CN113033323A - Gear fault identification method based on filter decomposition combination index - Google Patents
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Abstract
The invention relates to a gear fault identification method based on filter decomposition combination indexes, which comprises the following steps: carrying out a fault simulation experiment on a gear system test platform, and acquiring vibration signals of the gear under different operating conditions; decomposing the acquired vibration signal into a plurality of intrinsic mode function components through adaptive local iterative filter decomposition; calculating the permutation entropy of each intrinsic mode function; distinguishing the arrangement entropies of the first several intrinsic mode functions to represent the characteristics of different fault types by taking the arrangement entropies of the intrinsic mode functions corresponding to the frequency conversion signals of the gear system as boundaries; calculating the average value of the permutation entropies of the N training samples under the same type state as a standard fault mode; and calculating the arrangement entropy of the signal to be detected and the grey correlation degree of the standard fault mode in each state, thereby realizing classification and identification of different faults and being used for fault diagnosis of the gear system. The invention provides a new technical means for identifying different fault types of the gear system.
Description
Technical Field
The invention relates to a diagnosis technology of mechanical faults, in particular to a gear fault identification method based on adaptive local iterative filter decomposition, permutation entropy and grey correlation degree, which is called a gear fault identification method based on filter decomposition combination indexes for short.
Background
The gear box is a main part for motion and power transmission in mechanical equipment, and in gear transmission, equipment halt and even damage can be caused due to machine faults caused by gear failure, so that how to effectively extract gear fault characteristic parameters is a research hotspot of a plurality of scholars. Since Huang et al proposed empirical mode decomposition, the empirical mode decomposition method has attracted much attention from many scholars, spanning from traditional orthogonal basis function expansion to a fully data-driven representation of signals with the ability to adapt to arbitrarily complex signals. However, the empirical mode decomposition method has some problems, such as mode confusion caused by singular points in the signal, instability under noise interference, and the like. Under the inspiration of the idea of empirical mode decomposition, some scholars propose a new adaptive mode decomposition method, and adaptive local iterative filtering is a representative one. The self-adaptive local iterative filtering method effectively avoids the generation of false components in the decomposition process by introducing a Fokker-Planck equation to design a filter on the basis of keeping the idea of an empirical mode decomposition method, and is more suitable for analyzing nonlinear non-stationary signals. If the self-adaptive local iterative filtering method is used for the characteristic extraction of the non-stationary signals of the power system, a better effect is achieved; the method is used for extracting the fault characteristics of the rolling bearing, but in the fault characteristic extraction of the gear system, the research of the self-adaptive local iterative filtering method is less. Research has shown that gear failure signals exhibit typical non-stationarity and non-linearity characteristics. Therefore, how to effectively extract fault characteristics reflecting different working conditions of the gear is extremely important. However, no accurate extraction method is available for people to use at present.
Disclosure of Invention
Aiming at the problems, the invention provides a gear fault identification method based on self-adaptive local iterative filter decomposition, permutation entropy and grey correlation degree, which is called a gear fault identification method based on filter combination indexes for short, so that different fault types of a gear system can be classified and effectively identified, and a new technical means is provided for mechanical fault diagnosis of gear transmission.
The invention provides a gear fault identification method based on filter decomposition combination indexes, which is characterized by comprising the following steps:
(1) carrying out a fault simulation experiment on a gear system test platform, and acquiring vibration signals of the gear under different operating conditions;
(2) decomposing the acquired vibration signal into a plurality of intrinsic mode function components through adaptive local iterative filter decomposition;
(3) calculating the permutation entropy of each intrinsic mode function;
(4) distinguishing the arrangement entropies of the previous plurality of intrinsic mode functions to represent the characteristics of different fault types by taking the arrangement entropies of the intrinsic mode functions corresponding to the frequency conversion signals of the gear system as boundaries;
(5) calculating the average value of the permutation entropies of the N training samples under the same type state as a standard fault mode;
(6) and calculating the gray correlation degree or/and gray similar correlation degree of the permutation entropy of the signal to be detected and the standard fault mode in each state, thereby realizing classification and identification of different faults and being used for fault diagnosis of the gear system.
