**4.4 Motors**

Electrical, hydraulic motors as well as internal combustion engines are the dominant applications in the related literature. (Chen et al., 2006) worked on fault diagnosis of water hydraulic motors. A modelling of the monitored vibration signals based on the adaptive wavelet transform (AWT) was proposed. The model-based method by AWT was applied for de-noising and feature extraction. Scalograms acquired through the CWT revealed the characteristic signal's energy in time-scale domain and were used as feature values for fault diagnosis of water hydraulic motor. (Wu and Chen, 2006) presented a fault signal diagnosis technique for internal combustion engines based on CWT. The Morlet wavelet was used because in many mechanical dynamic signals, impulses are always the symptoms of faults and the Morlet wavelet is very similar to an impulse component. Different faults have shown different scalograms. A characteristic analysis and experimental comparison of the vibration signal and acoustic emission signal with the proposed algorithm were also presented in their work.

(Daviu et al., 2007) employed wavelet analysis on the stator startup currents in order to detect the presence of dynamic eccentricities in an induction motor. For this purpose, the DWT is applied on the stator startup monitored current signals. The approximation and details were obtained after the DWT decomposition via "db44" wavelet and 8 levels of analysis. The relative increment in the level energy of the wavelet coefficients was used as a quantitative indicator of the degree of severity of the fault. In (Chen et al., 2007) a novel method to process the vibration signals was presented for the fault diagnosis of water hydraulic motors. De-noising was initially conducted by thresholding in the wavelet domain and inversely transforming the de-noised wavelet coefficients. Feature extraction based on the second-generation wavelet of the vibration signals followed next. The statistical probability distributions of the mean, variance and the second-order statistical moment of the scaling coefficients at first, second and third scale were calculated and used to classify the different piston conditions. (Chendong et al., 2007) proposed a new sliding window feature extraction method based on the lifting scheme for extracting transient impacts from signals. A sliding window -designed according to the revolution cycle of rotating machinery- is applied to process the detail signals. By extracting modulus maxima from these windows, fault features and their locations in the original signals were revealed. An incipient impact fault caused by axis misalignment, mass imbalance and a bush broken

(center frequency and bandwidth) are optimized by differential evolution (DE) in order to eliminate the interferential vibrations and obtain the fault characteristic signal. Then, to further enhance the impulsive features and suppress residual noise, SCS which is a softthresholding method based on maximum likelihood estimation (MLE) is applied to the filtered signal. The results of simulated experiments and real bearing vibration signals verify the effectiveness of the proposed method in extracting impulsive features from noisy signals

(Chiementin et al., 2010) studied the effect of wavelet de-noising and other techniques on acoustic emission signals from faulty bearings. They applied DWT and attempted to optimize the various parameters selection involved in a wavelet-based de-noising scheme. They assessed the different de-noising techniques and concluded that the wavelet approach

Electrical, hydraulic motors as well as internal combustion engines are the dominant applications in the related literature. (Chen et al., 2006) worked on fault diagnosis of water hydraulic motors. A modelling of the monitored vibration signals based on the adaptive wavelet transform (AWT) was proposed. The model-based method by AWT was applied for de-noising and feature extraction. Scalograms acquired through the CWT revealed the characteristic signal's energy in time-scale domain and were used as feature values for fault diagnosis of water hydraulic motor. (Wu and Chen, 2006) presented a fault signal diagnosis technique for internal combustion engines based on CWT. The Morlet wavelet was used because in many mechanical dynamic signals, impulses are always the symptoms of faults and the Morlet wavelet is very similar to an impulse component. Different faults have shown different scalograms. A characteristic analysis and experimental comparison of the vibration signal and acoustic emission signal with the proposed algorithm were also

(Daviu et al., 2007) employed wavelet analysis on the stator startup currents in order to detect the presence of dynamic eccentricities in an induction motor. For this purpose, the DWT is applied on the stator startup monitored current signals. The approximation and details were obtained after the DWT decomposition via "db44" wavelet and 8 levels of analysis. The relative increment in the level energy of the wavelet coefficients was used as a quantitative indicator of the degree of severity of the fault. In (Chen et al., 2007) a novel method to process the vibration signals was presented for the fault diagnosis of water hydraulic motors. De-noising was initially conducted by thresholding in the wavelet domain and inversely transforming the de-noised wavelet coefficients. Feature extraction based on the second-generation wavelet of the vibration signals followed next. The statistical probability distributions of the mean, variance and the second-order statistical moment of the scaling coefficients at first, second and third scale were calculated and used to classify the different piston conditions. (Chendong et al., 2007) proposed a new sliding window feature extraction method based on the lifting scheme for extracting transient impacts from signals. A sliding window -designed according to the revolution cycle of rotating machinery- is applied to process the detail signals. By extracting modulus maxima from these windows, fault features and their locations in the original signals were revealed. An incipient impact fault caused by axis misalignment, mass imbalance and a bush broken

enhanced the signal kurtosis and crest factor more than the other techniques.

in condition monitoring.

presented in their work.

