CN114942133A - Optimal rank non-negative matrix factorization-based early fault diagnosis method for planetary gearbox - Google Patents
Optimal rank non-negative matrix factorization-based early fault diagnosis method for planetary gearbox Download PDFInfo
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Abstract
The invention provides an optimal rank non-negative matrix decomposition-based early fault diagnosis method for a planetary gearbox. Firstly, acquiring a fault vibration signal of the planetary gearbox, and calculating an STFT spectrum of the vibration signal; then, inputting the original vibration signal frequency spectrum as K-means clustering, and obtaining a curve graph with a clustering quality index (pkmcq) as a vertical coordinate and a clustering number K as a horizontal coordinate; secondly, selecting a k value corresponding to a first inflection point in a k-pkmcq curve as an optimal rank of nonnegative matrix decomposition to decompose the STFT spectrum of the vibration signal to obtain a base matrix W containing the spectrum characteristics of the original signal; then, selecting the basis vector with the maximum kurtosis value in the basis matrix W as the optimal basis vector to filter the original signal to obtain a filtered signal; finally, envelope demodulation is carried out on the filtered signals, characteristic frequency is extracted from an envelope spectrum, and the fault type of the gearbox is identified. The method can accurately diagnose the early weak fault of the planetary gear box.
Description
Technical Field
The invention belongs to the technical field of fault diagnosis and signal analysis of rotary machines, and relates to an early fault diagnosis method of a rotary machine, in particular to an early fault diagnosis method of a planetary gearbox based on optimal rank non-negative Matrix Factorization (non-negative Matrix Factorization), which can be used for fault diagnosis of gears and rolling bearing components in the planetary gearbox.
Background
Planetary gear transmission is widely used in the field of modern mechanical industry because of its advantages of small size, large transmission ratio, strong bearing capacity and the like. Considering the structural characteristics of the planetary gearbox, the planetary gearbox usually runs under severe working conditions such as heavy load, impact, pollution and the like, so that key parts such as gears and bearings are easy to break down, and the equipment is stopped even more seriously. Therefore, the method for monitoring the unfolding state of the planetary gear box, exploring an efficient fault diagnosis method, accurately extracting and identifying fault characteristics in the early stage of damage development and has important significance for ensuring the safe operation of equipment and reducing economic loss.
The operating conditions inside the planetary gearbox can be expressed by vibration information. The early failure characteristics of the gearbox are weak and are easily submerged in strong noise. Effective analysis and processing of vibration signals containing gearbox fault information are powerful ways to achieve accurate diagnosis of early stage faults of planetary gearboxes. Meanwhile, due to the influence of a transmission path and strong environmental noise, the vibration signals of the planetary gearbox can be considered to be mixed by a plurality of signal sources, and the planetary gearbox has a complex frequency spectrum structure. In order to eliminate noise interference, characteristic information representing a gearbox fault mode is separated from an original vibration signal, and various signal analysis technologies such as wavelet transformation, empirical mode decomposition, ensemble empirical mode decomposition, a basis function method, multi-parameter joint estimation and the like are widely applied. However, these methods have their own drawbacks. Wavelet transformation requires predetermination of wavelet bases and the number of decomposition layers, and lacks adaptivity. Although empirical mode decomposition has good adaptivity, the empirical mode decomposition can automatically decompose an input signal into a series of natural mode functions and the sum of residual errors. However, for gearbox vibration signals with weak characteristic information, modal aliasing is easily generated by decomposition. Although the ensemble empirical mode decomposition improves the modal aliasing problem of the decomposition to a certain extent, two input parameters of the intensity and the average times of the additional white noise are additionally introduced, and the operation amount is increased. Different from the method, the non-negative matrix decomposition is used as a matrix decomposition algorithm, the signal local features can be effectively extracted through the clustering analysis of the non-negative matrix, the algorithm is simple, has interpretability and definite physical significance, and is widely applied to the fields of signal processing, pattern recognition and the like. However, in the implementation process of the non-negative matrix factorization algorithm, the selection of the rank k is always a puzzling problem. For non-negative matrix decomposition of mechanical fault signals, most of the existing k selection means are selected based on experimental effects or manual experiences after traversal decomposition. The former is generally time consuming and the latter decomposition quality is not guaranteed. In addition, the precise screening of the components generated by the decomposition and how to extract the fault features based on the screened components also affect the application of the non-negative matrix decomposition in the aspect of weak signal feature extraction.
