Planetary Gearbox Fault Diagnosis Research Articles

A novel mathematical model of transmission path effect for the research of vibration characteristics of planetary gearboxes

Model-based vibration signal analysis to interpret and understand vibration characteristics can provide prior guidance for the condition monitoring and fault diagnosis of planetary gearboxes (PGs). Transmission path effects due to the rotational motion of planet gears with respect to the accelerometer mounted on the PG housing make understanding its real dynamic behavior challenging. To overcome this challenge, a novel mathematical model of the transmission path effect is proposed to support the construction of more realistic dynamic response of PGs. This model is derived only from the geometric parameters and material properties, and it has higher applicability than traditional models. Subsequently, a phenomenological vibration model is used to simulate all vibration sources, including sun–planet and ring–planet gear meshes. On these bases, a comprehensive vibration signal model is proposed by considering all vibration sources and the corresponding transmission path effects. Moreover, the theoretical spectral structure is deduced via Fourier series analysis. Finally, the vibration characteristics of the vibration signals obtained using the proposed mathematical model are analyzed and validated through simulations and experiments in the time and frequency domains.

Intelligent Fault Diagnosis for Planetary Gearbox Using Time-Frequency Representation and Deep Reinforcement Learning

Accurately and intelligently identifying faults of the planetary gearbox is essential in the safe and reliable operation and maintenance of the mechanical drive system. Recently, fault diagnosis of planetary gearbox has acquired tremendous progress, especially with the rising popularity of deep learning (DL). However, most methods are standard supervised learning where the input is directly mapped to a fault type, and with strong feedback. Also, their learning ways are static and unlike human learning that gradually acquires knowledge by interaction with the environment. To a certain extent, these deficiencies reduce the generalization and intelligence level of DL-based fault diagnosis methods. Besides, due to harsh working conditions, signals acquired often have strong noise and nonlinear features, leading to relatively low accuracy if raw signals are used as the input directly. Thus, this article proposes a new fault diagnosis method based on time-frequency representation and deep reinforcement learning (DRL). We first define fault diagnosis as a sequential decision-making problem in the classification Markov decision process. Next, the vibration signals are converted to uniform-sized TF maps by synchro-extracting transform to enhance the robustness of feature representation. Finally, a diagnosis agent is built and trained in the framework of DRL to learn the optimal classification policy automatically. Experimental results show that this method not only achieves better generalization and stability with an overall accuracy of over 99.5% in single-speed load cases but also outperforms others in multiwork conditions.

Refined time-shift multiscale diversity entropy: a novel feature extraction algorithm for fault diagnosis of planetary gearbox

Abstract Planetary gearboxes play a critical role in aerospace and heavy industry fields, such as wind turbines, heavy vehicles and construction machines. Intelligent fault diagnosis is significant for safe operation and fault prevention of planetary gearboxes. Recently, multiscale diversity entropy and related entropy methods are proposed to extract features of time series and applied for the fault diagnosis. However, there are still some limitations in fault feature representation and stability for multiscale diversity entropy. To solve the problem, in this paper, a novel planetary gearboxes fault diagnosis method via refined time-shift multiscale diversity entropy (RTSMDE) is proposed. First, a novel entropy algorithm called RTSMDE is proposed to measure the complexity of time series and extract fault features of the vibration signals, which is robust and efficient in performance. Then, the obtained features are utilized to fulfil automatically the fault pattern identifications using support vector machine. To confirm the superiority of the RTSMDE-based fault diagnosis method, simulated signals and experimental studies are constructed and three used widely methods are employed to present a comprehensive comparison. The results indicate that RTSMDE performs best and obtains the highest accuracy.

Cyclic symplectic component decomposition with application in planetary gearbox fault diagnosis

Due to the structural complexity of planetary gearbox, it is difficult to extract the fault information in the vibration signal of planetary gearbox, which seriously affects the accuracy of fault diagnosis. Although the existing fault diagnosis methods, such as local characteristic-scale decomposition (LCD) and ensemble empirical mode decomposition (EEMD), are widely used in the field of fault diagnosis, they are difficult to decompose complex signals effectively. Therefore, a new signal processing method, called cyclic symplectic component decomposition (CSCD) based on the Toeplitz matrix and the cyclic matrix, is proposed in this paper. In CSCD, to obtain the closed-loop solutions, each row is the right cyclic shift of the previous row, so as to avoid information leakage. Meanwhile, the combination of sample covariance and symplectic geometry similarity transformation is constructed to further protect the status information and weaken the influence of noise. In addition, the reconstruction of the same mode is completed by using the extreme difference similarity (EDS), which can realize the adaptive decomposition of the signal. The research results of simulation signal and actual planetary gearbox fault signal show that the proposed CSCD method has superior decomposition performance.

