CN112697477A - EMD equipment fault diagnosis method and system - Google Patents
EMD equipment fault diagnosis method and system Download PDFInfo
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Abstract
The invention discloses an EMD equipment fault diagnosis method and system. The method comprises the steps of decomposing a vibration signal of the equipment by using an EMD algorithm, removing a decomposed noise component and a trend term by using a nonlinear discrimination algorithm, retaining a fractal signal component, interpolating an extreme point by using a Hermite interpolation function, fitting an envelope by using a least square method, separating a frequency modulation part, estimating an instantaneous frequency by using a DQ algorithm, calculating a corresponding instantaneous scale, determining a detrending result of the vibration signal according to an analysis scale, calculating a multi-fractal spectrum of the detrending signal, extracting coordinates of a left end point, a right end point and an extreme point of the multi-fractal spectrum as characteristic parameters of the running state of the equipment to identify the running state of the equipment, and finally deploying the algorithm to an equipment state monitoring system.
Description
Technical Field
The invention relates to the field of equipment state monitoring and fault diagnosis, in particular to an EMD equipment fault diagnosis method and system.
Background
The device vibration signal contains rich fractal features that can describe the operating state of the device. The box dimension, power spectrum analysis and re-standard range method can estimate the single-fractal parameters of stationary signals, and the de-trend fluctuation analysis (DFA) can estimate the single-fractal dimension of non-stationary signals. However, when the device fails, the vibration signal is usually non-stationary and has a multi-fractal characteristic, and the conventional fractal dimension estimation method generates a relatively large error. The multi-fractal detrending fluctuation analysis (MFDF) can estimate multi-fractal parameters of non-stationary signals, but the MFDF method has the problems that the analysis scale needs to be manually determined, the fitting polynomial trend order is difficult to determine, and the data segment is discontinuous. Currently, there is a document that proposes an MFDFA version (MFDFAemd) based on EMD to solve the problem of MFDFA. However, the linear filtering method adopted by mfdfame is easy to destroy the fractal structure of the original signal, and there is a negative frequency phenomenon, and these defects seriously affect the application effect of mfdfame. In summary, in the prior art, it is difficult to accurately extract the multi-fractal features of the device vibration signal, and it is difficult to accurately detect the device operating state.
Disclosure of Invention
The invention provides a fault diagnosis method and system for EMD equipment (the method provided by the invention is abbreviated as MFDFoomd) aiming at the defects. The method provided by the invention is adopted to analyze the equipment vibration signal, can effectively extract the multi-fractal characteristics of the equipment vibration signal, overcomes the problems that the analysis scale of the MFDF method needs to be manually determined, the fitting polynomial trend order is difficult to determine and the data section is discontinuous, solves the phenomena of original signal fractal structure damage and negative frequency existing in the MFDF method, and has the advantages of high accuracy and precision of analysis results, high accuracy of equipment operation state identification results and the like.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: an EMD equipment fault diagnosis method is characterized in that: the method comprises the following steps:
step 1: measuring a device vibration signal x (k) by using an acceleration sensor at a sampling frequency fs, wherein k =1,2, …, N and N are lengths of the sampling signal;
step 2: empirical Mode Decomposition (EMD) is used) The algorithm decomposes the signal x (k) into the sum of n components and a trend term, i.e.
Wherein c isi(k) Representing the i-th component, r, obtained by the EMD algorithmn(k) Represents the trend term resulting from the EMD algorithm, in this example, n = 10;
and step 3: eliminating noise components and trend terms from EMD decomposition results by adopting a nonlinear discrimination algorithm, and reserving components c containing fractal featuresf(k) F =1,2, …, p, p represents the number of residual components after filtering;
and 4, step 4: determination of cf(k) Respectively using Hermite interpolation function to cf(k) The local maximum and local minimum are interpolated, and c is fitted by least square methodf(k) The upper envelope u (k) and the lower envelope l (k), then cf(k) Is defined as
The symbol | x | represents taking the absolute value of x;
and 5: repeatedly executing formula
m times, j =1,2, …, m, until
，
To obtain cf(k) Frequency modulation part FMm(k)，ej(k) Represents cj(k) Envelope of cj(k)=FM(j-1)(k)，c1(k)= cf（k）；
Step 6: FM calculation by Direct integration (DQ)m(k) Is instantaneous angle of, get cf(k) To obtain the instantaneous frequency of cf(k) S of instantaneous dimensionf；
And 7: when the scale is s, the detrending result of the vibration signal x (k) is
；
And 8: will be provided withY s (k) Divided into non-overlappingN s Length of segment beingsDue to data lengthNUsually cannot be removedsSo that a segment of data remains unavailable; in order to fully utilize the length of the data, the data is segmented with the same length from the reverse direction of the data, so that 2 is obtainedN s Segment data;
and step 9: calculate variance of each piece of data:
step 10: calculating a q-th order function:
step 11: changing the value of s, s = sfF =1,2, …, p, repeating the above steps 3 to 10, resulting in a variance function F about q and sq(s);
Step 12: if it is notx(k) Presence of fractal features, thenF q (s) And sizesThere is a power law relationship between:F q (s)~s H q()h (q) represents the generalized Hurst index of x (k);
when in useqWhen the value is not less than 0, the reaction time is not less than 0,H(0) determined by the logarithmic averaging procedure defined by:
step 13: calculating a standard scale index τ (q) = qH (q) -1 for the signal x (k), in this case q is taken in the range (-5, 5);
step 14: calculating the singular index α and the multifractal spectrum f (α) of the signal x (k):
α=H(q)+q H’(q),
f (alpha) = q (alpha-H (q)) +1, wherein H’(q) represents the first derivative of h (q);
step 15: extracting singular indexes corresponding to a left end point, a right end point and an extreme point of the multi-fractal spectrum f (alpha), and describing the running state of the equipment by using the 3 parameters;
step 16: the method in the steps is deployed on a state monitoring device to monitor the state of equipment.
