Gear Vibration Signal Research Articles

A tacholess order tracking method based on extended intrinsic chirp component decomposition for gears under large speed variation conditions

Abstract Order tracking has been considered as the most effective non-stationary signal analysis technique for condition monitoring and fault diagnosis. Conventional order tracking is performed with a reference signal measured by the auxiliary device, which is expensive and inconvenient to install. In order to to break the constraint of the traditional order tracking technique, some tacholess order tracking methods have been developed in the past few years. However, current tacholess order tracking approaches are only applicable to slightly varying speed applications. To overcome the shortcoming above, a novel tacholess order tracking method is proposed in this paper. In the proposed method, each mode of the vibration signal is reconstructed by a method called extended intrinsic chirp component decomposition, and the Hilbert transform is used to estimate the instantaneous phase of reference shaft. Then the vibration signal is resampled to the angle domain, and the fault characteristic orders can be identified in the order spectrum accurately. The effectiveness of the proposed method has been validated by a simulated meshing gear vibration signal. The result illustrates that the proposed method can realize gears fault diagnosis under large speed variation conditions.

Feature extraction based on generalized permutation entropy for condition monitoring of rotating machinery

Defective rotating machinery usually exhibits complex dynamic behavior. Therefore, feature representation of machinery vibration signals is always critical for condition monitoring of rotating machinery. Permutation entropy (PeEn), an adaptive symbolic description, can measure complexities of signals. However, PeEn, which compresses all the information into a single parameter, may lack the capability to fully describe the dynamics of complex signals. Afterward, multiscale PeEn (MPeEn) is put forward for coping with nonstationarity, outliers and artifacts emerging in complex signals. In MPeEn, a set of parameters serves to describe the dynamics of complex signals in different time scales. Nonetheless, an average procedure in MPeEn may withhold local information of complex signals and destroy internal structures of complex signals. To overcome deficiencies of PeEn and MPeEn, this paper proposes generalized PeEn (GPeEn) by introducing different orders and time lags into PeEn. In GPeEn, a complex signal is converted into a PeEn matrix rather than a single parameter. Moreover, minimal, maximal and average values of the PeEn matrix serve to briefly describe conditions of rotating machinery. Next, a numerical experiment proves that the proposed method in this paper performs better than skewness, kurtosis, PeEn and MPeEn in characterizing conditions of a Lorenz model. Subsequently, the proposed method in this paper is compared with skewness, kurtosis, PeEn and MPeEn by investigating gear and roll-bearing vibration signals containing different types and severity of faults. The results show that the proposed method in this paper outperforms the other four methods in distinguishing between different types and severity of faults of rotating machinery.

Vibration signal analysis of planetary gear with amplitude, frequency and phase modulation

In this paper, the vibration signal of planetary gear with amplitude, frequency and phase modulation is studied. The proposed mathematical model is employed to in- vestigate the modulation behavior of planetary gear. Based on this model, the ampli- tude modulation (AM) sidebands are analyzed to verify the correctness of theoretical calculation by Inalpolat and Kahraman. Then, the frequency modulation (FM) side- bands and phase modulation (PM) sidebands are also illustrated through an exam- ple analysis. The effects of parameters of planetary gear such as number of planets, teeth of sun and planet phasing relationships on the AM, FM and PM sidebands are analyzed. Finally, the specific expression of transmission error, time-varying mesh stiffness and dynamic mesh force including gear manufacturing error is developed. Time history signal and acceleration spectra of gear mesh interface excitations including AM, FM and PM are investigated for the meshes of sun-planet and ring- planet. The results show that gear parameters have important influence on the mod- ulation behavior. Additionally, manufacturing errors can be introduced to predict the sidebands of planetary gear. The amplitude, frequency and phase modulation study are extremely significant for the noise and vibration reduction, especially the fault diagnosis of planetary gear

Application of Generalized Composite Multiscale Lempel–Ziv Complexity in Identifying Wind Turbine Gearbox Faults