Vibration Separation Methodology Compensated by Time-Varying Transfer Function for Fault Diagnosis of Non-Hunting Tooth Planetary Gearbox.

Due to planetary movement of planet gears, the vibration signal perceived by a stationary sensor is modulated and difficult to diagnose. This paper proposed a vibration separation methodology compensated by a time-varying transfer function (TVTF-VS), which is a further development of the vibration separation (VS) method in the diagnosis of non-hunting tooth planetary gearboxes. On the basis of VS, multi-teeth VS is proposed to extract and synthesize the meshing signal of a planet gear using a single transducer. Considering the movement regularity of a planetary gearbox, the time-varying transfer function (TVTF) is represented by a generalized expression. The TVTF is constructed using a segment of healthy signal and an evaluation indicator is established to optimize the parameters of the TVTF. The constructed TVTF is applied to overcome the amplitude modulation effect and highlight fault characteristics. After that, experiments with baseline, pitting, and compound localized faults planet gears were conducted on a non-hunting tooth planetary gearbox test rig, respectively. The results demonstrate that incipient failure on a planet gear can be detected effectively, and relative location of the local faults can be determined accurately.

Research on fault diagnosis of planetary gearbox based on variable multi-scale morphological filtering and improved symbol dynamic entropy

Under complex working conditions with noise interference, the fault feature of planetary gearbox is difficult to be extracted and the fault mode is difficult to be identified. To tackle this problem, the technologies of variable multi-scale morphological filtering (VMSMF) and average multi-scale double symbolic dynamic entropy (AMDSDE) are proposed in this paper. VMSMF selects Chebyshev Window as the structural element and automatically selects the optimal-scale parameters according to the signal characteristics of the planetary gearbox, which improves the filtering accuracy and calculation efficiency. AMDSDE fully considers the correlation between various state modes. Once combined with relevant knowledge of Mathematical statistics, the algorithm can effectively reduce misjudgment. Firstly, the turn domain resampling (TDR) is used to transform the time domain signal of variable speed into the angle domain signal that is not affected by speed change. Secondly, the proposed VMSMF is used to de-noise the vibration signal, and the fault signal with a high signal-to-noise ratio is obtained. Finally, AMDSDE is used to extract the entropy value of the fault signal and judge the fault type. The proposed technology is verified by four kinds of signals collected from the sun gear of the planetary gearbox under non-stationary working conditions.

Deep residual networks-based intelligent fault diagnosis method of planetary gearboxes in cloud environments

With the widespread use of deep learning (DL) related techniques, many end-to-end planetary gearbox fault diagnosis models have been proposed. The input samples of DL models are often composed of time-domain signals, frequency-domain signals, or time–frequency domain signals from multiple rotation periods. So, redundant information is unavoidable, which may cause difficulty in the extraction of subtle fault features by the DL model and affect the accuracy of fault diagnosis. In addition, DL-based intelligent fault diagnosis (IFD) methods are developed based on a large amount of data. It is difficult to realize real-time fault diagnosis by relying on local equipment with limited computing power. Therefore, this paper proposes a deep residual networks-based IFD method of planetary gearboxes in cloud environments. A cloud-based IFD design is proposed to use the super computing power of cloud computing to solve the related issues caused by the insufficient computing power of local equipment. This method takes the wavelet time–frequency images of vibration signals as the network input. In order to obtain high accuracy, a method specialized for the selection of wavelet basis function (WBF) is developed based on the difference between the original signals and the reconstructed wavelet signals. Channel attention depth residual networks (CADRN) are used as the diagnosis model, and the channel attention module (CAM) is applied to enhance important fault features and improve the diagnosis accuracy. An ablation study and comparative experiments with three mainstream methods were carried out on a real-world dataset of planetary gearboxes, and the proposed method achieved more than 99% average accuracy rate, which verified the effectiveness of the proposed method.

