CN111638055A - Gearbox fault diagnosis method based on resonance sparse decomposition improved algorithm - Google Patents
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Abstract
The invention discloses a gear box fault diagnosis method based on a resonance sparse decomposition improved algorithm, which comprises the following steps of: 1) and setting preset parameters of the ant lion optimization algorithm. 2) And optimizing the high-quality factors and the low-quality factors by using the ant lion optimization algorithm by taking the minimum fuzzy entropy of the high-quality components as a target function. 3) With the optimized high-low quality factor QHAnd QLAnd as a preset parameter, carrying out resonance sparse decomposition on the vibration signal of the gearbox to form high and low resonance components. 4) And carrying out envelope spectrum analysis on the high resonance component containing the fault signal of the gearbox, and extracting fault characteristic frequency so as to identify the fault.
Description
Technical Field
The invention relates to the field of fault diagnosis of rotating machinery, in particular to a gearbox fault diagnosis method based on a resonance sparse decomposition improved algorithm.
Background
The planetary gear box is widely applied to various transmission systems of aviation, engineering machinery, wind power generation and the like, and has important significance for ensuring normal work and safe operation of a mechanical system because the working environment is complex, the surface bears alternating load, the fault rate is high, and the fault diagnosis and monitoring are carried out on the planetary gear box.
In practical engineering application, a vibration signal of the planetary gearbox is coupling of multiple excitation factors, the frequency components of the vibration signal are quite complex, and the vibration signal not only contains the rotation frequency of each part, the meshing frequency of a gear pair and the frequency multiplication of the meshing frequency, but also contains the natural frequency of excited equipment. The planet gears are meshed with the sun gear and other planet gears, and the meshing mode causes certain characteristic frequencies to be low; the relative position of the planet wheel and the sensor changes along with the operation, the vibration transmission path also changes continuously, the amplitude or frequency modulation of signals can be caused by installation and manufacturing errors, the passing effect of the planet wheel and the like, so that the side frequency band is complicated, in addition, the influence of environmental noise is caused, the fault frequency is easily submerged, and great difficulty is brought to the vibration analysis.
Aiming at the characteristics of strong background noise, nonlinearity and non-stability of the fault signal of the planetary gearbox, the time-frequency analysis method is widely applied to fault feature extraction. The fourier transform decomposes noise while decomposing a signal, and thus there is a contradiction between noise suppression and signal edge protection, and there is a certain obstacle to accurately recognizing and removing noise. The common time-frequency analysis methods mainly comprise short-time Fourier transform, Winger-Ville distribution, wavelet transform, empirical mode decomposition and the like, but have respective defects. Meanwhile, the envelope order ratio analysis cannot be effectively analyzed under the condition of strong interference, and the EMD method has the defects of frequency aliasing and the like.
Disclosure of Invention
The purpose of the invention is as follows: the technical problem to be solved by the invention is to provide an improved resonance sparse decomposition method and apply the improved resonance sparse decomposition method to gearbox fault diagnosis, and compared with the original resonance sparse decomposition method, the method provided by the invention can accurately extract the fault characteristic frequency of the wind power gearbox.
The technical scheme is as follows: in order to solve the technical problem, the invention provides a gearbox fault diagnosis method based on a resonance sparse decomposition improved algorithm, which comprises the following steps of:
(1) setting preset parameters of the ant lion optimization algorithm, including a target function, a maximum algebra, and upper and lower variable limits;
(2) optimizing high and low quality factors by using an ant lion optimization algorithm by taking the minimum fuzzy entropy of the high quality component after the resonance sparse decomposition of the planetary gear box as a target function;
(3) with the optimized high-low quality factor QHAnd QLAs a preset parameter, carrying out resonance sparse decomposition on the vibration signal of the gearbox to form high and low resonance components;
(4) and carrying out envelope spectrum analysis on the high resonance component containing the fault signal of the gearbox, and extracting fault characteristic frequency so as to identify the fault.
