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Traditional signal processing methods based on acceleration signals can determine whether a fault has occurred in a planetary gearbox. However, acceleration signals are severely affected by interference, causing difficulties in fault identification. This study proposes a gear fault classification method based on root strain and pseudo images. Firstly, fiber optic sensors are employed to directly acquire strain data from the ring gear root. Next, the strain signals are preprocessed using resampling and a time-domain synchronous averaging algorithm. The processed signals are encoded into two-dimensional images using Gramian Angular Fields (GAF). Then, CN-EfficientNet with contrast learning is proposed to analyze and extract deeper fault features from the image texture features. In the classification experiments for different types of faults, the accuracy reached 96.84%. The results indicate that the method can effectively accomplish the task of fault classification in planetary gearboxes. Comparative experiments with other common classification models further indicate the superior performance of the proposed learning model. Visualization based on Grad-CAM provides interpretability for the fault recognition network's results and reveals the underlying mechanism for its excellent classification performance. • A framework for planetary gearbox fault classification is proposed. • A method for measuring the root strain of ring gear tooth is designed. • A pseudo image-based gear strain signal processing algorithm is designed. • CN-EfficientNet network was built to classify pseudo images. [ABSTRACT FROM AUTHOR]

• Planet mistuning leads to coupling between lateral and torsional vibrations. • Planet gear mass and mesh stiffness have a larger influence on the modal response. • Torsional vibration modes are more sensitive to mesh stiffness. • Lateral vibration modes are more sensitive to plant gear mass. • Axial vibration modes are less sensitive to planet gear parameters. A parameter study is presented to determine effects of planet gear design parameters on the global modal behaviour of planetary geared rotor systems. The modal sensitivity analysis is conducted using a three-dimensional dynamic model of a planetary geared rotor system for the number of planet gears, planet mistuning, mass of planet gears, gear mesh stiffness and planet gear speed. These parameters have varying impacts on both natural frequencies and mode shapes, therefore the sensitivity of the planetary geared rotor vibration modes to the planet gear parameters is determined by computing the frequency shifts and comparing the mode shapes. The results show that the mass and mesh stiffness of planet gears have a larger influence on the global dynamic response. Torsional modes and coupled torsional-axial modes are more sensitive to gear mesh stiffness whereas lateral vibration modes are more sensitive to gearbox mass. Planet mistuning results in coupling between lateral and torsional vibrations. The planetary gearbox becomes more rigid in the torsional-axial modes and more flexible in the lateral modes with an increase in the number of planet gears. Planet gears are also found to be having significant gyroscopic effects inside the planetary gearbox. The main original findings in this study can be directly used as initial guidelines for planetary geared rotor design. [ABSTRACT FROM AUTHOR]

• An acoustic-based fault diagnosis system is proposed to accurately diagnose and orientate acoustic sources under low signal-to-noise ratios. • A multi-task TCN model is proposed to simultaneously calculate the orientation and the fault type of the faulty acoustic source. • An attentional mechanism that combines information from the sound field into the separation of fault sources is proposed. Planetary gearboxes are vital in industrial production due to their large transmission ratios. Therefore, accurate fault diagnosis of planetary gearboxes is crucial. However, in industrial applications, the acoustic fault signals from two different adjacent planetary gearboxes may overlap and interfere with each other, resulting in a low Signal-to-Noise Ratio (SNR) for each acoustic fault source, which in turn prevents accurate fault diagnosis. In this context, the Multi-Task Learning-Temporal Convolutional Network (MTL-TCN) is proposed to simultaneously output the orientation of the acoustic sources as well as the fault type to solve the problem of interference between adjacent acoustic sources. A Spatial information based Multi-Task Channel Attention (SMTCA) mechanism is also proposed to solve the problem of acoustic signal overlapping by using the orientation information to calculate the weight of the acoustic signal channel and assigning it to the fault diagnostic task, which combines the sound field information into the separation of fault sources. Finally, a Multi-Channel Acoustic based diagnose System (MC-ABDS) is proposed, which contains a customized microphone array as well as a sound field information and fault feature information extraction method called Multi-Task Attention TCN (MTA-TCN). The system is validated by the data collected in the anechoic chamber, and it is effective for the acoustic overlapping and interference that occurs when two adjacent planetary gearboxes are operating. The orientation accuracy of the acoustic source reached 99.98 %and the diagnostic accuracy of the fault reached 92.08 %. [ABSTRACT FROM AUTHOR]

• A novel method is proposed for diagnosing faults in planetary gearboxes. • The proposed method can effectively remove noise interference components in TFR. • The results of time-frequency representation have a prominent concentration of energy. • The method can extract the time-varying closely-spaced instantaneous frequency accurately. • No prior knowledge is required to achieve adaptive decomposition of signals. Instantaneous frequency (IF) time-varying closely spaced and severe background noise can introduce fake components into the time-frequency representation (TFR) of most time-frequency analysis (TFA) methods, especially for the vibration signals of variable-speed planetary gearboxes. These fake components lead to a decrease in the readability of the TFR, making it difficult to extract the true IF. To address this issue, a new TFA method called Synchronous Match-Reassigning Transform (SMRT) is proposed. Firstly, a polynomial chirp rate with a single parameter adjustment is constructed to achieve precise matching of the IF. Secondly, a frequency reassignment operator is constructed for the fine refinement of the IF ridge of Synchronous Match-Reassigning Operator (SMRO). Finally, SMRO is combined with VKF to achieve adaptive reconstruction of the true IF and to remove fake components. The TFR of SMRT has high readability and low energy leakage. The superiority and effectiveness of this method have been verified through synthetic signals and actual signals. [ABSTRACT FROM AUTHOR]

• Stacked wavelet auto-encoder with Morlet wavelet function is constructed. • A flexible weighted assignment of decision fusion strategy is designed. • Collaborative fault diagnosis framework driven by multisensory fusion is proposed. Collaborative fault diagnosis can be facilitated by multisensory fusion technologies, as these can give more reliable results with a more complete data set. Although deep learning approaches have been developed to overcome the problem of relying on subjective experience in conventional fault diagnosis, there are two remaining obstacles to collaborative efficiency: integration of multisensory data and fusion of maintenance strategies. To overcome these obstacles, we propose a novel two-part approach: a stacked wavelet auto-encoder structure with a Morlet wavelet function for multisensory data fusion and a flexible weighted assignment of fusion strategies. Taking a planetary gearbox as an example, we use noisy vibration signals from multisensors to test the diagnosis performance of the proposed approach. The results demonstrate that it can provide more accurate and reliable fault diagnosis results than other approaches. [ABSTRACT FROM AUTHOR]

