A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> Abstract A commonly used technique for the detection of faults which may occur in three-phase induction motors is to carry out a spectral analysis of the supply current to the motor under investigation. The presence of certain frequency components within the spectral analysis has been shown to be indicative of a fault condition (Hargis et al., 1982). Such techniques are becoming well established and are used regularly to monitor the health of large induction motors which are operated in critical applications within, for example, the nuclear and oil industries. This technique is generally applied to machines when they are operated under steady-state conditions. Recent work however has suggested that greater information may be obtained from a faulty motor if the same parameters which are monitored in the steady state are measured and analysed during transient conditions, such as the initial starting and acceleration periods of the motor. The frequency components which are indicative of motor faults are functions of speed, and hence, under these transient conditions are non-stationary in nature. This paper presents a review of modern signal processing techniques applicable to the analysis of signals whose frequency content is non-stationary. The individual techniques are compared using both test and actual data. Results are presented which identify the technique most appropriate for the task of fault detection in an induction motor under transient conditions. This technique is further investigated with regard to the possibility of locating as well as detecting machine faults. <s> BIB001 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> This paper presents a signal analysis technique for machine health monitoring based on the Hilbert-Huang Transform (HHT). The HHT represents a time-dependent series in a two-dimensional (2-D) time-frequency domain by extracting instantaneous frequency components within the signal through an Empirical Mode Decomposition (EMD) process. The analytical background of the HHT is introduced, based on a synthetic analytic signal, and its effectiveness is experimentally evaluated using vibration signals measured on a test bearing. The results demonstrate that HHT is suited for capturing transient events in dynamic systems such as the propagation of structural defects in a rolling bearing, thus providing a viable signal processing tool for machine health monitoring <s> BIB002 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> Based on the Morlet wavelet transformation and Wigner-Ville distribution (WVD), we present a wind turbine fault diagnosis method in this paper. Wind turbine can be damaged by moisture absorption, fatigue, wind gusts or lightening strikes. Due to this reason, there is an increasing need to monitor the health of these structures. Vibration analysis is the best-known technology applied in wind turbine condition monitoring, in which the time-frequency analysis techniques such as Wigner-Ville distribution (WVD) are widely used. Theoretically WVD has an infinite resolution in time-frequency domain. For early wind turbine fault signals, however, there are two main difficulties in WVD analysis. One is strong noise signals in the background and the other is cross terms in WVD itself. In this paper, continuous wavelet transformation (CWT) is employed to filter useless noise in raw vibration signals, and auto terms window (ATW) function is used to suppress the cross terms in WVD. In the CWT de-noising process, the Morlet wavelet, whose shape is similar to mechanical shock signals, is chosen to perform CWT on the raw vibration signals. The appropriate scale parameter for CWT is optimized by the cross validation method (CVM). An ATW based on the Smoothed Pseudo Wigner-Ville distribution (SPWVD) spectrum is taken to be a window function to suppress the cross terms in WVD. The new method can not only remove cross terms faraway from the auto terms, but also keep high energy close to every instantaneous frequency, the virtues such as high time-frequency resolution, and good energy aggregation etc. The wind turbine gear fault diagnosis experiment results indicate that the proposed method has a good de-nosing performance and is effective in suppressing the cross terms and extracting fault feature. <s> BIB003 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> Eccentricity-related faults in induction motors have been studied extensively over the last few decades. They can exist in the form of static or dynamic eccentricity or both, in which case it is called a mixed eccentricity fault. These faults cause bearing damage, excessive vibration and noise, unbalanced magnetic pull, and under extreme conditions, stator-rotor rub which may seriously damage the motors. Since eccentricity faults are often associated with large induction machines, the repair or replacement costs arising out of such a scenario may easily run into tens and thousands of dollars. Previous research works have shown that it is extremely difficult to detect such faults if they appear individually, rather than in mixed form, unless the number of rotor bars and the pole-pair number conform to certain relationships. In this paper, it is shown that the terminal voltages of induction machines at switch-off reveal certain features that can lead to the detection of these faults in individual form, even in machines that do not show these signatures in line-current spectrum in steady state, or to the detection of the main contributory factor in case of mixed eccentricity. <s> BIB004 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> Abstract Nonstationary signal analysis is one of the main topics in the field of machinery fault diagnosis. Time–frequency analysis can identify the signal frequency components, reveals their time variant features, and is an effective tool to extract machinery health information contained in nonstationary signals. Various time–frequency analysis methods have been proposed and applied to machinery fault diagnosis. These include linear and bilinear time–frequency representations (e.g., wavelet transform, Cohen and affine class distributions), adaptive parametric time–frequency analysis (based on atomic decomposition and time–frequency auto-regressive moving average models), adaptive non-parametric time–frequency analysis (e.g., Hilbert–Huang transform, local mean decomposition, and energy separation), and time varying higher order spectra. This paper presents a systematic review of over 20 major such methods reported in more than 100 representative articles published since 1990. Their fundamental principles, advantages and disadvantages, and applications to fault diagnosis of machinery have been examined. Some examples have also been provided to illustrate their performance. <s> BIB005 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> The aim of this paper is to present a diagnosis methodology for the detection of electrical faults in three-phase wound-rotor induction machines (WRIMs). In the considered application, the rotor windings are supplied by a static converter for the control of active and reactive power flows exchanged between the machine and the electrical grid. The proposed diagnosis approach is based on the use of wavelet analysis improved by a preprocessing of the rotor-voltage commands under time-varying conditions. Thus, the time evolution of fault components can be effectively analyzed. This paper proves also the importance of the fault components computed from rotor voltages in comparison to those coming from rotor currents