Preferably, in step (1): the ant lion optimization Algorithm (ALO) has the advantages of few adjusting parameters and high solving precision, and compared with other optimization algorithms, the ALO algorithm has better global optimization capability and convergence speed.
Preferably, in step (2): the fuzzy entropy is a parameter reflecting the disorder degree of the one-dimensional time sequence, and is used for regularly classifying sample characteristics by using fuzzy criteria, so that the method has high sensitivity to signal change and can well detect the dynamic mutation of a complex system. If a certain gear tooth in the planet wheel has local damage, then in a rotation period of the gear ring, the planet wheel and the sun wheel respectively generate regular impact, the more obvious the impact is, the more regular the sequence is, and the fuzzy entropy value is smaller.
The fuzzy entropy is defined as follows:
1) assume that a data sequence X with a number of sampling points N is [ X (1), X (2) ].x (N)]Is m, then the reconstruction generates a set of m-dimensional vectors, Xm(i)＝[x(i)，x(i+1)，...x(i+m-1)]U (i) in the present inventionThe sequence is planetary gearbox fault vibration data, where i is 1, 2.. N-m +1, let u (i) be the mean of the vectors, i.e.:
2) let vector xm(i)，Xm(j) The distance between
Wherein i, j is 1, 2.. N-m + 1;
3) solving two vectors X by fuzzy membership function of chaos pseudo-random sequence complexity predictionm(i)、Xm(j) The similarity between them is:
r is a resolution parameter;
4) defining a function:
the following results were obtained:
5) repeat steps 1) -4 for the m +1 dimension of the pattern dimension
6) The fuzzy entropy of the fault signal sequence of the planetary gearbox is obtained as follows:
FuzzyEn(m，r，N)＝lnφm(r)-lnφm+1(r)。
preferably, in the step (3), with QH and QL as preset parameters, the planetary gearbox signal may be decomposed into a high Resonance component and a low Resonance component by Resonance Sparse decomposition, and the Resonance Sparse decomposition method (RSSD) includes two parts, namely quality factor adjustable wavelet transform and signal Sparse decomposition.
The quality factor adjustable Wavelet Transform (TQWT) has the characteristics of simple concept, high calculation efficiency and easy quantification of quality factors and redundancy. The RSSD method thus separately obtains a library of basis functions for the high (low) quality factor transforms using TQWT and computes their corresponding transform coefficients.
The quality factor Q is defined as:
wherein f iscThe BW is the bandwidth of the signal, the size of Q reflects the resonance degree of the signal, the larger the Q is, the better the frequency aggregation of the signal is, and the higher the resonance property is. Therefore, the high (low) resonance signals can be sparsely represented by a basis function with high (low) Q, the Q range of the high resonance component is 1-1.5, and the Q value of the low resonance component is 3-8.
TQWT uses the two-channel decomposition filter bank shown in FIG. 1 to realize signal decomposition in an iterative manner, and FIG. 2 is a schematic diagram of L-layer TQWT, and v can be obtained0(n) and v1(n) the original signal is decomposed into a series of sub-bands by L layers TQWT as shown in FIG. 2, i.e. L low resonance sub-bands v0(n) and L high resonance sub-bands v1(n) of (a). Setting Q to QH, then obtaining S after reconstructing high resonance sub-band1Here, if the low resonance subband is discarded and Q is set to QL, the high resonance subband is reconstructed to obtain S2。
For example, β is a high pass scale factor in FIG. 1
α is a low pass scale factor
r1Representing redundancy, subband signals v0(n) has a sampling frequency of α fs，v1(n) has a sampling frequency of β fs，fsThe sampling frequency of the original signal x (n) of the planetary gearbox fault signal.
The calculation formula of the number of decomposition layers L in fig. 2 is:
in the formula, N1For signal scale, the greater the number of decomposition layers, the finer the decomposition, and the larger the calculation time, and the number of layers with high and low resonance components is selected to be 28 and 11, respectively, according to engineering experience.