• Tooth faults affect the morphology of the mesh force. • Internal mesh forces under various planet tooth faults are calculated. • Mesh force features are validated via the tooth root strain signal. • This work provides the basis for planet tooth faults classification. The mesh force of planetary gearboxes is the major excitation source of vibration. Thus, comprehending how gear faults impact the mesh force is essential in identifying specific fault information from the vibration response for accurate fault diagnosis. In this paper, the internal mesh force and mesh stiffness models of the planetary gearbox are established to depict the influence mechanism of planet tooth faults on the internal mesh force. Further, the theoretical internal mesh force features are validated via the ring tooth root strain, where the strain simulation and measurement are carried out, and a strain separation method is developed to obtain the actual mesh force features. The experimental and theoretical results both demonstrate that different planet tooth faults exhibit specific phase and trend features in the internal mesh force, which provides a foundation for tooth fault classification in planetary gearboxes. [ABSTRACT FROM AUTHOR]

This paper presents a novel signal processing scheme by combining refined composite hierarchical fuzzy entropy (RCHFE) and random forest (RF) for fault diagnosis of planetary gearboxes. In this scheme, we propose a refined composite hierarchical analysis based method to improve the feature extraction performance of existing MFE and HFE methods. First, RCHFE is applied to extract the fault-induced information from the vibration signals. Because a refined composite analysis is used in HFF, the feature extraction capability of HFF can be effectively enhanced. Then, the extracted features are fed into the RF for effective fault pattern identification. The superiority of the proposed RCHFE–RF method is validated using both simulated and experimental signals. Results show that the proposed method outperforms MFE-RF and HFE-RF in identifying fault types of planetary gearboxes. • RCHFE improves the feature extraction ability of FE and HFE. • RCHFE reduces the probability of undefined FE. • Simulated and experimental signals validate the advantage of our proposed RCHFE comparing with six existing entropy methods. [ABSTRACT FROM AUTHOR]

• A multitasking Y-Net that incorporates SE-Res modules in convolutional network is proposed. • A soft joint maximum mean discrepancy is proposed to extract domain-invariant features. • The domain adaptive fault diagnosis of different planetary gearbox under various operating conditions is realized. • The target-equipment dataset has no label, and the proportion of various categories is different from the source-equipment. • Y-Net remarkably outperforms related methods on all domain adaptation task. The planetary gearbox plays an important role in many advanced electromechanical mechanisms. The mechanical fault is a major factor that threatens the service performance of a planetary gearbox. Deep learning (DL) algorithms have been widely used to identify faults and health status of industrial equipment. However, owing to diversified equipment structures, variable working conditions and disparate data acquisition, the service performance of DL-based methods may degrade significantly when applied to different industrial sites. Domain adaptation emerges as a promising idea that aims to transfer knowledge from a source domain to a different but related target domain. In this paper, we introduce a novel deep domain-adaptive multi-task learning model Y-Net, which is exploited to enable domain-adaptive diagnosis of faults in planetary gearboxes. The SE-Res modules are utilized to reduce the redundancy of the model and improving the separability of deep features. Furthermore, a soft joint maximum mean discrepancy (SJMMD) is introduced to link the two pipeline in order to reduce both the marginal and conditional distribution discrepancy of the learned features, with the enhancement of auxiliary soft labels. The domain adaption between different planetary gearbox under variant operating condition is realized by the Y-Net. Experiments demonstrate the superiority of the proposed SJMMD over conventional maximum mean discrepancy, especially when the datasets of different domains suffer different imbalances. [ABSTRACT FROM AUTHOR]

Transient impulses are important information for machinery fault diagnosis. However, the transient features contained in the vibration signals generated by planetary gearboxes are usually immersed by a large amount of background noise and harmonic components. Even mathematical morphology (MM) is an excellent anti-noise signal processing method that can directly extract the geometry of impulse features in the time domain, but the four basic operators of MM can only extract one-way impulses while cannot extract the bidirectional impulses effectively at the same time. To accurately extract the impulse feature information, a novel method for fault detection of planetary gearbox based on an enhanced average (EAVG) filter and modulated signal bispectrum (MSB) is proposed. Firstly, the properties of the extracted impulses based on the four basic operators of MM will be divided into two categories of enhanced average operators. The four EAVG filters consist of the average weighted combination of enhanced average operators, and then the best EAVG filter is selected based on correlation coefficient to implement on the original vibration signal. It allows EAVG filter to extract positive and negative impulses of vibration signal, thereby improving the accuracy of planetary gearbox fault detection. Subsequently, the performance of the EAVG filter is influenced by the length of its structural element (SE), which is adaptively determined using an indicator based kurtosis. Then, the EAVG filter selects the optimal SE length to eliminate the interference of background noise and harmonic components to enhance the impulse components of the vibration signal. However, the nonlinear modulation components that are related to the fault types and severities are not extracted exactly and still remained in the filtered signal by EAVG. Finally, the MSB is utilized to the EAVG filtered signal to decompose the modulated components and extract the fault features. The advantages of EAVG over average (AVG) filter are clarified in the simulation study. In addition, the EAVG-MSB is validated by analyzing the vibration signals of planetary gearboxes with sun gear chipped tooth, sun gear misalignment and bearing inner race fault. The results indicate that the EAVG-MSB is effective and accurate in feature extraction compared with the combination morphological filter-hat transform (CMFH) and average combination difference morphological filter (ACDIF), and the feasibility of the EAVG-MSB are proved for planetary gearbox condition monitoring and fault diagnosis. • EAVG filter is used to extract the positive and negative impulses. • Kurtosis is taken as a novel criterion to optimize the SE length of EAVG. • MSB is used to extract fault feature for planetary gearbox fault detection. • Experimental results prove that the EAVG-MSB outperforms the ACDIF and CMFH. [ABSTRACT FROM AUTHOR]

Health monitoring, diagnostics and prognostics techniques have been deemed as the most promising and essential framework towards smart operation and maintenance of wind energy equipment. Wind turbine planetary gearboxes have remained the most intricate and challenging transmission units to implement intelligent health diagnostics in wind power generation systems. To resolve this issue, we present a novel spectral ensemble sparse representation classification (S-ESRC) approach for super-robust health diagnostics of wind turbine planetary gearboxes. Specifically, S-ESRC implements super-robust health diagnostics via three procedures consisting of data augmentation, spectral dictionary design, and spectral sparse approximation-based diagnostic scheme. Firstly, the prediction translation-invariance is exploited to accomplish vibrational data augmentation. Second, the spectral dictionary design with robust and strong reconstruction capability is achieved via spectrum construction and feature fusion considering the intra-class and inter-class attributes. Thirdly, the spectral sparse approximation error-based diagnostic scheme is applied to accomplish robust health diagnostics. Experimental validations using a wind turbine planetary gearbox system have demonstrated the applicability and superiority of S-ESRC for super-robust health diagnostics. Comparative studies have comprehensively shown the super-robust performances of S-ESRC including superior diagnostic accuracy, strong robustness to random noises, strong robustness to hyperparameters, and efficient computation costs in comparison with several state-of-the-art approaches. [Display omitted] [ABSTRACT FROM AUTHOR]