The adaptive local iterative filtering of the step (2) is a Fokker-Planck equation, and the formula is as follows:
in the formula:α，βthe value range of (A) is between (0,1),
the self-adaptive local iterative filtering algorithm is realized as follows:
(1) initialization: make the number of iterationsi=1, residual signalr 0(t) = x(t)
(2) Extraction ofiAn intrinsic mode function
(2.1) order the number of screeningsj =0, prototype intrinsic mode functionh ij (t) = r i-1(t)，
(2.2) designing an adaptive local Fokker-Planck filterg ij (t,τ) Determining the corresponding time-varying filter lengthl ij (t)，
(2.3) calculating the instantaneous mean:
m ij (t) = 
h ij (t+τ)g ij (t,τ)dτ （2）
(2.4) updating the prototype intrinsic mode function:
h ij (t) = h ij (t) - m ij (t) （3）
(2.5) if prototype intrinsic mode functionh ij (t) If the condition requirement of the intrinsic mode function is satisfied, order theiThe intrinsic mode function:
c i (t) = h ij (t) （4）
otherwise, make the screening timesj = j +1, return step (2.2)
(3) Updating the residual signal:
r i (t)=r i-1(t)-c i (t) （5）
(4) if the residual signalr i (t) When the termination criterion of the algorithm is satisfied, namely at most one extreme point becomes a trend item, the self-adaptive local iterative filter decomposition is terminated, otherwise, the iteration times are enabledi = i+1, return to extractiAn intrinsic mode function.
The arrangement entropy of the intrinsic mode function in the step (3) is calculated according to the following steps:
the sampling sequence is set as follows: [x(n)]=x(1)，x(2)，…，x(N) The sequence permutation entropy calculation step is as follows:
(1) and performing phase space reconstruction on the sampling sequence to obtain:
X(i)=[x(i)，x(i+τ)，…，x(i+(m-1)τ)] (6)
in the formula:mandτrespectively embedding dimension and delay time
(2) To pairX(i) Is/are as followsmThe data are sorted in ascending order to obtain:
x(i+(j 1-1)τ)≤x(i+(j 2-1)τ)≤…≤x(i+(j m -1)τ) (7)
in the formula:j 1，j 2，…，j m is composed ofX(i) Position index of reordered elements
(3) If it isX(i) In which two elements of equal size are present, i.e.
x(i+(j 1-1)τ)=x(i+(j 2-1)τ) (8)
Sorting by the size of the position index value, ifj 1<j 2Then, then
x(i+(j 1-1)τ)<x(i+(j 2-1)τ) (9)
(4) For any reconstructed signalX(i) A set of sequences in ascending order is available:
s(g)=(j 1，j 2，…，j m ) (10)
in the formula:g=1，2，…，kand is andk≤m| A And therefore, the first and second electrodes are,mthe different sequences reconstructed by the dimensional phase space havem| A Arrangement, sequences(g) Is one of the arrangements
(5) Calculating the probability of occurrence of each sequence, i.e.
P i =l/k (11)
In the formula:lis composed ofs(g) Number of occurrences
(6) In the form of Shannon entropy, permutation entropy can be defined as
H p (m, τ)=
(12)
(7) To pairH p (m, τ) Normalization processing can obtain:
H p = H p (m, τ)/In(m!) (13)
as can be seen from the definition of the permutation entropy,H p has a value range of [0,1 ]]The degree of randomness of the signal can be represented by the magnitude of the permutation entropy, and the smaller the permutation entropy, the more regular the signal, and vice versaThe complexity is high, the entropy of the arrangement of the sampled signals can be obtained, and local fine changes of the signals can be detected through the changes of the entropy.