under closed-loop operation. A periodical quantification of the fault, issued from the wavelet analysis, has been introduced for accurate stator- or rotor-fault detection. Simulation and experimental results show the validity of the proposed method, leading to an effective diagnosis procedure for both stator and rotor electrical faults in WRIMs. <s> BIB006 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> Nowadays industry pays much attention to prevent failures that may interrupt production with severe consequences in cost, product quality, and safety. The most-analyzed parameters for monitoring dynamic characteristics and ensuring correct functioning of systems are electric current, voltage, and vibrations. System-on-chip (SoC) design is an approach to increase performance and overcome costs during equipment monitoring. This work presents the design and implementation of a low-cost SoC design that utilizes reconfigurable hardware and a customized embedded processor for time-frequency analysis on industrial equipment through short-time Fourier transform and discrete wavelet transform. Three study cases (electric current supply to an induction motor during startup transient, voltage supply to an induction motor through a variable speed drive, and vibration signals from industrial-robot links) show the suitability of the proposed monitoring system for time-frequency analysis of different signals in distinct industrial applications, and early diagnosis and prognosis of abnormalities in monitored systems. <s> BIB007 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> During the last years, several time-frequency decomposition tools have been applied for the diagnosis of induction motors, for those cases in which the traditional procedures, such as motor current signature analysis, cannot yield the necessary response. Among them, the Cohen distributions have been widely selected to study transient and even stationary operation due to their high-resolution and detailed information provided at all frequencies. Their main drawback, the cross-terms, has been tackled either modifying the distribution, or carrying out a pretreatment of the signal before computing its time-frequency decomposition. In this paper, a filtering process is proposed that uses advanced notch filters in order to remove constant frequency components present in the current of an induction motor, prior to the computation of its distribution, to study rotor asymmetries and mixed eccentricities. In transient operation of machines directly connected to the grid, this procedure effectively eliminates most of the artifacts that have prevented the use of these tools, allowing a wideband analysis and the definition of a precise quantification parameter able to follow the evolution of their state. <s> BIB008 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Time-Frequency Signal-Based Methods <s> Local mean decomposition is a self-adaptive analysis method, which is suitable for the processing of multi-component amplitude-modulated and frequency-modulated signals. In this paper, the evaluating indicator of the end effect is put forward to characterize the advantages of local mean decomposition in non-stationary signal analysis. The comparisons between local mean decomposition and empirical mode decomposition show that the capabilities of the local mean decomposition on restraining the end effect and resisting the mode mixing are superior to those of empirical mode decomposition. Wigner–Ville distribution has had an important influence on non-stationary signal analysis, which keeps a higher time-frequency resolution and obtains superior distribution, but the cross-terms are its fatal disadvantages. Therefore, a new time-frequency analysis method, called self-adaptive Wigner-Ville distribution based on local mean decomposition, is proposed to effectively analyze non-stationary amplitude-modulated and... <s> BIB009
For machines under an unloaded condition, or unbalanced supply voltages, varying load, or load torque oscillations, the measured signals are generally transient and dynamic under the concerned time section. Therefore, analysis of the stationary quantities in some cases finds it difficult to monitor or detect faults via either a pure time-domain or a frequency-domain method. Due to the time-varying frequency spectrum of the transient signals, suitable time-frequency decomposition tools are needed for real-time monitoring and fault diagnosis. Time-frequency analysis can identify the signal frequency components and reveal their time-variant features, which has been an effective tool for monitoring and fault diagnosis by extracting feature information contained in nonstationary signals BIB005 . Various time-frequency analysis methods have been proposed and applied to machinery fault diagnosis. Among the time-frequency methods, short-time Fourier transform (STFT), wavelet transforms (WT), Hilbert-Huang transform (HHT), and Wigner-Ville distribution (WVD) are the most commonly used approaches. For instance, the STFT method allows determining signal frequency contents of local sections as the signal changes in time, which has been widely applied to detect both stator and rotor faults in inductor motors BIB004 . However, the STFT method suffers the high computational cost if it is required to obtain a good resolution. As a linear decomposition, WT-based method can provide a good resolution in time for high-frequency components of a signal and a good resolution in frequency for low-frequency components, which has demonstrated the effectiveness for tracking fault frequency components under nonstationary conditions BIB006 . In BIB007 , the STFT and the discrete WT were integrated to do early diagnosis and prognosis of the abnormalities in the monitored industrial systems. It is noticed that STFT and WT may suffer some uncertain limitations. For instance, the selection of a suitable window size in STFT is required, but it is generally not a known priori. The type of the basic wavelet function in WT has a direct effect on the effectiveness in identifying transient elements hidden within a dynamic signal. However, on the basis of the instantaneous frequencies resulting from the intrinsic-mode functions of the signal being analyzed, the HHT method is not constrained by the uncertain limitations with respect to the time and frequency resolutions suffered by some time-frequency techniques (e.g., STFT and WT), which has shown quite interesting performance in terms of fault severity evaluation BIB002 . The WVD method features a relatively low computational cost and high resolution, as the entire signal is utilized to obtain the energy at each time-frequency bin, which has been successfully applied to the fault diagnosis along with current analysis BIB001 or vibration analysis BIB003 . A significant defect of the conventional WVD method is the appearance of the cross terms in the distribution of artifacts, which hinders the application of WVD methods. Very recently, via combining advanced notch finiteimpulse-response filters and the conventional WVD method, an improved WVD-based fault diagnosis algorithm has been proposed in BIB008 , which can effectively minimize the cross terms and provide seamless high-resolution time-frequency diagrams enabling the diagnosis of rotor asymmetries and eccentricities in induction machines directly connected to the grid even in the worst cases. In BIB009 , a self-adaptive WVD method, based on local mean decomposition, was addressed, which can evidently remove the cross terms of WVD to improve the performance of the defect diagnosis.