• Deep learning is a promising tool to extract features for fault diagnosis. • Different measurement locations provide complementary information to the faults. • A data fusion method based on deep convolutional neural network is proposed. With the great ability of transforming data into deep and abstract features adaptively through nonlinear mapping, deep learning is a promising tool to improve the intelligence and accuracy of diagnosis. On the other hand, one acceleration sensor is not sensitive enough to position-variable faults and the collected signal is usually nonstationary and noisy. As different measurement locations provide complementary information to the faults, the paper proposes a deep convolutional neural network (DCNN) based data fusion method for health state identification. This method fuses the raw data from the horizontal and the vertical vibration signals and extracts features automatically. The effectiveness of the novel method is validated through the data collected from a planetary gearbox test rig, and experiments using DCNN, SVM and BPNN based model in different data processing methods are also carried out. The results show that the proposed method could obtain better identification results than the other methods. [ABSTRACT FROM AUTHOR]

• Dimensional parameters can be used to describe transmission properties. • Diameter has a larger influence on transmission properties than length. • Scaling laws facilitate the design process of transmissions. • The derived scaling laws fit catalog data from multiple manufacturers. In robotic actuators, low speeds and high torques are usually required. Small electric motors, which are more efficient at high speeds and low torques, do not fit the requirements directly. In order to transform the motor characteristics into the desired output characteristics, a transmission system is needed. Ideally, it should be optimally designed and adapted to the desired characteristics and the available space. Scaling laws can provide a way to design these desired output requirements as a function of the size parameters. These are however not yet available for transmission systems. To fill this gap, several scaling laws are developed throughout this paper for some of the most important robotic characteristics, i.e. maximum continuous output torque and reflected inertia, in function of the number of stages, the transmission ratio and the size parameters of different types of transmissions. These laws show that diameter has a much bigger influence on the characteristics of transmissions than length. All derived laws show good comparison with catalog data of manufacturers like Maxon, Moog, Neugart, Harmonic Drive®, Sumitomo and SKF. [ABSTRACT FROM AUTHOR]

Highlights • Torsional and axial vibrations on the shafts are coupled due to the gear helix angle. • Axial vibrations cannot transmit between the input and output shafts in spur gears. • Gearbox modes are fully isolated from the shafts because of no dynamic interaction. • Modal energy analysis shows coupling level between the shafts and planetary gearbox. • Global modes experience significant gyroscopic effects due to the planetary gearbox. Abstract A six degrees of freedom dynamic model of a planetary geared rotor system with equally spaced planets is developed by considering gyroscopic effects. The dynamic model is created using a lumped parameter model of the planetary gearbox and a finite element model of the rotating shafts using Timoshenko beams. The gears and carrier in the planetary gearbox are assumed to be rigid, and the gear teeth contacts and bearing elements are assumed to be flexible. The modal analysis results show that torsional and axial vibrations on the shafts are coupled in the helical gearing configuration due to the gear helix angle whereas these vibrations become uncoupled for spur gearing. Mainly, the vibration modes are classified as coupled torsional-axial, lateral and gearbox for the helical gear configuration, and torsional, axial, lateral and gearbox for the spur gear configuration. Modal energy analysis is used to quantify the coupling level between the shafts and the planetary gearbox, highlighting the impact of the gearbox on certain mode families. Gyroscopic effects of the planetary gearbox are found to be of great importance in the gearbox dominated modes. [ABSTRACT FROM AUTHOR]

Abstract The features signals of early fault collected from planetary gearbox are usually weak. It is difficult to extract effective fault features from the collected vibration signals under noise environment. In this paper, a new feature learning method for fault diagnosis of planetary gearbox based on deep conditional variational neural networks (CVNN) is proposed. First, the new method utilizes multi-layer perceptron (MLP) to model the normal distribution features of frequency spectra from noisy vibration signals. Second, the new features are obtained by resampling normal distribution features in order to eliminate the effect of noise. Then the denoised features are compressed and reduced dimensionally by MLP. Third, the effective denoised features are input to classifier. Finally, the trained CVNN is applied for intelligent fault diagnosis of planetary gearbox. The experimental results confirm that CVNN method can extract effective fault features from noisy vibration signals, and it has higher accuracy of fault diagnosis than other methods in the case of low signal to noise ratio (SNR) values. [ABSTRACT FROM AUTHOR]

• The overall transmission error (OTE) is directly applied to the planet fault differential diagnosis (DD) for the tooth flank spall and the gear fillet crack. • A novel reordered SVD approach guided by the sparse index L2/L1 norm is proposed for fault-dependent residual OTE extraction. • Fault components with different scales can be accurately extracted in residual OTE. • The proposed DD framework is robust in extremely low-speed or varying-speed conditions. Owing to recent studies on the relationship between the transmission error and the localized gear fault, TE-based differential diagnosis (DD) technology has emerged as a promising approach to identifying the tooth flank spall and the gear fillet crack which have similar signatures but quite different fault mechanisms and prognoses. However, due to complex structural factors, the fault modes can hardly be identified from the calculated overall transmission error (OTE). In light of this, a novel DD framework based on encoder-measured data is proposed in this work. Specifically, the OTE signal calculated from resampled data are filtered by flexible time synchronous average. A reordered singular values decomposition (RSVD) approach guided by the sparse index L2/L1 norm is then developed for fault-dependent residual OTE extraction. Experimental results validate that the faulty events can be accurately identified by the proposed framework without prior information under different speed conditions for planet gear DD. [ABSTRACT FROM AUTHOR]