Further, the EMD algorithm in step 2 includes the following steps:
1) the first screening process: finding out upper and lower local extreme points of data x (k), fitting the upper and lower local extreme points by cubic spline curve to obtain local maximum envelope and local minimum envelope of signal x (k), averaging values of corresponding points of the two envelopes to obtain an average curve m1；
Then, the original signal x (k) and the average curve m are obtained1A difference of (i) thath 10=x(k)-m 1Ending the first screening process;
2) the second screening process:h 10re-regarded as the original signal, and the above step 1) is repeated to obtain the signalh 11= h 10-m 11Here parameterm 11Representsh 10Is repeated j times until the mean value of the curve is 0.2<SD<0.3 the screening process is stopped, here
At this time, the process of the present invention,h j1= h j1(-1)-m j1in this case, it can be considered thath j1Is an Intrinsic Mode Function (IMF), and the 1 st IMF is defined asc 1=h j1；
3) Subtracting from the original signalc 1Is obtained byr 1=x(k)-c 1Then will ber 1When new data is taken, the two steps are repeated, and the 2 nd IMF can be obtained;
4) repeating the operation of step 3) to obtain a series of IMFs ifr n Having become a monotonic curve, the screening process stops, and the original signal is finally decomposed into the following form:
。
further, the step 3 nonlinear discrimination algorithm includes the following steps:
1) performing rearrangement operation and substitution operation on signals c (k), and using c as data obtained by rearrangement operationshuf(k) Indicating that data obtained after the substitution operation are csurr(k) Represents;
2) for c (k), cshuf(k) And csurr(k) Performing multi-fractal Detrended Fluctuation Analysis (MFDF) respectively to obtain a generalized Hurst index curve, wherein the generalized Hurst index curve of c (k) is represented by H (q); c. Cshuf(k) Generalized Hurst exponential curve of (1) using Hshuf(q) represents; c. Csurr(k) Generalized Hurst exponential curve of (1) using Hsurr(q) represents;
3) two parameters e are defined1And e2，
Further, the data rearrangement operation in the step 1) comprises the following steps: randomly randomizing the order of the components c (k).
Further, the data replacement operation in the step 1) comprises the following steps:
1) performing a discrete fourier transform on component c (k) to obtain the phase of component c (k);
2) replacing the original phase of component c (k) with a set of pseudo-independent identically distributed numbers located in the (-pi, pi) interval;
3) performing inverse discrete Fourier transform on the frequency domain data subjected to phase substitution to obtain data cIFFT(k) To obtain data cIFFT(k) The real part of (a).
Further, the MFDFA method in step 2) includes the following steps:
1) contour of construction x (k), k =1,2, …, NY(i)：
x (k) represents c (k) or c in step 2) of claim 3shuf(k) Or csurr（k）；
2) Signal profileY(i) Divided into non-overlappingN s Length of segment beingsDue to data lengthNUsually cannot be removedsSo that a segment of data remains unavailable; in order to fully utilize the length of the data, the data is segmented with the same length from the reverse direction of the data, so that 2 is obtainedN s Segment data;
3) fitting a polynomial trend of each section of data by using a least square method, and then calculating the variance of each section of data:
y v (i) Is a first of fittingvTrend of the segment data, if the fitted polynomial trend ismOrder, then note the de-trending process as (MF-) DFAm(ii) a In this example, m = 1;
4) calculate the firstqAverage of the order fluctuation function:
5) if it is notx(k) Presence of self-similar features thenqMean value of order fluctuation functionF q (s) And time scalesThere is a power law relationship between:
F q (s)~s H q()；
when in useqIf =0, the formula in step 4) diverges, at which timeH(0) Determined by the logarithmic averaging procedure defined by:
6) taking logarithm of both sides of the formula in step 5) to obtain ln [ 2 ]F q (s)]=H(q)ln(s)+c ，cIs constant, whereby the slope of the straight line can be obtainedH(q)。
Further, the least square method in the step 4 comprises the following steps: for x (t), t =1,2, …, n, x (t) represents the pair c in step 4f(k) A sequence or pair c generated by interpolating the local maxima off(k) The local minima of the sequence, n represents the length of the interpolated sequence,
1) a set of functions r is selected in advancek(t)，k=1,2,…,m，m<n, constructioning function
f(t)=a1r1(t)+a2r2(t)+…+ amrm(t) in which rk(t) represents a second order polynomial, a third order polynomial, a hyperbolic curve, an exponential curve, a logarithmic curve or a complex function curve;
2) calculating a least squares metric
；
3) Let J pair akPartial derivative of
K =1,2, …, m, when (a)1,a2,…,am)T =(RTR)-1RTX， X=(x(1),x(2),…,x(n)) T，
Wherein R isTRepresenting the transposed matrix of R, R-1An inverse matrix representing R;
4）rk(t) respectively selecting a second-order polynomial, a third-order polynomial, a hyperbolic curve, an exponential curve, a logarithmic curve and a composite function curve for calculation, then comparing least square indexes J generated by various curve forms, and selecting a curve form r corresponding to the minimum J as the curve formk(t) form (a).