In FIG. 2
Representing high-frequency coefficients, V, of the signal obtained by a j-th layer transforml jThe low-frequency coefficient obtained by the j-th layer transform is represented, and j is 1, …, L.
RSSD uses Morphological Component Analysis (MCA) to decompose the signal. The purpose of MCA is to estimate the source signals x with different resonance properties from the observed signals, i.e. the planetary gearbox fault signals x, respectively1And x2And the smaller the coupling degree of the two separated parts, the better. Suppose a signal x1And x2Respectively available basis function library S1And S2Sparse representation, the objective function of MCA is set to:
in the formula: w1，W2Respectively is a representation signal x1x2At S1、S2A transform coefficient of down; w1，iRepresents W1The ith component of (1), W2，jRepresents W2M and n are the number of high and low resonance components, lambda1，mRegularization parameter, λ, for the m component of high resonance components2，nRegularization parameter, λ, for the nth component of low resonance components1，mAnd λ2，nValue pair decomposition ofThe energy distribution of the high and low resonance components has an influence. If both values are increased, the residual signal energy will be increased, S1、S2The filter bank for displaying the high and low quality factor adjustable wavelets is obtained by the TQWT method, and the correlation is low.
Due to l in the above formula1Norm is not microminiature and parameters are more, so the resonance sparse decomposition method utilizes a split-augmented Lagrange search algorithm and updates the transformation coefficient W through iteration1、W2The objective function J is minimized, and finally an effective separation of the high and low resonance components is achieved. When the objective function is minimum, the corresponding transformation coefficients of the high resonance component and the low resonance component are respectively W1 *，W2 *Then, the estimated values of the high resonance component and the low resonance component are respectively:
the beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the improved RSSD algorithm can accurately extract the fault characteristic frequency of the wind turbine generator gearbox.
Drawings
FIG. 1 is a resonant sparse decomposition filter bank of the present invention;
FIG. 2 is a diagram of resonance sparse decomposition L-layer quality factor adjustable wavelet transform of the present invention;
FIG. 3 is a vibration waveform and an envelope spectrum of an original signal of the planetary gearbox according to the present invention;
(a) a 600r/min signal waveform diagram, (b) a 600r/min signal envelope spectrogram;
FIG. 4 is a graph of the fuzzy entropy change of the high resonance component of the ALO optimization process of the present invention;
FIG. 5 is the modified RSSD high-resonance component envelope spectrum of the present invention;
(a) a signal oscillogram processed by a RSSD and FastICA combined method, and (b) a signal envelope spectrogram processed by the RSSD and FastICA combined method.
Detailed Description
The structure of the wind power transmission system simulation test bed is as follows: the driving motor simulates the torque input of the wind wheel and is connected with the load motor after being transmitted by the secondary gear. In order to simulate the time-varying characteristic of the rotating speed of the wind wheel, a frequency converter is adopted to control the rotating speed of the motor. Various types of faults of the planetary gearbox are prepared in a defect manual processing mode, and the test bed can simulate the vibration conditions of the bearing, the main shaft and the gearbox when the rolling bearing and the gearbox have common faults. The broken tooth fault of the planet gear researched by the invention is also prepared manually, and a vibration sensor is arranged on the side of the planet gear box seat. The preparation of the broken tooth fault of the planetary gear box is to grind and flatten the tooth length of 0.5 time of a certain tooth on a planetary gear by an electric spark machining technology.
The parameters of the planetary gearbox are shown in table 1.
TABLE 1 planetary gearbox parameters
Table1 Planetary gearbox parameters
In the test of the planetary gearbox, the rotating speed of the motor is set to be 600r/min, namely the rotating frequency of the planet wheel is 10Hz, the rotating frequency of the planet carrier is 3.137Hz, and the rotating frequency of the sun wheel is 10 Hz. The sampling frequency is 4096 and the number of sampling points is 16384.