The grey correlation degree of the step (6) is obtained by the following steps:
is provided withX 0={x 0(j)}，j=1，2，…，nIn order to have a sequence of patterns to be recognized,X i ={x i (j)}，i=1，2，…，m；j=1，2，…，nis a reference pattern sequence, thenX 0AndX i the correlation coefficient of (a) is:
γ（x 0(j)，x i (j)）=
in the formulaρIn order to be able to determine the resolution factor,ρ∈（0,1]is generally preferredρ= 0.5. Therefore, it isX 0AndX i degree of association ofγ i Comprises the following steps:
γ i =
(15)
degree of associationγ i Size of (1) reflectsX 0AndX i degree of association of (1), use ofγ i Can identify the failure mode.
The grey similarity correlation degree in the step (6) is obtained according to the following steps:
is provided withX 0=(x 0(1), x 0(2),…,x 0(n) For the sequence of patterns to be recognized),X i =(x i (1), x i (2), …,x i (n)), (x i (k)>0) in order to refer to the pattern sequence,order to
σ i0,=(σ i0,(1), σ i0,(2),…,σ i0,(n))
(i=1,2,…,m;k=1,2,…,n).
Therefore, it isX 0AndX i degree of gray similarity ofγ i Comprises the following steps:
degree of gray similarityγ i Size of (1) reflectsX 0AndX i degree of association of (1), use ofγ i Can identify the failure mode. It can be seen that the gray similarity correlation eliminates the dependence on the resolution coefficient, and can faithfully reflect the similarity degree between the data sequences.
The method comprises the steps of firstly simulating working conditions such as normal, slight tooth surface abrasion, moderate tooth surface abrasion, tooth breakage and the like on a gear box simulation experiment platform, then carrying out self-adaptive decomposition on sampling signals by adopting self-adaptive local iterative filtering, then calculating the arrangement entropy of each intrinsic mode function component obtained by decomposition, and finally carrying out fault identification and classification by calculating the gray correlation degree between a sample to be identified and a standard fault mode. Provides a new and more effective technical means for the field diagnosis of gear faults.
Drawings
FIG. 1 is a block flow diagram of steps performed by the present invention.
FIG. 2 is a waveform diagram of a fault signal adaptive local iterative filter decomposition result of a medium-wear gear.
FIG. 3 is a waveform of the EEMD decomposition result of the medium wear gear fault signal.
Fig. 4 is a waveform diagram of EMD decomposition results of a medium wear gear fault signal.
FIG. 5 is a plot of the array entropy for different operating conditions of the gear system.
In FIGS. 2 to 4, the ordinate of each waveform indicates the amplitude (acceleration a) in m/s2The abscissa is time in seconds.
The ordinate of each graph in fig. 5 is the rank entropy value, and the abscissa is the number of IMFs.
Detailed Description
The implementation process and the beneficial technical effects of the invention are further explained by combining the drawings and the examples.
The adaptive local iterative filter decomposition, permutation entropy, and gray correlation are obtained as described above.
As shown in fig. 1-5. In order to verify the identification effect of the gear fault identification device on the gear fault, four common gear working conditions of normal gear, slight tooth surface abrasion, moderate tooth surface abrasion, broken gear and the like are respectively tested on a gear system test platform. The tested gear has the frequency conversion off r =23.6 Hz, meshing frequency off z =686 Hz, and the sampling frequency of the vibration signal is 16384 Hz. Sampling four gear working conditions respectively, taking 20 samples respectively, and performing adaptive decomposition on a sampling signal by using adaptive local iterative filtering, wherein the signal is subjected to adaptive local iterative filtering decomposition to obtain 8 IMF components and 1 residual component as shown in FIG. 2 by taking a tooth surface moderate wear fault signal as an example.
