Gear Vibration Signal Research Articles

Anomaly Detection and Remaining Useful Life Estimation for the Health and Usage Monitoring Systems 2023 Data Challenge.

Gear fault detection and remaining useful life estimation are important tasks for monitoring the health of rotating machinery. In this study, a new benchmark for endurance gear vibration signals is presented and made publicly available. The new dataset was used in the HUMS 2023 conference data challenge to test anomaly detection algorithms. A survey of the suggested techniques is provided, demonstrating that traditional signal processing techniques interestingly outperform deep learning algorithms in this case. Of the 11 participating groups, only those that used traditional approaches achieved good results on most of the channels. Additionally, we introduce a signal processing anomaly detection algorithm and meticulously compare it to a standard deep learning anomaly detection algorithm using data from the HUMS 2023 challenge and simulated signals. The signal processing algorithm surpasses the deep learning algorithm on all tested channels and also on simulated data where there is an abundance of training data. Finally, we present a new digital twin that enables the estimation of the remaining useful life of the tested gear from the HUMS 2023 challenge.

A distinguished deep learning method for gear fault classification using time–frequency representation

Fault diagnosis of gearboxes has attracted increasing interest in recent decades due to their ubiquity and importance in the industry. Modern research trends focus on developing a diagnosis system that works automatically with the application of artificial intelligence. These previous studies have used the Deep Learning (DL) network without adequately addressing noise of the input data, requiring more data to achieve effective training. Thus, this work proposes a novel Transfer Learning method using the time–frequency representation of gear vibration signals, which enables more accurate classification in complex working conditions and reduces necessary input data to train. Using fine-tuning techniques proposed in this paper requires only a limited data set while ensuring acceptable classification results. An experiment test rig within different gear faults and load conditions was set up to evaluate the algorithm’s effectiveness.

Research on a Wind Turbine Gearbox Fault Diagnosis Method Using Singular Value Decomposition and Graph Fourier Transform.

Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singular value decomposition (SVD) and graph Fourier transform (GFT). Singular values, commonly employed in feature extraction and fault diagnosis, effectively encapsulate various fault states of mechanical equipment. However, prior methods neglect the inter-relationships among singular values, resulting in the loss of subtle fault information concealed within. To precisely and effectively extract subtle fault information from gear vibration signals, this study incorporates graph signal processing (GSP) technology. Following SVD of the original vibration signal, the method constructs a graph signal using singular values as inputs, enabling the capture of topological relationships among these values and the extraction of concealed fault information. Subsequently, the graph signal undergoes a transformation via GFT, facilitating the extraction of fault features from the graph spectral domain. Ultimately, by assessing the Mahalanobis distance between training and testing samples, distinct defect states are discerned and diagnosed. Experimental results on bearing and gear faults demonstrate that the proposed method exhibits enhanced robustness to noise, enabling accurate and effective diagnosis of gearbox faults in environments with substantial noise.

A novel gearbox local fault feature extraction method based on quality coefficient and dictionary learning

The performance of sparse decomposition is directly determined by the similarity between impact atoms and the actual fault impact waveform. The shift-invariant K-singular value decomposition (K-SVD) dictionary learning algorithm is capable of training impact patterns from vibration signals collected by sensors to construct impact atoms, thereby extracting fault impact components from the vibration signals. However, the impact pattern training using the shift-invariant K-SVD algorithm is influenced by the presence of harmonics and white noise in the gear transmission system vibration signals. To solve the above problems, a novel gearbox local fault feature extraction method based on the quality coefficient and dictionary learning is proposed in this paper. Firstly, the original signal is decomposed into a series of intrinsic mode functions (IMFs) by empirical mode decomposition. Then, a new quality coefficient is proposed by comprehensively considering the intensity of the impact, harmonics and noise components in each IMF, as well as the degree of correlation with the original signal. The IMF with the largest quality coefficient is used to train the impact pattern and solve the sparse coefficients. Finally, the orthogonal matching pursuit algorithm is adopted to solve the sparse coefficients, which are used to reconstruct the fault impact response signal from the dictionary. Simulation and experimental analysis demonstrate the superior performance of the proposed method compared to other state-of-the-art methods.

