Comparisons of MFDFA, EMD and WT by Neural Network, Mahalanobis Distance and SVM in Fault Diagnosis of Gearboxes

A method for gearbox fault diagnosis consists of feature extraction andfault identification. Many methods for feature extraction have beendevised for exposing nature of vibration data of a defective gearbox. Inaddition, features extracted from gearbox vibration data are identifiedby various classifiers. However, existing literatures leave much to bedesired in assessing performance of different combinatorial methods forgearbox fault diagnosis. To this end, this paper evaluated performance ofseveral typical combinatorial methods for gearbox fault diagnosis byassociating each of multifractal detrended fluctuation analysis (MFDFA),empirical mode decomposition (EMD) and wavelet transform (WT) witheach of neural network (NN), Mahalanobis distance decision rules(MDDR) and support vector machine (SVM). Following this,performance of different combinatorial methods was compared using agroup of gearbox vibration data containing slightly different faultpatterns. The results indicate that MFDFA performs better in featureextraction of gearbox vibration data and SVM does the same in faultidentification. Naturally, the method associating MFDFA with SVMshows huge potential for fault diagnosis of gearboxes. As a result, thispaper can provide some useful information on construction of a methodfor gearbox fault diagnosis.

Acoustics Based Monitoring and Diagnostics for the Progressive Deterioration of Helical Gearboxes

Gearbox condition monitoring(CM)plays a significant role in ensuring the operational reliability and efficiency of a wide range of critical industrial systems such as wind turbines and helicopters.Accurate and timely diagnosis of gear faults will improve the maintenance of gearboxes operating under sub-optimal conditions,avoid excessive energy consumption and prevent avoidable damages to systems.This study focuses on developing CM for a multi-stage helical gearbox using airborne sound.Based on signal phase alignments,Modulation Signal Bispectrum(MSB)analysis allows random noise and interrupting events in sound signals to be suppressed greatly and obtains nonlinear modulation features in association with gear dynamics.MSB coherence is evaluated for selecting the reliable bi-spectral peaks for indication of gear deterioration.A run-to-failure test of two industrial gearboxes was tested under various loading conditions.Two omnidirectional microphones were fixed near the gearboxes to sense acoustic information during operation.It has been shown that compared against vibration based CM,acoustics can perceive the responses of vibration in a larger areas and contains more comprehensive and stable information related to gear dynamics variation due to wear.Also,the MSB magnitude peaks at the first three harmonic components of gear mesh and rotation components are demonstrated to be sufficient in characterizing the gradual deterioration of gear transmission.Consequently,the combining of MSB peaks with baseline normalization yields more accurate monitoring trends and diagnostics,allowing the gradual deterioration process and gear wear location to be represented more consistently.

The Effect of Signal Propagation Delay on the Measured Vibration in Planetary Gearboxes

Modulation of the gear mesh vibration is a major field of research for the condition monitoring of planetary gearboxes.The modulation creates sidebands around the gearmesh frequency in the vibration spectrum,and the distribution of these sidebands has been researched in numerous papers.All publications on the subject assume that the effect of the time varying signal propagation delay between the main vibration source–the gear mesh point(s)–and the(usually fixed)transducer can be neglected.This paper investigates the validity of this assumption.To do so,a planetary gearbox with a transducer mounted on the(fixed)ring gear is studied,and the effect of the propagation delay is modelled as a phase modulation of the gear mesh vibration.General expressions are then derived for the distribution and strength of the modulation sidebands,and these expressions are applied to quantify the effect of the propagation delay on five industrial gearboxes.The results show that the amplitude of the sidebands is negligible and would not interfere with condition assessment based on analysis of the modulation of the gear mesh frequency,and thus the propagation delay can be neglected for practical purposes.