Multi-Scale Attention Based Deep Reinforcement Learning for Intelligent Fault Diagnosis of Planetary Gearbox

Multi-Scale Attention Based Deep Reinforcement Learning for Intelligent Fault Diagnosis of Planetary Gearbox

Effective Convolutional Transformer for Highly Accurate Planetary Gearbox Fault Diagnosis

To extract the global temporal correlations and local features together to enhance the accuracy for fault diagnosis, this paper proposes an effective convolutional Transformer (ECT), which can learn the global temporal correlations using Transformer and local features with convolution at the same time. The proposed method designs a multi-stage hierarchical structure of Transformer, which utilizes convolutional tokenization to distill dominating sequence features from raw vibration signals while increasing the dimension of token embedding across stages at the same time as that in CNNs. The spatial-reduction attention (SRA) and the linear dimension reduction projections are introduced respectively to Transformer at different stages to reduce the resource consumption of the model. Finally, the proposed method utilizes a sequence pooling strategy on the output of Transformer to eliminate the requirement of the class token and make the model accurate for classification. The specially designed structure makes the model flexible and effective for planetary gearbox fault diagnosis. Experiments performed on planetary gearbox fault simulators indicate that the ECT method has significant effectiveness and high accuracy compared with the state-of-the-art methods for planetary gearbox fault diagnosis.

Matching Synchroextracting Transform for Mechanical Fault Diagnosis Under Variable-Speed Conditions

Time–frequency (TF) analysis (TFA) technique has been widely used to the analysis of rotating machine vibration. However, vibration signal from practical sources contains complicated components and noise, so the fault diagnosis to variable-speed machinery is full of challenges. In this study, inspired by the demodulated synchrosqueezing transform (DSST), the synchroextracting transform (SET) is extended to a prior instantaneous frequency (IF) based method, named matching synchroextracting transform (MSET). To achieve the fault diagnosis using MSET, the follow-up works mainly include two parts. First, a demodulation filtering strategy is developed for multicomponent signal separation. Second, the order analysis based multiple IFs estimation idea and the second-order difference operator based IF smoothing scheme are introduced to obtain the reliable initial IFs. The effectiveness of the proposed technique is verified via some simulation studies. Finally, the proposed technique is successfully applied to the fault diagnosis of rolling bearing and planetary gearbox.

Feature Enhancement Based on Regular Sparse Model for Planetary Gearbox Fault Diagnosis

The planetary gearbox, widely used in many machinery fields, suffers from harmful vibration excited by bearings fault, which always causes machine breakdowns. Thus, fault diagnosis is the necessary approach to keeping machines safe, which often takes fault features, which are extracted from signals, as critical information. However, limited to various interferences caused by gear meshing and background noise, fault characteristic information is always weak and difficult to identify, bringing an increasing emphasis on feature enhancement. In this paper, based on the feature enhancement problem under strong interferences, a sparse regular diagnosis algorithm is studied. Firstly, a new fault sensitivity indicator is constructed to distinguish different periodic impulse signals and enhance the energy of the fault impulse. Combined with tunable Q-factor wavelet transform multi-scale representation, the guided enhanced vector is introduced to guide the directional gathering of the fault frequency band. Then a weighted regular term is constructed to establish the Guided Enhanced Regular Sparse (GERS) model. Iterative soft threshold algorithm is employed to solve the model. Compared with state-of-the-art methods, through numerical simulation and fault experiment, the effectiveness and superiority of the proposed algorithm is verified successfully.

Degree of cyclic target protrusion defined on squared envelope spectrum for rotating machinery fault diagnosis

Rotating machinery fault diagnosis is critical for safe operation of modern mechanical equipment so as to avoid serious damage and economic loss caused by malfunctions. Envelope analysis is an effective method in the field of rotating machinery fault diagnosis, in which the selection of optimal demodulated band containing the most obvious fault features by fault index is a critical step. However, the existing fault indexes are often defined on the basis of global ratio in their domains of definitions, which may result in incorrect band selection. To address the problem, a novel index named degree of cyclic target protrusion (DCTP) for fault diagnosis is proposed in this paper. DCTP is defined on squared envelope spectrum to take adequately fault characteristic frequency (FCF) into consideration. Specifically, Otsu method is utilized to calculate local threshold for determining cyclic target amplitude and cyclic background in two elaborate bands. In this aspect, DCTP is defined as a weighted local ratio of cyclic target amplitude to cyclic background. Because it focuses on FCF, DCTP can avoid interference by extraneous components. DCTP is used to replace the kurtosis index of fast kurtogram (FK) to establish the DCTPgram which is compared with FK and ratio of cyclic content based method in roller bearing fault diagnosis and planetary gearbox fault diagnosis. Experimental results and comparison studies demonstrate that the DCTPgram has a significant advantage for rotating machinery fault diagnosis.

