, wherein each sample contains N-1024 sampling points, and forming an experimental data set consisting of 50 samples in each health state. Wherein, 10 samples in each health state are used as a training set, and 40 samples are used as a testing set.
Rolling bearing fault feature extraction experiment:
before the rolling bearing fault feature extraction is carried out, inherent time scale decomposition (ITD) is adopted to carry out preprocessing on the vibration signal, and morphological features such as inherent instantaneous amplitude, frequency and the like of the signal are further highlighted. The result of the ITD decomposition of the ball failure at a failure diameter of 7mils is shown in fig. 4, and the ITD decomposes the failure vibration signal into 5 PR components and 1 monotone trend component. From the decomposition results, it can be seen that the optimal PR component with the highest kurtosis value contains the dominant amplitude and frequency characteristics that characterize ball failure.
TABLE 1 Fault types and severity compositions of Experimental samples
Tab.1Compositionoffaulttypesandseverityinexperimentalsamples
After the vibration signal of the rolling bearing is decomposed by ITD, the improved multi-scale amplitude perception permutation entropy (IMAAPE) is adopted for feature extraction. And carrying out IMAAPE feature extraction on the optimal PR component, setting the embedding dimension d to be 4, the time delay l to be 1, the time scale tau to be 20, and adjusting the coefficient A to be 0.5. And carrying out IMAAPE characteristic extraction on the vibration signal samples of the test set to obtain a 20-dimensional rolling bearing vibration signal fault characteristic vector. As shown in fig. 5, which is an imape feature clustering diagram of different fault types under 0 load, it can be seen from the first 3 dimensions of the feature vector that the feature extraction method provided by the present invention can better describe normal, inner ring fault, outer ring fault and ball fault, and the feature vector has strong clustering property. As shown in fig. 6, which is an imape feature clustering chart of different fault severity under 0 load, it can be seen that the first 2 dimensions in the feature vector are selected, and the feature extraction method provided by the present invention also has good clustering performance on the feature extraction results of different fault severity.
TABLE 2 comparison of the Performance of the Rolling bearing Fault feature extraction Algorithm
Tab.2Performancecomparisonofrollingbearingfaultfeatureextractionalgorithm
In order to illustrate the performance of the IMAAPE rolling bearing vibration signal characteristic extraction method, the invention compares the effects of the IMAAPE and the existing rolling bearing fault characteristic extraction method. The experiment was performed using 40 samples each of the inner ring failure, the outer ring failure, and the ball failure under 0 load, and the experimental results are shown in table 2.
Under the condition of different fault types, the larger the average value of the inter-class distance of the feature vector is, the larger the feature difference of different fault types extracted by the feature extraction method is; the smaller the intra-class distance average value of the feature vector under the condition of different fault types is, the smaller the feature difference of the same fault type extracted by the feature extraction method is. As can be seen from table 2, the average inter-class distance of imape is greater than the improved multi-scale permutation entropy (IMPE) and the fine composite multi-scale permutation entropy (RCMPE), but less than the improved multi-scale sample entropy (IMSE), the improved multi-scale fuzzy entropy (IMFE), and the fine composite multi-scale sample entropy (RCMSE), while the average intra-class distance of imape is the smallest among all feature extraction methods. The experimental result shows that the rolling bearing fault characteristics extracted by IMAAPE have better clustering property. In addition, as can be seen from table 2, when the same number of sampling points is calculated, the average time consumption of imape is the smallest among all the feature extraction methods, and the real-time performance is better.
TABLE 3 Rolling bearing Fault feature extraction Algorithm Performance comparison
Tab.3Performancecomparisonofrollingbearingfaultfeatureextractionalgorithm
In order to further explain the separability of the imape fault feature extraction method provided by the invention, the feature extraction method described in table 2 is respectively combined with a random forest classifier, the number of CART decision trees is set to be 50, 40 test samples of each category of 10 rolling bearings in different health states are analyzed, and the experimental results are shown in table 3. Compared with the current different rolling bearing fault feature extraction methods, the IMAAPE fault feature extraction method provided by the invention has better fault severity description capability, and the extracted feature vector has higher separability.
