ARX model-based gearbox fault detection and localization under varying load conditions

The development of the fault detection schemes for gearbox systems has received considerable attention in recent years. Both time series modeling and feature extraction based on wavelet methods have been considered, mostly under constant load. Constant load assumption implies that changes in vibration data are caused only by deterioration of the gearbox. However, most real gearbox systems operate under varying load and speed which affect the vibration signature of the system and in general make it difficult to recognize the occurrence of an impending fault.This paper presents a novel approach to detect and localize the gear failure occurrence for a gearbox operating under varying load conditions. First, residual signal is calculated using an autoregressive model with exogenous variables (ARX) fitted to the time-synchronously averaged (TSA) vibration data and filtered TSA envelopes when the gearbox operated under various load conditions in the healthy state. The gear of interest is divided into several sections so that each section includes the same number of adjacent teeth. Then, the fault detection and localization indicator is calculated by applying F-test to the residual signal of the ARX model. The proposed fault detection scheme indicates not only when the gear fault occurs, but also in which section of the gear. Finally, the performance of the fault detection scheme is checked using full lifetime vibration data obtained from the gearbox operating from a new condition to a breakdown under varying load.     

Vibration signal models for fault diagnosis of planetary gearboxes

A thorough understanding of the spectral structure of planetary gear system vibration signals is helpful to fault diagnosis of planetary gearboxes. Considering both the amplitude modulation and the frequency modulation effects due to gear damage and periodically time variant working condition, as well as the effect of vibration transfer path, signal models of gear damage for fault diagnosis of planetary gearboxes are given and the spectral characteristics are summarized in closed form. Meanwhile, explicit equations for calculating the characteristic frequency of local and distributed gear fault are deduced. The theoretical derivations are validated using both experimental and industrial signals. According to the theoretical basis derived, manually created local gear damage of different levels and naturally developed gear damage in a planetary gearbox can be detected and located.     

Constrained adaptive lifting and the CAL4 metric for helicopter transmission diagnostics

This paper presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting (CAL) algorithm, an adaptive manifestation of the lifting scheme. Lifting is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Adaptivity is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation synchronous signal-averaging algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have approximately the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local waveform changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. A diagnostic metric based on the lifting prediction error vector termed CAL4 is developed. The CAL diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the CAL4 metric is compared with the classic metric FM4.     

基于BP神经网络的变速箱故障诊断方法研究

针对变速箱的工作时间不能真实反映实际健康状况的问题,通过提取变速箱的振动信号作为状态参数,建立了基于BP神经网络的变速箱故障诊断模型。该模型首先提取振动信号中对故障反映灵敏的成分作为特征值,获得BP神经网络的训练数据,并通过对比确定最优的隐含层节点数,确定BP神经网络的结构参数。模型训练结束后,以验证数据为例进行故障诊断研究,并对诊断结果进行评估。评估结果表明,该模型准确度高,具有较好的应用和推广价值。     

Complex signal analysis for wind turbine planetary gearbox fault diagnosis via iterative atomic decomposition thresholding

The vibration signals from complex structures such as wind turbine (WT) planetary gearboxes are intricate. Reliable analysis of such signals is the key to success in fault detection and diagnosis for complex structures. The recently proposed iterative atomic decomposition thresholding (IADT) method has shown to be effective in extracting true constituent components of complicated signals and in suppressing background noise interferences. In this study, such properties of the IADT are exploited to analyze and extract the target signal components from complex signals with a focus on WT planetary gearboxes under constant running conditions. Fault diagnosis for WT planetary gearboxes has been a very important yet challenging issue due to their harsh working conditions and complex structures. Planetary gearbox fault diagnosis relies on detecting the presence of gear characteristic frequencies or monitoring their magnitude changes. However, a planetary gearbox vibration signal is a mixture of multiple complex components due to the unique structure, complex kinetics and background noise. As such, the IADT is applied to enhance the gear characteristic frequencies of interest, and thereby diagnose gear faults. Considering the spectral properties of planetary gearbox vibration signals, we propose to use Fourier dictionary in the IADT so as to match the harmonic waves in frequency domain and pinpoint the gear fault characteristic frequency. To reduce computing time and better target at more relevant signal components, we also suggest a criterion to estimate the number of sparse components to be used by the IADT. The performance of the proposed approach in planetary gearbox fault diagnosis has been evaluated through analyzing the numerically simulated, lab experimental and on-site collected signals. The results show that both localized and distributed gear faults, both the sun and planet gear faults, can be diagnosed successfully.     

