CN107228766B - Based on the Fault Diagnosis of Roller Bearings for improving multiple dimensioned fuzzy entropy - Google Patents

Based on the Fault Diagnosis of Roller Bearings for improving multiple dimensioned fuzzy entropy Download PDF

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CN107228766B
CN107228766B CN201710363095.7A CN201710363095A CN107228766B CN 107228766 B CN107228766 B CN 107228766B CN 201710363095 A CN201710363095 A CN 201710363095A CN 107228766 B CN107228766 B CN 107228766B
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fuzzy entropy
entropy
bearing
fault
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CN107228766A (en
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朱可恒
李郝林
陈龙
景璐璐
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University of Shanghai for Science and Technology
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    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00Testing of machine parts
    • G01M13/04Bearings
    • G01M13/045Acoustic or vibration analysis
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    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
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    • G06F18/241Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2411Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on the proximity to a decision surface, e.g. support vector machines
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00Pattern recognition
    • G06F18/20Analysing
    • G06F18/24Classification techniques
    • G06F18/241Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2413Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on distances to training or reference patterns
    • G06F18/24133Distances to prototypes
    • G06F18/24137Distances to cluster centroïds
    • G06F18/2414Smoothing the distance, e.g. radial basis function networks [RBFN]

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Abstract

The present invention relates to a kind of based on the Fault Diagnosis of Roller Bearings for improving multiple dimensioned fuzzy entropy, acquires the vibration signal of rolling bearing;Calculate the multiple dimensioned fuzzy entropy of improvement of vibration signal;Using the improvement fuzzy entropy on the first eight scale as bearing fault characteristics vector;Fault feature vector is divided into training set and test set;Support vector machines is trained using training set and test set is predicted with trained model;The working condition and fault type of rolling bearing are identified according to prediction result.Fuzzy entropy algorithm is improved, the traditional fuzzy entropy replaced with a population mean calculate in local mean value, calculate the improvement fuzzy entropy under different scale.Improved multiple dimensioned fuzzy entropy can more fully reflect the feature of signal, to more accurately assess the operating status of bearing.The present invention can extract bearing state information more abundant, there is higher discrimination during Fault Pattern Recognition.