Wind turbine gearboxes operate in harsh environments; therefore, the resulting gear vibration signal has characteristics of strong nonlinearity, is non-stationary, and has a low signal-to-noise ratio, which indicates that it is difficult to identify wind turbine gearbox faults effectively by the traditional methods. To solve this problem, this paper proposes a new fault diagnosis method for wind turbine gearboxes based on generalized composite multiscale Lempel–Ziv complexity (GCMLZC). Within the proposed method, an effective technique named multiscale morphological-hat convolution operator (MHCO) is firstly presented to remove the noise interference information of the original gear vibration signal. Then, the GCMLZC of the filtered signal was calculated to extract gear fault features. Finally, the extracted fault features were input into softmax classifier for automatically identifying different health conditions of wind turbine gearboxes. The effectiveness of the proposed method was validated by the experimental and engineering data analysis. The results of the analysis indicate that the proposed method can identify accurately different gear health conditions. Moreover, the identification accuracy of the proposed method is higher than that of traditional multiscale Lempel–Ziv complexity (MLZC) and several representative multiscale entropies (e.g., multiscale dispersion entropy (MDE), multiscale permutation entropy (MPE) and multiscale sample entropy (MSE)).

Wavelet Packet Transform-Assisted Least Squares Support Vector Machine for Gear Wear Degree Diagnosis

Wear degree detection of gears is an effective way to prevent faults. However, due to the interference of high-speed meshing vibration and environmental noise, the weak vibration signal generated by the gear is easily covered by the noise, which makes it difficult to detect the degree of wear. To address this issue, this paper proposes a novel gear wear degree diagnosis method based on local weighted scatter smoothing method (LOWESS), wavelet packet transform (WPT), and least square support vector machine (APSO-LSSVM) optimized by adaptive particle swarm algorithm. According to the low signal-to-noise ratio characteristic of gear vibration signal, LOWESS is first used to preprocess the signal spectrum. Then, the characteristic parameters used to characterize gear wear are extracted from different decomposition depths by WPT and, finally, combined with APSO-SVM to diagnose the degree of gear wear. Compared with the basic least squares support vector machine, the improved method has better performance in sample classification. The experimental results show that the method in this paper can effectively reduce the diagnosis error caused by background noise, and the diagnosis accuracy reaches 98.33%, which can provide a solution for the health status monitoring of gears.

Harnessing fuzzy neural network for gear fault diagnosis with limited data labels

Diagnosis and prognosis of gear systems play an important role in modern manufacturing. While first-principle-based inverse analysis is subject to various limitations, data-driven approaches such as many machine learning techniques have shown great promise in recent years. Nevertheless, major challenges remain. Machine learning generally requires large amount of high-quality training data which may not be available for many industrial systems. In particular, while gear faults are continuous in nature and exhibit many different scenarios, in practical situations owing to the high cost in data acquisition especially for fault scenarios, only a small number of discrete classes of faults, i.e., fault types and severities, can be recorded and employed in training. As such, the neural networks trained will need to deal with unseen faults when they are actually implemented. To tackle this challenge, in this research, we develop a fuzzy classification approach capable of handling fault scenarios that are not included in the training dataset. Through the integration of a fuzzification procedure, this fuzzy neural network (FNN) can produce classification outcome with probability and confidence level. An unseen fault scenario will be classified into the nearest fault class with probability, effectively yielding the diagnosis result under limited data. While fault features in gear vibration signals are hidden and have complex nonlinear relations with respect to fault scenarios, it is found that the kernel principal component analysis (KPCA) can enable the FNN to facilitate the correlation of fault features. Systematic case studies using experimental data acquired from a lab-scale gear system are carried out to validate the new approach.