A time domain approach to diagnose gearbox fault based on measured vibration signals

Spectral analysis techniques to process vibration measurements have been widely studied to characterize the state of gearboxes. However, in practice, the modulated sidebands resulting from the local gear fault are often difficult to extract accurately from an ambiguous/blurred measured vibration spectrum due to the limited frequency resolution and small fluctuations in the operating speed of the machine that often occurs in an industrial environment. To address this issue, a new time-domain diagnostic algorithm is developed and presented herein for monitoring of gear faults, which shows an improved fault extraction capability from such measured vibration signals. This new time-domain fault detection method combines the fast dynamic time warping (Fast DTW) as well as the correlated kurtosis (CK) techniques to characterize the local gear fault, and identify the corresponding faulty gear and its position. Fast DTW is employed to extract the periodic impulse excitations caused from the faulty gear tooth using an estimated reference signal that has the same frequency as the nominal gear mesh harmonic and is built using vibration characteristics of the gearbox operation under presumed healthy conditions. This technique is beneficial in practical analysis to highlight sideband patterns in situations where data is often contaminated by process/measurement noises and small fluctuations in operating speeds that occur even at otherwise presumed steady-state conditions. The extracted signal is then resampled for subsequent diagnostic analysis using CK technique. CK takes advantages of the periodicity of the geared faults; it is used to identify the position of the local gear fault in the gearbox. Based on simulated gear vibration signals, the Fast DTW and CK based approach is shown to be useful for condition monitoring in both fixed axis as well as epicyclic gearboxes. Finally the effectiveness of the proposed method in fault detection of gears is validated using experimental signals from a planetary gearbox test rig. For fault detection in planetary gear-sets, a window function is introduced to account for the planet motion with respect to the fixed sensor, which is experimentally determined and is later employed for the estimation of reference signal used in Fast DTW algorithm.     

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 and fault identification. Many methods for feature extraction have been devised for exposing nature of vibration data of a defective gearbox. In addition, features extracted from gearbox vibration data are identified by various classifiers. However, existing literatures leave much to be desired in assessing performance of different combinatorial methods for gearbox fault diagnosis. To this end, this paper evaluated performance of several typical combinatorial methods for gearbox fault diagnosis by associating each of multifractal detrended fluctuation analysis (MFDFA), empirical mode decomposition (EMD) and wavelet transform (WT) with each of neural network (NN), Mahalanobis distance decision rules (MDDR) and support vector machine (SVM). Following this, performance of different combinatorial methods was compared using a group of gearbox vibration data containing slightly different fault patterns. The results indicate that MFDFA performs better in feature extraction of gearbox vibration data and SVM does the same in fault identification. Naturally, the method associating MFDFA with SVM shows huge potential for fault diagnosis of gearboxes. As a result, this paper can provide some useful information on construction of a method for gearbox fault diagnosis.     

Feature separation using ICA for a one-dimensional time series and its application in fault detection

Principal component analysis (PCA) is a method that transforms multiple data series into uncorrelated data series. Independent component analysis (ICA) is a method that separates multiple data series into independent data series. Both methods have been used in fault detection. However, both require signals from at least two separate sensors. To overcome this requirement and utilize the fault detection capability of ICA and PCA, we propose to use wavelet transform to pre-process the data collected from a single sensor and then use the coefficients of the wavelet transforms at different scales as input to ICA and PCA. The effectiveness of this method is demonstrated by applying it to both a simulated signal series and a vibration signal series collected from a gearbox. The results show that the method of combining wavelet transform and ICA works better than the method of combining wavelet transform and PCA for impulse detection based on a one-dimensional vibration data series.     