**4.4 Motors** 

fault have been successfully detected by using the proposed approach. In (Peng et al., 2007) the wavelet transform modulus maximal (WTMM) method was used to calculate the Lipschitz exponents of the vibration signals with different faults. The Lipschitz exponent can give a quantitative description of the signal's singularity. The proposed singularity based parameters proved a set of excellent diagnostic features, which could separate the four kinds of faults very well. The results showed that, with the fault severity increasing, the vibration signals' singularities and singularity ranges increased as well, and therefore one could evaluate the fault severity through measuring the vibration signals' singularities and singularity ranges.

(Wu and Liu, 2008) instead of WPT utilized a DWT technique combined with a feature selection of energy spectrum and fault classification using ANNs for analyzing fault signals of internal combustion engines. The features of the sound emission signals at different resolution levels were extracted by multi-resolution analysis and Parseval's theorem. (Niu et al., 2008) applied multi-level wavelet decomposition on transient stator current signals for fault diagnosis of induction motors. After the signal preprocessing using smoothing– subtracting and wavelet transform techniques, features were extracted from each level of detail component of decomposed signals using DWT and "db10" mother wavelet. 21 features in total are acquired from each sensor consisting of the time domain (10 features), frequency domain (three features) and regression estimation (eight features). Totally, two 70 321 features sets are calculated from seven types of signals collected by three current probes at each wavelet decomposition level. The calculated two features sets consisted of the training and test sets respectively and consist of the input in four different classifiers for pattern recognition with quite satisfactory results. (Chen et al., 2008) proposed a methodology based on Wavelet Packet Analysis (WPA) and Kolmogorov-Smirnov (KS) test to analyze monitored vibration signals from the water hydraulic motor to assess the fault degradation of the pistons in water hydraulic motor. The fault detection procedure applied is summarized in the following. First, the time-domain vibration signals were decomposed through the WPT in two levels. The soft-thresholding technique was used in the wavelet and approximation coefficients to get the de-noised coefficients. The reconstructed denoised vibration signal with improved signal-to-noise ratio (SNR) was obtained by reconstructing the de-noised coefficients in the multi-decomposition of the vibration signal. Then the kurtosis of the de-noised signal was calculated and finally the KS test was used to classify the kurtosis statistical probability distribution (SPD) under seven different piston conditions. Thus the piston condition in water hydraulic motor was successfully assessed. (Widodo and Yang, 2008) introduced an intelligent system for faults detection and classification of induction motor using wavelet support vector machines (W-SVMs). W-SVMs were built by utilizing the kernel function using wavelets. Transient current signals were monitored in various damage conditions of the induction motor. The acquired signals were preprocessed through DWT ("db5", 5 levels) and various statistical features were extracted. Principal component analysis (PCA) and kernel PCA were utilized to reduce the dimension of features and to extract the useful features for classification process. Finally the classification process for diagnosing the faults was carried out using W-SVMs and conventional SVMs based on one against-all multi-class classification.

(Wu and Liu, 2009) proposed a fault diagnosis system for internal combustion engines using wavelet packet transform (WPT) and artificial neural network (ANN) techniques on monitored sound emission signals. In the preprocessing phase, WPT coefficients are used,

Utilising the Wavelet Transform in Condition-Based Maintenance: A Review with Applications 303

Tool condition monitoring is a very interesting industrial application. (Velayudham et al., 2005) used wavelet packet transform to study the condition of the drill during drilling of glass/phenolic composite under acoustic emission (AE) monitoring. The energy of the wavelet packet is considered as criterion for the selection of feature packets. Thus, the AE signals were decomposed into four levels, that is, splitting into 16 wavelet packets. Each wavelet packet corresponds to a frequency band ranging from 0–156.25 to 2343.75–2500 kHz. Out of the 16 packets resulted, it is necessary to select the packets (feature packets) that contain useful information. Based on the energy in each packet those with the maximum energy were selected. The monitoring index extracted from wavelet coefficients of highest energy packets could reliably detect the condition of the tool. (Shao et al., 2011) utilized a modified blind sources separation (BSS) technique to separate source signals in milling process. A single-channel BSS method based on wavelet transform and independent component analysis (ICA) was developed, and source signals related to a milling cutter and spindle were separated from a single-channel power signal. The experiments with different tool conditions illustrate that the separation strategy is robust and promising for cutting process monitoring. In (Liao et al., 2007) a wavelet-based methodology for grinding wheel condition monitoring based on acoustic emission (AE) signals was presented. Features were then extracted from each raw AE signal segment using the DWT via "db1" and 12 levels of analysis. An adaptive genetic clustering algorithm was finally applied to the extracted features in order to distinguish between different states of grinding wheel condition. (Li et al., 2005) utilized the DWT to recognize the tool wear states in automatic machining processes. The wavelet coefficients *d*(*j*, *k*) of cutting force signals were calculated after the application of DWT. *d(5,k)* coefficients proved sensitive and able to identify the different tool wear states and different cutting conditions. (Velayudham et al., 2005) used the WPT in order to characterize the acoustic emission signals released from glass/phenolic polymeric composite during drilling. In their work, the energy of the wavelet packets was taken as criterion for the selection of feature packets, with those having the higher energy to contain the characteristic features of the signal. The results showed that the selected monitoring indices from the wavelet packet coefficients were capable of detecting the drill condition