Discrepancy representation metric completely determines the transfer diagnosis performance of deep domain adaptation methods. Maximum mean discrepancy (MMD) based on the mean statistic, as the commonly used metric, has poor discrepancy representation in some cases. MMD is generally known from the aspect of kernel function, but the inherent relationship between the two is unknown. To deal with these issues, the authors theoretically explore their relationship first. With the revealed relationship, a novel discrepancy representation metric named maximum mean square discrepancy (MMSD), which can comprehensively reflect the mean and variance information of data samples in the reproducing kernel Hilbert space, is constructed for enhancing domain confusion. Additionally, for the real application under limited samples and ensuring the effectiveness of MMSD, biased and unbiased empirical MMSD statistics are developed, and the error bounds between the two empirical statistics and the real distribution discrepancy are derived. The proposed MMSD is successfully applied to the end-to-end fault diagnosis of planetary gearbox of wind turbine without labeled target-domain samples. The experimental results on twelve cross-load transfer tasks validate that MMSD has a better ability of discrepancy representation and a higher diagnosis accuracy compared with other well-known discrepancy representation metrics. The related code can be downloaded from https://qinyi-team.github.io/2023/06/Maximum-mean-square-discrepancy. [ABSTRACT FROM AUTHOR]

Abstract Rotary encoder signal, as the built-in position information, possesses a wide variety of advantages over vibration signal and has aroused great interest in the field of health monitoring for rotating machinery. However, there are two major issues when attempting to detect and diagnose failures with encoder information. First of all, a series of proper signal processing methods need to be designed for fault feature extraction, which largely relies on the expert experience and domain knowledge. Furthermore, existing studies primarily concentrate on a single transform, such as instantaneous angular speed, which neglects the diversity of encoder information. In view of above deficiencies, a multivariate encoder information based convolutional neural network (MEI-CNN) is proposed for intelligent diagnosis in this paper. In this framework, three different types of dynamic encoder information are firstly acquired by analyzing and processing the raw position sequence, after that multivariate encoder information (MEI) data are constructed by data fusion. Finally, a concise and effective convolutional neural network is designed to extract discriminating features and provide diagnosis results. The proposed method not only overcomes drawbacks of traditional techniques based on vibration analysis, but also provides an intelligent way to achieve satisfactory diagnosis results. The effectiveness and superiority of MEI-CNN are validated by experimental data from a planetary gearbox test rig. The results also indicate that the proposed method may offer a promising tool for intelligent diagnosis of rotating machinery. [ABSTRACT FROM AUTHOR]

Planetary gearbox has complex structures and works under various non-stationary operating conditions. The vibration signals of planetary gearbox are complicated and usually polluted by noise and interference. It is difficult to extract effective features of early faults. In addition, there are only a small number of fault samples for planetary gearbox fault diagnosis. All of these increase the difficulty of planetary gearbox fault diagnosis. Aiming at these problems, a novel fault diagnostic method is proposed which combines Generative Adversarial Networks (GAN) and Stacked Denoising Autoencoders (SDAE). The generator of GAN can generate new samples which has similar distribution with original samples from planetary gearbox vibration signals. Then, generated samples are transformed to the discriminator together with original samples which expand the sample size. SDAE is used as the discriminator of GAN which can automatically extract effective fault features from input samples and discriminate their authenticity and fault categories. Through novel adversarial machine learning mechanism, the generator and discriminator are concurrently optimized to enhance the quality of generation samples and the ability of fault mode classification. The experimental results show that the developed SDAE-GAN method for planetary gearbox has good anti-noise ability and achieve better fault diagnosis performance in the case of small samples. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel fault diagnosis method based on variational mode decomposition (VMD) and generalized composite multi-scale symbol dynamic entropy (GCMSDE) to identify the different health conditions of planetary gearboxes. First, VMD is adopted to remove the noises and highlight the fault symptoms. Second, GCMSDE is utilized to extract the fault features from the denoised vibration signals. Third, the Laplacian score (LS) approach is employed to refine the fault features. Finally, the new features are fed into Softmax regression to identify the health conditions of planetary gearboxes. The proposed method is numerically and experimentally demonstrated to be able to differentiate seven localized fault types on the sun gear, planet gear and ring gear of planetary gearboxes. Highlights • A method called GCMSDE is developed to enhance the fault extraction ability. • We first combined VMD and GCMSDE, which highlight the fault signatures. • Simulated and experiments have validated good performance of the proposed method. [ABSTRACT FROM AUTHOR]

Envelope analysis (EA) is one of the most usually used demodulation methods for fault diagnosis of gearboxes, the main problem for EA is to find a frequency subband that contains more fault-related components. However, modulation phenomenon can be observed for both healthy and damaged situations in planetary gearboxes. And most of the traditional EA techniques cannot distinguish the fault-related modulation components from fault-unrelated modulation components, which may leads to a degradation of the fault diagnosis method for planetary gearbox. In order to overcome the problem of finding the subband that contains the most fault-related modulation components, this paper proposed a new optimal demodulation subband selection method (ODSSM) for fault diagnosis of planetary gearbox. With the proposed method, the fault-related degree of each subband is evaluated based on a new index that measuring the ratio of fault-related modulation components to fault-unrelated modulation components in envelope spectrum. The index then is employed to find the optimal demodulation subband in the entire frequency range based on genetic algorithm (GA). Finally, fault diagnosis results can be obtained based on EA method. For validation, the proposed method and other two methods are utilized to detect the sun gear crack fault in planetary gearbox. The results show that the proposed method can detect the gear fault in both simulation signals and experiment signals, and achieves improved demodulation performance than the other two methods. [ABSTRACT FROM AUTHOR]

Identifying the differences between the spectra or envelope spectra of a faulty signal and a healthy baseline signal is an efficient planetary gearbox local fault detection strategy. However, causes other than local faults can also generate the characteristic frequency of a ring gear fault; this may further affect the detection of a local fault. To address this issue, a new filtering algorithm based on the meshing resonance phenomenon is proposed. In detail, the raw signal is first decomposed into different frequency bands and levels. Then, a new meshing index and an MRgram are constructed to determine which bands belong to the meshing resonance frequency band. Furthermore, an optimal filter band is selected from this MRgram. Finally, the ring gear fault can be detected according to the envelope spectrum of the band-pass filtering result. [ABSTRACT FROM AUTHOR]

Along with the development of the Hybrid Electric Vehicles (HEVs), the permanent magnetic synchronous motor (PMSM) and the planetary gearbox is widely used because of its high power density. There is much significant electro-mechanical coupling phenomenon in the mechanical installations. The aim of this paper is the analytical study of a planetary gearbox by using the stator current signature analysis in the PMSM based on the electro-mechanical coupling mechanism. This paper proposes a mathematical framework based on the electro-mechanical coupling model of the PMSM-planetary gearbox system, considering the load torque oscillation and the time-varying mesh stiffness. The model simulation result shows that from the mathematical framework, the load torque oscillation frequency and the time-varying mesh stiffness frequency can be predicted through the current frequency. The proposed mathematical model is verified by the model simulation. And a test-bed based on a 60 kW three-phase PMSM connected to a planetary gearbox has been used. Fourier transform is applied to the demodulated torque signal and current signal for denoising and removing the intervening neighbouring features. [ABSTRACT FROM AUTHOR]