Rolling bearing fault type identification experiment
In order to verify the performance of the bearing fault diagnosis method based on the combination of the improved amplitude perception permutation entropy (IMAAPE) and the Random Forest (RF), the experimental verification is carried out on 40 test samples of each category of 10 rolling bearings in different health states, and the result is shown in Table 4. Therefore, the provided fault diagnosis method for the rolling bearing can effectively identify normal faults, inner ring faults, outer ring faults and ball faults, can effectively analyze the severity of the faults, and is low in false alarm rate, and the average identification accuracy rate is up to 99.25%.
Table 4 shows the identification rate of the rolling bearing failure diagnosis method
Tab.4 Identification rate of the proposed rolling bearing faultdiagnosis method
In order to further explain the performance of the method for diagnosing the fault of the rolling bearing, the method for diagnosing the fault of the rolling bearing is compared with the prior art, and the experimental results are shown in table 5. Therefore, the method provided by the invention can realize the identification of the fault type of the rolling bearing and can further analyze the severity of the fault of the bearing. Under the condition of single fault severity, the fault type can be accurately identified; under the condition that the fault severity is complex, the average fault identification rate is still relatively high.
TABLE 5 comparison of identification rates of different rolling bearing fault diagnosis methods
Tab.5Comparisonofidentificationratesofdifferentfaultdiagnosismethodsforrollingbearings
Conclusion
1) The ITD can stably decompose the rolling bearing fault signal into a group of PR components, wherein the optimal PR component can highlight the main time-frequency characteristic of the rolling bearing fault signal, so that the subsequent fault characteristic extraction is facilitated;
2) IMAAPE improves the coarse graining process in multi-scale analysis, and utilizes the characteristic that amplitude perception permutation entropy is sensitive to signal amplitude and frequency change to calculate AAPE values under different time scales and form a characteristic vector, so that the method has strong fault description capability;
3) the rolling bearing fault diagnosis method based on IMAAPE and RF can further analyze the fault severity on the basis of accurately identifying the fault type, and the average identification accuracy rate reaches 99.25% under the condition that the fault severity is relatively complex.
The method researched by the invention is only suitable for identifying the fault type and analyzing the fault severity degree of the rolling bearing under the fixed load at present. In order to further improve the generalization capability of the rolling bearing fault diagnosis method, the subsequent research focuses on analyzing the fault type and the fault severity of the rolling bearing under the condition of variable load.
The second embodiment is as follows: this embodiment mode is a further description of the first embodiment modeThe difference between this embodiment and the first embodiment is that in the second step, X is settFor a known signal to be analyzed, defining
An operator is extracted for the base line,
can extract XtMiddle base line signal
And obtaining corresponding inherent rotation component
Signal XtIs decomposed into
The inherent time scale decomposition algorithm mainly comprises the following steps:
step two, firstly: let { τ bekK is 1, 2. } denotes the signal XtLocal extreme of, default τ0＝0；
Step two: in the interval [0, τ ]k]In definition of LtAnd HtAnd XtIn the interval t ∈ [0, τ ∈ [ ]k+2]At intervals of consecutive extrema (τ)k,τk+1]Extracted baseline signal L oftExpressed as:
wherein the content of the first and second substances,
wherein alpha is a linear scaling factor used to adjust the amplitude of the extracted intrinsic rotation component, 0< alpha < 1;
step two and step three: according to the formulas (2) and (3), the inherent rotation component HtCan be expressed as:
wherein the content of the first and second substances,
extracting an operator for the inherent rotation, and obtaining an inherent rotation component of 3 bits in a formula;
step two, four: will baseline signal LtRepeating the steps two-three as input signal of next decomposition to obtain a series of PR components, and terminating the decomposition by using the baseline signal LtBecome monotonous or less than a certain preset value;
after decomposition by intrinsic time scale decomposition, the time series XtThe method is characterized by comprising the following steps of decomposing the PR component into a series of PR components and a monotone trend component, wherein the kurtosis value of a signal can effectively describe the pulse characteristic of the signal, the higher the kurtosis value is, the richer the pulse characteristic contained in the signal is, and obtaining the PR component with the maximum kurtosis value as the optimal inherent rotation component, wherein the calculation process is as follows:
wherein, KiDenotes a kurtosis value of the ith PR component, n denotes a time series length, UiSelecting U for the normalized kurtosis value of the ith PR component, wherein m is the number of the PR components, and the best inherent rotation componentiThe PR component corresponding to the maximum value,
is the fourth power sum of all data points in the aforementioned intrinsic rotation (PR) component, i referring to the ith PR component.