Torque effect on vibration behavior of high-speed train gearbox under internal and external excitations

The high-speed train transmission system,experiencing both the internal excitation originating from gear meshing and the external excitation originating from the wheel-rail interaction,exhibits complex dynamic behavior in the actual service environment.This paper focuses on the gearbox in the high-speed train to carry out the bench test,in which various operat-ing conditions(torques and rotation speeds)were set up and the excitation condition covering both internal and external was created.Acceleration responses on multiple positions of the gearbox were acquired in the test and the vibration behavior of the gearbox was studied.Meanwhile,a stochastic excitation modal test was also carried out on the test bench under different torques,and the modal parameter of the gearbox was identified.Finally,the sweep frequency response of the gearbox under gear meshing excitation was analyzed through dynamic modeling.The results showed that the torque has an attenuating effect on the amplitude of gear meshing frequency on the gearbox,and the effect of external excitation on the gearbox vibration cannot be ignored,especially under the rated operating condition.It was also found that the torque affects the modal param-eter of the gearbox significantly.The torque has a great effect on both the gear meshing stiffness and the bearing stiffness in the transmission system,which is the inherent reason for the changed modal characteristics observed in the modal test and affects the vibration behavior of the gearbox consequently.

Multiple fault separation and detection by joint subspace learning for the health assessment of wind turbine gearboxes

The gearbox of a wind turbine （WT） has dominant failure rates and highest downtime loss among all WT subsystems. Thus, gearbox health assessment for maintenance cost reduction is of paramount importance. The concurrence of multiple faults in gearbox components is a common phenomenon due to fault induction mechanism. This problem should be considered before planning to replace the components of the WT gearbox. Therefore, the key fault patterns should be reliably identified from noisy observation data for the development of an effective maintenance strategy. However, most of the existing studies focusing on multiple fault diagnosis always suffer from inappropriate division of fault information in order to satisfy various rigorous decomposition principles or statistical assumptions, such as the smooth envelope principle of ensemble empirical mode decomposition and the mutual independence assumption of independent component analysis. Thus, this paper presents a joint subspace learning-based multiple fault detection （JSLMFD） technique to construct different subspaces adaptively for different fault pattems. Its main advantage is its capability to learn multiple fault subspaces directly from the observation signal itself. It can also sparsely concentrate the feature information into a few dominant subspace coefficients. Furthermore, it can eliminate noise by simply performing coefficient shrinkage operations. Consequently, multiple fault patterns are reliably identified by utilizing the maximum fault information criterion. The superiority of JSL-MFD in multiple fault separation and detection is comprehensively investigated and verified by the analysis of a data set of a 750 kW WT gearbox. Results show that JSL-MFD is superior to a state-of-the-art technique in detecting hidden fault patterns and enhancing detection accuracy.

Measured load spectra of the bearing in high-speed train gearbox under different gear meshing conditions

The load spectrum is a crucial factor for assess-ing the fatigue reliability of in-service rolling element bear-ings in transmission systems.For a bearing in a high-speed train gearbox,a measurement technique based on strain detection of bearing outer ring was used to instrument the bearing and determine the time histories of the distributed load in the bearing under different gear meshing conditions.Accordingly,the load spectrum of the total radial load car-ried by the bearing was compiled.The mean value and class interval of the obtained load spectrum were found to vary non-monotonously with the speed and torque of gear mesh-ing,which was considered to be caused by the vibration of the shaft and the bearing cage.As the realistic service load input of bearing life assessment,the measured load spectrum under different gear meshing conditions can be used to pre-dict gearbox bearing life realistically based on the damage-equivalent principle and actual operating conditions.

Intelligent Fault Diagnosis for Planetary Gearbox Using Transferable Deep Q Network Under Variable Conditions with Small Training Data

Effective fault diagnosis of planetary gearboxes is critical for ensuring the safety and dependability of mechanical drive systems.Nevertheless,variable conditions and inadequate fault data bring huge challenges to its practical fault diagnosis.Taking this into account,this study presents a new intelligent fault diagnosis(IFD)approach for planetary gearbox using a transferable deep Q network(TDQN)that merges deep reinforcement learning(DRL)and transfer learning(TL).First,a DRL environment simulation is designed by a predefined classification Markov decision process.Then,leveraging varied-size convolutions and residual learning,a multiscale residual convolutional neural network agent for TDQN is created to automatically learn meaningful features directly from vibration signals while avoiding model degradation.Next,a large source dataset is obtained from complex conditions,and this agent learns an IFD policy via autonomous interaction with the data environment.Finally,a parameter-based TL strategy is adopted to retrain the model on target datasets with variable conditions and small training data,which is conducted by fine-tuning the model parameters gained from the source task to accomplish target tasks.The results show that this TDQN outperforms not only state-of-the-art methods in a source task with an accuracy of 98.53%but also in two target tasks with 99.63%and 98.37%,respectively.