Tacholess order tracking method is an effective tool for condition monitoring of planetary gearbox under varying-speed operation to reduce the measurement cost and avoid the inconvenience in the installation and adjustment. The robust ridge estimation is an indispensable procedure in the tacholess order tracking. However, conventional ridge estimation methods are difficult to extract the targeted ridge from the highly nonstationary signals. In this paper, we propose a novel method, termed dual path optimization ridge estimation (DPORE), which implants the idea of local integration to adapt with the intensively oscillated ridge. An in-situ vibration signal collected from a wind turbine planetary gearbox provided by the contest during the conference CMMNO December 2014 is employed to validate the proposed method. As a result, an important time-frequency ridge with weak energy and intricate shape is successfully extracted by the proposed method, while two popular ridge estimation methods cannot well track the complete time-frequency ridge. Moreover, the results obtained by the proposed method outperform those provided by the contestants in the conference contest. Finally, the accuracy of estimated ridge is further demonstrated by order analysis and one of the planet bearings in planetary gearbox with an inner race defect can be detected based on the order spectrum. [ABSTRACT FROM AUTHOR]

Vold-Kalman order tracking filter is an effective technique for dealing with non-stationary vibrations which offshore wind turbines often encounter. It has a unique capability to extract and track the time waveforms of harmonics in short transients without phase bias, and this capability is beneficial to the condition monitoring of offshore wind turbines. In general, the accuracy of the tracking results of the Vold-Kalman filer for condition monitoring is heavily dependent on the selection of filter bandwidth. A fixed filter bandwidth becomes problematic when processing different types of signals under varying operating conditions. Significant errors may arise in the tracking, rendering the condition monitoring of offshore wind turbines unreliable. To address this issue, this paper proposes a novel scheme for Vold-Kalman filter bandwidth selection to guarantee the consistency and accuracy of the offshore wind turbine condition monitoring process, ensuring reliable fault diagnosis. A numerical model is used to evaluate the effectiveness of the proposed bandwidth selection scheme first. Then the proposed scheme is further validated through the offshore wind turbine planetary gearbox datasets, together with the demonstration of the fault diagnosis capability of the filtered results. • We propose a novel bandwidth selection method for Vold-Kalman filtering. • Vold-Kalman filtering process can be achieved with controllable accuracy. • A more practical bandwidth selection scheme is provided to maintain a consistent monitoring. • Effectiveness of approach is validated using wind turbine planetary gearbox datasets. [ABSTRACT FROM AUTHOR]

Planetary gearbox vibration signals are intricate due to the unique structure, complex kinetics and background noise interference. Moreover, they have time shift invariant feature because of the periodical rotation of the mechanical components. Reliable feature extraction from such signals is the key to success in planetary gearbox fault diagnosis. The recently proposed shift invariant K-means singular value decomposition (SI-K-SVD) dictionary learning method offers a good approach to analyze such signals. This method requires neither a priori knowledge on signals to construct any analytic dictionary, nor a large number of sample signals to form a training dictionary. It is therefore data-driven in nature, and highly flexible and adaptive to represent signals. In this paper, such properties of the SI-K-SVD are exploited to extract the latent constituent components of complex signals and use them to represent signals sparsely, thus suppressing background noise and revealing the true vibration patterns. To apply the SI-K-SVD method to planetary gearbox signals, the criteria for determining the key parameters used in the SI-K-SVD, i.e., the length of pattern and number of decompositions, are suggested. The method has been illustrated by analyzing numerically simulated signals. It has been favorably compared with the frequently used matching pursuit (MP) and K-means singular value decomposition (K-SVD) methods. Its effectiveness in real planetary gearbox fault diagnosis has been validated by analysis of lab experimental signals of a planetary gearbox. The results show that both localized and distributed gear faults can be diagnosed successfully. [ABSTRACT FROM AUTHOR]

Planetary gearbox fault diagnosis under nonstationary conditions is important for many engineering applications in general and for wind turbines in particular because of their time-varying operating conditions. This paper focuses on the identification of time-varying characteristic frequencies from complex nonstationary vibration signals for fault diagnosis of wind turbines under nonstationary conditions. We propose a time–frequency analysis method based on the Vold-Kalman filter and higher order energy separation (HOES) to extract fault symptoms. The Vold-Kalman filter is improved such that it is encoders/tachometers-free. It can decompose an arbitrarily complex signal into mono-components without resorting to speed inputs, thus satisfying the mono-component requirement by the HOES algorithm. The HOES is then used to accurately estimate the instantaneous frequency because of its high adaptability to local signal changes. The derived time–frequency distribution features fine resolution without cross-term interferences and thus facilitates extracting time-varying frequency components from highly complex and nonstationary signals. The method is illustrated and validated by analyzing simulated and experimental signals of a planetary gearbox in a wind turbine test rig under nonstationary running conditions. The results have shown that the method is effective in detecting both distributed (wear on every tooth) and localized (chipping on one tooth) gear faults. [ABSTRACT FROM AUTHOR]

In this study a single stage planetary multiplying gearbox with helical gears was tested on a back-to-back gearbox test rig with recirculating power under the operating conditions that matched the tangential velocities and operating contact pressures found in a planetary stage of a 2.5 MW wind turbine. The study was done with four different wind turbine gear oils. The gearbox oil sump temperature was set free. The load and no-load losses were measured and compared with the results yielded by an existing numerical model which takes into account the influence of the lubricant formulation in the load losses. The results have indicated that each gear oil formulation promoted different power loss results resulting in distinct stabilized operating temperatures. [ABSTRACT FROM AUTHOR]

• A novel mathematical model of the transmission path effect is proposed. • Path effect depends only on the geometric parameters and material properties. • A phenomenological vibration model is used to simulate all vibration sources. • Vibration characteristics are analyzed and validated through experiments. 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. [ABSTRACT FROM AUTHOR]

Planetary gearboxes exhibit unique challenges in bearing fault detection. This paper presents a hybrid approach for fault diagnosis of planetary bearings using an internal vibration sensor and novel signal processing strategies. An accelerometer is mounted internally on the planet carrier to address the issues of variable transmission path. An effective bearing faults detection algorism is developed by employing several advanced signal processing techniques, including Cepstrum whitening, minimum entropy deconvolution (MED), spectral kurtosis (SK) and envelope analysis. The adverse effect of the electromagnetic interference in the signal due to the use of a slip ring is tackled by optimizing the SK technique for demodulation band selection. The proposed method is assessed by analyzing experimental data from a planetary gearbox test rig with seeded bearing faults. The result shows that the new method can effectively detect both inner race and outer race faults of the planetary bearing. [ABSTRACT FROM AUTHOR]

