Research on Instantaneous Angular Speed Signal Separation Method for Planetary Gear Fault Diagnosis

Planetary gear train is a critical transmission component in large equipment such as helicopters and wind turbines. Conducting damage perception of planetary gear trains is of great significance for the safe operation of equipment. Existing methods for damage perception of planetary gear trains mainly rely on linear vibration analysis. However, these methods based on linear vibration signal analysis face challenges such as rich vibration sources, complex signal coupling and modulation mechanisms, significant influence of transmission paths, and difficulties in separating damage information. This paper proposes a method for separating instantaneous angular speed (IAS) signals for planetary gear fault diagnosis. Firstly, this method obtains encoder pulse signals through a built-in encoder. Based on this, it calculates the IAS signals using the Hilbert transform, and obtains the time-domain synchronous average signal of the IAS of the planetary gear through time-domain synchronous averaging technology, thus realizing the fault diagnosis of the planetary gear train. Experimental results validate the effectiveness of the calculated IAS signals, demonstrating that the time-domain synchronous averaging technology can highlight impact characteristics, effectively separate and extract fault impacts, greatly reduce the testing cost of experiments, and provide an effective tool for the fault diagnosis of planetary gear trains.

Small Sample Gear Fault Diagnosis Method Based on Transfer Learning

Aiming at the problems of lack of fault diagnosis samples and low model generalization ability of cross-working gear based on deep transfer learning, a fault diagnosis method based on improved deep residual network and transfer learning was proposed. Firstly, one-dimensional signal is transformed into two-dimensional time-frequency image by continuous wavelet transform. Then, a deep learning model based on ResNet50 is constructed. Attention mechanism is introduced into the model to make the model pay more attention to the useful features for the current task. The network parameters trained by ResNet50 network on ImageNet dataset were used to initialize the model and applied to the fault diagnosis field. Finally, to solve the problem of gear fault diagnosis under different working conditions, a small sample training set is proposed for fault diagnosis. The method is applied to gearbox fault diagnosis, and the results show that: The proposed deep model achieves 99.7% accuracy of gear fault diagnosis, which is better than the four models such as VGG19 and MobileNetV2. In the cross-working condition fault diagnosis, only 20% target dataset is used as the training set, and the proposed method achieves 93.5% accuracy.

Gear Vibration Analysis and Gear Fault Diagnosis based on Mathematical Morphology

Gear vibration analysis and gear fault diagnosis are related to the multi-objective decision-making process of machinery equipment production, in which a large amount of data and information should be collected, and the relationship between supply/demand needs and available resources, between production and labor, and between enterprise benefit and social benefit should be balanced generally. Thus, the gear fault diagnosis technologies as well as the professional quality and technical quality are required to be very high. To conform to the forward development of mathematical modeling technology, it is urgent to implement safety product management with computer by using gear vibration analysis and gear fault diagnosis as methods for aiding the research and development of machinery gear fault diagnosis system. 7

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

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

Generalized Demodulation Transform for Bearing Fault Diagnosis Under Nonstationary Conditions and Gear Noise Interferences

It is a challenging issue to detect bearing fault under nonstationary conditions and gear noise interferences. Meanwhile, the application of the traditional methods is limited by their deficiencies in the aspect of computational accuracy and e ciency, or dependence on the tachometer. Hence, a new fault diagnosis strategy is proposed to remove gear interferences and spectrum smearing phenomenon without the tachometer and angular resampling technique. In this method, the instantaneous dominant meshing multiple(IDMM) is firstly extracted from the time-frequency representation(TFR) of the raw signal, which can be used to calculate the phase functions(PF) and the frequency points(FP). Next, the resonance frequency band excited by the faulty bearing is obtained by the band-pass filter. Furthermore, based on the PFs, the generalized demodulation transform(GDT) is applied to the envelope of the filtered signal. Finally, the target bearing is diagnosed by matching the peaks in the spectra of demodulated signals with the theoretical FPs. The analysis results of simulated and experimental signal demonstrate that the proposed method is an e ective and reliable tool for bearing fault diagnosis without the tachometer and the angular resampling.