Numerical Visualization of Grease Flow in a Gearbox

Lubricating greases are widely used in e.g.open gear drives and gearboxes with difficult sealing conditions.The efficiency and heat balance of grease-lubricated gearboxes depend strongly on the lubrication mechanisms channeling and circulating,for which the grease flow is causal.The computational fluid dynamics opens up the possibility to visualize and understand the grease flow in gearboxes in more detail.In this study,a single-stage gearbox lubricated with an NLGI 1-2 grease was modeled by the finite-volume method to numerically investigate the fluid flow.Results show that the rotating gears influence the grease sump only locally around the gears.For a low grease fill volume,the rotation of the gears is widely separated from the grease sump.For a high grease fill volume,a pronounced geargrease interaction results in a circulating grease flow around the gears.The simulated grease distributions show good accordance with high-speed camera recordings.

A Noise Reduction Method for Multiple Signals Combining Computed Order Tracking Based on Chirplet Path Pursuit and Distributed Compressed Sensing

With the development of multi-signal monitoring technology,the research on multiple signal analysis and processing has become a hot subject.Mechanical equipment often works under variable working conditions,and the acquired vibration signals are often non-stationary and nonlinear,which are difficult to be processed by traditional analysis methods.In order to solve the noise reduction problem of multiple signals under variable speed,a COT-DCS method combining the Computed Order Tracking(COT)based on Chirplet Path Pursuit(CPP)and Distributed Compressed Sensing(DCS)is proposed.Firstly,the instantaneous frequency(IF)is extracted by CPP,and the speed is obtained by fitting.Then,the speed is used for equal angle sampling of time-domain signals,and angle-domain signals are obtained by COT without a tachometer to eliminate the nonstationarity,and the angledomain signals are compressed and reconstructed by DCS to achieve noise reduction of multiple signals.The accuracy of the CPP method is verified by simulated,experimental signals and compared with some existing IF extraction methods.The COT method also shows good signal stabilization ability through simulation and experiment.Finally,combined with the comparative test of the other two algorithms and four noise reduction effect indicators,the COT-DCS based on the CPP method combines the advantages of the two algorithms and has better noise reduction effect and stability.It is shown that this method is an effective multi-signal noise reduction method.

Characterization,identification and life prediction of acoustic emission signals of tensile damage for HSR gearbox housing material

Purpose-This study aims to ensure the operation safety of high speed trains,it is necessary to carry out nondestructive monitoring of the tensile damage of the gearbox housing material in rail time,yet the traditional tests of mechanical property can hardly meet this requirement.Design/methodology/approach-In this study the acoustic emission(AE)technology is applied in the tensile tests of the gearbox housing material of an high-speed rail(HSR)train,during which the acoustic signatures are acquired for parameter analysis.Afterward,the support vector machine(SVM)classifier is introduced to identify and classify the characteristic parameters extracted,on which basis the SVM is improved and the weighted support vector machine(WSVM)method is applied to effectively reduce the misidentification of the SVM classifier.Through the study of the law of relations between the characteristic values and the tensile life,a degradation model of the gearbox housing material amid tensile is built.Findings-The results show that the growth rate of the logarithmic hit count of AE signals and that of logarithmic amplitude can well characterize the stage of the material tensile process,and the WSVM method can improve the classification accuracy of the imbalanced data to above 94%.The degradation model built can identify the damage occurred to the HSR gearbox housing material amid the tensile process and predict the service life remains.Originality/value-The results of this study provide new concepts for the life prediction of tensile samples,and more further tests should be conducted to verify the conclusion of this research.

Multi-objective Optimization of a Two-Stage Helical Gearbox to Improve Efficiency and Reduce Height

The goal of this research is to look at multi-target optimization of a two-stage helical gearbox in order to determine the best key design elements for reducing gearbox height and enhancing gearbox efficiency.To do this,the method known as Taguchi and GRA(Grey Relation Analysis)were used in two stages to address the problem.The single-objective optimization problem was addressed first to close the gap between variable levels,and then the multi-objective optimization problem was solved to determine the best primary design variables.The first and second stage CWFWs(Coefficients of Wheel Face Width),ACS(Permissible Contact Stresses),and first stage gear ratio were also calculated.The study’s findings were utilized to identify the best values for five critical design aspects of a two-stage helical gearbox.