Incipient fault diagnosis of planetary gearboxes based on an adaptive parameter-induced stochastic resonance method

The stochastic resonance (SR) method is commonly used in incipient fault diagnosis to extract weak fault features from complex diagnostic signals. However, the extraction effect of a SR system is highly dependent on the choice of system parameters as well as the complexity of input signals. To solve this problem, the present study proposes an adaptive parameter-induced SR method, in which high pass filter and Teager energy operator (TEO) are combined to pre-process the original signal while the grasshopper optimization algorithm is introduced to optimize the SR system parameters. The proposed method is employed to diagnose a set of experimental vibration signals of a planetary gearbox with incipient localized root crack and incipient distributed surface wear as well, leading to satisfactory diagnosis results. Comparing with the existing adaptive stochastic resonance methods, the present method claims the merits of a high signal-to-noise ratio and low computation cost.

Intelligent Fault Diagnosis Method of Wind Turbines Planetary Gearboxes Based on a Multi-Scale Dense Fusion Network

Due to the powerful capability of feature extraction, convolutional neural network (CNN) is increasingly applied to the fault diagnosis of key components of rotating machineries. Due to the shortcomings of traditional CNN-based fault diagnosis methods, the continuous convolution and pooling operations result in the constant decrease of feature resolution, which may cause the loss of some subtle fault information in the samples. This paper proposes a CNN-based model with improved structure multi-scale dense fusion network (MSDFN) to realize the fault diagnosis of wind turbines planetary gearboxes under complicated working conditions. First, the continuous wavelet transform is applied to preprocess the vibration signals, and the two-dimensional wavelet time-frequency diagrams are used as the network input. Then, the multi-scale feature fusion (MSFF) module and a feature of maximum (FoM) module are used in the extraction and classification stages of fault features, respectively. Next, the multi-scale features of each network layer are fused to enhance the fault features. Finally, the high fault diagnosis accuracy is achieved by extracting the separable fusion result of fault features. The proposed method achieves more than 99% fault diagnosis average accuracy on a planetary gearbox dataset. The comparative experimental results verify the effectiveness of the proposed method and its superiority to some mainstream approaches. The ablation study further confirms that MSFF module and FoM module play the positive role in fault diagnosis.

Novel multi-scale dilated CNN-LSTM for fault diagnosis of planetary gearbox with unbalanced samples under noisy environment

Lots of recent deep learning based intelligent fault diagnosis methods of planetary gearbox have achieved satisfactory accuracy with balanced training samples. Nevertheless, the fault samples are generally far less than healthy samples in practical engineering, and the collected data samples usually contain lots of noise, making it difficult to achieve accurate fault diagnosis. In order to solve these problems, this paper proposes a new method called novel multi-scale dilated convolutional neural network with long short-term memory (CNN-LSTM). Firstly, a novel multi-scale dilated CNN is constructed using new dilated strategy to enrich the coverage of the fields of view and avoid the loss of original information, which could adequately mine the distinguishing features of small samples. Secondly, an adaptive weight unit combined with LSTM is designed to fuse the distinguishing features and improve their robustness to noise. Finally, to pay more attention to the small samples and easily confused samples, a new-type loss function called enhanced cross entropy is developed. The test and analysis of the planetary gearbox data sets prove that the proposed method shows better diagnosis performance than other comparison methods using unbalanced training samples.

An adaptive order-band energy ratio method for the fault diagnosis of planetary gearboxes

Condition monitoring of planetary gearboxes in time-varying speed service is an important and actual engineering requirement, however, also an intractable task. The traditional sideband energy ratio (SER) method limits its application to complex operational conditions due to the frequency spectrum based and manual bandwidth selection. To this end, this paper proposes an adaptive order-band energy ratio (AOER) method, an enhanced version of the SER, to quantitatively and intelligently diagnose gear faults under different operational conditions. First, a signal model based on angular increment and order components is proposed to properly describe the vibrations for both stationary and non-stationary conditions. The proposed model provides the theoretical source and reliance for the order spectrum analysis and the diagnostic mechanism of the OER. Second, the OER is theoretically proved to be a reliable fault indicator by analyzing the proposed signal model. The offset of the uncertainty terms highlighting the fault symptoms demonstrates the potential success of using OER for the fault diagnosis. Finally, OERs generated from the vibration data and three typical machine learning algorithms are used to adaptively obtain the optimal bandwidth and thus the AOER. The AOER can be directly used for the remaining vibration data of the corresponding operational condition. Comparing with SER and the convolutional neural network, the experimental results demonstrate the effectiveness and outperformance of AOER for both stationary and non-stationary operational conditions. More importantly, since AOER can cope with diagnostic tasks for different operational conditions, it enables an improved ability to monitor a PG’s health in the actual complex environment.