Model Parameter Transfer for Gear Fault Diagnosis under Varying Working Conditions

Gear fault diagnosis technologies have received rapid development and been effectively implemented in many engineering applications.However,the various working conditions would degrade the diagnostic performance and make gear fault diagnosis(GFD)more and more challenging.In this paper,a novel model parameter transfer(NMPT)is proposed to boost the performance of GFD under varying working conditions.Based on the previous transfer strategy that controls empirical risk of source domain,this method further integrates the superiorities of multi-task learning with the idea of transfer learning(TL)to acquire transferable knowledge by minimizing the discrepancies of separating hyperplanes between one specific working condition(target domain)and another(source domain),and then transferring both commonality and specialty parameters over tasks to make use of source domain samples to assist target GFD task when sufficient labeled samples from target domain are unavailable.For NMPT implementation,insufficient target domain features and abundant source domain features with supervised information are fed into NMPT model to train a robust classifier for target GFD task.Related experiments prove that NMPT is expected to be a valuable technology to boost practical GFD performance under various working conditions.The proposed methods provides a transfer learning-based framework to handle the problem of insufficient training samples in target task caused by variable operation conditions.

NEW DEMODULATION TECHNOLOGY OF OPTIMIZING ENERGY OPERATOR AND APPLICATION TO GEAR FAULT DIAGNOSIS

Although many methods have been applied to diagnose the gear thult currently, the sensitivity of them is not very good. In order to make the diagnosis methods have more excellent integrated ability in such aspects as precision, sensitivity, reliability and compact algorithm, and so on, and enlightened by the energy operator separation algorithm （EOSA）, a new demodulation method which is optimizing energy operator separation algorithm （OEOSA） is presented. In the algorithm, the non-linear differential operator is utilized to its differential equation： Choosing the unit impulse response length of filter and fixing the weighting coefficient for inportant points. The method has been applied in diagnosing tooth broden and fatiguing crack of gear faults successfully. It provides demodulation analysis of machine signal with a new approach.

A Method for Gear Fault Diagnosis Based on the Empirical Mode Decomposition

According to the characteristics of gear fault vibration signals, a methodfor gear fault diagnosis based upon the empirical mode decomposition (EMD) is proposed in thispaper. By using EMD, any complicated signal can be decomposed into a finite and often small numberof intrinsic mode functions (IMFs) , which are based upon the local characteristic time scale of thesignal. Thus, EMD is perfectly suitable for non-stationary signal processing and faultcharacteristics extracting. It is well known that a gear vibration signal consists of a number offrequency family components, each of which is a modulated signal. Thus, we can use EMD to decomposea gear fault vibration signal into a number of IMF components, some of which correspond to thefrequency families, and the others are noises. Therefore, the frequency families can be separatedand the noise can be decreased at the same time. The proposed method has been applied to gear faultdiagnosis. The results show that both the sensitivity and the reliability of this method aresatisfactory.

Study on Rolling Mill Gear Box and Design of Multichannel Fault Diagnosis

Gear box places an important role rolling mill.Its reliability decides the machine operation.Due to the important role,if the key machine is broken because of gear box′s malfunction,the whole production devices will be influeued.Therefore,it′s very important to monitor the gear box online.Good monitoring system can help companies to better process fault diagnosis.The design sets up a monitoring system with Enwatch polled mode on-line acquisition module and Odyssey software.By calculating the data,the problem of the monitoring system is find,the plans to collect signal is made,the problems of monitoring gear box′s multichannel vibration are solved and the malfunctions initially are estimated according to the signal,which has theoretical basis and practical meanings.

Faults Analysis and Diagnosis of DRJ-460 Dish Centrifugal Separator′s Helical Gear

The main faults of dish centrifugal separator's helical gear are described inthis paper. In order to diagnose the DRJ-460 dish centrifugal separator correctly, the vibration istested with a helical gear under both normal and abnormal conditions. After comparing severalgeneral methods of the gear's fault feature extraction, a new convenient and effective method ispresented on the basis of analyzing the vibration spectrum under different rotary velocities.