Description

Based on the Fault Diagnosis of Roller Bearings for improving multiple dimensioned fuzzy entropy
Technical field
It is the present invention relates to a kind of fault diagnosis technology, in particular to a kind of based on the rolling bearing for improving multiple dimensioned fuzzy entropy Method for diagnosing faults.
Background technique
Rolling bearing is one of component crucial in rotating machinery, and operating status often decides the property of entire machine Energy.Therefore, the fault diagnosis of rolling bearing has important meaning.In various Method for Bearing Fault Diagnosis, it is based on vibration signal Diagnosis be one of the most frequently used, most efficient method.And rolling bearing inevitably will receive friction, gap and non-in the process of running The influence of the non-linear factors such as linear rigidity, vibration signal collected often show very strong non-linear, unstable state feature. Therefore, traditional time domain and time-frequency domain signal analysis method based on linear system is difficult accurately to extract the fault signature of bearing Information.With the development of nonlinear kinetics, there are some nonlinear dynamic analysis technologies, for the non-of analysis bearing complexity Linear dynamics behavior provides a kind of selection well.Approximate entropy, Sample Entropy, multi-scale entropy and multiple dimensioned fuzzy entropy among these Deng being all introduced in the fault diagnosis of rolling bearing, and achieve good diagnosis effect.Approximate entropy is multiple to time series A kind of measurement of miscellaneous degree, Sample Entropy are a kind of improvement of pairing approximation entropy, reduce and overcome while dependence sequence length closely Like the shortcomings that entropy itself matching.Fuzzy entropy is that the concept of fuzzy set is introduced into the calculating of Sample Entropy, the dependence to parameter Property is smaller, relative uniformity is stronger and anti-noise ability is more preferable.Multiple dimensioned fuzzy entropy is defined in the fuzzy entropy under different scale, uses Carry out complexity of the measure time sequence under different scale, than the fuzzy entropy of single scale can more fully gauge signal it is complicated Degree.
However, fuzzy entropy has subtracted a local mean value when building calculates required vector, this calculating entropy When have ignored the overall trend of signal.And for the fault diagnosis of rolling bearing, only consider that vibration signal is wrapped comprehensively The feature contained could extract the fault characteristic information that can reflect bearing operating status more fully hereinafter.
Summary of the invention
The present invention be directed to traditional multiple dimensioned fuzzy entropy algorithms to have limitation when extracting bearing state information, A kind of Fault Diagnosis of Roller Bearings based on the multiple dimensioned fuzzy entropy of improvement is proposed, fuzzy entropy algorithm is improved, is used The local mean value in the calculating of traditional fuzzy entropy that one population mean replaces, calculates the improvement fuzzy entropy under different scale.It improves Multiple dimensioned fuzzy entropy afterwards can more fully reflect the feature of signal, to more accurately assess the operating status of bearing.
The technical solution of the present invention is as follows: a kind of based on the Fault Diagnosis of Roller Bearings for improving multiple dimensioned fuzzy entropy, tool Body includes the following steps:
1) vibration signal of rolling bearing, is measured;
2) the multiple dimensioned fuzzy entropy of improvement of bearing vibration signal, is calculated:
Coarse is carried out to the bearing vibration signal that measurement obtains;For limitation present in fuzzy entropy calculating process, Fuzzy entropy algorithm is improved;The improvement fuzzy entropy of coarse grain sequence under different scale factors is calculated, improving fuzzy entropy algorithm point is Utilize population meanInstead of the local mean value u in former fuzzy entropy algorithmic formula0(i), i.e., for a N point time series { u }, (i): 1≤i≤N a m dimensional vector is constructed
Wherein,Indicate that the continuous m u value since i-th point subtracts population mean
3) the improvement fuzzy entropy on the first eight scale, is chosen as bearing fault characteristics vector;
4) obtained bearing fault characteristics, are divided into training sample and test sample;
5), support vector machines is trained using training sample to obtain prediction model;
6), test sample is predicted using obtained prediction model;
7) working condition and fault type of rolling bearing, are identified according to prediction result.
The beneficial effects of the present invention are: the present invention is based on the rolling bearing fault diagnosis sides for improving multiple dimensioned fuzzy entropy Method improves traditional fuzzy entropy algorithm, can extract bearing state information more abundant, have during Fault Pattern Recognition Higher discrimination.
Detailed description of the invention
Fig. 1 is the multi-scale entropy analysis chart of analog signal primal algorithm;
Fig. 2 is the multi-scale entropy analysis chart of analog signal innovatory algorithm of the present invention;
Fig. 3 is that improvement of ten kinds of the present invention different bearing faults on eight different scales obscures entropy diagram;
Fig. 4 is that the present invention is based on the rolling bearing fault diagnosis flow charts for improving multiple dimensioned fuzzy entropy and support vector machines;
Fig. 5 is that the present invention is based on the recognition result figures for improving multiple dimensioned fuzzy entropy and SVM;
Fig. 6 is the recognition result figure based on original multiple dimensioned fuzzy entropy and SVM.
Specific embodiment
The present invention in order to overcome traditional fuzzy entropy to ignore this limitation of the overall trend of signal when calculating, while in order to Efficiency of fault diagnosis is improved, interference of the human factor to diagnostic result is reduced, is provided a kind of based on improved multiple dimensioned fuzzy The Fault Diagnosis of Roller Bearings of entropy and support vector machines specifically uses following technical scheme:
