Copula-Based Time-Frequency Distribution Analysis for Planetary Gearbox Fault Detection

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

Enhanced Cohen class time–frequency methods based on a structure tensor analysis: Applications to ISAR processing

This thesis proposes analytical models and monitoring methods based on these models to carry out fault diagnosis of planetary gearboxes and assist in developing robust fault alarm framework for early detection of gear failures. The proposed techniques can be applied not only to planetary wind turbine gearboxes but also to other general planetary gearboxes in varied engineering applications. The equally-spaced planetary gearbox is an important power-train component employed in many electro-mechanical engineering systems whose failures can result in significant capital losses and pose safety concerns. For example, a modern wind turbine is usually designed for a life span of over 20 years. Failure of its drive train components, such as the planetary gearbox and the generator, can leave the wind turbine out of service for long periods and therefore contribute to majority of the downtime and incurred maintenance costs over the entire lifetime of the wind turbine. Vibration based diagnostic techniques to detect gear tooth damage in gearboxes haven been widely studied. However, the complex nature of measured vibration spectra, resulting from rotating planet pinions with respect to the stationary sensor mounted on the gearbox housing, makes an effective implementation of these techniques as a challenge. The research presented in this thesis addresses the challenges of vibration based monitoring of planetary gearbox by (1) understanding the dynamic behavior of planetary gears and the amplitude modulation (AM) phenomena due to the relative motions of the planet pinions with respect to the stationary sensor through a lumped parameter modeling based approach, (2) identifying the location of the additional frequency components in measured vibration spectra resulting due to general gear faults, which are shown to depend on the geometry of the planetary gear-set and the gear carrying the local fault and (3) developing a fault alarm algorithm to diagnose incipient gear failure for industrial applications. The results are validated through dynamic simulations and experimental data from two planetary gearbox test rigs: a 4KW laboratory planetary gearbox test rig with the artificial seeded gear failure and a 750 kW tested gearbox for wind turbine application installed in a 2.5 MW dynamometer test facility at the National Renewable Energy Laboratory (NREL) at Golden, Colorado, US. The second facility is capable of providing static, highly accelerated life and model-in-the-loop tests. Both experiments collected vibration data through stationary accelerometers attached to the housing of the gearbox. The original contribution of the thesis include: (1) A mathematical AM-FM (amplitude modulated/frequency modulated) signal model developed to simulate the distinct spectrum of planetary gearboxes operating under healthy and faulty conditions; (2) Fourier series analysis based on this mathematical signal model that identifies the additional frequency components appearing due to local faults and describe the relationship between the location of these frequency components and the geometry of the planetary gear-set and (3) a new time domain approach that combines dynamic time warping and correlated kurtosis to detect gear faults and identify their location, thus assisting in the development of a robust fault alarm system.

A method of range and depth estimation was studied using a single hydrophone based on the dispersive characteristic and time-frequency analysis for low frequency underwater acoustic pulse signals in shallow water environment. First, the signal received on a single hydrophone can be decomposed into a series of modes within the frame work of normal mode theory, and then the dispersive characteristic of the propagating modes can be analyzed using the time-frequency analysis. In order to improve the time-frequency resolution, the use of the time-frequency distribution with adaptive radial-Gaussian kernel extracts the arrival time difference of propagating modes in dispersion curve, which can be used to estimate source range. Mode energy can be extracted using binary time-frequency mask filtering based on multi-mode joint matching processing; and the source depth can be estimated by comparing the differences of the mode energy of the real data and simulated replica data, yielding a contrast function. Simulation results from a shallow-water Pekeris waveguide show that the time-frequency distribution with adaptive radial-Gaussian kernel represents well the dispersion characteristics of the underwater acoustic pulse signals, provides higher time-frequency resolution and overcomes the problem of the inherent limit for the time resolution and frequency resolution in the traditional short-time Fourier transform, so that the modes can be separated and identified more easily in the time-frequency plane. From the result of the range estimation, the different mode combinations have different results of the range estimation. The range estimation result can be obtained accurately by using the mode with high energy in the time-frequency plane. The relative error in range estimation is less than 2% by using the mode with high energy. In terms of the depth estimation, the more the number of joint matching mode, the more sharp peak and low fake peaks the contrast function has, so that the depth estimation is further improved by incorporating more modes. This research has great significance for studying the extraction and separation of low frequency underwater acoustic pulse signals.

Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions

Time–frequency analysis based on Vold-Kalman filter and higher order energy separation for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions

Heart beat causes the synchronous body vibration, which can be measured on the spine axis by sensitive force sensor called ballistocardiogram. Ballistocardiogram was a kind of nonstationary physiological signal, which couldn't be analyzed and processed by traditional signal processing method. The generation and acquisition method of ballistocardiogram were explained. As examples of bilinear and linear time-frequency distribution, the Cohen class distribution and wavelet transform were discussed and used in ballistocardigram pseudo-period segment. In addition, the frequency range of ballistocardiogram and the levels of wavelet decomposition were determined by Cohen class distribution, but the performance of exponential distribution is better than that of Wigner-Ville distribution and has a fine correspondence to time domain wave of actual ballistocardigram. The experiment results show that, bilinear and linear time-frequency distribution are both able to divide ballistocardiogram into pseudo-periods corresponding to cardiac cycle, but the segment performance of wavelet decomposition is better than that of Cohen class distribution, and the latter one is terser to realize.