Fault diagnosis of AMT gear shifting process based on semi-quantitative SDG model

In order to diagnose gear shifting process in automated manual transmission（AMT）,a semi-quantitative signed directed graph（SDG）model is applied.Mathematical models are built by analysis of the power train dynamic and the gear shifting control process.The SDG model is built based on related priori knowledge.By calculating the fuzzy membership degree of each compatible passway and its possible fault source,we get the possibilities of failure for each possible fault source.We begin with the nodes with the maximum possibility of failure in order to find the failed part.The diagnosis example shows that it is feasible to use the semi-quantitative SDG model for fault diagnosis of the gear shifting process in AMT.

Detection and Diagnosis of Gear Fault By the Single Gear Tooth Analysis Technique

This paper presents a procedure of sing le gear tooth analysis for early detection and diagnosis of gear faults. The objec tive of this procedure is to develop a method for more sensitive detection of th e incipient faults and locating the faults in the gear. The main idea of the sin gle gear tooth analysis is that the vibration signals collected with a high samp ling rate are divided into a number of segments with the same time interval. The number of signal segments is equal to that of the gear teeth. The analysis of i ndividual segments reveals more sensitively the changes of the vibration signals in both time and frequency domain caused by gear faults. In addition, the locat ion of a failed tooth can be indicated in terms of the position of the segment t hat deviates from the normal segments. An experimental investigation verified th e advantages of the single gear tooth analysis.

Bispectrum Analysis in Fault Diagnosis of Gears

The application ofbispectrum analysis in fault diagnosis o f gears is studied in this paper. Bispectrum analysis is capable of removing Gau ssian or symmetric non-Gaussian noise and providing more information than power spectrum analysis.The results of the research show that normal gear sig nals, cracked gear signals and broken gear signals can be easily distinguished b y using bispectrumas the signal features. The bispectrum diagonal slice B_x(ω_1,ω_2) can be used to identifythe gear condition automatically.

CVRgram for Demodulation Band Determination in Bearing Fault Diagnosis under Strong Gear Interference

Fault-related resonance frequency band extraction-based demodulation methods are widely used for bearing diagnostics.However,due to the high peaks of strong gear meshing interference,the classical band selection methods have poor performance and cannot work well for bearing fault type detection.As such,the CVRgram-based bearing fault diagnosis method is proposed in this paper.In the proposed method,inspired by the conditional variance(CV)index and root mean square(RMS),a novel index,named the CV/root mean square(CVR),is first proposed.The CVR index has high robustness for the interference of non-Gaussian or Gaussian noise and has the ability to determine the center frequency of the weak bearing fault-related resonance frequency band under strong interference.Secondly,motived by the Kurtogram,the CVRgram algorithm is developed for adaptively determining the optimal filtering parameters.Finally,the CVRgram-based bearing fault diagnosis method under strong gear meshing interference is proposed.The performance of the CVRgram-based method is verified by both the simulation signal and the experiment signal.The comparison analysis with the Kurtogram,Protrugram,and CVgram-based method shows that the proposed technique has a much better ability for bearing fault detection under strong noise interference.

CLASSIFICATION OF GEAR FAULTS USING HIGHER-ORDER STATISTICS AND SUPPORT VECTOR MACHINES

Gears alternately mesh and detach in driving process, and then workingconditions of gears are alternately changing, so they are easy to be spalled and worn. But becauseof the effect of additive gaussian measurement noises, the signal-to-noises ratio is low; theirfault features are difficult to extract. This study aims to propose an approach of gear faultsclassification, using the cumulants and support vector machines. The cumulants can eliminate theadditive gaussian noises, boost the signal-to-noises ratio. Generalisation of support vectormachines as classifier, which is employed structural risk minimisation principle, is superior tothat of conventional neural networks, which is employed traditional empirical risk minimisationprinciple. Support vector machines as the classifier, and the third and fourth order cumulants asinput, gears faults are successfully recognized. The experimental results show that the method offault classification combining cumulants with support vector machines is very effective.