Failure analysis of gear using continuous wavelet transform applied in the context of wind turbines

One of the main reasons for failure in the wind turbine is the wear between the gear teeth during the power conversion and changes in the rotation speed, which is also generally associated with changes in the lubrication regimes. In this sense, vibration and signal analysis are frequently used in predictive maintenance as they usually permit the identification of deviations in the proper functioning of the equipment. Thus, this work aims to apply the continuous wavelet transform (CWT) to correlate gear wear and vibration signals, using visual and straightforward analysis. An experimental setup of a gear system was used to analyze vibration signals from different tooth gear damages. Gears with different levels and modes of damage were used in order to evaluate the sensitivity of vibration signals to them. The features from vibration signals were extracted by Morlet wavelet analysis. Results demonstrate that the proposed method accurately detected the early failure by visualization in frequency–time maps.

Early pitting fault detection for polymer gears using kurtosis-VMD based condition indicators

The vibration signals of a polymer gear are considerably weak and susceptible to ambient noise at the early stage of the fault, which makes the fault difficult to detect. Efficient detection of an early fault in a polymer gear may improve the operation safety of the machinery system that utilizes it for power transmission. This study introduces an innovative approach for the early detection of pitting faults in polymer gears, utilizing condition indicators (CIs) derived from kurtosis-variational mode decomposition (VMD). First, the vibration signal of the polymer gear is decomposed using VMD into several components. Second, the sensitive components are selected to construct a new signal from the first two largest kurtosis values. Third, the CIs are extracted from newly constructed signals, and envelope spectrum analysis is performed. It is observed from the results that the kurtosis-VMD based CIs are effective in the early pitting fault detection of polymer gears. Finally, it is found that the proposed method performs better in all operating conditions considered in the experiment, compared with raw signal and kurtosis-empirical mode decomposition (EMD) based analysis. The proposed method’s response to noise is also explored. Furthermore, the proposed method is compared with the existing time synchronous averaging (TSA), difference, and residual methods.

Gear fault diagnosis based on complex network theory and error-correcting output codes: Multi class support vector machine

Gearbox failures have a detrimental effect on the machine performance that affects the production capacity and economic benefits of a manufacturing industry in an adverse manner. Early detection of faults in gears helps to prevent sudden machine failures. Previously, many signal processing and artificial intelligence techniques have been successfully applied to diagnose gear faults by analyzing the machine vibrations. These techniques have repeatedly emphasized on the need to extract quality features from gear vibration signals and using artificial intelligence techniques that can identify multiple types of faults simultaneously. As such, in this article, new features called as visibility graph features based on complex network theory have been proposed to extract fault information from vibration signals. In addition, a new artificial intelligence framework for multifault classification known as error-correcting output codes-multiclass support vector machine is proposed to detect gear faults. To the best of authors’ knowledge, these features along with the error-correcting output codes-artificial intelligence framework have been rarely utilized for fault diagnosis purpose. The proposed approach has been applied on experimental gear vibration data to validate its effectiveness. First, the vibration signals are transformed to graphs, and various graph properties are computed to serve as fault features. Then, the fault features are supplied to train the error-correcting output codes-multiclass support vector machine model and learn the fault patterns. Finally, the gear fault classification accuracies are determined for various gear test conditions and compared with those of existing methods. It is observed that the proposed approach provides an average improvement of 4.22%, 9.93% and 11.8% over the time-domain features, time–frequency domain features and voting-based multiclass support vector machine classifier, respectively, for different operating conditions. Furthermore, the suggested technique augments the classification accuracies by 10%, 7.5% and 6.7%, respectively, as compared with the deep-learning models, namely standard stacked sparse autoencoder, deep neural network and convolution neural network.

Research on Gearbox Fault Diagnosis Method Based on VMD and Optimized LSTM

The reliability of gearboxes is extremely important for the normal operation of mechanical equipment. This paper proposes an optimized long short-term memory (LSTM) neural network fault diagnosis method. Additionally, a feature extraction method is employed, utilizing variational mode decomposition (VMD) and permutation entropy (PE). Firstly, the gear vibration signal is subjected to feature decomposition using VMD. Secondly, PE is calculated as a feature quantity output. Next, it is input into the improved LSTM fault diagnosis model, and the LSTM parameters are iteratively optimized using the chameleon search algorithm (CSA). Finally, the output of the fault diagnosis results is obtained. The experimental results show that the accuracy of the method exceeds 97.8%.