 
 
 Planetary gearboxes are widely used in the drivetrain of helicopters and wind turbines. Any planetary gearbox failure could lead to breakdown of the whole drivetrain and major loss of helicopters and wind turbines. Therefore, planetary gearbox fault diagnosis is an important topic in prognostics and health management (PHM). Planetary gearbox fault diagnosis has been done mostly through vibration analysis over the past years. Vibration signals theoretically have the amplitude modulation effect caused by time variant vibration transfer paths due to the rotation of planet carrier and sun gear, and therefore their spectral structure is complex. It is difficult to diagnose planetary gearbox faults via vibration analysis. Strain sensor signals on the other hand have less amplitude modulation effect. Thus, it is potentially easy and effective to diagnose planetary gearbox faults via stain sensor signal analysis. In this paper, a research investigation on planetary gearbox fault diagnosis via strain sensor signal analysis is reported. The investigation involves using time synchronous average technique to process signals acquired from a single piezoelectric strain sensor mounted on the housing of a planetary gearbox and extracting condition indicators for fault diagnosis. The reported investigation includes analysis results on a set of seeded fault tests performed on a planetary gearbox test rig in a laboratory. The results have showed a satisfactory planetary gearbox fault diagnostic performance using strain sensor signal analysis.
 
 

Smoothing localized directional cyclic autocorrelation and application in oil-film instability analysis

Time-frequency representations (TFRs) of Cohen's class are not always the best TFRs for analyzing a given signal. Using algorithms to find Cohen's-class TFRs, it is possible to find TFRs of an infinite number of classes, including the hyperbolic class. Optimal TFRs of various signals illustrate that for many signals, certain optimum TFRs outside of Cohen's class outperform optimal Cohen's-class TFRs in analysing these signals. >

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

A Cohen's class time-frequency (TF) distribution has high resolution in time and frequency simultaneously on a TF plane. It is a powerful tool for nonstationary signal analysis of the type observed commonly in speech and biological signals. A kernel of high resolution was investigated for its applicability to biological signals. To apply the TF analysis with the new kernel to the analysis of a signal from a blood flow, an ultrasound Doppler sinusoidal shift signal was studied. Experimental data were obtained in olive oil by moving a steel ball to and fro by continuously irradiating it with ultrasound. The movement of the steel ball was controlled by various functions. Three kernels were used: (1) a Wigner kernel, (2) a Choi-Williams kernel, and (3) our new kernel. The demodulation accuracy with our new kernel was higher and negative components were smaller than with the Choi-Williams kernel.

Planetary gearboxes are widely used in the modern mechanical transmission equipment. The fault diagnosis of the planetary gearboxes is an important work. When the planetary gearbox fault occurs, its vibration signal has the characteristics of complex frequency components and amplitude modulation-frequency modulation. In view of these problems, a signal demodulation analysis method based on complementary ensemble empirical mode decomposition (CEEMD) and Teager energy operator is proposed to extract instantaneous amplitude and instantaneous frequency information of the fault signals. First, the CEEMD method is used to decompose the vibration signals of the complex multi component planetary gearbox into a series of single component intrinsic mode functions (IMFs). Then, the Teager energy operator is used to estimate the amplitude envelope and the instantaneous frequency of each single component signal. The intrinsic mode function is selected as the sensitive component according to the fluctuation characteristic of the instantaneous frequency. Finally, the Fourier transformation is applied in the obtained amplitude envelope and instantaneous frequency of the sensitive component to identify the gear fault characteristic frequencies, and achieve the accurate diagnosis of the planetary gearbox fault. The effectiveness and superiority of the method is verified through the analysis of the fault simulation experiment data of the planetary gearbox.

This paper presents the implementation of linear time-frequency distribution (TFD) techniques to analyze power quality signals. The power quality signals are swell, sag, interruption, transient, harmonic, interharmonic, notching and normal voltage based on IEEE Std. 1159-1995. The time-frequency analysis techniques selected are spectrogram and Gabor transform. From the time-frequency representation (TFR) obtained, the signal parameters are estimated to identify the signal characteristics. Identified signal characteristics that are used as input to a classifier includes the average of root mean square (RMS) voltage, total waveform distortion, total harmonic distortion and total nonharmonic distortion and duration of swell, sag, interruption and transient. From the linear time-frequency analysis techniques used, the optimal technique is chosen in terms of accuracy, computation complexity and memory size.

Time-frequency distribution (TFD) methods have been widely used for planetary gearbox fault detection. The aim of TFD is to represent a signal by a joint energy distribution in the time-frequency domain. Positivity is one of the most important properties for TFDs. Copula-based positive TFD construction methods utilize the time marginal, the frequency marginal and the dependence structure between the marginals. In this study, the dependence between the time marginal and the frequency marginal is studied explicitly by numerical and graphical rank-based statistics. Rank-based statistics are invariant with monotone transformations of the marginal distributions. This study demonstrates that the dependence does exist between the time marginal and the frequency marginal. The findings build one theoretical foundation for further study on copula-based TFD construction for one planetary gearbox vibration. Moreover, the results show that with the increase of the gearbox degradation, the Kendall's Tau's absolute value increases as well. This indicates that the more severe the fault is, the stronger the dependence would be.