As can be seen from FIG. 2, the adaptive local iterative filtering decomposes the non-stationary gear fault signal into a plurality of stationary IMF components, and in the IMF8 components, a more obvious periodic component can be seen, and the frequency of the component is calculated to know that the component corresponds to the frequency conversion signal of the gear. For comparison, FIG. 3 shows the result of adaptive decomposition of the same signal using the EEMD method. In the EEMD decomposition, although the modal aliasing is mitigated by adding noise during the decomposition process, the modal aliasing phenomenon is still more significant compared to the adaptive local iterative filter decomposition. Also, the rotational frequency component of the gear is not visible in the decomposition result of the EEMD. The method also fully shows that the self-adaptive iterative filtering can effectively inhibit the modal aliasing phenomenon due to the introduction of the Fokker-Planck equation.
To further highlight the adaptive decomposition capability of the adaptive local iterative filtering, fig. 4 shows the result of EMD decomposing the same signal. Comparing fig. 2, fig. 3, fig. 4, it can be seen that 12 IMF components and 1 residual component are obtained by EMD decomposition, 11 IMF components and 1 residual component are obtained by EEMD decomposition, 8 IMF components and 1 residual component are obtained by adaptive local iterative filter decomposition, from the view of modal aliasing degree of decomposed signals, the EEMD method reduces the degree of modal aliasing to a certain extent by adding white noise in the decomposition process on the basis of EMD decomposition, and in the signal obtained by adaptive local iterative filter decomposition, the modal aliasing degree is effectively improved, which is more beneficial to the improvement of fault characteristics of the gear system.
Now, 10 samples of each state are randomly extracted as training samples, and the permutation entropy of the 8 intrinsic mode functions obtained by decomposing each state is solved according to the fault identification principle steps shown in fig. 1, as shown in fig. 5. The value in the graph is the average value of the permutation entropies of 10 training samples, and it can be seen from the graph that the shapes of the permutation entropies of four working conditions are similar, and because the magnitude of the permutation entropy reflects the random degree of the signal, it can be seen that along with the continuous decomposition of the signal, the components contained in the components tend to be simple, and thus the permutation entropies show a gradually decreasing trend. Since the IMF8 corresponds to the gear rotation frequency, the first 7 IMFs can be considered to contain gear failure information, which indicates that the permutation entropy can effectively represent the change of the gear failure characteristics. The permutation entropies of the first 7 IMF components are taken as fault characteristics, and the permutation entropy curves under four working conditions are similar, so that whether different fault types can be effectively distinguished or not in subsequent fault type classification and identification is critical if a proper identification method is selected.
Randomly extracting 5 samples from the remaining 10 samples obtained by sampling in each state as samples to be detected, and giving the arrangement obtained by calculating the samples to be detected in table 1.
TABLE 1 arrangement entropy under different working conditions of gear system
And finally, calculating the gray correlation degree between the permutation entropy of the sample to be detected and the average value of the permutation entropies of the training samples in all states by using a gray correlation degree method. And carrying out classification and identification on fault modes of the gear system according to the value of the correlation degree, wherein the resolution coefficient is 0.5. The results are shown in Table 2.
TABLE 2 Grey correlation between samples to be tested and Standard failure modes
It can be seen from table 2 that the gray correlation method has an ideal effect on gear system fault pattern recognition, in the arrangement entropy curve chart of fig. 5, the arrangement entropy curve shapes of four working conditions are relatively similar, and four different fault types can be effectively classified and recognized by the gray correlation method, which shows that the gray correlation can accurately classify the small sample fault recognition problem. And the residual fault samples are identified, and the correct classification result can be obtained. However, because the gray correlation degree calculation has the influence of the value of the resolution coefficient, different classification results can be obtained by different resolution coefficients. Table 3 gives the gear-system failure-mode identification results using the grey-likeness correlation.
TABLE 3 Grey similarity correlation between the samples to be tested and the standard failure modes
Comparing tables 2 and 3, it can be seen that although the grey correlation value can also distinguish different gear failure modes, the obtained correlation value is low, and different correlation values can be obtained due to different values of the resolution coefficient. And the method of the similarity correlation degree is adopted, the interference of the resolution coefficient is eliminated, the obtained similarity correlation degree value is obviously higher than the traditional correlation degree value, and the similarity degree of the data sequence can be reflected better.