Disclosure of Invention
In order to solve the problems, the invention aims to provide an optimal rank non-negative matrix factorization-based early fault diagnosis method for the planetary gearbox. The method can get rid of dependence on priori knowledge such as a signal processing technology, diagnosis experience and the like, and solves the problems that the prior condition of the traditional nonnegative matrix decomposition algorithm on the decomposition rank is difficult, weak diagnosis of fault information of the planetary gear box under the background of strong noise is difficult and the like.
The technical scheme of the invention is as follows:
an optimal rank non-negative matrix factorization-based early fault diagnosis method for a planetary gearbox comprises the following steps:
step S1: arranging an acceleration sensor right above a shell on which the sensor is easily placed along the planetary gear box, collecting a failure original vibration signal s (t) of the planetary gear box, and performing fast Fourier transform to obtain an original signal frequency spectrum S (f);
step S2: and taking the original signal spectrum S (f) of the gearbox as input, sequentially adding one to the initial clustering center number K of 2, and traversing to perform K-Means clustering to obtain a line graph with the clustering center number K as an abscissa and the spectrum K-Means clustering quality (pkmcq) as an ordinate. The horizontal and vertical coordinates are dimensionless parameters;
wherein, the new index pkmcq is defined as the ratio of the intra-class average distance to the inter-class average distance of the signal spectrum K-means cluster:
in the formula, C i Denotes the ith cluster, num (C) i ) Number of samples representing ith cluster, c i Is C i Is p is C i Sample point(s) in (c). pkmcq represents how good the clustering effect is. As the cluster number k gradually approaches the true cluster number from small to large, the rate of decrease of the pkmcq value also gradually decreases. When the number of clusters k exceeds the true number of clusters and gradually moves away from the true number of clusters, the rate of decrease in the pkmcq value shows a gentle tendency. And drawing a k-pkmcq curve by taking the clustering number k as an abscissa and the pkmcq value as an ordinate. Therefore, an obvious inflection point appears in the k-pkmcq curve for the first time, and the corresponding k value is the estimated clustering number;
step S3: carrying out short-time Fourier transform on the original vibration signal s (t) to obtain a short-time Fourier transform spectrogram matrix V, and taking the short-time Fourier transform spectrogram matrix V as an input matrix of nonnegative matrix decomposition;
wherein, the spectrogram matrix V is obtained according to the following formula:
in the formula, γ (t) represents a short-time fourier transform window function. t denotes time and τ denotes time delay. With the change of time t, the window function will be displaced on the time axis, and the Fourier transform of the section intercepted by the window function is calculated s (t);
step S4: taking the optimal clustering number k obtained according to the k-pkmcq curve as a nonnegative matrix to decompose the optimal rank, and guiding the nonnegative matrix decomposition of the spectrogram matrix V to obtain two matrixes W ═ W 1 ,w 2 ,…,w k ]∈R m×k And H ═ H 1 ,h 2 ,…,h k ] T ∈R k×n The specific decomposition process is as follows:
V m×n ≈W m×k ×H k×n (s.t.W≥0,H≥0)
in the formula, W is referred to as a base matrix, and H is a weight matrix.
Step S5: calculating kurtosis value of each basis vector in the basis matrix W, and selecting the basis vector W with the largest kurtosis value o Performing next processing as the optimal component;
step S6: according to the optimal basis vector w o Filtering the original signal spectrum S (f) to obtain a filtered signal spectrum S w (f) Then obtaining a filtered signal s by inverse fast Fourier transform w (t) of (d). The specific implementation process of the filtering is represented as follows:
step S7: for the filtered signal s w And (t) performing Hilbert transform demodulation processing, extracting characteristic information (local fault frequency, frequency conversion and combined frequency of the local fault frequency and the frequency conversion of the gear) reflecting the fault of the planetary gearbox from the envelope spectrum, and accurately judging the fault type.
The invention has the beneficial effects that:
(1) the method gives play to the advantages of a non-negative matrix factorization algorithm in the aspect of self-adaptive signal matrix factorization, and solves the problem that early weak fault diagnosis of the planetary gearbox is difficult through effective screening and processing of internal components of the matrix obtained through factorization.