In this paper is reviewing rotation sealed lead-in unit of submersible mechanisms. Reviewable mechanisms are used at sea depth more than 2000 meter. The main idea of research is based on consideration of influence distance between magnetic couplings transmitting rotation through a membrane of a tough box. The emphasis was made on variation magnetic fields depending on membrane width and material. As a result is received a theoretical correlation between transferable torque and depth of submergence. Is shown a rotation sealed lead-in unit design. Is suggested a circular membrane design. [ABSTRACT FROM AUTHOR]

• A new low-frequency fault detection method is proposed. • The proposed method overperforms wavelet decomposition method in weak feature extraction. • The acoustic signals present more significant fault features than vibration signals. • The effect of feature extraction is evaluated quantitatively. In some practical application of construction machinery and equipment, the planetary gearbox in the walking parts is wrapped with tires, and its speed is very low. When this planetary gearbox fails, the fault frequency is very low (less than 1 Hz) due to its complex transmission relationship. Because the planetary gearbox has the characteristics of low speed, low fault frequency and surrounded by tires, it is difficult to detect its fault condition in practical engineering. This work proposes a new low-frequency fault detection method. First, the pre-processing is used for the measured acoustic signals. Second, the pre-processed acoustic signals are decomposed into components by the multi-resolution singular value decomposition. Third, the autoregressive model is constructed to select fault-related component. Finally, the output component is further analyzed by envelope spectrum analysis. The results indicate that the proposed method can accurately detect the characteristic information of low frequency faults of planetary gearbox in practical engineering. [ABSTRACT FROM AUTHOR]

• A new cyclic symplectic component decomposition (CSCD) is proposed. • CSCD can avoid information leakage during decomposition. • CSCD can keep the structural information of the original signal unchanged. • CSCD has good robustness and decomposition performance. 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. [ABSTRACT FROM AUTHOR]

Abstract: Planetary gearboxes play an important role in wind turbine (WT) drivetrains. WTs usually work under time-varying running conditions due to the volatile wind conditions. The planetary gearbox vibration signals in such an environment are hence highly nonstationary. Conventional spectral analysis and demodulation analysis methods are unable to identify the characteristic frequency of gear fault from such nonstationary signals. As such, this paper presents a time–frequency analysis methods to reveal the constituent frequency components of nonstationary signals and their time-varying features for WT planetary gearbox monitoring. More specifically, we exploit the adaptive optimal kernel (AOK) method for this challenging application because of its fine time–frequency resolution and cross-term free nature, as demonstrated by our simulation analysis. In this study, the AOK method has been applied to identify the time-varying characteristic frequencies of gear fault or to extract different levels of impulses induced by gear faults from lab WT experimental signals and in-situ WT signals under time-varying running conditions. We have demonstrated that the AOK is effective diagnosis of: (a) both the local damage (a single chipped tooth) and distributed faults (wear of all teeth), (b) both sun gear and planet gear faults, and (c) faults with very weak signature (e.g., the sun gear fault at the low speed stage of a WT planetary gearbox). [Copyright &y& Elsevier]

Highlights: [•] Novel hybrid approach for dimensionality reduction is proposed. [•] Non-linear and linear approach have been tested. [•] Multivariate linear regression (MLR) was used assuming linearity of data. [•] Least absolute selection and shrinkage method (Lasso) was proposed as a non-linear approach. [ABSTRACT FROM AUTHOR]

Abstract: In the last decade, the use of acoustic emissions has received growing acceptance for its application in machine condition monitoring. This is because it offers good possibilities to diagnose failures at early stages and low rotational speeds. The use of acoustic emissions for condition monitoring of gears, however, is still an active field of research, because several questions remain unanswered. One of these questions is the effect of operating conditions on the AE generated during gear meshing. In this work, the results of experiments carried out on a non-faulty planetary gearbox test bench are presented. A planetary gearbox is considered, because of its usual application on machines subjected to variable operating conditions. The effects of lubricant temperature, load and rotational speed are investigated. The conclusions obtained from the experiments are used for the analysis of the AE measured on the planetary gearbox of a bucket wheel excavator. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

• An improved phenomenological model of a gear pair with local fault is proposed. • Relative phases of planetary gearboxes are calculated by a modified phase model. • The local fault characteristic frequencies of gears are deduced based on models. • The conclusions are validated based on five experiments conducted on a test rig. Planetary gearboxes (PGs) are prone to gear local faults, such as cracking, pitting, and spalling, because of their difficult working environment. These faults may lead to significant capital losses and catastrophic events. Numerous phenomenological modulation models of vibration signals of PGs have been proposed for diagnosis purposes. However, local fault diagnosis remains extremely challenging due to two aspects: (1) Most vibration modulation models cannot reflect the local fault-induced pulse modulation characteristic. (2) Studies on local fault characteristic frequencies (LFCFs) of gears lack a unified mechanism explanation. To solve these problems, an improved phenomenological vibration model of a gear pair with local fault is first proposed. This model can reflect the pulse modulation characteristic. Then, relative phases between multiple gear pairs in the PG are calculated based on a modified phase model. Based on these, phenomenological vibration models of PGs with/without local faults are established, spectral structures are derived using Fourier series analysis, and LFCFs are deduced for local fault diagnosis. Simulation and experimental studies demonstrate the effectiveness of the proposed models, which exhibit higher descriptive capability than traditional models. [ABSTRACT FROM AUTHOR]

Abstract: Effective diagnosis of damage levels is important for condition based preventive maintenance of gearboxes. One special characteristic of damage levels is the inherent ordinal information among different levels. Retaining the ordinal information is therefore important for diagnosing damage levels. Classification, a machine learning technique, has been widely adopted for automated diagnosis of gear faults. However, classification cannot keep the ordinal information because the damage levels are treated as nominal variables. This paper employs ordinal ranking, another machine learning technique, to preserve the ordinal information in automated diagnosis of damage levels. As to ordinal ranking, feature selection is important. However, most existing feature selection methods are for classification, which are not suitable for ordinal ranking. This paper designs a feature selection method for ordinal ranking based on correlation coefficients. A diagnosis approach based on ordinal ranking and the proposed feature selection method is then introduced. This method is tested on diagnosis of artificially created surface damage levels of planet gear teeth in a planetary gearbox. Experimental results show the effectiveness of the proposed diagnosis approach. The advantages of using ordinal ranking for diagnosing gear damage levels are also demonstrated. [Copyright &y& Elsevier]