The third concrete implementation mode: the embodiment is further described with respect to the first embodiment, and the difference between the first embodiment and the second embodiment is that the improved coarse granulation process in the first step is obtained by:
step three is one: assume a time series of length N { Xi}＝{x1,x2,...,xNThe sequence was coarsely granulated with a scale factor τ of 1, 2.., n, as shown in the following formula,
wherein the content of the first and second substances,
representing a new time sequence obtained after coarse graining when the scale factor is tau;
step three, step two: calculating the sample entropy value of each coarse-grained new time sequence, and obtaining n multi-scale entropy values under different time scales to describe the signal characteristics of the original time sequence;
step three, one step and three steps: the coarse graining process of the multi-scale entropy is improved, and the improved coarse graining time sequence is expressed as
Wherein the content of the first and second substances,
the fourth concrete implementation mode: the present embodiment is a further description of the first specific embodiment, and the difference between the present embodiment and the first specific embodiment is that the step of obtaining the amplitude perceptual arrangement entropy of the time series in the step two is as follows;
step three, step two and step one: let us assume that a given time series x of length N is { x1,x2,...,xNFor each time point t, embedding the signal x into a d-dimensional space to obtain a reconstruction vector,
wherein d and l represent the embedding dimension and time delay, respectively;
step three, step two: per vector
The size of the medium elements is arranged in ascending order, i.e.
wherein, f (pi)i) Representing a statistical arrangement order piiFunction of number of occurrences, each time
The internal elements are arranged in the order of piiWhen, f (pi)i) Then 1 is added, and the definition of the permutation entropy is shown as the following formula,
step three, step two and step three: suppose that
Is 0 for time series
During the process that t is gradually increased from 1 to N-d + 1, every time the arrangement sequence is
When the temperature of the water is higher than the set temperature,
it is necessary to perform the update,
adjusting the weight of the mean value of the signal amplitude and the deviation between the amplitudes, and generally taking 0.5;
step three, step two and step four: for the whole time series
Probability of occurrence
Comprises the following steps:
the magnitude-aware permutation entropy of the time series is expressed as:
the fifth concrete implementation mode: the embodiment is further described with respect to the first embodiment, and the difference between the embodiment and the first embodiment is that the random forest classifier in the fourth step includes the following specific steps: suppose that the random forest classifier consists of multiple decision trees hj(x,Θk) K 1,2,. n }, { ΘkK is 1,2, and n represents random vectors which are independent and distributed identically; training sample set representation for random forest classifier
D＝{(x1,y1),(x2,y2),...,(xN,yN)}，xi＝(xi,1,...,xi,p)TRepresents the ith training sample xiHaving p characteristic values, yiRepresenting a training sample xiCorresponding markSigning; performing Bootstrap sampling on the training sample set D for n times to obtain n Bootstrap sub-samples Dj(j ═ 1,2, …, n); for each subsample DjBuilding a decision tree model hj(x) (generally, CART decision tree is selected) to finally obtain a set of decision trees h1(x),h2(x),…,hk(x) A decision tree classifier; for a new test sample, voting through n decision trees to obtain the category with the most votes as the final category of the test sample, wherein the classification decision is as follows:
wherein h isj(x) Representing the jth decision tree, and I (-) is an indicative function, namely, when the value of the number in the set is 1, otherwise, the value is 0; y denotes a category label yiThe target variable of the composition.