An Improved Coupled Dynamic Modelling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery,in which gear,shaft and bearing operate together to transmit motion and power.The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis.Dynamic modelling can study the mechanism under different faults and provide theoretical foundation for fault detection.However,current commonly used gear dynamic model usually neglects the influence of bearing and shaft,resulting in incomplete understanding of gearbox fault diagnosis especially under the effect of local defects on gear and shaft.To address this problem,an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects.Firstly,an eighteen degree-of-freedom gearbox dynamic model is proposed,taking into account the interaction among gear,bearing and shaft.Secondly,the dynamic model is iteratively solved.Then,vibration responses are expounded and analysed considering gear spalling and shaft crack.Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum.Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general.An experiment is designed to verify the rationality of the proposed gearbox model.Lastly,comprehensive analysis under different spalling size and shaft crack angle are analysed.Results show that when spalling size and crack angle are larger,RMS and the amplitude of shaft rotating frequency will not increase linearly.The dynamic model can accurately simulate the vibration of gear transmission system,which is helpful for gearbox fault diagnosis.

Discussion on Maintenance Cases of Wind Turbine Components

At present,the greenhouse effect is caused by excessive emission of carbon dioxide.As a result the Arctic ice has melted and sea levels have risen.If it continues to deteriorate,it will cause human catastrophe.In order to avoid direct crisis and development,green energy is the only necessary way.Here,wind power plays an important role.Onshore wind power has been developed in Taiwan for more than 15 years.There are 341 onshore wind turbines that have been built so far.The total installed capacity is 678 MW high.Among them,Tai power occupies a total of 169 stations with a total installed capacity of 294 MW.Offshore wind turbines are also under construction.By 2025,the capacity will be 5 to 6 GW.It can be seen that the supply of wind power in the overall power market will become an important area in the future.Therefore,how to improve the availability and capacity factors of wind turbine power generation will become a top priority for owners.Since most of the world’s best wind farms are in the Taiwan Strait,this is a unique feature of Taiwan,although Taiwan lacks traditional fuels,petroleum,coal,natural gas and other resources.If these abundant solar and wind energy resources can be effectively utilized,in addition to reducing carbon emissions and contributing to the world,the development of green energy can also drive the development of the domestic green energy industry,also through the development of green energy to establish domestic operation and maintenance technology for wind turbines.

Wind Turbine Planetary Gearbox Fault Diagnosis via Proportion-Extracting Synchrosqueezing Chirplet Transform

Wind turbine planetary gearboxes usually work under time-varying conditions,leading to nonstationary vibration signals.These signals often consist of multiple time-varying components with close instantaneous frequencies.Therefore,high-quality time-frequency analysis(TFA)is needed to extract the time-frequency feature from such nonstationary signals for fault diagnosis.However,it is difficult to obtain high-quality timefrequency representations(TFRs)through conventional TFA methods due to low resolution and time-frequency blurs.To address this issue,we propose a new TFA method termed the proportion-extracting synchrosqueezing chirplet transform(PESCT).Firstly,the proportion-extracting chirplet transform is employed to generate highresolution underlying TFRs.Then,the energy concentration of the underlying TFRs is enhanced via the synchrosqueezing transform.Finally,wind turbine planetary gearbox fault can be diagnosed by analysis of the dominant time-varying components revealed by the concentrated TFRs with high resolution.The proposed PESCT is suitable for achieving high-quality TFRs for complicated nonstationary signals.Numerical and experimental analyses validate the effectiveness of the PESCT in characterizing the nonstationary signals from wind turbine planetary gearboxes.

基于非均匀连续时间马尔可夫原理的海上浮式风机齿轮箱最优维修策略研究（英文）

Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.

Gearbox Fault Diagnosis using Adaptive Zero Phase Time-varying Filter Based on Multi-scale Chirplet Sparse Signal Decomposition

When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.