Condition monitoring of a single-stage gearbox with artificially induced gear cracks utilizing on-line vibration and acoustic emission measurements

The condition monitoring of a lab-scale, single stage, gearbox using different non-destructive inspection methodologies and the processing of the acquired waveforms with advanced signal processing techniques is the aim of the present work. Acoustic emission (AE) and vibration measurements were utilized for this purpose. The experimental setup and the instrumentation of each monitoring methodology are presented in detail. Emphasis is given on the signal processing of the acquired vibration and acoustic emission signals in order to extract conventional as well as novel parameters-features of potential diagnostic value from the monitored waveforms. Innovative wavelet-based parameters-features are proposed utilizing the discrete wavelet transform. The evolution of selected parameters/features versus test time is provided, evaluated and the parameters with the most interesting diagnostic behaviour are highlighted. The differences in the parameters evolution of each NDT technique are discussed and the superiority of AE over vibration recordings for the early diagnosis of natural wear in gear systems is concluded.     

基于Polytec激光测振仪和第二代小波的齿轮箱故障诊断

齿轮箱是机械设备中一种必不可少的通用零部件,也是故障多发部件,而齿轮失效又是诱发其故障的重要因素。因此发展新型齿轮箱故障诊断技术具有重要意义。搭建了基于Polytec激光测振仪的光学测量系统,拾取齿轮箱振动信号,采用第二代小波提取故障特征,达到了故障诊断的目的,可用于齿轮箱故障预知和智能维修。     

Low-Pass Filtering Empirical Wavelet Transform Machine Learning Based Fault Diagnosis for Combined Fault of Wind Turbines

Fault diagnosis of wind turbines is of great importance to reduce operating and maintenance costs of wind farms. At present, most wind turbine fault diagnosis methods are focused on single faults, and the methods for combined faults usually depend on inefficient manual analysis. Filling the gap, this paper proposes a low-pass filtering empirical wavelet transform (LPFEWT) machine learning based fault diagnosis method for combined fault of wind turbines, which can identify the fault type of wind turbines simply and efficiently without human experience and with low computation costs. In this method, low-pass filtering empirical wavelet transform is proposed to extract fault features from vibration signals, LPFEWT energies are selected to be the inputs of the fault diagnosis model, a grey wolf optimizer hyperparameter tuned support vector machine (SVM) is employed for fault diagnosis. The method is verified on a wind turbine test rig that can simulate shaft misalignment and broken gear tooth faulty conditions. Compared with other models, the proposed model has superiority for this classification problem.     

Application of Generalized Composite Multiscale Lempel–Ziv Complexity in Identifying Wind Turbine Gearbox Faults

Wind turbine gearboxes operate in harsh environments; therefore, the resulting gear vibration signal has characteristics of strong nonlinearity, is non-stationary, and has a low signal-to-noise ratio, which indicates that it is difficult to identify wind turbine gearbox faults effectively by the traditional methods. To solve this problem, this paper proposes a new fault diagnosis method for wind turbine gearboxes based on generalized composite multiscale Lempel–Ziv complexity (GCMLZC). Within the proposed method, an effective technique named multiscale morphological-hat convolution operator (MHCO) is firstly presented to remove the noise interference information of the original gear vibration signal. Then, the GCMLZC of the filtered signal was calculated to extract gear fault features. Finally, the extracted fault features were input into softmax classifier for automatically identifying different health conditions of wind turbine gearboxes. The effectiveness of the proposed method was validated by the experimental and engineering data analysis. The results of the analysis indicate that the proposed method can identify accurately different gear health conditions. Moreover, the identification accuracy of the proposed method is higher than that of traditional multiscale Lempel–Ziv complexity (MLZC) and several representative multiscale entropies (e.g., multiscale dispersion entropy (MDE), multiscale permutation entropy (MPE) and multiscale sample entropy (MSE)).     