Abstract: Planetary gearboxes play an important role in wind turbine drive trains. Fault diagnosis of planetary gearboxes is a key topic for maintenance of wind turbines. Considering the spectral complexity of planetary gearbox vibration signals as well as their amplitude modulation and frequency modulation (AMFM) nature, we propose a simple yet effective method to diagnose planetary gearbox faults based on amplitude and frequency demodulations. We use the energy separation algorithm to estimate the amplitude envelope and instantaneous frequency of modulated signals for further demodulation analysis, by exploiting the adaptability of Teager energy operator to instantaneous changes in signals and the fine time resolution. However, the energy separation algorithm requires signals to be mono-components. To satisfy this requirement, we decompose signals into intrinsic mode functions (IMFs) using the ensemble empirical mode decomposition (EEMD) method as it can decompose any signal into mono-components. We further propose a criterion to guide the selection of the most relevant IMF for demodulation analysis according to the wavelet-like filter nature of EEMD and the AMFM characteristics of the planetary gearbox vibration signals. By matching the dominant peaks in the Fourier spectra of the obtained amplitude envelope and instantaneous frequency with the theoretical characteristic frequency of each gear, we can diagnose planetary gearbox faults. The principle and effectiveness of the proposed method are illustrated by simulation and the experimental analysis of signals from a planetary gearbox of a wind turbine test rig. With the proposed method, both the wear and chipping faults can be detected and located for a sun gear of the planetary gearbox test rig. [Copyright &y& Elsevier]

Abstract: Fault detection and diagnosis in mechanical systems during their time-varying nonstationary operation is one of the most challenging issues. In the last two decades or so researches have noticed that machines work in nonstationary load/speed conditions during their normal operation. Diagnostic features for gearboxes were found to be load dependent. This was experimentally confirmed by a smearing effect in the spectrum. In order to better understand the involved phenomena and to ensure agreement between simulation and experimental results, two models of gearboxes (a fixed-axis two-stage gearbox and a planetary gearbox) operating under varying load conditions are proposed. The models are based on two mechanical systems used in the mining industry, i.e. the belt conveyor and the bucket wheel excavator. An original transmission error function expressing changes in technical condition and load variation is presented. Energy based parameters (the signal RMS value or the arithmetic sum of the amplitudes of spectral gearmesh components) are adopted as the diagnostic features. Simulation results show a strong correlation between load values, changes in condition and the diagnostic features. The findings are key to condition monitoring. Thanks to the use of the models one can better understand the phenomena identified through an analysis of vibration signals captured from real machines. [Copyright &y& Elsevier]

• An adaptive parameter-induced SR method is proposed for diagnosing the incipient faults in planetary gearboxes. • A combined strategy of 'HPF + TEO demodulation' is proposed to improve the detectability of raw vibration signals. • A GOA-optimized CBSR system is constructed to enhance the incipient fault features. • The effectiveness of the proposed method is validated by experimental data. 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. [ABSTRACT FROM AUTHOR]

• Mean-Squared Energy features of DWT are extracted from planetary gearbox. • The signal features of various defect are analyzed with SVM and ANN • The ANN out-performs with 99.7 % accuracy compared to other reported ML classifiers Monitoring the condition of unreachable gears of epicyclic gearbox in real-time increases the asset reliability by anticipating the failures through preventive maintenance. Machine vibrations exhibit fruitful information about the failure at different operating conditions when measured at a convenient location through signal processing techniques. This study demonstrates the potency of discrete wavelet analysis for fault diagnosis of the planetary gearbox using Artificial Neural Network and Support Vector Machine. The mean squared energy of the detail coefficients at eight decomposed levels for different wavelet families is considered a feature. The J48 algorithm selects the prominent features which form an input to the classifiers. Afterward, their relative ability in classifying faults is compared in detail. Further, the classification performance of commonly used machine learning algorithms in the literature is also compared. It is found that the mean square energy of detailed coefficients of Discrete Wavelet Transform exhibit excellent fault diagnosing characteristics with various classifiers and is highly recommended. [ABSTRACT FROM AUTHOR]

• A cepstrum-assisted empirical wavelet transform (CEWT) is proposed for fault diagnostics. • Cepstrum is adopted to identify the modulation sideband clusters around gear mesh harmonics. • Envelope averaging is proposed to improve demodulation analysis for fault diagnostics. • Simulation and experimental results demonstrate the superiority of the proposed method for fault diagnostics. Demodulation analysis is a widely used approach for fault diagnostics of planetary gearboxes by identifying the fault-induced modulation effect buried in noise with complicated characteristics. To enhance the performance of demodulation analysis, previous studies have employed signal decomposition, including empirical wavelet transform (EWT), to decompose a signal with a clear modulation effect. However, EWT requires a physical understanding of the modulation effect to isolate the fault-related signals. To solve this challenge, we propose a cepstrum-assisted empirical wavelet transform (CEWT). In the proposed method, the vibration signal is decomposed using empirical wavelet filters designed based on the smoothed spectrum from cepstrum analysis. To further enhance the fault-related signal, the proposed method employs averaging for the envelopes of the decomposed signals for the demodulation analysis. The proposed method is validated by examining numerical simulation and experiment. The results show that the proposed method improves fault diagnostic performance, as compared to existing methods. [ABSTRACT FROM AUTHOR]

The reliability of planetary gearbox is extremely important for safe and reliable operation. In this work, a fault diagnosis method based on acoustic signals is proposed for planetary gearbox, where the generated acoustic signals are nonlinear and non-stationary. First, the Fourier decomposition method (FDM) is utilized to decompose the measured acoustic signals into Fourier intrinsic band functions (FIBFs). Compared with the traditional empirical mode decomposition (EMD) method, FDM has better decomposition effect results without end effects and mode aliasing issues. Second, the comprehensive feature parameters of energy and TESK (time and envelope spectrum kurtosis) are adopted for overcoming the noisy and weak acoustic signals. Compared with a single feature parameter, the comprehensive feature parameters can significantly improve the accuracy of fault diagnosis. Third, the Random Forest (RF) classification algorithm is adopted for setting up the fault diagnosis method. Experimental results show that the fault diagnosis accuracy rate of the proposed FDM-based method using the acoustic signals reaches up to 96.32% under the limited sample data conditions, which achieved better fault diagnosis effect than vibration signals in the experimental conditions. [ABSTRACT FROM AUTHOR]

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. • An improved method is proposed for planetary gearbox fault diagnosis. • The novel feature selection strategy uses mean and variance of cosine similarity. • A multiclass SVDD model is established to perform fault diagnosis in kernel space. • Experiments are carried out to demonstrate the effectiveness and merits. [ABSTRACT FROM AUTHOR]