The sixth specific implementation mode: this embodiment mode is a further description of embodiment mode two, and differs from embodiment mode two in that α in step two is 0.5.
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.
Claims (6)
1. The rolling bearing fault diagnosis method based on the improved multi-scale amplitude perception permutation entropy is characterized by comprising the following steps of:
the method comprises the following steps: acquiring known rolling bearing vibration signals under different fault types and different fault degrees, and forming rolling bearing vibration signal sample sets under different fault types and different fault degrees;
step two; performing inherent time scale decomposition on each vibration signal in the sample set to obtain a series of inherent rotating PR components, and selecting an optimal PR component from the inherent rotating PR components to perform subsequent feature extraction;
step three; extracting the characteristics of rolling bearing vibration signals contained in the optimal PR component under different time scales by using the improved multi-scale amplitude perception permutation entropy to form characteristic sets under different fault types and different fault degrees, wherein the acquisition step of the improved multi-scale amplitude perception permutation entropy is as follows:
step three, firstly: assume that the time series to be analyzed is { x }1,x2,...,xNCreating a new set of coarse-grained time series using an improved coarse-grained process
Wherein the content of the first and second substances,
τ＝1,2，...，n；
step three: for each time scale factor τ and embedding dimension d, a separate calculation is made
(i ═ 1,2, …, τ) and defining its average as the improved multi-scale magnitude-aware permutation entropy,
wherein AAPE is amplitude perception permutation entropy;
step four; the method comprises the steps that a rolling bearing vibration signal sample set is subjected to feature extraction to form a rolling bearing vibration signal fault feature set, and the feature set is input into a random forest classifier;
step five: and inputting the test set into a random forest classifier to obtain the fault type and the fault severity of the rolling bearing of the test set.
2. The rolling bearing fault diagnosis method based on the improved multi-scale amplitude perception arrangement entropy as claimed in claim 1, characterized in that: in the second step, X is settIs a known standbyDefinition of the signal analyzed
An operator is extracted for the base line,
can extract XtMiddle base line signal
And obtaining corresponding inherent rotation component
Signal XtIs decomposed into
The inherent time scale decomposition algorithm mainly comprises the following steps:
step two, firstly: let { τ bekK is 1, 2. } denotes the signal XtLocal extreme of, default τ0＝0；
Step two: in the interval [0, τ ]k]In definition of LtAnd HtAnd XtWhere t is [0, τ ]k+2]At intervals of consecutive extrema (τ)k,τk+1]Extracted baseline signal L oftExpressed as:
wherein the content of the first and second substances,
wherein alpha is a linear scaling factor used to adjust the amplitude of the extracted intrinsic rotation component, 0< alpha < 1;
step two and step three: according to the formulas (2) and (3), the inherent rotation component HtCan be expressed as:
wherein the content of the first and second substances,
extracting an operator for the inherent rotation;
step two, four: will baseline signal LtRepeating the steps two-three as input signal of next decomposition to obtain a series of PR components, and terminating the decomposition by using the baseline signal LtBecome monotonous or less than a certain preset value;
after decomposition by intrinsic time scale decomposition, the time series XtThe method is characterized by comprising the following steps of decomposing the PR component into a series of PR components and a monotone trend component, wherein the kurtosis value of a signal can effectively describe the pulse characteristic of the signal, the higher the kurtosis value is, the richer the pulse characteristic contained in the signal is, and obtaining the PR component with the maximum kurtosis value as the optimal inherent rotation component, wherein the calculation process is as follows:
wherein, KiDenotes a kurtosis value of the ith PR component, n denotes a time series length, UiSelecting U for the normalized kurtosis value of the ith PR component, wherein m is the number of the PR components, and the best inherent rotation componentiThe PR component corresponding to the maximum value.