Signal Identification of Gear Vibration in Engine-Gearbox Systems Based on Auto-Regression and Optimized Resonance-Based Signal Sparse Decomposition

As an essential part of the transmission system, gearboxes are considered as a major source of vibration. Signal identification of gear vibration is necessary for online monitoring of the mechanical systems. However, in engine-gearbox systems, the ignition impact of the engine is strong, so that the gear vibration is generally submerged. To overcome this issue, the resonance-based signal sparse decomposition (RSSD) method is used in this paper based on different oscillatory behaviors of the gear meshing impact and the engine ignition impact. To improve the accuracy of RSSD under interferences, the meshing frequency energy ratio (MF–ER) index is introduced into RSSD to adaptively choose the decomposition parameters. Before applying the RSSD method, the auto-regression (AR) model is used as a pre-whitening step to eliminate the normal gear meshing vibration, which improves the decomposition performance of RSSD. The effectiveness of the proposed AR-ORSSD (AR-based optimized RSSD) algorithm is tested using both simulated signals and measured vibration signals from an engine-gearbox system in a forklift. Comparisons were made with the RSSD algorithm based on a genetic algorithm. Experimental results indicate that the AR-ORSSD algorithm is superior at identifying gear vibration signals especially when under strong interferences.

New Gear Fault Diagnosis Method Based on MODWPT and Neural Network for Feature Extraction and Classification

Abstract Gear fault diagnosis using vibration signals has become the subject of intensive studies to detect any sudden failure. However, these signals exhibit nonlinear and nonstationary behaviors when the rotating machine operates under multiple working conditions. Furthermore, fault features extraction and classification of multiple gear states are always unsatisfactory and considered as a huge task. This is the main reason that motivates us to develop a new intelligent gear fault diagnosis method in order to automatically identify and classify several kinds of gear defects under different work conditions. So in this article, we propose a combination between the maximal overlap discrete wavelet packet transform (MODWPT), entropy indicator, and a multilayer perceptron (MLP) neural network as a new automatic fault diagnosis approach. MODWPT decomposes the data signal into several components using a uniform frequency bandwidth. Each decomposed component is selected to extract feature vector using entropy indicator. Finally, MLP provides a powerful automatic tool for identifying and classifying the aforementioned extracted features. Experimental vibration signals of healthy gear; gear with general surface wear; gear with chipped tooth in length; gear with chipped tooth in width; gear with missing tooth; and gear with tooth root crack are recorded under fifteen different work conditions to test the effectiveness of the suggested technique. Experimental results affirm that our proposed approach can successfully detect, identify, and classify the gear fault pattern in all cases.

Fault feature extraction method of gear based on optimized minimum entropy deconvolution and accugram

Gear fault vibration signals are commonly non-stationary, and useful fault information is often buried in heavy noise, which makes it difficult to extract gear fault features. How to select the suitable fault frequency bands is the key to gear fault diagnosis. To address the above problems, a method combining the improved minimum entropy deconvolution (MED) and accugram, named IMEDA, is proposed for extracting gear fault features. Firstly, a selection index based on permutation entropy (PE) and correlation coefficient is defined. Then, the optimal filter length can be effectively selected by the step-length searching method using the proposed index as objective function, and the improved MED is employed to preprocess the gear vibration signals. Finally, the accugram analysis is performed for the preprocessed signals to obtain the optimal frequency band, and the fault characteristic frequencies are extracted from the square envelope spectrum of the signals in the optimal band. The method is validated by gear experimental data with gear wear-out failure. The analysis results demonstrate that the proposed method owns superior effect by comparing with the fast kurtogram (FK), MED combined with FK (MED-FK), accugram and infogram.