1. improved multi-scale entropy algorithm
1.1 multiple dimensioned fuzzy entropies
Approximate entropy and Sample Entropy are all based on the similitude that Heaviside function (unit-step function) carrys out definition vector , result in traditional two-value classification as a result, and in real world the boundary of class be it is fuzzy, be difficult to directly determine one to Whether mould-fixed fully belongs to certain one kind.Fuzzy entropy introduces the concept of fuzzy set, and utilization index function is as ambiguity function Calculate the similitude of vector.
Fuzzy entropy is defined as follows:
(1) for a N point time series { u (i): 1≤i≤N }, a m dimensional vector is constructed
Wherein,Indicate that the continuous m u value since i-th point subtracts local mean value u0(i),
Wherein
(2) it definesWithThe distance between for both corresponding element maximum difference
(3) it is defined using ambiguity functionWithSimilarityFor
R is similar tolerance, i.e. similarityFor the maximum difference of the two corresponding element and the function of similar tolerance;
(4) to eachIts with it is allSimilarity it is average, be expressed as
(5) defined functionFor
(6) similarly, m+1 is tieed up, repeats above step and obtains
(7) ambiguity in definition entropy is
(8) when N is finite value, (8) formula can be expressed as
FuzzyEn (m, r, N)=ln φm(r)-lnφm+1(r) (9)
The exponential function that fuzzy entropy is initially selected as ambiguity function is
In order to make exponential function have more specific physical significance, formula (10) has carried out following improvement
Fuzzy entropy is calculated using (11) formula herein.
Fuzzy entropy is all the measurement to time sequence complexity on single scale as Sample Entropy, and entropy is bigger, sequence The complexity of column is higher.For complexity and self-similarity of the measure time sequence under different scale, original time sequence is constructed The coarse sequence of column is as follows:
Wherein, τ represents scale factor, 1 < < j < < N/ τ.In fact, as τ=1,As former sequence.To non-zero τ original time series are divided into the coarse grain sequence that τ every segment length are N/ τCalculate the mould of coarse grain sequence under different scale Entropy is pasted, as multiple dimensioned fuzzy entropy analysis.If entropy of the time series on most of scale is all than another sequence Greatly, then representing the former has higher complexity.
1.2 improved multiple dimensioned fuzzy entropies
However, fuzzy entropy has subtracted a mean value when building calculates the vector of similitude, the purpose designed in this way be for The local similarity occurred in of short duration electro-physiological signals can more accurately be described, but this has ignored the overall trend of signal. And for the performance degradation assessment of rolling bearing, the feature that vibration signal is included only is considered comprehensively, it could be more complete Reflect to face the state of bearing operation.Based on analysis above, population mean is utilized when calculating hereinInstead of formula (1) In local mean value u0(i), it is changed to
Wherein,It is defined as follows:
Then fuzzy entropy is calculated with (13) formula, and combines calculating axis with improved fuzzy entropy algorithm and multiscale analysis Vibration signal is held, the multiple dimensioned fuzzy entropy analysis improved.Analog signal and practical bearing fatigue life accelerated test number According to demonstrating the validity and superiority of improved multiple dimensioned fuzzy entropy.
The selection of 1.3 parameters
According to the definition of fuzzy entropy, obscure entropy calculating depend on Embedded dimensions m, similar tolerance r, sequence length N with And the gradient n of ambiguity function.Embedded dimensions m indicates the length of comparison window, and r represents the width of similar tolerance.M value is bigger, weight The development process of construction system is more careful, however big m value needs enough data length (N=10m~30m) or similar appearance It limits sufficiently large.But similar excessive will lead to of tolerance loses many statistical informations, similar tolerance is too small in turn and will increase meter Result is calculated to the sensibility of noise.The value range of general r is 0.1~0.25SD (standard deviation that SD is original series).It is comprehensive Consider, the present invention takes m=2, r=0.2SD, N=2048.Compared with Sample Entropy, the more parameter n of the calculating of fuzzy entropy, It decides the gradient of similar tolerance boundaries.N plays a part of weight during calculating vector similitude, as n > 1, more Ground is included in contribution of the closer vector to its similarity, and is less included in the similarity contribution of farther away vector;As n < 1, Effect is then opposite.Excessive n can lose detailed information, and when n is infinitely great, it is Heaviside function that exponential function, which is degenerated, this When can lose the full details information at edge.Therefore, in order to obtain detailed information more as far as possible, n takes lesser integer value, and such as 2 Or 3 etc., the present invention takes n=2.
2. the analysis of analog signal
Utilize analog signal preliminary identification primal algorithm and resolution capability of the algorithm to different complexity signals after improvement, mould Quasi- signal is made of a logic sequence L, a sinusoidal signal S and a random signal R:
Lj=L+Aj×(S+R)
A indicates that the Amplitude Ration of S and L, L represent the logic sequence produced by following formula in formula:
X (n+1)=ω × x (n) × (1-x (n))
ω is the constant of determining sequence complexity, changes the analog signal of the available different complexities of different A and ω. When taking A1=A2=0.1, ω1=3.7, ω2It is found that it meets such relationship: L to the complexity of induction signal when=3.81<L2。 Fig. 1 is the multi-scale entropy analysis of primal algorithm, calculates the fuzzy entropy of the first eight scale, as seen from the figure, L2On some scales The entropy of (τ=1,2,3,6,7,8) is greater than L1, but at τ=4 and 5, entropy is less than L1, this is carrying out L1And L2Complexity It will cause confusion when analysis.As a comparison, Fig. 2 is the multi-scale entropy analysis of innovatory algorithm, from the figure, it can be seen that L2At 8 Entropy on scale is both greater than L1.Therefore, compared with primal algorithm, improved multiple dimensioned fuzzy entropy has more signal complexity Good separating capacity.