Diagnostics and prognostics of planetary gearbox using CWT, auto regression (AR) and K-means algorithm

Condition monitoring of machine is recognized as effective strategy for undertaking the maintenance in wide variety of industries. Planetary gearbox is a critical component in helicopters, wind turbines, hybrid vehicles and so forth. Planetary gearbox are complex in nature due to its size and meshing components. Condition monitoring and fault diagnosis of planetary gearbox is challenging due to complexity in dependable fault extraction from raw vibration signal. The mechanism of planetary gearbox is complex as there are several gears meshing at the same time. To find out the nature of fault and defective component in planetary gearbox is difficult. In this paper, the fault detection and fault type identification diagnostic approach using auto regression model (AR) and continuous wavelet transforms (CWT) by considering different frequency range is established. The experimental research conducted with different type of fault vibration signals in the gearbox have been diagnosed and identified the fault type using AR Modelling, Impulse and Shape Factor for validation purposes. The unique behaviors and fault characteristics of planetary gearboxes are identified and analyzed. The fault frequency identification and extraction of features from the non-stationary signals in different fault severity level of vibration data demonstrates the reliability of proposed method. The developed algorithm adds efficacy in detecting the nature of fault and defective component without performing a visual inspection.

Improved multiclass support vector data description for planetary gearbox fault diagnosis

Planetary gearbox is one of the most important components of rotating machinery and plays a key role in modern industry. Due to the complex physical structures and harsh working conditions, planetary gearbox often suffers from different fault types, so it is of vital importance to investigate its fault diagnosis task. In this paper, a novel feature selection strategy is proposed to improve the multiclass support vector data description (SVDD) algorithm for planetary gearbox fault diagnosis. First, a novel feature selection method based on the cosine similarity measure in kernel space of Gaussian radial basis function (GRBF) is presented, so as to determine features that are sensitive to faults. Then, based on the selected features, an improved multiclass SVDD algorithm is developed to classify multiple classes of planetary gear faults, thus completing the fault diagnosis task. Finally, the effectiveness and advantage of the proposed method are demonstrated via experiments using wind turbine drivetrain diagnostics simulator (WTDDS), with comparison to several traditional methods.

Multiscale Symbolic Diversity Entropy: A Novel Measurement Approach for Time-Series Analysis and Its Application in Fault Diagnosis of Planetary Gearboxes

The health condition monitoring of planetary gearboxes has drawn increasing attention due to the importance for safety operation and failure prevention. A novel diagnosis methodology based on multiscale symbolic diversity entropy (SDivEn) is proposed in this article. Herein, dynamical complexity of measured data is quantified by SDivEn. Compare to other entropy-based descriptors, SDivEn has advantages in its robustness and computation efficiency. To increase the feature representation capability of entropy descriptors, multiscale analysis is performed, where the measurement data in time series is decomposed into multiple scaled series by using the coarse graining process and then processed individually by using SDivEn method. The proposed multiscale SDivEn method is applied for fault recognition of planetary gearboxes. Experimental results indicate that the proposed method obtains the highest accuracy in recognizing seven health conditions of planetary gearboxes in comparison with three other existing entropy-based methods.

Variational nonlinear component decomposition for fault diagnosis of planetary gearboxes under variable speed conditions

Planetary gearboxes are extensively used in various heavy equipment and their failures may cause equipment breakdown. Since planetary gearboxes under variable speed conditions will induce time-varying complicated characteristics, which are often contaminated by strong noise and other irrelevant vibration components, fault diagnosis of varying-speed planetary gearboxes is still a challenging task. Although variational nonlinear chirp mode decomposition (VNCMD) can deal with nonstationary signals, it requires some prior knowledge, which limits its practical applications. In this paper, a novel scheme called variational nonlinear component decomposition (VNCD) is proposed as an improved version of the VNCMD to overcome the limitations of the VNCMD. Firstly, the VNCD adopts a new algorithmic framework by modifying the optimization function of the VNCMD to eliminate an upper bound determined by noise, which makes the VNCD more adaptive in practical applications. Secondly, in order to automatically determine initial frequencies and the number of signal components, we propose a novel initial frequencies estimation method based on optimizing a spectrum concentration index and a resampling technique. The initial frequencies estimation method is potential and effective under a strong noise environment, which is suitable to deal with very close time-frequency components. In addition, a high-resolution time-frequency distribution is generated to precisely exhibit time-varying fault features of planetary gearboxes and it improves the signal-to-noise ratio of raw vibration signals. Both our simulated and experimental studies have demonstrated the effectiveness of the proposed VNCD method in fault diagnosis and weak fault feature detection of planetary gearboxes under variable speed conditions.