Further, the DQ method in step 6 includes the following steps:
1) let cos (phi (t)) = F (t)), then
Phi (t) stands for FMm(k) T =1,2, …, N, f (t) = FMm(k)；
2) Instantaneous angle
Then the instantaneous frequency is
，
Representing the first derivative of phi (t), the instantaneous scale is defined as
。
Based on the EMD equipment fault diagnosis method, the system for realizing the method is characterized in that: the state monitoring system in the step 16 comprises the following parts: the system comprises a data line, an acceleration sensor, a data acquisition card, a case, a notebook computer and signal analysis software, wherein the acceleration sensor is connected with the data acquisition card through the data line, the data acquisition card is installed in the case, the case is connected with the notebook computer through the data line, the signal analysis software is installed on the notebook computer, and the signal analysis software is used for realizing the algorithm.
The method comprises the following steps:
step 1), the following steps: collecting a vibration signal;
step 2), the step of: decomposing an original signal into different component sum forms, wherein some components correspond to noise and trend terms, and some components contain fractal features;
and 3, step 3: removing noise components and trend items in the signal decomposition result by using a nonlinear discrimination algorithm, and only reserving signal components containing fractal features;
4) to 6): separating the frequency modulation part of each fractal signal component, and estimating the instantaneous frequency and the instantaneous scale of each fractal signal component by using DQ;
step 7), the steps of: selecting proper fractal signal components according to the analysis scale, and summing the selected fractal signal components to be used as a signal de-trend result corresponding to the analysis scale;
8) to 14): performing fluctuation analysis on the signal detrending result corresponding to each analysis scale to obtain a multi-fractal spectrum of the original signal;
step 15): extracting the vertical coordinates of the left end point, the right end point and the extreme point of the multi-fractal spectrum, and taking the three parameters as the characteristic parameters of the running state of the equipment;
16) step: deploying the algorithm on an equipment state monitoring system, and monitoring the equipment state;
by adopting the technical scheme, compared with the prior art, the invention has the following advantages:
1) the vibration signal is adaptively decomposed by adopting an EMD method, the noise component and the trend term are removed according to a nonlinear filtering method, the fractal structure of the original signal can be protected, and the damage of the linear filtering method to the fractal structure of the original signal is avoided;
2) the frequency modulation part for separating the signal component estimates the instantaneous frequency of the signal component by using DQ, which can ensure that the instantaneous frequency keeps a positive value and avoid the negative frequency phenomenon;
3) calculating corresponding instantaneous scale according to the instantaneous frequency of the signal component, and performing fluctuation analysis according to the instantaneous scale of the signal component, so that the defect of manually setting the scale is avoided;
4) the EMD method is used for automatically determining the type of the signal trend, the continuity of the signal trend is ensured, and the defects of the prior art are effectively overcome;
5) the accuracy and precision of the analysis result are high, and the accuracy of the identification result of the running state of the equipment is high.
The invention is further illustrated with reference to the following figures and examples.
Drawings
FIG. 1 is a flow chart of the method of the present invention in an embodiment of the present invention;
FIG. 2 is a schematic diagram of an apparatus state monitoring device according to an embodiment of the present invention;
fig. 3 is a multi-fractal simulation signal generated by a multi-fractal cascade model in the embodiment of the present invention;
fig. 4 is an instantaneous frequency of a multi-fractal simulation signal obtained by using the MFDFAemd method in the embodiment of the present invention, where the number of signal components is 10;
fig. 5 is an instantaneous frequency of a multi-fractal simulation signal obtained by using the mfdfoomd method in the embodiment of the present invention, where the number of signal components is 10;
FIG. 6 is a comparison graph of the multi-fractal simulation signal analysis results respectively using MFDF, MFDFEMd and MFDFEMd methods in the embodiment of the present invention;
FIG. 7 is a diagram illustrating the calculation results of two non-linear discriminant parameters, wherein the symbols "circle" and "square" represent e1 and e2, respectively; FIG. 8 is a comparison diagram of analysis results of noisy multi-fractal simulation signals respectively using MFDF, MFDFame, and MFDFAEmd methods in the embodiment of the present invention;
FIG. 9 is a diagram illustrating correlation coefficients between each signal component and an original signal obtained by EMD according to an embodiment of the present invention;
FIG. 10 is a comparison diagram of analysis results of noisy multi-fractal simulation signals respectively using MFDFA, MFDFAEmd based on correlation filtering, and MFDFAEmd based on correlation filtering in the embodiment of the present invention;
FIG. 11 is a vibration signal of five gear boxes in the embodiment of the invention, wherein (a) - (e) respectively represent normal, abrasion, pitting, tooth breakage and abrasion + pitting gear states;
FIG. 12 is a multi-fractal spectrum of the five gearbox vibration signals obtained using MFDFA in an embodiment of the present invention;
FIG. 13 is a multi-fractal spectrum of vibration signals of the five gearboxes obtained by using MFDFame in the embodiment of the present invention;
FIG. 14 is a multi-fractal spectrum of vibration signals of the five gearboxes obtained by using MFDFOAmd in the embodiment of the present invention;
FIG. 15 shows the results of the classification of the left, right and extreme coordinates of the multi-fractal spectrum obtained from MFDFA into the five gear box states in the example of the present invention, where the "circle", "square", "plus", "diamond" and "left triangle" symbols represent the normal, wear, pitting, tooth breakage and wear + pitting gear states, respectively;
FIG. 16 shows the results of the classification of the left, right, and extreme coordinates of the multi-fractal spectrum obtained from MFDFame on the states of the five gearboxes according to the present invention, where the "circle", "square", "plus", "diamond", and "left triangle" symbols represent the normal, wear, pitting, tooth breakage, and wear + pitting gear states, respectively;
fig. 17 shows the classification results of the coordinates of the left end point, the right end point, and the extreme point of the multi-fractal spectrum obtained from MFDFAoemd according to the embodiment of the present invention on the states of the five gearboxes, where the symbols "circle", "square", "plus", "diamond", and "left triangle" represent the normal, worn, pitting, tooth breakage, and worn + pitting gear states, respectively.
