CN112697470A - SSD device fault diagnosis method and system - Google Patents
SSD device fault diagnosis method and system Download PDFInfo
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Abstract
The invention discloses a SSD equipment fault diagnosis method and system, which decomposes equipment vibration signals by using an SSD algorithm, removes noise components and trend terms by using a nonlinear discrimination algorithm, reserves fractal signal components, interpolates extreme points by using a Lagrange interpolation function, fits envelopes by using a least square method, separates a frequency modulation part, estimates instantaneous frequency by using a DQ algorithm and calculates corresponding instantaneous scale, determining a vibration signal detrending result according to the analysis scale, calculating a multi-fractal spectrum of a 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, identifying the running state of the equipment, deploying the algorithm to an equipment state monitoring system, and being capable of accurately distinguishing the running state of the equipment.
Description
Technical Field
The invention relates to the field of equipment state monitoring and fault diagnosis, in particular to a method and a system for diagnosing a fault of SSD (solid state drive) equipment.
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 method and a system for diagnosing the fault of the SSD device (the method is abbreviated as MFDFOSsd) 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: a SSD device fault diagnosis method is characterized by comprising the following steps: 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 Singular Spectrum Decomposition (SSD) algorithm is adopted to solve the problemThe number x (k) is decomposed into the sum of n components and a trend term, i.e.
Wherein c isi(k) Representing the i-th component, r, derived by the SSD algorithmn(k) Represents the trend term derived from the SSD algorithm, in this example, n = 10; SSD algorithms are well known, see literature
P. Bonizzi, J.M. KAREL, O. Meste, R.L. Peeters, Singular spectrum decomposition: A new method for time series decomposition, Advances in Adaptive Data Analysis, 2014，6 (4) : 1-29；
And step 3: noise components and trend items are eliminated from the SSD decomposition result by adopting a nonlinear discrimination algorithm, and components c containing fractal features are reservedf(k) F =1,2, …, p, p represents the number of residual components after filtering;
and 4, step 4: determination of cf(k) The local maximum value and the local minimum value of c are respectively compared with c by adopting Lagrange interpolation functionf(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) In the momentAngle of time, 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 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 2shuf(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 SSD 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: the algorithm is deployed on an equipment state monitoring system to monitor 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 SSD (solid State disk) method, the noise component and the trend item 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 SSD 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 mfdfoosd 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 MFDFOSsd 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 MFDFoosd 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, mfdfame based on correlation filtering, and mfdfoss 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 using MFDFoossd in an 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 results of classifying the states of the five gearboxes by the coordinates of the left end point, the right end point and the extreme point of the multi-fractal spectrum obtained from mfdfoosd according to the embodiment of the present invention, and the symbols "circle", "square", "plus", "diamond" and "left triangle" represent the normal, worn, pitting, broken tooth and worn + pitting gear states, respectively.