Gearbox vibration monitoring using extended Kalman filters and hypothesis tests

The efficiency of many maintenance programs is heavily dependent on the detection accuracy of the condition monitoring system. Condition indicators that are sensitive to environmental or operational variables of no interest will inevitably reflect irrelevant fluctuations and thus mislead the subsequent analysis. In consideration of this phenomenon, a fully automatic and robust vibration monitoring system for gearboxes is proposed in this study. The primary objective here is on how to exclude the effects of variable load conditions. The proposed technique features a number of appealing advantages, which include extended Kalman filter-based time-varying autoregressive modeling, automatic autoregressive model order selection with the aid of a non-paired two-sample Satterthwaite's t′-test, a highly effective and robust condition indicator (the means of one-sample Kolmogorov-Smirnov goodness-of-fit test), and an automatic alert generating mechanism for incipient gear faults with the aid of a Wilcoxon rank-sum test. Two sets of entire lifetime gearbox vibration monitoring data with distinct variable load conditions were used for experimental validation. The proposed condition indicator was compared with other well-known and/or recently proposed condition indicators. The results demonstrate excellent performance of the proposed technique in four aspects: the effectiveness of identifying the optimum model order, a minimum number of false alerts, constant behavior under variable load conditions, and to some extent an early alert for incipient gear faults. Furthermore, the proposed condition indicator can be directly employed by condition-based maintenance programs as a condition covariate for operational maintenance decision analysis. It provides a quantitative and more efficient means for exchanging condition information with maintenance programs in comparison with the widely used non-parametric time-frequency techniques such as wavelets, which rely on visual inspection.     

Application of multi-scale chirplet path pursuit and fractional Fourier transform for gear fault detection in speed up and speed-down processes

Demodulation is very important for gear fault detection. However, the demodulation is substantially complicated by the non-stationary nature of the signal during the speed-up and speed-down processes. As such, we propose a new technique to detect gear faults under such conditions based on the multi-scale chirplet path pursuit (MSCPP) algorithm and the fractional Fourier transform (FrFT) method. With the MSCPP algorithm, the instantaneous frequency of the signal component with the largest energy in the multi-components gear vibration signal can be estimated. Then according to the estimated instantaneous frequency, the vibration signal segment whose instantaneous frequency curve approximated as either an ascending or descending linear segment can be obtained from the original gear vibration signal. In other words, the vibration signal segment that can be regarded as a multi-component linear frequency modulated (LFM) signal is extracted. As the FrFT is suitable for multi-component LFM signal analysis, it is then applied to demodulating this vibration signal segment and hence detecting local gear faults based on the revealed modulation phenomenon. The effectiveness of the proposed method has been demonstrated by both simulation and experimental data.     

Subway Gearbox Fault Diagnosis Algorithm Based on Adaptive Spline Impact Suppression

In the signal processing of real subway vehicles, impacts between wheelsets and rail joint gaps have significant negative effects on the spectrum. This introduces great difficulties for the fault diagnosis of gearboxes. To solve this problem, this paper proposes an adaptive time-domain signal segmentation method that envelopes the original signal using a cubic spline interpolation. The peak values of the rail joint gap impacts are extracted to realize the adaptive segmentation of gearbox fault signals when the vehicle was moving at a uniform speed. A long-time and unsteady signal affected by wheel–rail impacts is segmented into multiple short-term, steady-state signals, which can suppress the high amplitude of the shock response signal. Finally, on this basis, multiple short-term sample signals are analyzed by time- and frequency-domain analyses and compared with the nonfaulty results. The results showed that the method can efficiently suppress the high-amplitude components of subway gearbox vibration signals and effectively extract the characteristics of weak faults due to uniform wear of the gearbox in the time and frequency domains. This provides reference value for the gearbox fault diagnosis in engineering practice.     

基于HHT变换的起动电动机特征信号时频分析

针对车辆起动电动机电气和机械故障发生时特征信号的时变不平稳特性,进行了时频域分析处理,提出了利用现代信号处理方法对故障信号提取特征向量的方法,主要对起动电动机的电枢和轴承故障进行诊断。在构建电机故障测试实验平台的基础上,利用破坏性实验构造了故障类型,测取了电枢电流和振动信号,分别采用小波分析理论和HHT变换对信号进行分析,通过分解再重构的方式将信号分解成了频率由高到低的不同分量,并获得了故障的特征频率,提取了特征向量。实验结果表明,基于HHT变换的现代信号处理方法在处理时变非平稳信号方面比小波分析理论更具有自适应性,更易识别。     