Detailed Description
In an embodiment, as shown in fig. 1 and 2, a method for diagnosing faults of an EMD device is characterized in that: the method comprises the following steps:
step 1: measuring a device vibration signal x (k) by using an acceleration sensor at a sampling frequency fs, wherein k =1,2, …, N and N are lengths of the sampling signal;
step 2: the signal x (k) is decomposed into the sum of n components and a trend term, i.e., using an Empirical Mode Decomposition (EMD) algorithm
Wherein c isi(k) Representing the i-th component, r, obtained by the EMD algorithmn(k) Represents the trend term resulting from the EMD algorithm, in this example, n = 10;
and step 3: eliminating noise components and trend terms from EMD decomposition results by adopting a nonlinear discrimination algorithm, and reserving components c containing fractal featuresf(k) F =1,2, …, p, p represents the number of residual components after filtering;
and 4, step 4: determination of cf(k) Respectively using Hermite interpolation function to cf(k) The local maximum and local minimum are interpolated, and c is fitted by least square methodf(k) The upper envelope u (k) and the lower envelope l (k), then cf(k) Is defined as
The symbol | x | represents taking the absolute value of x;
and 5: repeatedly executing formula
m times, j =1,2, …, m, until
，
To obtain cf(k) Frequency modulation part FMm(k)，ej(k) Represents cj(k) Envelope of cj(k)=FM(j-1)(k)，c1(k)= cf（k）；
Step 6: FM calculation by Direct integration (DQ)m(k) Is instantaneous angle of, get cf(k) To obtain the instantaneous frequency of cf(k) S of instantaneous dimensionf；
And 7: when the scale is s, the detrending result of the vibration signal x (k) is
；
And 8: will be provided withY s (k) Divided into non-overlappingN s Length of segment beingsDue to data lengthNUsually cannot be removedsSo that a segment of data remains unavailable; in order to fully utilize the length of the data, the data is segmented with the same length from the reverse direction of the data, so that 2 is obtainedN s Segment data;
and step 9: calculate variance of each piece of data:
step 10: calculating a q-th order function:
step 11: changing the value of s, s = sfF =1,2, …, p, repeating the above steps 3 to 10, resulting in a variance function F about q and sq(s);
Step 12: if it is notx(k) Presence of fractal features, thenF q (s) And sizesThere is a power law relationship between:F q (s)~s H q()h (q) represents the generalized Hurst index of x (k);
when in useqWhen the value is not less than 0, the reaction time is not less than 0,H(0) determined by the logarithmic averaging procedure defined by:
step 13: calculating a standard scale index τ (q) = qH (q) -1 for the signal x (k), in this case q is taken in the range (-5, 5);
step 14: calculating the singular index α and the multifractal spectrum f (α) of the signal x (k):
α=H(q)+q H’(q),
f (alpha) = q (alpha-H (q)) +1, wherein H’(q) represents the first derivative of h (q);
step 15: extracting singular indexes corresponding to a left end point, a right end point and an extreme point of the multi-fractal spectrum f (alpha), and describing the running state of the equipment by using the 3 parameters;
step 16: the method in the steps is deployed on a state monitoring device to monitor the state of equipment.
The EMD algorithm in the step 2 comprises the following steps:
1) the first screening process: finding out upper and lower local extreme points of data x (k), fitting the upper and lower local extreme points by cubic spline curve to obtain local maximum envelope and local minimum envelope of signal x (k), averaging values of corresponding points of the two envelopes to obtain an average curve m1；
Then, the original signal x (k) and the average curve m are obtained1A difference of (i) thath 10=x(k)-m 1Ending the first screening process;
2) the second screening process:h 10re-regarded as the original signal, and the above step 1) is repeated to obtain the signalh 11= h 10-m 11Here parameterm 11Representsh 10Is repeated j times until the mean value of the curve is 0.2<SD<0.3 the screening process is stopped, here
At this time, the process of the present invention,h j1= h j1(-1)-m j1in this case, it can be considered thath j1Is an Intrinsic Mode Function (IMF), and the 1 st IMF is defined asc 1=h j1；
3) Subtracting from the original signalc 1Is obtained byr 1=x(k)-c 1Then will ber 1When new data is taken, the two steps are repeated, and the 2 nd IMF can be obtained;
4) repeating the operation of step 3) to obtain a series of IMFs ifr n Having become a monotonic curve, the screening process stops, and the original signal is finally decomposed into the following form:
。
the step 3 of the nonlinear discriminant algorithm comprises the following steps:
1) performing rearrangement operation and substitution operation on signals c (k), and using c as data obtained by rearrangement operationshuf(k) Indicating that data obtained after the substitution operation are csurr(k) Represents;
2) for c (k), cshuf(k) And csurr(k) Performing multi-fractal Detrended Fluctuation Analysis (MFDF) respectively to obtain a generalized Hurst index curve, wherein the generalized Hurst index curve of c (k) is represented by H (q); c. Cshuf(k) Generalized Hurst exponential curve of (1) using Hshuf(q) represents; c. Csurr(k) Generalized Hurst exponential curve of (1) using Hsurr(q) represents;
3) two parameters e are defined1And e2，
The data rearrangement operation in the step 1) comprises the following steps: randomly randomizing the order of the components c (k).