Calculating the meshing frequency of the planetary gearbox at 600r/min
fm＝fcZr＝3.137×72＝225.8Hz
In the formula (f)cThe rotational frequency Z of the planet carrierrNumber of teeth of the ring gear
Planet wheel fault characteristic frequency:
fmis the rotational speed of the gear shaft, zpThe number of teeth of the planet wheel.
The 600r/min lower planetary gear case waveform is collected and subjected to envelope analysis as shown in figure 1. As shown in fig. 1a), the vibration waveform has no obvious periodic characteristics, many peaks, and rough and unstable waveform; the waveform changes sharply and instantly, even in a straight line shape. This is due to the friction of the laboratory bench itself and the false signal interference due to more noise and signal modulation. Fig. 1b) a vibration signal envelope spectrogram has more low-frequency components in a fault state, has no clear spectral line peak value, but cannot acquire fault characteristic frequency of a signal.
The modified RSSD algorithm steps are as follows:
The objective function is: fuzzy entropy values for high resonance components.
The maximum algebra is: 500.
variable upper and lower limits: qHBetween 3 and 8, QLBetween 1 and 1.5.
And 2, optimizing the high-quality factors and the low-quality factors by using an ant lion optimization algorithm by taking the minimum fuzzy entropy of the high-quality components after resonance sparse decomposition of the planetary gearbox as a target function.
And 3, performing resonance sparse decomposition on the vibration signal of the gearbox by taking the optimized high-low quality factors QH and QL as preset parameters to form high-low resonance components. The parameters of the resonance sparse decomposition are set as: the redundancy factor was 3.5, the number of decomposition layers for the high resonance component was 28, and the number of decomposition layers for the low resonance component was 11.
And 4, carrying out envelope spectrum analysis on the high resonance component containing the fault signal of the gearbox, and extracting fault characteristic frequency so as to identify the fault.
In the step 2, the fuzzy entropy is a parameter reflecting the disorder degree of the one-dimensional time sequence, and the sample characteristics are regularly classified by using a fuzzy criterion, so that the method has high sensitivity to the change of signals and can well detect the dynamic mutation of a complex system. The fuzzy entropy calculation steps are as follows:
step 2.1: assume that a data sequence X with a number of sampling points N is [ X (1), X (2) ].x (N)]Is m, then the reconstruction generates a set of m-dimensional vectors: xm(i)＝[x(i)，x(i+1)，...x(i+m-1)]-u (i), wherein i ═ 1, 2.. N-m + 1. Let u (i) be the mean of the vectors, i.e.:
step 2.2: let vector Xm(i)，Xm(j) The distance between
Wherein i, j is 1,2
Step 2.3: solving two vectors X by fuzzy membership function of chaos pseudo-random sequence complexity predictionm(i)、Xm(j) The similarity between them is:
step 2.4: defining a function:
can obtain
Step 2.5: repeat steps 1) -4 for the m +1 dimension of the pattern dimension
Step 2.6: the fuzzy entropy of the high resonance component after the fault signal of the planetary gear box is decomposed is obtained
FuzzyEn(m，r，N)＝lnφm(r)-lnφm+1(r) (1-9)
In step 3, the resonance sparse decomposition decomposes the complex signal into a high resonance component mainly based on the continuous oscillation signal and a low resonance component mainly based on the transient impact signal according to the difference of the quality factors Q of the continuous oscillation signal and the transient impact signal. The fault signal of the planetary gear box is a narrow-band signal with frequency modulation and amplitude modulation, and belongs to high resonance components. The method can effectively reduce the influence of broadband signals (such as bearing fault signals and eccentricity) containing transient impact, and realize the dimension reduction of the number of vibration source signals in the signals.