Exchanged ridge demodulation of time-scale manifold for enhanced fault diagnosis of rotating machinery

The vibration or acoustic signal from rotating machinery with localized fault usually behaves as the form of amplitude modulation (AM) and/or frequency modulation (FM). The demodulation techniques are conventional ways to reveal the fault characteristics from the analyzed signals. One of these techniques is the time-scale manifold (TSM) ridge demodulation method with the merits of good time–frequency localization and in-band noise suppression properties. However, due to the essential attribute of wavelet ridge, the survived in-band noise on the achieved TSM will still disturb the envelope extraction of fault-induced impulses. This paper presents an improved TSM ridge demodulation method, called exchanged ridge demodulation of TSM, by combining the benefits of the first two TSMs: the noise suppression of the first TSM and the noise separation of the second TSM. Specifically, the ridge on the second TSM can capture the fault-induced impulses precisely while avoiding the in-band noise smartly. By putting this ridge on the first TSM, the corresponding instantaneous amplitude (IA) waveform can represent the real envelope of pure faulty impulses. Moreover, an adaptive selection method for Morlet wavelet parameters is also proposed based on the smoothness index (SI) in the time-scale domain for an optimal time-scale representation of analyzed signal. The effectiveness of the proposed method is verified by means of a simulation study and applications to diagnosis of bearing defects and gear fault.     

Research on dynamics and fault mechanism of spur gear pair with spalling defect

This study focuses on the nonlinear dynamic and vibration characteristics of spur gear pair with local spalling defect to explore the spalling mechanism. The dynamic model of the gear pair with spalling defect and time-variant mesh stiffness is established to investigate the effect of spalling defect on mesh stiffness and dynamic response. The analytical solutions of the system which is deduced into four different stages of the gear with the time-variant stiffness in a mesh period are obtained. The dynamic responses with the evolvement of sapll are analyzed by using time history, phase contrail, Poincaré section and spectrum analysis. The spalling characteristics are also evaluated by employing statistical techniques, which shows that the spalling failure is suitable to be detected under low velocity and small excitation. The gearbox with spalling defect is designed and the experiments are carried out to get the dynamic characteristics of the spalling vibration signals. The results obtained herein show the good agreement qualitatively with the theoretical analysis, which provides a theoretical basis to spalling fault diagnosis of gearbox.     

THE APPLICATION OF PSEUDO-PHASE PORTRAIT IN MACHINE CONDITION MONITORING

This paper presents a robust phase space reconstruction method based on singular value decomposition technique and its applications to large rotating machine and gear system condition monitoring and fault diagnosis. The singular value decomposition is used to determine the effective embedding space and to reduce the noise level of a measured vibration signal. Following the singular value decomposition, a pseudo-phase portrait can be obtained in the effective embedding space. This pseudo-phase portrait is then used to extract qualitative features of machine faults. Experience has shown that when one compares the pseudo-phase portraits obtained under different machine conditions, it is often possible to detect major differences due to different dynamic and kinematic mechanisms. In the case of gear system condition monitoring, correlation dimension has been introduced to evaluate these differences in order to obtain more accurate and reliable diagnosis. The pseudo-phase portrait is conceptually simple and has been found to be sensitive to some fault types. It is promising therefore that such pseudo-phase portraits can be used to realize real-time, online computer-aided diagnosis of machine faults.     

基于RBF神经网络的强流LIA故障诊断与性能评价技术

 用于流体动力学诊断的强流LIA是庞大而复杂的系统，其性能预测和评估是十分困难的。针对强流LIA大量的单次快脉冲非平稳信号，提出基于小波包分析与RBF神经网络技术相结合实现故障智能诊断和性能评价的方法。该方法以强流LIA高维信号的小波包结点能量提取的特征向量来表征信号平顶、脉宽以及暂态特性。在此基础上，建立了“神龙一号”加速器腔电压及注入器出口束流故障诊断与性能评价原型系统，该系统不仅可进行故障诊断和性能评价，还可探测到加速器运行参数的变化趋势，为加速器的精细维护提供预测信息。