The data replacement operation in the step 1) comprises the following steps:
1) performing a discrete fourier transform on component c (k) to obtain the phase of component c (k);
2) replacing the original phase of component c (k) with a set of pseudo-independent identically distributed numbers located in the (-pi, pi) interval;
3) performing inverse discrete Fourier transform on the frequency domain data subjected to phase substitution to obtain data cIFFT(k) To obtain data cIFFT(k) The real part of (a).
The MFDF method in the step 2) comprises the following steps:
1) contour of construction x (k), k =1,2, …, NY(i)：
x (k) represents c (k) or c in step 2) of claim 3shuf(k) Or csurr（k）；
2) Signal profileY(i) Divided into non-overlappingN s Length of segment beingsDue to data lengthNUsually cannot be removedsSo that a segment of data remains unavailable; in order to fully utilize the length of the data, the data is segmented with the same length from the reverse direction of the data, so that 2 is obtainedN s Segment data;
3) fitting a polynomial trend of each section of data by using a least square method, and then calculating the variance of each section of data:
y v (i) Is a first of fittingvTrend of the segment data, if the fitted polynomial trend ismOrder, then note the de-trending process as (MF-) DFAm(ii) a In this example, m = 1;
4) calculate the firstqAverage of the order fluctuation function:
5) if it is notx(k) Presence of self-similar features thenqMean value of order fluctuation functionF q (s) And time scalesThere is a power law relationship between:
F q (s)~s H q()；
when in useqIf =0, the formula in step 4) diverges, at which timeH(0) Determined by the logarithmic averaging procedure defined by:
6) taking logarithm of both sides of the formula in step 5) to obtain ln [ 2 ]F q (s)]=H(q)ln(s)+c ，cIs constant, whereby the slope of the straight line can be obtainedH(q)。
The least square method in the step 4 comprises the following steps: for x (t), t =1,2, …, n, x (t) represents the pair c in step 4f(k) A sequence or pair c generated by interpolating the local maxima off(k) The local minima of the sequence, n represents the length of the interpolated sequence,
1) a set of functions r is selected in advancek(t)，k=1,2,…,m，m<n, constructioning function
f(t)=a1r1(t)+a2r2(t)+…+ amrm(t) in which rk(t) represents a second order polynomial, a third order polynomial, a hyperbolic curve, an exponential curve, a logarithmic curve or a complex function curve;
2) calculating a least squares metric
；
3) Let J pair akPartial derivative of
K =1,2, …, m, when (a)1,a2,…,am)T =(RTR)-1RTX， X=(x(1),x(2),…,x(n)) T，
Wherein R isTRepresenting the transposed matrix of R, R-1An inverse matrix representing R;
4）rk(t) respectively selecting a second-order polynomial, a third-order polynomial, a hyperbolic curve, an exponential curve, a logarithmic curve and a composite function curve for calculation, then comparing least square indexes J generated by various curve forms, and selecting the corresponding curve when J is minimumThe line has the form of rk(t) form (a).
The DQ method in step 6 includes the steps of:
1) let cos (phi (t)) = F (t)), then
Phi (t) stands for FMm(k) T =1,2, …, N, f (t) = FMm(k)；
2) Instantaneous angle
Then the instantaneous frequency is
，
Representing the first derivative of phi (t), the instantaneous scale is defined as
。
Based on the above-mentioned fault diagnosis method for the EMD device, the system for implementing the method, the state monitoring system in step 16 includes the following parts: the system comprises a data line, an acceleration sensor, a data acquisition card, a case, a notebook computer and signal analysis software, wherein the acceleration sensor is connected with the data acquisition card through the data line, the data acquisition card is installed in the case, the case is connected with the notebook computer through the data line, the signal analysis software is installed on the notebook computer, and the signal analysis software is used for realizing the algorithm.