As can be seen from the above embodiments, the present invention has the following features:
(1) the self-adaptive local iterative filtering is used as a new self-adaptive mode decomposition method, a priori basis function is not required to be constructed, and a single-component signal reflecting the fluctuation nature of the signal can be extracted in a self-adaptive mode according to the local change characteristics of the signal.
(2) The self-adaptive local iterative filtering method can effectively avoid false fluctuation generated in the iterative filtering process by designing a filter as a Fokker-Planck equation, is more beneficial to decomposing the true intrinsic mode component of a signal, and particularly effectively separates a gear frequency conversion signal in the self-adaptive decomposition of a tooth surface moderate abrasion fault signal, which cannot be realized by EEMD and EMD methods.
(3) The permutation entropy is one of the information entropies, has better anti-noise and anti-interference capabilities, and components contained in the components tend to be simple along with the continuous decomposition of the signals, and the permutation entropy shows the trend of gradually reducing. By adopting the gray correlation degree method, different fault types of the gear system are effectively classified and identified, and the arrangement entropy can really represent the characteristics of the different fault types.
Claims (6)
1. A gear fault identification method based on filter decomposition combination indexes is characterized by comprising the following steps:
(1) carrying out a fault simulation experiment on a gear system test platform, and acquiring vibration signals of the gear under different operating conditions;
(2) decomposing the acquired vibration signal into a plurality of intrinsic mode function components through adaptive local iterative filter decomposition;
(3) calculating the permutation entropy of each intrinsic mode function;
(4) distinguishing the arrangement entropy of the previous intrinsic mode function to represent the characteristics of different fault types by taking the arrangement entropy of the intrinsic mode function corresponding to the frequency conversion signal of the gear system as a boundary;
(5) calculating the average value of the permutation entropies of the N training samples under the same type state as a standard fault mode;
(6) and calculating the gray correlation degree or/and gray similar correlation degree of the permutation entropy of the signal to be detected and the standard fault mode in each state, realizing classification and identification of different faults and being used for fault diagnosis of the gear system.
2. The method for identifying the gear fault based on the filter decomposition combination index according to claim 1, wherein the adaptive local iterative filtering in the step (2) is a Fokker-Planck equation, which is as follows:
in the formula:α，βthe value range of (A) is between (0,1),
the self-adaptive local iterative filtering algorithm is realized as follows:
(1) initialization: make the number of iterationsi=1, residual signalr 0(t) = x(t)
(2) Extraction ofiAn intrinsic mode function
(2.1) order the number of screeningsj =0, prototype intrinsic mode functionh ij (t) = r i-1(t)，
(2.2) designing an adaptive local Fokker-Planck filterg ij (t,τ) Determining the corresponding time-varying filter lengthl ij (t)，
(2.3) calculating the instantaneous mean:
m ij (t) = 
h ij (t+τ)g ij (t,τ)dτ （2）
(2.4) updating the prototype intrinsic mode function:
h ij (t) = h ij (t) - m ij (t) （3）
(2.5) if prototype intrinsic mode functionh ij (t) If the condition requirement of the intrinsic mode function is satisfied, order theiThe intrinsic mode function:
c i (t) = h ij (t) （4）
otherwise, make the screening timesj = j +1, return step (2.2)
(3) Updating the residual signal:
r i (t)=r i-1(t)-c i (t) （5）
(4) if the residual signalr i (t) When the termination criterion of the algorithm is satisfied, namely at most one extreme point becomes a trend item, the self-adaptive local iterative filter decomposition is terminated, otherwise, the iteration times are enabledi = i+1, return to extractiAn intrinsic mode function.