3. case verification
In order to further illustrate the multiple dimensioned fuzzy entropy of improvement in the validity for extracting Rolling Bearing Fault Character, to actual Bearing test data are analyzed.Meanwhile in order to realize the intelligence of fault diagnosis and reduce human factor to fault identification As a result influence establishes the multi-faults classification based on support vector machines to realize the automatic diagnosis of different bearing faults.Branch It holds that vector machine algorithm is simple, and generalization ability is strong, is excellent in small sample classification, is widely used in fault diagnosis field.
3.1 test data
Bearing data center of the test data used herein from U.S.'s Case Western Reserve University, test bearing model SKF 6205-2RS JEM deep groove ball bearing utilizes the different Single Point of Faliure of spark erosion technique arrangement failure size.Bearing Revolving speed is 1797r/min, sample frequency 12kHz, comprising normal condition, inner ring failure, outer ring failure and rolling element failure with And totally 10 kinds of fault types, each data length are 2048 points to different faults size, specific test data set as shown in table 1.
Table 1
3.2 test results and analysis
Vibration data under above-mentioned ten kinds of different Rolling Bearing Status is analyzed using improved multiple dimensioned fuzzy entropy, as a result as schemed Shown in 3.It can be seen from the figure that improvement of the signal on different scale obscures Entropy change trend and fault-signal under normal condition Difference, apparent downward trend is presented with the increase of scale in the entropy of signal under malfunction, and normal signal is with scale Increase first increase and then gradually tend to be steady, the entropy on most of scale is all bigger than fault-signal, illustrates normal condition The complexity of lower signal is higher than fault-signal.This is because when operate normally under health status when, vibration be it is random, do not advise Then, interaction, coupling and the ambient noise between component of machine are mostly come from, therefore, normal signal, which has, to be compared Low self-similarity, high complexity.Relatively, when bearing breaks down, the impact as caused by failure can bring many true Qualitatively impact ingredient reduces its complexity to increase the self-similarity of fault-signal.Though from fig. 3 it can also be seen that Signal under right different faults state has similar variation tendency under different scale, but is different malfunction in different rulers Entropy on degree is of different sizes, illustrates that the complexity of signal under different malfunctions is different, therefore, improved multiple dimensioned mould Paste entropy is the method for a kind of effective reflection and differentiation Rolling Bearing Fault Character.
In order to reduce influence of the human factor to fault identification result, and verify improved multiple dimensioned fuzzy entropy relative to Superiority of the multiple dimensioned fuzzy entropy of primal algorithm when extracting bearing state information, support vector machines are used to realize the axis of rolling Hold the automatic diagnosis of failure.Due to carrying out multicategory classification, the present invention establishes multi-category support vector machines using one-to-one method. Kernel function selects Radial basis kernel function, and optimal punishment parameter and kernel function are found using the method for cross validation and grid search Parameter.It is as shown in Figure 4 using the rolling bearing fault diagnosis step for improving multiple dimensioned fuzzy entropy and support vector machines.It specifically includes Following steps:
Step (1), the vibration signal for measuring rolling bearing;
Step (2), the multiple dimensioned fuzzy entropy of improvement for calculating bearing vibration signal:
Coarse is carried out to the bearing vibration signal that measurement obtains;For limitation present in fuzzy entropy calculating process, Fuzzy entropy algorithm is improved;The improvement fuzzy entropy of coarse grain sequence under different scale factors is calculated, calculates fuzzy entropy using upper State formula (13) and (14);
Step (3) chooses improvement fuzzy entropy on the first eight scale as bearing fault characteristics vector;
Obtained bearing fault characteristics are divided into training sample and test sample by step (4);
Step (5) is trained support vector machines using training sample to obtain prediction model;
Step (6) predicts test sample using obtained prediction model;
Step (7), the working condition and fault type that rolling bearing is identified according to prediction result.
Every kind of state of ten kinds of bearing states chooses 50 groups of data, considers that fault sample hardly results in practice, wherein 10 groups For training, remaining 40 groups are used to test, altogether 500 groups of data.Training sample input support vector machines is trained, with instruction The model prediction test data perfected, all training samples are all correctly validated, the recognition result of test sample such as Fig. 5 institute Show, 400 groups of test samples only have 3 to be divided by mistake, predictablity rate 99.25%.Multi-scale entropy algorithm is improved in order to protrude Superiority calculates the original multi-scale entropy of above-mentioned data, using same step training and establishes SVM prediction mould Then type carries out Classification and Identification to test data.All training samples are all correctly validated, and the recognition result of test sample is shown in Fig. 6,400 groups of test samples one share 14 by mistake point, classification accuracy 96.5%.This comparing result also illustrates improvement Multiple dimensioned fuzzy entropy afterwards can more effectively extract the status information lain in bearing vibration signal than primal algorithm, thus It can more accurately identify different bearing fault states.