Firstly, a multi-fractal cascade model is adopted
The generated multi-fractal simulation signal verifies the performance of the MFDFA, the MFDFAemd and the MFDFAemd. In this example, p =0.375N =14, the resulting multi-fractal simulation signal is shown in fig. 3. The instantaneous frequency of the multi-fractal simulation signal is calculated by using the MFDFAemd, and the result is shown in fig. 4. As can be seen from fig. 4, the instantaneous frequency calculated by mfdfame has many negative frequencies, and the mfdfame analysis result has a large error because the negative frequencies have no physical significance. The instantaneous frequency of the multi-fractal simulation signal is calculated by using the MFDFAoemd, and the result is shown in fig. 5. As can be seen from fig. 5, the instantaneous frequencies calculated by MFDFAoemd are all positive frequencies, so the MFDFAoemd analysis result is in line with the actual situation. Next, a multi-fractal spectrum of the multi-fractal simulation signal is calculated using MFDFA, MFDFAemd, and MFDFAoemd, respectively, and the result is shown in fig. 6. According to the results shown in fig. 6, it can be found through calculation that the average of the absolute errors between the fractal spectrum obtained from MFDFA and the theoretical value is 0.064, the average of the relative errors is 12.21%, the average of the absolute errors between the fractal spectrum obtained from MFDFAemd and the theoretical value is 0.035, the average of the relative errors is 6.57%, the average of the absolute errors between the fractal spectrum obtained from MFDFAemd and the theoretical value is 0.026, and the average of the relative errors is 5.30%, so that the average of the absolute errors between the fractal spectrum obtained from MFDFAemd is 59.38% smaller than the average of the absolute errors between the fractal spectrum obtained from MFDFAemd, the average of the relative errors is 56.59%, the average of the absolute errors between the fractal spectrum obtained from MFDFAemd is 25.71% smaller than the average of the absolute errors between the fractal spectrum obtained from MFDFAemd, and the average of the relative errors is. Fig. 7 shows the calculation results of two non-linear discrimination parameters in the embodiment of the present invention, and it can be seen that all signal components include fractal signal components. Then, a noisy signal with a signal-to-noise ratio of 20dB is constructed by a method of adding white Gaussian noise to the multi-fractal simulation signal. The multi-fractal spectrum of the noise-containing multi-fractal simulation signal was calculated by using MFDFA, MFDFAemd, and MFDFAemd, respectively, and the result is shown in fig. 8. According to the results shown in fig. 8, the multi-fractal spectrum obtained from mfdfaamd completely deviates from the theoretical value, the mean absolute error value of the multi-fractal spectrum obtained from MFDFAemd and the theoretical value is 0.084, the mean relative error value is 11.81%, the mean absolute error value of the multi-fractal spectrum obtained from MFDFAoemd and the theoretical value is 0.037, and the mean relative error value is 5.53%, so that the MFDFAoeThe multi-fractal spectrum obtained by md is reduced by 55.95% compared with the mean absolute error value and 53.18% compared with the multi-fractal spectrum obtained by MFDFAEmd. It follows that MFDFAoemd has better noise immunity than MFDFA and mfdfaeemd. Fig. 9 shows the correlation coefficient between each signal component and the original signal obtained by EMD in the embodiment of the present invention, and it can be seen that the 7 th component has the weakest correlation with the original signal and should be removed from the original signal. Fig. 10 is a comparison diagram of analysis results of a noisy multi-fractal simulation signal by using MFDFA, mfdfame based on correlation filtering, and mfdfame based on correlation filtering, respectively, in the embodiment of the present invention. As can be seen from fig. 10, the analysis result of the noise-containing multi-fractal simulation signal by the mfdfame based on the correlation filtering and the mfdfame based on the correlation filtering completely deviates from the theoretical value, so that the fractal structure of the original signal is easily damaged by the correlation filtering method.
The gearbox vibration data used in the invention is from a gearbox fault simulation experiment table. This experiment simulates three single point gear failures: wear, pitting and tooth breakage, and one compound gear failure: wear + pitting. The collected vibration signals comprise five gear running states of normal, abrasion, pitting corrosion, tooth breakage and abrasion + pitting corrosion. The motor speed was 1500RPM, the vibration signal sampling frequency was 5120Hz, and 5 segments of data with a length of 10000 points were collected at each gear state, and the five gearbox vibration signals are shown in fig. 11. Firstly, the five gearbox vibration signals are analyzed by adopting an MFDF method, and the multi-fractal spectrums corresponding to the five gearbox vibration signals are obtained as shown in figure 12, so that the multi-fractal spectrums corresponding to normal, abrasion, broken tooth and compound fault states are seriously overlapped, and the multi-fractal spectrum corresponding to a pitting state is abnormal in shape. Then, the five gearbox vibration signals are analyzed by using an MFDFame method, and the multi-fractal spectrums corresponding to the five gearbox vibration signals are obtained as shown in FIG. 13, so that the multi-fractal spectrums corresponding to normal, abrasion, broken teeth and compound fault states are seriously overlapped. Finally, the vibration signals of the five gear boxes are analyzed by using an MFDFoomd method, and the multi-fractal spectrums corresponding to the vibration signals of the five gear boxes are obtained as shown in fig. 14, so that the multi-fractal spectrums corresponding to the five gear states can be separated. Singular indexes corresponding to the left end point, the right end point and the extreme point of the multi-fractal spectrum obtained by the MFDF, MFDFAemd and MFDFAemd methods are respectively extracted to classify the states of the five gear boxes, and the results are respectively shown in FIGS. 15-17. As can be seen from fig. 15, the pitting gear states can be correctly distinguished by using the singular indexes corresponding to the left end point, the right end point, and the extreme point of the multi-fractal spectrum obtained by the MFDFA method, but the remaining four gear states cannot be distinguished, so the gear box state recognition rate is 20%. As can be seen from fig. 16, the left end point, the right end point, and the singular index corresponding to the extreme point of the multi-fractal spectrum obtained by the MFDFAemd method can correctly distinguish the states of the pitting gears, but cannot distinguish the remaining four gear states, so the gear box state recognition rate is 20%. As can be seen from fig. 17, the states of the five gears can be correctly distinguished by using the singular indexes corresponding to the left end point, the right end point and the extreme point of the multi-fractal spectrum obtained by the MFDFAoemd method, so that the gear box state recognition rate is 100%. It can be seen that the accuracy of the state identification of the gearbox can be improved by 80% by adopting the MFDFoomed method.