(2) The invention provides a new estimation strategy for decomposing the optimal rank by a signal non-negative matrix, constructs a line graph of the number K of clustering centers and the clustering quality of a frequency spectrum K-Means, effectively overcomes the prior dependence of a non-negative matrix decomposition algorithm on the decomposed rank, and enables the non-negative matrix decomposition algorithm to be suitable for a strong noise background.
(3) The invention designs a novel self-adaptive filtering method, which is used for self-adaptively selecting the optimal basis vector containing fault information in the basis matrix obtained by processing the non-negative matrix decomposition algorithm by means of the maximum kurtosis criterion to perform subsequent frequency domain filtering processing. On one hand, the stability of the selection of the optimal basis vector is ensured, and on the other hand, the problem that the useful information is easy to filter out when the prior fault information is insufficient by the traditional filtering means is solved.
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FIG. 1 is a flow chart of an optimal rank non-negative matrix factorization-based planetary gearbox early fault diagnosis method provided by the invention;
FIG. 2 is a time domain waveform, Fourier spectrum and envelope spectrum of a sun gear tooth root crack fault vibration signal in an embodiment of the invention; in the figure, (a) is a time-domain waveform of the failure vibration signal, (b) is a fourier spectrum of the failure vibration signal, and (c) is an envelope spectrum of the failure vibration signal.
FIG. 3 is a short-time Fourier transform spectrum of a sun gear fault vibration signal in an embodiment of the present invention;
FIG. 4 is a line graph of the clustering center number K and the clustering quality pkmcq obtained by performing K-means clustering on the sun gear fault vibration signal frequency spectrum in the embodiment of the present invention.
FIG. 5 is a result diagram of adaptive filtering of sun gear fault vibration signals by using an optimal rank non-negative matrix factorization algorithm according to an embodiment of the present invention; in the figure, (a) is a time-domain waveform of the filtered signal, (b) is a fourier spectrum of the filtered signal, and (c) is an envelope spectrum of the filtered signal.
Detailed Description
The following detailed description of the embodiments of the present invention is provided in connection with the accompanying drawings.
In the embodiment of the invention, an optimal rank non-negative matrix factorization-based early fault diagnosis method for a planetary gearbox is shown in fig. 1, which is a flow chart of the early fault diagnosis method for the planetary gearbox, and comprises the following steps:
the method comprises the following steps: an acceleration sensor is arranged right above a box body of the planetary gear box fault experiment table. The internal parameters of the planetary gearbox are shown in table 1. The output rotating speed of the motor is 600r/min (the rotating frequency is 10 Hz). And continuously acquiring the original vibration signal of the sun gear fault at a sampling frequency of 12800Hz for 2 s. To simulate a strong noise background, white Gaussian noise with a signal-to-noise ratio of-3 dB is added to the original vibration signal. And carrying out fast Fourier transform and Hilbert demodulation on the noisy vibration signal, and obtaining a frequency spectrum and an envelope spectrum. In fig. 2, (a), (b) and (c) are respectively time domain waveform, frequency spectrum and envelope spectrum of the sun gear fault vibration signal, the interference of noise makes (a) signal time domain waveform exhibit disorder, and (b) frequency spectrum information in fig. 2 is disordered. Meanwhile, no obvious frequency information characterizing the local failure of the sun gear is observed in the envelope spectrum shown in (c) of fig. 2.
TABLE 1 planetary gearbox internal parameters
Step two: and (3) taking the noisy fault signal frequency spectrum S (f) obtained in the step one as an input to carry out K-means clustering processing, and calculating the clustering quality pkmcq under different clustering center numbers K to obtain a K-pkmcq line drawing shown in figure 3. And selecting an abscissa value k which corresponds to the first inflection point of the line graph as 6 as an estimated non-negative matrix factorization optimal rank.
Step three: and carrying out short-time Fourier transform on the original vibration signal to obtain a time-frequency spectrogram as shown in figure 4. Noise is widely distributed in each frequency band of the signal, and the number of the frequency bands of the signal cannot be effectively distinguished in fig. 4. The empirical non-negative matrix factorization optimal rank estimation method proved to be ineffective.
Step four: and (4) carrying out non-negative matrix decomposition on the spectrogram matrix V obtained in the step three to obtain a component set containing a series of original signal characteristic information and a base matrix W.
Step five: calculating kurtosis value of each basis vector in the basis matrix W, and selecting the basis vector W with the largest kurtosis value o The next processing is performed as the best component.