Claims (1)

1. a kind of based on the Fault Diagnosis of Roller Bearings for improving multiple dimensioned fuzzy entropy, which is characterized in that specifically include as follows Step:
1) vibration signal of rolling bearing, is measured;
2) the multiple dimensioned fuzzy entropy of improvement of bearing vibration signal, is calculated:
Coarse is carried out to the bearing vibration signal that measurement obtains;For limitation present in fuzzy entropy calculating process, to mould Paste entropy algorithm improves;The improvement fuzzy entropy of coarse grain sequence under different scale factors is calculated, improving fuzzy entropy algorithm point is benefit Use population meanInstead of the local mean value u in former fuzzy entropy algorithmic formula0(i), i.e., for a N point time series { u }, (i): 1≤i≤N a m dimensional vector is constructed
Wherein,Indicate that the continuous m u value since i-th point subtracts population mean
3) the improvement fuzzy entropy on the first eight scale, is chosen as bearing fault characteristics vector;
4) obtained bearing fault characteristics vector, is divided into training sample and test sample;
5), support vector machines is trained using training sample to obtain prediction model;
6), test sample is predicted using obtained prediction model;
7) working condition and fault type of rolling bearing, are identified according to prediction result.
CN201710363095.7A 2017-05-22 2017-05-22 Based on the Fault Diagnosis of Roller Bearings for improving multiple dimensioned fuzzy entropy Expired - Fee Related CN107228766B (en)

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