Analysis of Vibration Characteristics of Planetary Gearbox with Broken Sun Gear Based on Phenomenological Model

To investigate the vibration properties in healthy and fault conditions of planetary gearboxes, a phenomenological model is constructed to present the vibration spectrum structure. First, the effects of the base deflection of the gear fillet and the flexibility between the root circle and the base circle on the time-varying meshing stiffness are considered in order to construct an equivalent model of time-varying mesh stiffness and broken tooth faults, exploring the law of variation for meshing stiffness when differently sized faults occur on the sun gear. Then, considering both the effect of the vibration transfer path and the meshing impacts, we establish phenomenological models of planetary gears under healthy and fault conditions. By comparing and analyzing the phenomenological model based on the cosine function to verify the effectiveness of the proposed model. The experimental results show that the error of the proposed model is 1.38% lower than that of the traditional phenomenological model, and the proposed model can accurately analyze the frequency, amplitude, and sideband characteristics of the vibration signals of sun gear with different degrees of broken tooth, which can be used for the local fault diagnosis of planetary gearboxes.

Dual-Thread Gated Recurrent Unit for Gear Remaining Useful Life Prediction

Remaining useful life (RUL) prediction can provide a foundation for the operation and maintenance of industrial equipment. In order to improve the predictive ability for the complex degradation trajectory, a new dual-thread gated recurrent unit (DTGRU) is explored. It uses a dual-thread learning strategy to mine the stationary and non-stationary information from the input data and the difference of hidden states at two adjacent time steps. Then the state transition updating formulas of DTGRU are derived. Using the collected gear vibration signals and degradation-trend-constrained variational autoencoder, the gear health indicator (HI) is constructed. Based on the constructed HI and DTGRU, a novel RUL prediction method is developed. Via multiple gear life-cycle datasets, the effectiveness of the DTGRU-based RUL prediction approach is verified. Furthermore, compared with the existing typical prediction methods, the experimental results show that DTGRU has higher predictive ability in terms of HI fitting precision and RUL prediction performance.

Dynamic modeling and vibration analysis of planetary gear sets concerning mesh phasing modulation

This paper studies the changes in behavior, in terms of mesh phasing modulation, of planetary gear transmissions (PGTs) due to various gear pinhole position errors. An advanced model of the spur PGT is established to explore the effects of the position errors on mesh phasing relations and an analytical determination of the relative mesh phasing variation is derived. Furthermore, the vibration performance of planetary gears is investigated by developing a novel dynamic model and components of the vibration signals are clarified using the proposed model. Additionally, we further perform several experiments to measure the mesh phasing variations using strain gauges and collect the gear vibration signals using accelerometers. Finally, simulation and experimental results are compared to verify the proposed models, and the results indicate that the presented models provide the opportunity for the researchers to quantify the mesh phasing relations relative to the gear position errors as well as clarify the frequency modulation mechanism of gear vibrations in PGTs.

A new noise reduction method based on re-weighted group sparse decomposition and its application in gear fault feature detection

Aiming at the problem that gear vibration signals are susceptible to noise and the difficulty of extracting fault features, this paper proposes a new noise reduction method based on re-weighted group sparse decomposition (RWGSD). RWGSD introduces group sparse mode decomposition theory to protect the structural information of signal components in the frequency domain. On this basis, vital components are screened according to the time-domain characteristics of fault information, and the re-weighted enhancement is carried out. The fault characteristics are easy to identify in the final noise reduction result. In addition, RWGSD defines two new indicators, cyclic re-weighted kurtosis (CRWK) and re-weighted cyclic intensity (RWCI). CRWK can assess the intensity of periodic characteristic components and has some resistance to strong impact interference. RWCI can evaluate the magnitude of fault information, overcoming the limitations of traditional noise reduction techniques that screen out vital components based on energy size. Numerical simulation and real-world experiment results show that the proposed method has excellent performance in noise removal, increases the reliability of gear fault feature detection, and has certain practical values.

Difference mode decomposition for adaptive signal decomposition

Adaptive extraction of concerned components (CC) from mixed frequency components remains to be a challenging topic in various research domains. Most existing adaptive mode decomposition algorithms for extracting CC, such as wavelet transform, wavelet packet transform, singular value decomposition, empirical mode decomposition, empirical wavelet transform, and variational mode decomposition, are intrinsically adaptive band-pass filter banks and they face the following two tough problems. The first problem is that they cannot separate CC from interferential components in same frequency bands. The second problem is that it is not fully effective in automatically selecting CC distributed in different frequency bands by using some designed criteria. In this paper, a new decomposition approach called difference mode decomposition (DMD) is proposed to adaptively decompose a mixed signal into CC, reference components, and noise, and enrich the domain of adaptive mode decomposition. The proposed DMD relies on convex optimization and Fourier transform, and its decomposition is mathematically justified and composes physical interpretations. Analyses of simulated and real-world bearing and gear vibration signals are used to verify the effectiveness and superiority of the proposed DMD over existing adaptive mode decomposition algorithms. It is demonstrated that the proposed DMD can effectively extract CC such as repetitive transients caused by bearing and gear faults. Moreover, since the proposed DMD is based on Fourier transform expanded by trigonometric basis functions, the proposed DMD can be easily extended to other domains by expanding basis functions besides the frequency domain.