DETECTION OF INCIPIENT LOCALIZED GEAR FAULTS IN GEARBOX BY COMPLEX CONTINUOUS WAVELET TRANSFORM

As far as the vibration signal processing is concerned, composition ofvibration signal resulting from incipient localized faults in gearbox is too weak to be detected bytraditional detecting technology available now. The method, which includes two steps: vibrationsignal from gearbox is first processed by synchronous average sampling technique and then it isanalyzed by complex continuous wavelet transform to diagnose gear fault, is introduced. Twodifferent kinds of faults in the gearbox, i.e. shaft eccentricity and initial crack in tooth fillet,are detected and distinguished from each other successfully.

Analysis and Simulation for Planetary Gear Fault of Helicopter Based on Vibration Signal

Fault diagnosis for helicopter's main gearbox based on vibration signals by experiments always requires high costs. To solve this problem,a helicopter's planetary gear system is taken as an example. Firstly,a simulation model is established by McFadden,and analyzed under ideal condition. Then this model is developed and improved as the delay-time model of the vibration signal which determines the phase-change of sidebands when the system is running. The cause and change-rules of planetary gear system's vibration signal are analyzed to establish the fault diagnosis model.At the same time,the vibration signal of fault condition is simulated and analyzed. This simulation method can provide a reference for fault monitoring and diagnosis for planetary gear system.

Gear Transmission Fault Classification using Deep Neural Networks and Classifier Level Sensor Fusion

Gear transmissions are widely used in industrial drive systems.Fault diagnosis of gear transmissions is important for maintaining the system performance,reducing the maintenance cost,and providing a safe working environment.This paper presents a novel fault diagnosis approach for gear transmissions based on convolutional neural networks(CNNs)and decision-level sensor fusion.In the proposed approach,a CNN is first utilized to classify the faults of a gear transmission based on the acquired signals from each of the sensors.Raw sensory data is sent directly into the CNN models without manual feature extraction.Then,classifier level sensor fusion is carried out to achieve improved classification accuracy by fusing the classification results from the CNN models.Experimental study is conducted,which shows the superior performance of the developed method in the classification of different gear transmission conditions in an automated industrial machine.The presented approach also achieves end-to-end learning that ean be applied to the fault elassification of a gear transmission under various operating eonditions and with signals from different types of sensors.

Incipient Gear Fault Detection Using Adaptive Impulsive Wavelet Filter Based on Spectral Negentropy

Adaptive wavelet filtering is a very important fault feature extraction method in the domain of condition monitoring;however, owing to the time-consuming computation and difficulty of choosing criteria used to represent incipient faults, the engineering applications are limited to some extent. To detect incipient gear faults at a fast speed, a new criterion is proposed to optimize the parameters of the modified impulsive wavelet for constructing an optimal wavelet filter to detect impulsive gear faults. First, a new criterion based on spectral negentropy is proposed. Then, a novel search strategy is applied to optimize the parameters of the impulsive wavelet based on the new criterion. Finally,envelope spectral analysis is applied to determine the incipient fault characteristic frequency. Both the simulation and experimental validation demonstrated the superiority of the proposed approach.

NEW METHOD OF EXTRACTING WEAK FAILURE INFORMATION IN GEARBOX BY COMPLEX WAVELET DENOISING

Because the extract of the weak failure information is always the difficulty and focus of fault detection. Aiming for specific statistical properties of complex wavelet coefficients of gearbox vibration signals, a new signal-denoising method which uses local adaptive algorithm based on dual-tree complex wavelet transform （DT-CWT） is introduced to extract weak failure information in gear, especially to extract impulse components. By taking into account the non-Gaussian probability distribution and the statistical dependencies among wavelet coefficients of some signals, and by taking the advantage of near shift-invariance of DT-CWT, the higher signal-to-noise ratio （SNR） than common wavelet denoising methods can be obtained. Experiments of extracting periodic impulses in gearbox vibration signals indicate that the method can extract incipient fault feature and hidden information from heavy noise, and it has an excellent effect on identifying weak feature signals in gearbox vibration signals.