An improved sideband energy ratio for fault diagnosis of planetary gearboxes

Frequency spectrum analysis is an effective and direct way to understand the vibration behavior of a planetary gearbox (PG). Sideband structures, as useful and detectable fault information, have drawn widespread research attention to track and indicate the health conditions of the internal gears. However, for planetary gearboxes, different characteristic fault sidebands may mislead the diagnostic decisions, therefore, expert knowledge must be heavily relied on. The sideband related indicators, such as Sideband Energy Ratio (SER) and Sideband Index (SI), which synthesized the amplitudes of characteristic frequencies, have demonstrated their effectiveness in fault diagnosis of a PG. Whereas, the diagnostic mechanisms behind these sideband related indicators were not adequately studied. Moreover, how to properly select the numbers of sidebands to form a reliable indicator so far still has not yet been seriously considered. In this article, the diagnostic mechanisms of SER and SI are reexamined and analyzed via planetary gear vibration signal models with faulty gear. The drawbacks of these indicators are revealed over the theoretical analysis. According to the theoretical derivations, a selection of fewer sideband numbers is applied. A novel indicator, namely an Improved Sideband Energy ratio (ISER), is then proposed for the diagnostic task. The ISER and other sidebands indicators are testified through experimental data under different gear fault scenarios. Three typical intelligent classification algorithms, namely support vector machine (SVM), XGBoost, and deep neural network (DNN) are employed to demonstrate their diagnostic abilities. The results show that the ISER outperforms than SER, SI, and other statistical sideband indicators.

Research on a Noise Reduction Method Based on DTCWT and the Cyclic Singular Energy Difference Spectrum

The gear is the most important part of the transmission system of mechanical equipment, and the monitoring and diagnosis of it can improve the reliability of mechanical equipment. However, mechanical equipment generally works in harsh working conditions. The gear vibration signal is subjected to strong noise interference in working conditions, which brings great challenges for the effective diagnosis of gear faults. This paper proposed a noise reduction method based on the dual-tree complex wavelet transform (DTCWT) and cyclic singular energy difference spectrum. First, the gear vibration signal containing strong noise interference is decomposed into a series of signal components with different frequency characteristics by using the time-frequency analysis ability of DTCWT. Then, cyclic singular energy difference spectrum is proposed based on the idea of a cascaded cycle and the successive elimination of noise interference to process each signal component with different frequency characteristics, and the termination conditions of cyclic singular energy difference spectrum can be set according to the noise interference distribution characteristics in different frequency bands. The final noise reduction of the original gear vibration signal can be realized based on signal reconstruction after the noise reduction processing of each signal components with different frequency bands. Finally, experiments are carried out to verify the effectiveness of the proposed method, which is effective and suitable for the noise reduction of the vibration signal.

Application of morphological wavelet and permutation entropy in gear fault recognition

In this paper, a new gear fault recognition method was proposed by using morphological wavelet and permutation entropy. Firstly, the morphological Haar wavelet was proposed based on morphological wavelet, and it was used to pre-process the measured gear vibration signal. Then, the permutation entropy was used as the eigenvalue of gear fault to be extracted from the vibration signal, which included four working conditions: normal, mild wear, moderate wear, and broken teeth. Finally, according to different faults corresponding to different permutation entropy distributions, the various fault states were classified, and the permutation entropy distributions of non-denoised signals were compared. It could be seen that the morphological Haar wavelet had good de-noising effectiveness, and permutation entropy could express the feature of different gear conditions. The example of gear fault recognition proved that the combination of morphological wavelet and permutation entropy could effectively improve the ability of gear fault classification.

Research on gear fault degree recognition method based on multi sensor fusion

The fatal fault of gear will inevitably experience the evolution of different fault degrees, and the accurate recognition of the fault degree of gear has more practical significance for predictive maintenance and efficient operation. A gear fault degree recognition method based on multi sensor fusion is proposed. Ensemble local mean decomposition (ELMD) is used to decompose the vibration signal of gear, which can eliminate the aliasing effect of LMD. Then, the fault feature is extracted by using envelope spectrum information entropy and time-domain kurtosis. Based on the initial recognition of the sub evidence formed by a signal sensor based on wavelet neural network (WNN), the basic belief function assignment and fusion methods of Dempster-Shafer (D-S) evidence theory are determined, and the accurate recognition based on multi sensor fusion for different fault degree of gear is realized, which is verified by experiments.