Optimization Application of Deep Belief Network in Gear Fault Diagnosis

Deep belief networks (DBNs) in the process of the application of the gear vibration signal fault diagnosis, vector network depth, the number of neurons in hidden layer, set the initial parameters, such as there is a certain blindness, and for different data sets, the influence of initial parameters is different also, in order to get ideal fault recognition rate, the initial parameters have to be repeatedly debugging, This process is not only time-consuming and laborious, but also disadvantageous to its universal application in fault diagnosis. To solve this problem, this paper mainly optimizes the number of hidden layer neurons and learning rate of DBNs. The diagnosis example shows that after optimization, the initial parameter setting is more accurate and efficient, and the fault identification rate is significantly improved.

A Fault Diagnosis Scheme for Gearbox Based on Improved Entropy and Optimized Regularized Extreme Learning Machine

The performance of a gearbox is sensitive to failures, especially in the long-term high speed and heavy load field. However, the multi-fault diagnosis in gearboxes is a challenging problem because of the complex and non-stationary measured signal. To obtain fault information more fully and improve the accuracy of gearbox fault diagnosis, this paper proposes a feature extraction method, hierarchical refined composite multiscale fluctuation dispersion entropy (HRCMFDE) to extract the fault features of rolling bearing and the gear vibration signals at different layers and scales. On this basis, a novel fault diagnosis scheme for the gearbox based on HRCMFDE, ReliefF and grey wolf optimizer regularized extreme learning machine is proposed. Firstly, HRCMFDE is employed to extract the original features, the multi-frequency time information can be evaluated simultaneously, and the fault feature information can be extracted more fully. After that, ReliefF is used to screen the sensitive features from the high-dimensional fault features. Finally, the sensitive features are inputted into the optimized regularized extreme learning machine to identify the fault states of the gearbox. Through three different types of gearbox experiments, the experimental results confirm that the proposed method has better diagnostic performance and generalization, which can effectively and accurately identify the different fault categories of the gearbox and outperforms other contrastive methods.

Research on a Denoising Method of Vibration Signals Based on IMRSVD and Effective Component Selection

This paper proposes a denoising method of vibration signal based on improved multiresolution singular value decomposition (IMRSVD) and effective component selection. A new construction method of trajectory matrix is used, which can enhance the oscillating component of the original signal. Next, based on the improved trajectory matrix, singular value decomposition (SVD), which plays the role of pre-decomposition, is used to obtain multiple one-dimensional components, and the further decomposition of that is achieved by multiresolution singular value decomposition (MRSVD). Finally, the effective components selection of a series of decomposed signal components is achieved based on the proposed feature evaluation index (FEI). The denoising experiments are carried out using the simulation signal and the vibration signal of planetary gear, respectively. The experimental results show that the proposed method performs better than the traditional SVD denoising method, and the weak fault feature in the vibration signal can be extracted successfully. In addition, the comparison between periodic modulation intensity (PMI) and FEI displays that the proposed method has better robustness and accuracy than the interference components with similar frequency. Thus, the proposed method is an effective weak fault feature extraction and denoising tool of vibration signals for fault diagnosis.

Gear Fault Diagnosis Based on Variational Modal Decomposition and Wide+Narrow Visual Field Neural Networks

In modern industrial production, rotating machinery plays an important role. The gears in this machinery adjust the speed and transmission of torque. Therefore, when the gear fails, it is very important to be able to diagnose the fault quickly and accurately. Gear vibration signals are often used in gear fault diagnosis, but the fault signal is often overwhelmed by noises. To enable the scientific and efficient detection of faults, this study proposes a gear fault diagnosis method based on variational modal decomposition (VMD) and wide+narrow visual field neural networks (WNVNNs), namely VMD-WNVNN. VMD-WNVNN consists of two stages. In the feature extraction stage, VMD and Pearson correlation coefficients are used to decompose and reconstruct the original data to obtain the features of these data in the frequency domain. In the classification stage, WNVNN is used to classify the data based on features. The final results of the gear fault diagnosis experiments show that this method not only has higher classification accuracy but also has higher classification stability than other recently proposed methods. Note to Practitioners—The gearbox is composed of many mechanical parts, such as gears, shafts, and bearings. Therefore, the vibration signal collected by the vibration sensor on the gearbox housing will contain the vibration signal of each part and the noise caused by processing errors. Therefore, if some methods can be used to efficiently extract the characteristic signals required for diagnosis in the data processing stage, the efficiency of fault diagnosis will be greatly improved. This article takes the health of gears as the research object and proposes a method that combines adaptive signal decomposition and deep learning technology. Experimental results show that this method has higher classification accuracy and classification stability than other methods proposed recently.