3. The rolling bearing fault diagnosis method based on the improved multi-scale amplitude perception arrangement entropy as claimed in claim 1, wherein the improved coarse graining process in the first step is obtained by the following steps:
step three is one: assume a time series of length N { Xi}＝{x1,x2,...,xNThe sequence was coarsely granulated with a scale factor τ of 1, 2.., n, as shown in the following formula,
wherein the content of the first and second substances,
representing a new time sequence obtained after coarse graining when the scale factor is tau;
step three, step two: calculating the sample entropy value of each coarse-grained new time sequence, and obtaining n multi-scale entropy values under different time scales to describe the signal characteristics of the original time sequence;
step three, one step and three steps: the coarse graining process of the multi-scale entropy is improved, and the improved coarse graining time sequence is expressed as
Wherein the content of the first and second substances,
4. the rolling bearing fault diagnosis method based on the improved multi-scale amplitude perception arrangement entropy of claim 1, wherein the time-series amplitude perception arrangement entropy in the third step is obtained by the following steps;
step three, step two and step one: suppose a given time series X of length N ═ X1,x2,...,xNFor each time point t, embedding the signal x into a d-dimensional space to obtain a reconstruction vector,
1, 2., N- (d-1) l wherein d and l represent the embedding dimension and time delay, respectively;
step threeII, secondly: per vector
The size of the medium elements is arranged in ascending order, i.e.
wherein, f (pi)i) Representing a statistical arrangement order piiFunction of number of occurrences, each time
The internal elements are arranged in the order of piiWhen, f (pi)i) Then 1 is added, and the definition of the permutation entropy is shown as the following formula,
step three, step two and step three: suppose thatIs 0 for time series
During the process that t is gradually increased from 1 to N-d +1, every time the arrangement sequence is
When the temperature of the water is higher than the set temperature,
it is necessary to perform the update,
adjusting the weight of the mean value of the signal amplitude and the deviation between the amplitudes, and taking 0.5;
step three, step two and step four: for the whole time series
Probability of occurrence
Comprises the following steps:
the magnitude-aware permutation entropy of the time series is expressed as:
a is the adjustment coefficient.
5. The rolling bearing fault diagnosis method based on the improved multi-scale amplitude perception permutation entropy as claimed in claim 1, wherein the random forest classifier in the fourth step comprises the following specific steps: suppose that the random forest classifier consists of multiple decision trees hj(x,Θk) K 1,2,. n }, { ΘkK is 1,2, and n represents random vectors which are independent and distributed identically; training sample set representation D { (x) for random forest classifier1,y1),(x2,y2),...,(xN,yN)}，xi＝(xi,1,...,xi,p)TRepresents the ith training sample xiHaving p characteristic values, yiRepresenting a training sample xiA corresponding label; performing Bootstrap sampling on the training sample set D for n times to obtain n Bootstrap sub-samples DjJ is 1,2, …, n; for each subsample DjBuilding a decision tree model hj(x) Finally, a decision tree consisting of a set of decision trees { h }is obtained1(x),h2(x),…,hk(x) A decision tree classifier; for a new test sample, voting through n decision trees to obtain the category with the most votes as the final category of the test sample, wherein the classification decision is as follows:
wherein h isj(x) Representing the jth decision tree, and I (-) is an indicative function, namely, when the value of the number in the set is 1, otherwise, the value is 0; y denotes a category label yiThe target variable of the composition.
6. The rolling bearing fault diagnosis method based on the improved multiscale amplitude perception permutation entropy of claim 2, wherein α is 0.5 in the second step.
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