The resonance sparse decomposition method of the signal adopts Morphological component analysis to decompose the signal, and the Morphological component analysis (Morphological component analysis, MCA) sets that the signal to be processed is formed by linearly overlapping components with obvious differences of various Morphological characteristics, respectively selects different over-complete dictionaries to perform sparse representation on each component according to the characteristics of different component components, and finally decomposes the signal into components with different Morphological characteristics through T times of decomposition iteration. It is assumed that the input signal x is linearly combined from a plurality of different morphological components, each component xkAll correspond to an overcomplete dictionary SkThen the signal x can be decomposed into:
in resonance sparse decomposition, let the input signal x be represented as two signals x1、x2Sum, x1Including a high resonant component of the sustained oscillation signal, x2Including the low resonance component of the transient impulse.
x＝x1+x2x，x1，x2∈RN
The objective of the morphological component analysis is to estimate the source signals x with different resonance properties from the input signal x1And x2And the smaller the coupling degree of the two separated parts, the better. Suppose a signal x1And x2Respectively available basis function library S1And S2Sparse representation, S1、S2The high and low quality factors are adjustableThe wavelet filter bank is obtained by a quality factor adjustable wavelet transform TQWT method, and the objective function of the morphological component is set as follows:
wherein S is1、S2Respectively representing a base function library containing high-quality factor and low-quality factor transformation; w1、W2Respectively is a representation signal x1、x2In the frame S1、S2A transform coefficient of down; m and n are the numbers of high and low resonance components respectively, and m is set to be 28 and n is set to be 11 according to experience in the embodiment; lambda [ alpha ]1，iRegularization parameter, λ, for the ith component of the high-resonance component2，jA regularization parameter for the jth component of the low resonance components; lambda [ alpha ]1，iAnd λ2，jThe value of (2) has an influence on the energy distribution of the decomposed high and low resonance components, and if the values of both are increased, the residual signal energy is increased.
Because norm in the above formula is not microminiature and has more parameters, the resonance sparse decomposition method utilizes a split-augmented Lagrange search algorithm to update the transformation coefficient W through iteration1、W2The objective function J is minimized, and finally an effective separation of the high and low resonance components is achieved. When the objective function is minimized, the corresponding transformation coefficients of the high resonance component and the low resonance component are respectively
Then the estimated values of the high resonance component and the low resonance component are respectively:
the vibration signal of the planetary gearbox is diagnosed by adopting an improved RSSD method, fig. 3 is an envelope spectrum of the broken tooth fault signal processed by the method, and the main components in the envelope spectrum are at the first, second and third frequency multiplication positions of the rotation frequency of the planet carrier, and the fault characteristic frequency and second frequency multiplication positions of the planet wheel. The improved resonance sparse decomposition can reduce the dimension of the original signal, can more accurately decompose each independent component, and is favorable for extracting the fault characteristic frequency of the planetary gear box.
While the invention has been shown and described with respect to the preferred embodiments, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the scope of the invention as defined in the following claims.
Claims (6)
1. A gearbox fault diagnosis method based on a resonance sparse decomposition improved algorithm is characterized by comprising the following steps:
(1) setting preset parameters of the ant lion optimization algorithm, including a target function, a maximum algebra, and upper and lower variable limits;
(2) optimizing high and low quality factors by using an ant lion optimization algorithm by taking the minimum fuzzy entropy of the high quality component after the resonance sparse decomposition of the planetary gear box as a target function;
(3) with the optimized high-low quality factor QHAnd QLAs a preset parameter, carrying out resonance sparse decomposition on the vibration signal of the gearbox to form high and low resonance components;
(4) and carrying out envelope spectrum analysis on the high resonance component containing the fault signal of the gearbox, and extracting fault characteristic frequency so as to identify the fault.