An Enhanced CICA Method and Its Application to Multistage Gearbox Low-frequency Fault Feature Extraction

Background: The vibration signals acquired from multistage gearbox’s slow-speed gear with localized fault may be directly mixed with source noise and measured noise. In addition, Constrained Independent Component Analysis (CICA) method has strong immunity to the measured noise but not to the source noise. These questions cause the difficulty for applying CICA method to directly extract lowfrequency and weak fault characteristic from the gear vibration signals with source noise. Methods: In order to extract the low-frequency and weak fault feature from the multistage gearbox, the source noise and measured noise are introduced into the independent component analysis (ICA) algorithm model, and then an enhanced Constrained Independent Component Analysis (CICA) method is proposed. The proposed method is implemented by combining the traditional Wavelet Transform (WT) with Constrained Independent Component Analysis (CICA). Results: In this method, the role of a supplementary step of WT before CICA analysis is explored to effectively reduce the influence of strong noise. Conclusion: Through the simulations and experiments, the results show that the proposed method can effectively decrease noise and enhance feature extraction effect of CICA method, and extract the desired gear fault feature, especially the low-frequency and weak fault feature.

A Fast Multi-tasking Solution: NMF-Theoretic Co-clustering for Gear Fault Diagnosis under Variable Working Conditions

Most gear fault diagnosis (GFD) approaches suffer from inefficiency when facing with multiple varying working conditions at the same time. In this paper, a non-negative matrix factorization (NMF)-theoretic co-clustering strategy is proposed specially to classify more than one task at the same time using the high dimension matrix, aiming to offer a fast multi-tasking solution. The short-time Fourier transform (STFT) is first used to obtain the time-frequency features from the gear vibration signal. Then, the optimal clustering numbers are estimated using the Bayesian information criterion (BIC) theory, which possesses the simultaneous assessment capability, compared with traditional validity indexes. Subsequently, the classical/modified NMF-based co-clustering methods are carried out to obtain the classification results in both row and column tasks. Finally, the parameters involved in BIC and NMF algorithms are determined using the gradient ascent (GA) strategy in order to achieve reliable diagnostic results. The Spectra Quest’s Drivetrain Dynamics Simulator gear data sets were analyzed to verify the effectiveness of the proposed approach.

Cyclostationary modeling for local fault diagnosis of planetary gear vibration signals

Owing to the rotation and reciprocation of mechanical equipment, their vibration signals inherently exhibit cyclic stationary characteristics. This paper provides a phenomenological signal model of the planetary gear vibrations under the cyclostationarity paradigm. The model is helpful to give comprehensive demodulation information which is the limit of classic spectral analysis of deterministic signals, so that the diagnosis of local faults in planetary gear sets can be more explicit. First, the effects of rotating speed fluctuation on periodic gear meshing vibrations are analyzed. It is shown that the stationary speed fluctuation will turn the periodicity of signals into second-order cyclostationarity. Next, an impulsive oscillation sequence with interval timing jitter is used to describe the dynamic response of the meshing stiffness change caused by local defects. Meanwhile, the influence of a vibration transfer path is also considered in the model. Based on the above analysis, the following procedure is utilized to analyze planetary gearbox vibrations: remove the periodic components by the self-adaptive noise cancellation method and then, apply the second-order frequency descriptor to reveal fault features of the signals. Both the simulation and experiment are used to validate the correctness of model derivation and the superiority of the cyclostationary analysis.