Crack Fault Classification for Planetary Gearbox Based on Feature Selection Technique and K-means Clustering Method

During the condition monitoring of a planetary gearbox, features are extracted from raw data for a fault diagnosis.However, different features have different sensitivity for identifying different fault types, and thus, the selection of a sensitive feature subset from an entire feature set and retaining as much of the class discriminatory information as possible has a directly effect on the accuracy of the classification results. In this paper, an improved hybrid feature selection technique(IHFST) that combines a distance evaluation technique(DET), Pearson’s correlation analysis, and an ad hoc technique is proposed. In IHFST, a temporary feature subset without irrelevant features is first selected according to the distance evaluation criterion of DET, and the Pearson’s correlation analysis and ad hoc technique are then employed to find and remove redundant features in the temporary feature subset, respectively, and hence,a sensitive feature subset without irrelevant or redundant features is selected from the entire feature set. Further, the k-means clustering method is applied to classify the different kinds of health conditions. The effectiveness of the proposed method was validated through several experiments carried out on a planetary gearbox with incipient cracks seeded in the tooth root of the sun gear, planet gear, and ring gear. The results show that the proposed method can successfully distinguish the different health conditions of a planetary gearbox, and achieves a better classification performance than other methods. This study proposes a sensitive feature subset selection method that achieves an obvious improvement in terms of the accuracy of the fault classification.

Application of particle swarm optimization blind source separation technology in fault diagnosis of gearbox

Blind source separation (BBS) technology was applied to vibration signal processing of gearbox for separating different fault vibration sources and enhancing fault information. An improved BSS algorithm based on particle swarm optimization (PSO) was proposed. It can change the traditional fault-enhancing thought based on de-noising. And it can also solve the practical difficult problem of fault location and low fault diagnosis rate in early stage. It was applied to the vibration signal of gearbox under three working states. The result proves that the BSS greatly enhances fault information and supplies technological method for diagnosis of weak fault.

Gearbox Deterioration Detection under Steady State,Variable Load, and Variable Speed Conditions

Multiple dominant gear meshing frequencies are present in the vibration signals collected from gearboxes and the conventional spiky features that represent initial gear fault conditions are usually difficult to detect. In order to solve this problem, we propose a new gearbox deterioration detection technique based on autoregressive modeling and hypothesis testing in this paper. A stationary autoregressive model was built by using a normal vibration signal from each shaft. The established autoregressive model was then applied to process fault signals from each shaft of a two-stage gearbox. What this paper investigated is a combined technique which unites a time-varying autoregressive model and a two sample Kolmogorov-Smimov goodness-of-fit test, to detect the deterioration of gearing system with simultaneously variable shaft speed and variable load. The time-varying autoregressive model residuals representing both healthy and faulty gear conditions were compared with the original healthy time-synchronous average signals. Compared with the traditional kurtosis statistic, this technique for gearbox deterioration detection has shown significant advantages in highlighting the presence of incipient gear fault in all different speed shafts involved in the meshing motion under variable conditions.

Approach to the Design Calculation of Sucker Rod Pumping Systems in Coalbed Methane Wells

The existing design of the pumping systems mainly focuses on the approximate computational formulae and procedures,which are developed based on the analytic approaches of conventional oil/gas fields.The calculation of polished rod loads usually just concerns about the static and inertial loads.And the computation of gearbox torque generally uses empirical formulae and correction factors.The above modeling procedures,if applied to the coalbed methane（CBM） wells,can not give the desired accuracy of the system design and its pertinent analysis.In this paper,based on the kinematic and dynamic analysis of the pumping system,the kinematic relation of polished rod is analyzed,and the variation of the total loads of polished rod is developed with the limits of CBM well conditions along the string.The gearbox torque calculation model is established by combining the counterbalance effect with the calculated dynamometer cards and torque factors.The application characteristics of this model are demonstrated by the example of ZH002-4 well in Qinshui basin.The interpretations of results show that the cranks of beam units should rotate in a counter clockwise direction viewed with the wellhead to the right.Compared with oil？gas fields,the dynamic and friction to polished rod load ratios are relatively high and the computation of polished rod loads should involve the static and inertial loads,as well as vibration and friction loads.And the dynamic load ratio decreases rapidly during the production.Besides,the total deformation of the string is small in CBM wells.As for balanced operation,the gearbox torque load usually has two approximately equal peaks and the magnitudes of instantaneous torque are just within 50% of unbalanced gearbox loadings.The proposed research improves efficiency of the pumping system,loads the pumping unit more uniformly,and provides the reasonable basis for selecting the units.