Removal of transfer function effects from gear vibration signals under constant and variable speed conditions

Gear faults generally cause changes to the forcing functions of the system, which are usually hard to measure. Vibration is a common tool for gear condition monitoring, it being generated by a forcing function exciting responses through a transmission path from the excitation to the measurement point. The diagnostic information in the vibration measurements is often distorted by transfer function effects, in particular for local faults, such as cracks, where the waveform is important. In such cases, more direct diagnostic information can be extracted by removing the transfer function effects. However, a very limited amount of research has been carried out to reconstruct the time-domain waveforms of the forcing functions, except some making the assumption that the forcing functions are impulsive. A method was previously developed to identify and remove the transfer function effects from transmission error (TE) measurements at constant speeds to reconstruct the excitations, utilising a cepstrum-based operational modal analysis (OMA) method. In the current paper, this method is extended to vibration signals under constant and variable speed conditions. Since vibration has more complex transfer functions than TE, this paper establishes an additional pre-processing procedure, which removes the deterministic components in order to facilitate the OMA process. After removing the transfer function effects from measured vibration signals, the proposed technique reconstructs forcing functions that are much more clearly indicative of the faults at all speeds and which approximate the meshing forces at the gear teeth. The fault features are effectively enhanced and localised in the forcing functions, and the importance of phase modification to the reconstruction of forcing function waveforms is demonstrated. The technique was validated using vibration measurements obtained from a single stage spur gear box with a tooth root crack.

A general fault diagnosis framework for rotating machinery and its flexible application example

When dealing with the fault diagnosis of different rotating machines (gear or bearing), different working conditions (such as rotating speed), different signals (acoustic signal or vibration signal), it is usually necessary to establish different models, which is, however, time-consuming and laborious. At the same time, the models have poor generality and portability. In order to solve above problems, a general fault diagnosis framework (GFDF) is proposed in this paper. Firstly, the collected signals, whether vibration signals or acoustic signals, are directly converted into two-dimensional gray images; secondly, the FAST-Enhanced-Unoriented-SIFT (FEUS) feature extraction algorithm proposed in this paper is used to extract feature vectors; then, the feature vectors are encoded by using the bag-of-words (BoW) model to obtain the basic words and codebook vectors; finally, the fault diagnosis is completed by calculating the distance between the description vector of the signal to be diagnosed and the codebook vectors. GFDF’s main feature lies in the evitable frequency domain transformation and noise reduction, which makes GFDF insensitive to signal type and has high diagnostic efficiency. The experimental results show that GFDF has high diagnostic accuracy and stability for acoustic signals and vibration signals of rolling bearing and planetary gear at different rotating speeds, which proves that GFDF has generality and portability and is potential for the application in other scenes. Comparative experiments show that GFDF outperforms the representative traditional classification methods and deep learning models in diagnostic accuracy and stability. In addition, GFDF is applied to the fault diagnosis of the acoustic signals collected in motion to simulate the working state of inspection robots, and the ideal diagnostic result is also achieved. The flexible application example of this framework provides experience for other researchers.

Semi-supervised fault diagnosis of machinery using LPS-DGAT under speed fluctuation and extremely low labeled rates

Recent research in semi-supervised fault diagnosis of machinery based on graph neural networks (GNNs) still has some problems, such as insufficient label information mining, static feature extraction of neighbor nodes, and relatively ideal diagnosis scenarios. In engineering practice, machinery often runs under speed fluctuation such as start-stop process, and labeling samples becomes increasingly expensive. To deal with the above challenges, a new semi-supervised fault diagnosis method called label propagation strategy and dynamic graph attention network (LPS-DGAT) is proposed in this paper. The designed LPS can take full advantage of the label co-dependency between samples, so as to realize the full utilization of the limited label information. The constructed DGAT by dynamic attention can effectively extract feature information of the different neighbor nodes under speed fluctuation. The proposed method is used to analyze the vibration signals of bearing and gear under speed fluctuation, and the comparison results show that even in the extreme situations where the labeled rates are no more than 1%, the proposed method can still accurately extract discriminative features and diagnose different fault modes, which is better than other GNNs.