Gear Fault Feature Extraction Based on Fuzzy Function and Improved Hu Invariant Moments

To intelligently identify gear fault types on the basis of gear vibration signals, due to the non-linear and non-stationary characteristics of gear vibration signals, a fuzzy function is used to represent the gear vibration signals in different states as two-dimensional time-frequency images. To solve the problem that the recognition effect of discontinuity area in the image by traditional Hu invariant moments is not ideal, improved Hu invariant moments are proposed, and the feature parameters of time-frequency images of gear vibration signals are extracted based on the improved Hu invariant moments. Different intelligent classifiers are used to recognize the gear vibration signals in different states. The recognition accuracy is higher by improved Hu invariant moments than by traditional Hu invariant moments, which shows that the method of gear fault feature extraction based on a fuzzy function and improved Hu invariant moments is quite ideal, and can be used in intelligent diagnosis of gear faults.

Gear Fault Diagnosis Based on Genetic Mutation Particle Swarm Optimization VMD and Probabilistic Neural Network Algorithm

The decomposition number $K$ and penalty factor $\alpha $ in the variational mode decomposition (VMD) algorithm have a great influence on the decomposition effect and the accuracy of subsequent fault diagnosis. Therefore, a gear fault diagnosis method based on genetic mutation particle swarm optimization VMD and probabilistic neural network (GMPSO-VMD-PNN) algorithm is proposed in this paper. Firstly, the GMPSO algorithm is used to optimize the $[K,\alpha]$ parameter combination in the VMD algorithm, and the optimal $[K,\alpha]$ parameter combination of each gear fault vibration signal to be decomposed is selected. Then, the gear fault vibration signal is decomposed into several intrinsic mode functions (IMFs) by VMD, and the sample entropy value of each IMFs is extracted to form the feature vector of subsequent fault diagnosis. Finally, the characteristic vector of gear fault vibration signal is input into PNN model, and gear fault is accurately classified. By comparing with fixed parameter VMD algorithm, empirical mode decomposition (EMD) and complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithm, the superiority of this method in gear fault diagnosis is verified. Therefore, the GMPSO-VMD-PNN algorithm proposed in this paper has certain application value for gear fault diagnosis.

Macroscopic–Microscopic Attention in LSTM Networks Based on Fusion Features for Gear Remaining Life Prediction

In the mechanical transmission system, the gear is one of the most widely used transmission components. The failure of the gear will cause serious accidents and huge economic loss. Therefore, the remaining life prediction of the gear is of great importance. In order to accurately predict the remaining life of the gear, a new type of long-short-term memory neural network with macroscopic–microscopic attention (MMA) is proposed in this article. First, some typical time-domain and frequency-domain characteristics of vibration signals are calculated, respectively, such as the maximum value, the absolute mean value, the standard deviation, the kurtosis, and so on. Then, the principal component of these characteristics is extracted by the isometric mapping method. The importance of fusional characteristic information is filtered via a proposed MMA mechanism so that the input weight of neural network data and recursive data can reach multilevel real-time amplification. With the new long short-term memory neural network, the health characteristics of gear vibration signals can be predicted based on the known fusion features. The experimental results show that this method can predict the remaining life of gears and bearings well, and it has higher prediction accuracy than the conventional prediction methods.

Gear Fault Diagnosis Based on Kurtosis Criterion VMD and SOM Neural Network

A gear fault diagnosis method based on kurtosis criterion variational mode decomposition (VMD) and self-organizing map (SOM) neural network is proposed. Firstly, the VMD algorithm is used to decompose the gear vibration signal, and the instantaneous frequency mean is calculated as the evaluation index, and the characteristic curve is drawn to screen out the most relevant intrinsic mode functions (IMFs) of the original vibration signal. Then, the number of VMD decompositions is determined, and the kurtosis value of IMFs are extracted to form the feature vectors. Then, the kurtosis value feature vectors of IMFs are normalized to form the kurtosis value normalized vectors. Finally, the normalized vectors of kurtosis value are input into SOM neural network to realize gear fault diagnosis. When the number of training times of SOM neural network is 100, the gear fault category is accurately classified by SOM neural network. The results show that when the training times of SOM neural network is 100 times, the gear fault diagnosis method, based on the kurtosis criterion VMD and SOM neural network is 100%, which indicates that the new method has a good effect on gear fault diagnosis.