From the test results, it was assumed after analysis that:
1) the vibration signal is adaptively decomposed by adopting an EMD method, the noise component and the trend term are removed according to a nonlinear filtering method, the fractal structure of the original signal can be protected, and the damage of the linear filtering method to the fractal structure of the original signal is avoided;
2) the frequency modulation part for separating the signal component estimates the instantaneous frequency of the signal component by using DQ, which can ensure that the instantaneous frequency keeps a positive value and avoid the negative frequency phenomenon;
3) calculating corresponding instantaneous scale according to the instantaneous frequency of the signal component, and performing fluctuation analysis according to the instantaneous scale of the signal component, so that the defect of manually setting the scale is avoided;
4) the EMD method is used for automatically determining the type of the signal trend, the continuity of the signal trend is ensured, and the defects of the prior art are effectively overcome;
5) the accuracy and precision of the analysis result are high, and the accuracy of the identification result of the running state of the equipment is high.
It should be appreciated by those skilled in the art that the foregoing embodiments are merely exemplary for better understanding of the present invention, and should not be construed as limiting the scope of the present invention as long as the modifications are made according to the technical solution of the present invention.
Claims (9)
1. An EMD equipment fault diagnosis method is characterized in that: the method comprises the following steps:
step 1: measuring a device vibration signal x (k) by using an acceleration sensor at a sampling frequency fs, wherein k =1,2, …, N and N are lengths of the sampling signal;
step 2: the signal x (k) is decomposed into the sum of n components and a trend term, i.e., using an Empirical Mode Decomposition (EMD) algorithm
Wherein c isi(k) Representing the i-th component, r, obtained by the EMD algorithmn(k) Represents a trend term derived from the EMD algorithm;
and step 3: eliminating noise components and trend terms from EMD decomposition results by adopting a nonlinear discrimination algorithm, and reserving components c containing fractal featuresf(k) F =1,2, …, p, p represents the number of residual components after filtering;
and 4, step 4: determination of cf(k) Respectively using Hermite interpolation function to cf(k) The local maximum and local minimum are interpolated, and c is fitted by least square methodf(k) The upper envelope u (k) and the lower envelope l (k), then cf(k) Is defined as
The symbol | x | represents taking the absolute value of x;
and 5: repeatedly executing formula
m times, j =1,2, …, m, until
，
To obtain cf(k) Frequency modulation part FMm(k)，ej(k) Represents cj(k) Envelope of cj(k)=FM(j-1)(k)，c1(k)= cf（k）；
Step 6: FM calculation by Direct integration (DQ)m(k) Is instantaneous angle of, get cf(k) To obtain the instantaneous frequency of cf(k) S of instantaneous dimensionf；
And 7: when the scale is s, the detrending result of the vibration signal x (k) is
；
And 8: will be provided withY s (k) Divided into non-overlappingN s Length of segment beingsDue to data lengthNUsually cannot be removedsSo that a segment of data remains unavailable; in order to fully utilize the length of the data, the data is segmented with the same length from the reverse direction of the data, so that 2 is obtainedN s Segment data;
and step 9: calculate variance of each piece of data:
step 10: calculating a q-th order function:
step 11: changing the value of s, s = sfF =1,2, …, p, repeating the above steps 3 to 10, resulting in a variance function F about q and sq(s);
Step 12: if it is notx(k) Presence of fractal features, thenF q (s) And sizesThere is a power law relationship between:F q (s)~s H q()h (q) represents the generalized Hurst index of x (k);
when in useqWhen the value is not less than 0, the reaction time is not less than 0,H(0) determined by the logarithmic averaging procedure defined by:
step 13: calculating a standard scale index τ (q) = qH (q) -1 for the signal x (k);
step 14: calculating the singular index α and the multifractal spectrum f (α) of the signal x (k):
α=H(q)+q H’(q),
f (alpha) = q (alpha-H (q)) +1, wherein H’(q) represents the first derivative of h (q);
step 15: and extracting singular indexes corresponding to a left end point, a right end point and an extreme point of the multi-fractal spectrum f (alpha), and describing the running state of the equipment by using the 3 parameters.