2. The gearbox fault diagnosis method based on the resonance sparse decomposition improvement algorithm as claimed in claim 1, wherein the fuzzy entropy in the step (2) is defined as follows:
1) assume that a data sequence X with a number of sampling points N is [ X (1), X (2) ].x (N)]Is m, then the reconstruction generates a set of m-dimensional vectors, Xm(i)＝[x(i),x(i+1),...x(i+m-1)]U (i), the sequence being epicyclic gearbox fault vibration data, where i is 1, 2.. N-m +1, let u (i) be the mean of the vectors, i.e.:
2) let vector Xm(i),Xm(j) The distance between
Wherein i, j is 1, 2.. N-m + 1;
3) solving two vectors X by fuzzy membership function of chaos pseudo-random sequence complexity predictionm(i)、Xm(j) The similarity between them is:
r is a resolution parameter;
4) defining a function:
the following results were obtained:
5) repeat steps 1) -4 for the m +1 dimension of the pattern dimension
6) The fuzzy entropy of the fault signal sequence of the planetary gearbox is obtained as follows:
FuzzyEn(m,r,N)＝lnφm(r)-lnφm+1(r)。
3. a gearbox fault diagnosis method based on resonance sparse decomposition improvement algorithm according to claim 1 or 2, characterized in that in step (3), with QH and QL as preset parameters, the resonance sparse decomposition can decompose the planetary gearbox signal into high resonance component and low resonance component, and the quality factor Q is defined as:
wherein f iscThe central frequency of the signal is BW, the bandwidth of the signal is BW, the magnitude of Q reflects the resonance degree of the signal, the QH range of the high resonance component after optimization is 1-1.5, and the QL value of the low resonance component is 3-8.
4. The gearbox fault diagnosis method based on resonance sparse decomposition improvement algorithm as claimed in claim 3, wherein in step (3), the original signal is decomposed into a series of sub-bands through L layers of TQWT by high pass scale factor and low pass scale factor, namely L low resonance sub-bands v0(n) and L high resonance sub-bands v1(n) when Q is set to QH, S is obtained after reconstruction of the high-resonance subband1Setting Q as QL, then obtaining S after low resonance sub-band reconstruction2。
5. The gearbox fault diagnosis method based on the resonance sparse decomposition improved algorithm according to claim 4, wherein the number L of decomposition layers meets the following condition:
in the formula, N1For signal scaling, β is a high-pass scale factor
α is a low pass scale factor
r1Representing redundancy, subband signals v0(n) has a sampling frequency of α fs，v1(n) has a sampling frequency of β fs，fsThe sampling frequency of the original signal x (n) of the planetary gearbox fault signal.
6. The gearbox fault diagnosis method based on the resonance sparse decomposition improved algorithm as claimed in claim 5, wherein: the method for calculating the high and low resonance components in the step (3) comprises the following steps:
(3.1) respectively estimating source signals x with different resonance properties from observation signals, namely fault signals x of the planetary gearbox1And x2Suppose a signal x1And x2Can be respectively used as S1And S2Sparse representation, the objective function to construct the MCA is set to:
in the formula: w1，W2Respectively is a representation signal x1x2At S1、S2A transform coefficient of down; w1,iRepresents W1The ith component of (1), W2,jRepresents W2M and n are the number of high and low resonance components, lambda1,iRegularization parameter, λ, for the ith component of high resonance components2,jRegularization parameters for the jth component of low resonance components;
(3.2) resonance sparse decomposition method utilizing split-augmented Lagrange search algorithm, updating transformation coefficient W through iteration1、W2Minimizing the objective function J to realize effective separation of high resonance component and low resonance component, wherein when the objective function is minimized, the corresponding high resonance component and low resonance component transformation coefficients are W1 *，W2 *Then, the estimated values of the high resonance component and the low resonance component are respectively:
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| CN114427972A (en) * | 2022-02-09 | 2022-05-03 | 中国人民解放军战略支援部队航天工程大学士官学校 | Rolling bearing performance degradation feature extraction method and system |
| CN115434872A (en) * | 2022-08-11 | 2022-12-06 | 兰州理工大学 | Wind turbine generator gearbox composite fault diagnosis method based on AVMD and improved RSSD |
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