3. The gear fault identification method based on the filter decomposition combination index according to claim 1, wherein the arrangement entropy of the intrinsic mode functions in the step (3) is calculated according to the following steps:
the sampling sequence is set as follows: [x(n)]=x(1)，x(2)，…，x(N) The sequence permutation entropy calculation step is as follows:
(1) and performing phase space reconstruction on the sampling sequence to obtain:
X(i)=[x(i)，x(i+τ)，…，x(i+(m-1)τ)] (6)
in the formula:mandτrespectively embedding dimension and delay time
(2) To pairX(i) Is/are as followsmThe data are sorted in ascending order to obtain:
x(i+(j 1-1)τ)≤x(i+(j 2-1)τ)≤…≤x(i+(j m -1)τ) (7)
in the formula:j 1，j 2，…，j m is composed ofX(i) Position index of reordered elements
(3) If it isX(i) In which two elements of equal size are present, i.e.
x(i+(j 1-1)τ)=x(i+(j 2-1)τ) (8)
Sorting by the size of the position index value, ifj 1<j 2Then, then
x(i+(j 1-1)τ)<x(i+(j 2-1)τ) (9)
(4) For any reconstructed signalX(i) A set of sequences in ascending order is available:
s(g)=(j 1，j 2，…，j m ) (10)
in the formula:g=1，2，…，kand is andk≤m| A And therefore, the first and second electrodes are,mreconstructing different sequences in a dimensional phase spaceTotal sum of allm| A Arrangement, sequences(g) Is one of the arrangements
(5) Calculating the probability of occurrence of each sequence, i.e.
P i =l/k (11)
In the formula:lis composed ofs(g) Number of occurrences
(6) In the form of Shannon entropy, permutation entropy can be defined as
H p (m, τ)=
(12)
(7) To pairH p (m, τ) Normalization processing can obtain:
H p = H p (m, τ)/In(m!) (13)。
4. the method for identifying the gear fault based on the filter decomposition combination index as claimed in claim 1, wherein the grey correlation degree in the step (6) is obtained by the following steps:
is provided withX 0={x 0(j)}，j=1，2，…，nIn order to have a sequence of patterns to be recognized,X i ={x i (j)}，i=1，2，…，m；j=1，2，…，nis a reference pattern sequence, thenX 0AndX i the correlation coefficient of (a) is:
γ（x 0(j)，x i (j)）=
in the formulaρIn order to be able to determine the resolution factor,ρ∈（0,1]is generally preferredρNot less than 0.5, thereforeX 0AndX i degree of association ofγ i Comprises the following steps:
γ i =
(15)。
5. the method for identifying the gear fault based on the filter decomposition combination index according to claim 1, wherein the gray similarity correlation degree in the step (6) is obtained by the following steps:
is provided withX 0=(x 0(1), x 0(2),…,x 0(n) For the sequence of patterns to be recognized),X i =(x i (1), x i (2), …,x i (n)), (x i (k)>0) for reference to the pattern sequence, order
σ i0,=(σ i0,(1), σ i0,(2),…,σ i0,(n))
(i=1,2,…,m;k=1,2,…,n).
Therefore, it isX 0AndX i degree of gray similarity ofγ i Comprises the following steps:
6. the method for identifying gear failure based on filter decomposition combination index according to claim 1, wherein the permutation entropy of the pre-identification intrinsic mode function in the step (4) is multiple.
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| CN114187266A (en) * | 2021-12-13 | 2022-03-15 | 江苏鑫丰源机电有限公司 | Tooth surface gluing degree evaluation method based on artificial intelligence |
| CN114896559A (en) * | 2022-04-29 | 2022-08-12 | 盐城工学院 | Self-adaptive noise complete set empirical mode decomposition method based on permutation entropy |
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| CN114187266A (en) * | 2021-12-13 | 2022-03-15 | 江苏鑫丰源机电有限公司 | Tooth surface gluing degree evaluation method based on artificial intelligence |
| CN114896559A (en) * | 2022-04-29 | 2022-08-12 | 盐城工学院 | Self-adaptive noise complete set empirical mode decomposition method based on permutation entropy |
| CN114896559B (en) * | 2022-04-29 | 2023-03-07 | 盐城工学院 | Self-adaptive noise complete set empirical mode decomposition method based on permutation entropy |
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