2. The fault diagnosis method for the EMD equipment according to claim 1, wherein: the EMD algorithm in the step 2 comprises the following steps:
1) the first screening process: finding out upper and lower local extreme points of data x (k), fitting the upper and lower local extreme points by cubic spline curve to obtain local maximum envelope and local minimum envelope of signal x (k), and fitting the corresponding points of the two envelopesIs averaged to obtain an average curve m1；
Then, the original signal x (k) and the average curve m are obtained1A difference of (i) thath 10=x(k)-m 1Ending the first screening process;
2) the second screening process:h 10re-regarded as the original signal, and the above step 1) is repeated to obtain the signalh 11= h 10-m 11Here parameterm 11Representsh 10Is repeated j times until the mean value of the curve is 0.2<SD<0.3 the screening process is stopped, here
At this time, the process of the present invention,h j1= h j1(-1)-m j1in this case, it can be considered thath j1Is an Intrinsic Mode Function (IMF), and the 1 st IMF is defined asc 1=h j1；
3) Subtracting from the original signalc 1Is obtained byr 1=x(k)-c 1Then will ber 1When new data is taken, the two steps are repeated, and the 2 nd IMF can be obtained;
4) repeating the operation of step 3) to obtain a series of IMFs ifr n Having become a monotonic curve, the screening process stops, and the original signal is finally decomposed into the following form:
。
3. the fault diagnosis method for the EMD equipment according to claim 1, wherein: the step 3 of the nonlinear discriminant algorithm comprises the following steps:
1) performing rearrangement operation and substitution operation on the signals c (k), and performing rearrangement operation on the obtained dataBy cshuf(k) Indicating that data obtained after the substitution operation are csurr(k) Represents;
2) for c (k), cshuf(k) And csurr(k) Performing multi-fractal Detrended Fluctuation Analysis (MFDF) respectively to obtain a generalized Hurst index curve, wherein the generalized Hurst index curve of c (k) is represented by H (q); c. Cshuf(k) Generalized Hurst exponential curve of (1) using Hshuf(q) represents; c. Csurr(k) Generalized Hurst exponential curve of (1) using Hsurr(q) represents;
3) two parameters e are defined1And e2，
4. The fault diagnosis method for the EMD equipment according to claim 3, wherein: the data rearrangement operation in the step 1) comprises the following steps: randomly randomizing the order of the components c (k).
5. The fault diagnosis method for the EMD equipment according to claim 3, wherein: the data replacement operation in the step 1) comprises the following steps:
1) performing a discrete fourier transform on component c (k) to obtain the phase of component c (k);
2) replacing the original phase of component c (k) with a set of pseudo-independent identically distributed numbers located in the (-pi, pi) interval;
3) performing inverse discrete Fourier transform on the frequency domain data subjected to phase substitution to obtainData cIFFT(k) To obtain data cIFFT(k) The real part of (a).
6. The fault diagnosis method for the EMD equipment according to claim 3, wherein: the MFDF method in the step 2) comprises the following steps:
1) contour of construction x (k), k =1,2, …, NY(i)：
x (k) represents c (k) or c in step 2) of claim 3shuf(k) Or csurr（k）；
2) Signal profileY(i) Divided into non-overlappingN s Length of segment beingsDue to data lengthNUsually cannot be removedsSo that a segment of data remains unavailable; in order to fully utilize the length of the data, the data is segmented with the same length from the reverse direction of the data, so that 2 is obtainedN s Segment data;
3) fitting a polynomial trend of each section of data by using a least square method, and then calculating the variance of each section of data:
y v (i) Is a first of fittingvTrend of the segment data, if the fitted polynomial trend ismOrder, then note the de-trending process as (MF-) DFAm；
4) Calculate the firstqAverage of the order fluctuation function:
5) if it is notx(k) Presence of self-similar features thenqMean value of order fluctuation functionF q (s) And time scalesThere is a power law relationship between:
F q (s)~s H q()；
when in useqIf =0, the formula in step 4) diverges, at which timeH(0) Determined by the logarithmic averaging procedure defined by:
6) taking logarithm of both sides of the formula in step 5) to obtain ln [ 2 ]F q (s)]=H(q)ln(s)+c ，cIs constant, whereby the slope of the straight line can be obtainedH(q)。
7. The fault diagnosis method for the EMD equipment according to claim 1, wherein: the least square method in the step 4 comprises the following steps: for x (t), t =1,2, …, n, x (t) represents the pair c in step 4f(k) A sequence or pair c generated by interpolating the local maxima off(k) The local minima of the sequence, n represents the length of the interpolated sequence,
1) a set of functions r is selected in advancek(t)，k=1,2,…,m，m<n, constructioning function
f(t)=a1r1(t)+a2r2(t)+…+ amrm(t) in which rk(t) represents a second order polynomial, threeAn order polynomial, hyperbolic, exponential, logarithmic or complex function curve;
2) calculating a least squares metric
；
3) Let J pair akPartial derivative of
K =1,2, …, m, when (a)1,a2,…,am)T =(RTR)-1RTX， X=(x(1),x(2),…,x(n)) T，
Wherein R isTRepresenting the transposed matrix of R, R-1An inverse matrix representing R;
4）rk(t) respectively selecting a second-order polynomial, a third-order polynomial, a hyperbolic curve, an exponential curve, a logarithmic curve and a composite function curve for calculation, then comparing least square indexes J generated by various curve forms, and selecting a curve form r corresponding to the minimum J as the curve formk(t) form (a).
8. The fault diagnosis method for the EMD equipment according to claim 1, wherein: the DQ method in step 6 includes the steps of:
1) let cos (phi (t)) = F (t)), then
Phi (t) stands for FMm(k) T =1,2, …, N, f (t) = FMm(k)；
2) Instantaneous angle
Then the instantaneous frequency is
，
Representing the first derivative of phi (t), the instantaneous scale is defined as
。
9. A system for implementing a fault diagnosis method for an EMD device according to any one of claims 1 to 8, characterized in that: the system comprises the following parts: the system comprises a data line, an acceleration sensor, a data acquisition card, a case, a notebook computer and signal analysis software, wherein the acceleration sensor is connected with the data acquisition card through the data line, the data acquisition card is installed in the case, the case is connected with the notebook computer through the data line, the signal analysis software is installed on the notebook computer, and the signal analysis software is used for realizing the algorithm.
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