Step six: according to the sensitive component w o Filtering the original signal spectrum S (f) shown in fig. 2 (b) to obtain a filtered signal spectrum S w (f) Then obtaining a filtered signal s by inverse fast Fourier transform w (t) of (d). The waveform and spectrum of the corresponding filtered signal are shown in fig. 5 (a) and (b).
Step seven: for the filtered signal s w (t) hilbert transform demodulation processing is performed, and (c) in fig. 5 shows an envelope spectrum after demodulation. Clear sun gear local fault frequency f appears in envelope spectrum su Sun gear frequency conversion f r And a series of frequency doubling and combined frequencies f su -f r ，f su +f r ，2*f su ，3*f su ，4*f su ，5*f su ，6*f su ，4*f su -f r ，6*f su -f r . These are all favorable indicators of sun gear failure. The analysis result shows the effectiveness and feasibility of the planetary gearbox early fault diagnosis method based on the optimal rank nonnegative matrix decomposition.
Claims (1)
1. An optimal rank non-negative matrix factorization-based early fault diagnosis method for a planetary gearbox is characterized by comprising the following steps of:
step S1: arranging an acceleration sensor right above a shell on which the sensor is easily placed along the planetary gear box, collecting a failure original vibration signal s (t) of the planetary gear box, and performing fast Fourier transform to obtain an original signal frequency spectrum S (f);
step S2: taking the original signal spectrum S (f) of the gearbox as input, sequentially adding one to the initial clustering center number K which is 2, and traversing to perform K-Means clustering to obtain a line graph with the clustering center number K as a horizontal coordinate and the spectrum K-Means clustering quality pkmcq as a vertical coordinate; the horizontal and vertical coordinates are dimensionless parameters;
wherein the index pkmcq is defined as the ratio of the intra-class average distance to the inter-class average distance of the signal spectrum K-means cluster:
in the formula, C i Denotes the ith cluster, num (C) i ) Number of samples representing ith cluster, c i Is C i Has a centroid of p is C i The sample point of (1); pkmcq represents the quality of the clustering effect; as the clustering number k gradually approaches to the real clustering number from small to large, the decreasing rate of the pkmcq value is gradually decreased; when the clustering number k exceeds the real clustering number and gradually gets away from the real clustering number, the reduction rate of the pkmcq value presents a gentle trend; drawing a k-pkmcq curve by taking the clustering number k as an abscissa and the pkmcq value as an ordinate; therefore, an obvious inflection point appears in the k-pkmcq curve for the first time, and the corresponding k value is the estimated clustering number;
step S3: carrying out short-time Fourier transform on the original vibration signal s (t) to obtain a short-time Fourier transform spectrogram matrix V, and taking the short-time Fourier transform spectrogram matrix V as an input matrix of nonnegative matrix decomposition;
wherein, the spectrogram matrix V is obtained according to the following formula:
wherein γ (t) represents a short-time fourier transform window function; t represents time, τ represents time delay; shifting the window function on the time axis along with the change of the time t, and calculating s (t) Fourier transform of a part intercepted by the window function;
step S4: taking the optimal clustering number k obtained according to the k-pkmcq curve as a nonnegative matrix to decompose the optimal rank, and guiding the nonnegative matrix decomposition of the spectrogram matrix V to obtain two matrixes W ═ W 1 ,w 2 ,…,w k ]∈R m×k And H ═ H 1 ,h 2 ,…,h k ] T ∈R k×n The specific decomposition process is as follows:
V m×n ≈W m×k ×H k×n (s.t.W≥0,H≥0)
in the formula, W is called a base matrix, and H is a weight matrix;
step S5: computingSelecting the kurtosis value of each basis vector in the basis matrix W, and selecting the basis vector W with the largest kurtosis value o Taking the component as a sensitive component to be processed in the next step;
step S6: according to the sensitive component w o Filtering the original signal spectrum S (f) to obtain a filtered signal spectrum S w (f) Then obtaining a filtered signal s by inverse fast Fourier transform w (t); the specific implementation process of the filtering is represented as follows:
step S7: for the filtered signal s w And (t) performing Hilbert transform demodulation processing, extracting characteristic information (local fault frequency, rotation frequency and combined frequency of the gear and the rotation frequency) reflecting the faults of the planetary gearbox from the envelope spectrum, and accurately judging the fault type.
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