Detailed Description
An embodiment, as shown in fig. 1 and fig. 2, is a method for diagnosing a failure of an SSD device, wherein: 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. into the sum of n components using a Singular Spectral Decomposition (SSD) algorithm
Wherein c isi(k) Representing the i-th component, r, derived by the SSD algorithmn(k) Represents the trend term derived from the SSD algorithm, in this example, n = 10; SSD algorithms are well known, see literature
P. Bonizzi, J.M. KAREL, O. Meste, R.L. Peeters, Singular spectrum decomposition: A new method for time series decomposition, Advances in Adaptive Data Analysis, 2014，6 (4) : 1-29；
And step 3: noise components and trend items are eliminated from the SSD decomposition result by adopting a nonlinear discrimination algorithm, and components c containing fractal features are reservedf(k) F =1,2, …, p, p represents the number of residual components after filtering;
and 4, step 4: determination of cf(k) The local maximum value and the local minimum value of c are respectively compared with c by adopting Lagrange interpolation functionf(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 step 3 of the nonlinear discriminant algorithm comprises the following steps:
1) for signal c (k)Performing a rearrangement operation and a substitution operation, the data obtained by the rearrangement operation being used as 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，
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 2shuf(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 a curve form r corresponding to the minimum J as the curve formk(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 SSD device failure diagnosis method, the system 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 MFDFA, MFDFAemd and MFDFOAssd. In this example, p =0.375 and n =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 was calculated using mfdfoosd, and the result is shown in fig. 5. As can be seen from fig. 5, the instantaneous frequencies calculated from the mfdfoossd are all positive frequencies, and therefore the mfdfoossd 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 MFDFAossd, respectively, and the result is shown in fig. 6. As shown in fig. 6, it can be found through calculation that the average of the absolute errors between the multi-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 multi-fractal spectrum obtained from mfdfaamd and the theoretical value is 0.035, the average of the relative errors is 6.57%, the average of the absolute errors between the multi-fractal spectrum obtained from mfdfaosd and the theoretical value is 0.023, and the average of the relative errors is 5.34%, so that the average of the absolute errors between the multi-fractal spectrum obtained from mfdfaosd is 64.06% smaller than that obtained from MFDFA, the average of the relative errors is 56.27%, the average of the absolute errors between the multi-fractal spectrum obtained from mfdfaosd is 34.29% smaller than that obtained from mfdfaamd, and the average of the relative errors is 18.72%. 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. Is divided intoThe multi-fractal spectrum of the noise-containing multi-fractal simulation signal was calculated by using MFDFA, MFDFAemd, and MFDFAossd, respectively, and the results are 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 mfdfaamd from 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 mfdfaosd from the theoretical value is 0.030, and the mean relative error value is 5.57%, so that the mean absolute error value of the multi-fractal spectrum obtained from mfdfaosd is 64.29% smaller, and the mean relative error value is 52.84% smaller. It follows that mfdfoossd has better noise immunity than MFDFA and MFDFAemd. 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 noisy multi-fractal simulation signals by using MFDFA, mfdfame based on correlation filtering, and mfdfoss 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 MFDFAossd 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.
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 MFDFoosd 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 a left end point, a right end point and an extreme point of a multi-fractal spectrum obtained by the MFDF, MFDFEMd and MFDFOSsd 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 five 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 mfdfoosd method, and therefore the gear box state recognition rate is 100%. It can be seen that the MFDFoosd method can improve the accuracy of the state identification of the gearbox by 80%.
From the test results, it was assumed after analysis that:
1) the vibration signal is adaptively decomposed by adopting an SSD (solid State disk) method, the noise component and the trend item 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 SSD 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 (8)
1. A SSD device fault diagnosis method is characterized by comprising the following steps: 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. into the sum of n components using a Singular Spectral Decomposition (SSD) algorithm
Wherein c isi(k) Representing the i-th component, r, derived by the SSD algorithmn(k) Represents a trend term derived from the SSD algorithm;
and step 3: noise components and trend items are eliminated from the SSD decomposition result by adopting a nonlinear discrimination algorithm, and components c containing fractal features are reservedf(k) F =1,2, …, p, p represents the number of residual components after filtering;
and 4, step 4: determination of cf(k) Local maximum sum ofLocal minima, using Lagrange 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 SSD device failure diagnosis method of claim 1, wherein: 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，
3. The SSD device failure diagnosis method of claim 2, wherein: the data rearrangement operation in the step 1) comprises the following steps: randomly randomizing the order of the components c (k).
4. The SSD device failure diagnosis method of claim 2, 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 obtain data cIFFT(k) To obtain data cIFFT(k) The real part of (a).
5. The SSD device failure diagnosis method of claim 2, 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 2shuf(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 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)。
6. The SSD device failure diagnosis method of 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, 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).
7. The SSD device fault diagnosis method and system of 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
。
8. A system for implementing a method of fault diagnosis of an SSD device according to any of claims 1 to 7, characterized by: 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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