• A novel ANCNN model is developed to accurately diagnose planetary gearbox fault. • TCO-spectrum is applied to avoid the influences of variable speed and loads. • The BN algorithm is adopted to eliminate the feature distribution differences. • The PSO is used to flexibly decide the key hyperparameters of the designed model. • Experiments and applications validate the presented method and shown its superiority. In real industrial application, the operating conditions of the planetary gearbox are always variable speed and variable load according to production. Meanwhile, the scarcity of fault data and different working conditions lead to serious data imbalance and distribution differences, which make a great challenge for planetary gearbox fault detection and diagnosis. To address these issues, a novel adaptive normalized convolutional neural network (ANCNN) is developed to accurately and automatically diagnose the different fault locations and severities of planetary gearbox considering the scenarios of complex variable working conditions and data imbalance. First, Teager calculated order (TCO) spectrum is applied to avoid the influences of large speed fluctuations and variable loads, which is an efficient pretreatment approach for the proposed ANCNN. Then, the batch normalization algorithm is adopted to eliminate the feature distribution differences caused by variable operating modes and data imbalance. Finally, in order to automatically adapt to different planetary gearbox diagnosis circumstances, the particle swarm optimization (PSO) strategy is used for optimizing and flexibly deciding the key hyperparameters of the designed model, thereby improving the overall performance of the model. The effectiveness of the presented method is confirmed through experiments on two different planetary gearbox datasets, which are from a generic planetary gearbox for industrial applications and a drivetrain dynamic simulator test rig. In addition, comparison with other mainstream intelligent diagnosis techniques validates the superiority of the presented method. The experimental results demonstrate that the presented method can achieve diagnostic accuracies of better than 99.8%, and also shows excellent stability for the unbalanced data classification. [ABSTRACT FROM AUTHOR]

• A supervised adaptive spectral graph wavelet transform (SASGWT) is proposed. • The acoustic signal is converted into the graph spectral domain for analysis. • An optimization algorithm using combination parameter index is proposed in SGWT. • The SASGWT method achieved excellent weak fault detection effect in the test. This article describes an acoustic-based fault detection technique of three-stage planetary gearbox in actual engineering applications. The proposed technique was used to extract weak fault signal features. The measured acoustic signals were converted into the path graph from a new perspective in the graph spectral domain. Then an optimized spectral graph wavelet transform method is proposed to decompose the path graph into multiple components. Furthermore, reference signal was constructed based on the structure of planetary gearbox, and the fault-related component is output by comparing the similarity between the constructed reference signal and the decomposed components. Finally, the envelope spectrum analysis is further adopted to identify faults. The proposed supervised adaptive spectral graph wavelet transform (SASGWT) method has better performance than traditional wavelet decomposition method. The weak fault detection effect based on acoustic signals is superior to vibration signals under the experimental conditions of this work. [ABSTRACT FROM AUTHOR]

• A method for estimating the fault size of gear tooth is proposed. • The law between the exit time of the faulty gear tooth and the fault size is deduced. • An improved phenomenological model of planetary gearbox vibration signal is established. • The assisted phase for verifying the correctness of the signal model is proposed. Multiple vibration signal models for planetary gearboxes have been built, but details in the signals are often ignored when verifying their correctness. The main reason is that the vibration mechanism of the gearbox is not well studied. To overcome this problem, the stiffness model of the faulty external gear pair is firstly developed and the end meshing time of the broken tooth under different fault sizes is explored. Based on this, an improved phenomenological model is established, and the assisted phases for verifying its correctness are proposed. Subsequently, the simulated signal is decomposed into two components, which mainly contain meshing impacts and fault impacts, respectively. Based on the time difference between these two types of impacts, the mapping relationship between the assisted phases and the fault size is verified. Finally, the correctness of the vibration mechanism of the gearbox and the improved phenomenological model are verified by simulation and experiments. [ABSTRACT FROM AUTHOR]

• A new method for generating the vibration signal of planetary gearbox is proposed. • The bolt constraint of the ring gear is considered in the new vibration signal model. • The transmission mechanism of the signal from vibration source to sensor is analyzed. • Effect of bolt constraint on the modulation and overlapping phenomenon is studied. The lumped parameter model (LPM) is a common modeling method for simulating the vibration signal of the planetary gearbox. Generally, the simulation results are not directly used for the subsequent analysis, because two factors need to be considered: the transmission paths of vibration signals and the amplitude modulation effect of the carrier. However, both of these factors are subjectively affected. In order to overcome this problem, a new method for generating the gearbox vibration signal is proposed. Based on LPM, the vibration displacement of each component is solved, and meshing forces of the internal gear pairs are calculated. Then, the ring gear with bolt constraints is simplified to the Euler-Bernoulli beam, and the vibration signal of any point on the ring gear is established by solving the vibration of the beam. Subsequently, based on the new signal model, the transmission mechanism, the amplitude modulation and the overlapping phenomenon of the vibration signal, and the effect of bolt constraint on the vibration of the gearbox are analyzed. Finally, the correctness of the new method and the effect of bolt constraint on the vibration signal are verified by experiments. [ABSTRACT FROM AUTHOR]

In real-world applications, fault detection and diagnosis of planetary gearboxes are vital if it can be employed to avert catastrophic failure consequences in rotating machinery. Fault diagnosis usually starts with collecting vibration signals from rotating machinery. These vibration signals are usually produced in non-stationary operating conditions with time-varying loads and speeds, which makes fault diagnosis more challenging. Signal processing methods are typically selected for fault diagnosis to capture either time, frequency, or time-frequency based diagnostic features from measured vibration signals. Yet, it is usually a costly or time-consuming process and, sometimes, heavily dependent on human expertise. Although current deep learning algorithms offer an efficient and intelligent diagnostic strategy for fault diagnosis, unfortunately, most of the reported algorithms are basically only valid for the stationary operating conditions. To address the challenges of non-stationary operating conditions, in this paper, an Automatic Speed Adaption Neural Network (ASANN) model within the incorporation of instantaneous rotating speed is proposed, and it provides an end-to-end learning fashion with the guidance of rotating speed information. With the incorporating of instantaneous rotating speed information, the proposed ASANN model enables the extraordinary capacity for planetary gearbox fault detection under varying operational scenarios. The validity of the ASANN model is verified by an experimental investigation of fault diagnosis in a planetary gearbox. • An automatic speed adaption neural network (ASANN) model is proposed. • ASANN can adaptively learn features from measured vibration signals. • ASANN provides a better ability to accommodate fluctuating operating conditions. • ASANN is a true end-to-end learning model under the guidance of the instantaneous rotating speed information. [ABSTRACT FROM AUTHOR]