(Borghetti et al., 2006) proposed a methodology based on the continuous-wavelet transform (CWT) for the analysis of voltage transients due to line faults, and discussed its application to fault location in power distribution systems. The analysis showed that correlation exists between typical frequencies of the CWT-transformed signals and specific paths in the network covered by the traveling waves originated by the fault. (Belotti et al., 2006) presented a diagnostic tool, based on the DWT, for the detection of wheel-flat defect of a test train at different speeds. DWT was applied on the rail acceleration signals via "db4" wavelet and 10-level decomposition. The results, achieved after an exhaustive experimental campaign, allowed the validation of the effectiveness of

(Xu and Li, 2007) utilized oil spectrometric data from air-compressors. In the first stage denoising of the original signals through WPT (db4", 3 levels) and "*rigsure"* threshoding

**4.5 Tool wear** 

effectively.

**4.6 Other applications** 

the diagnostic tool.

their entropy is calculated and treated as the input to the ANN in order to distinguish the various fault conditions. ''db4", ''db8" and ''db20" from the Daubechies family were used as mother wavelets with no clear advantage of one of them in the ANN performances.

(Lin et al., 2010) utilized vibration measurements to distinguish effectively between aligned and misaligned motors. The proposed method calculates the difference between the MSE of the original vibration signal and that of the signal after the signal is de-noised by wavelet transform. This study presents a novel use of the multiscale entropy technique by comparing the difference of sample entropy of a signal before and after the signal is denoised using wavelet transform. De-noising was performed using the Daubechies wavelet transform, which was implemented with Matlab wavelet function with the following parameter settings: threshold type is ''rigrsure"; number of decomposition levels is 4; mother wavelet is ''db4". (Cusido et al.,2010) have monitored motor current for fault diagnosis in induction machines. The power detail density (PDD) function resulting from a wavelet transformation has proven to be one of the best methods for motor fault estimation under variable load. Power detail density was calculated as the squares of the coefficients of one detail. (Wang and Jiang, 2010) utilized an adaptive wavelet de-noising scheme by combining advantages of both hard and soft thresholding, to de-noise vibration signals from the aircraft engine rotor experimental test rig by block to light rub-impact rotational plate. After the de-noising procedure, the correlation dimension of the vibration signal is computed, and is used as the characteristic feature for identifying the fault deterioration grade.

(Ece and Basaran, 2011) applied wavelet packet decomposition (WPD) in supply-side current signals for the condition monitoring of induction motors with adjustable speed and load levels. In this work, acquired data, sampled at 20 kHz, is analyzed using 11 level WPD. This way, the coefficients of three nodes at the 11th level corresponding to 43.92–48.8 Hz, 48.8–53.68 Hz, and 53.68–58.56 Hz that cover the region of both side-bands as well as the 50 Hz fundamental, are obtained. Using the coefficients of each resulted node, 5 statistical features (i.e. mean, variance, standard deviation, skewness, and kurtosis) are calculated resulting 15 element feature vectors. (Konar and Chattopadhyay, 2011) employed a hybrid CWT–Support Vector Machine approach (CWT-SVM) to analyze the frame vibrations of healthy and faulty induction motors during start-up. Various mother wavelets were utilized in the implementation of CWT. 'Morlet' and 'db10' wavelets were found to be the best choice and used throughout the study. Three statistical features (i.e. root mean square (RMS), crest and kurtosis values) were calculated from the CWT coefficients for each loading condition and consisted of the input in the SVM to classify between healthy and faulty states. In (Anami et al., 2011), a methodology to determine the health condition of motorcycles, based on discrete wavelet transform (DWT) of sound measurements is proposed. The 1-D central contour moments and invariant contour moments, of approximation coefficients of DWT form the feature vectors corresponding to various health states. The sound samples are subjected to wavelet decomposition using Daubechies 'db4' wavelets. The decomposition into approximation and detailed coefficients is carried out for the first 14 levels. The feature vector comprises of four 1D central contour moments (l2;l3; l4 and l5) and their four invariants (F1; F2; F3 and F4) computed on approximation coefficients of a wavelet sub-band. A dynamic time warping (DTW) classifier along with Euclidean distance measure is successfully used for the classification of the feature vectors.

#### **4.5 Tool wear**

302 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

their entropy is calculated and treated as the input to the ANN in order to distinguish the various fault conditions. ''db4", ''db8" and ''db20" from the Daubechies family were used as

(Lin et al., 2010) utilized vibration measurements to distinguish effectively between aligned and misaligned motors. The proposed method calculates the difference between the MSE of the original vibration signal and that of the signal after the signal is de-noised by wavelet transform. This study presents a novel use of the multiscale entropy technique by comparing the difference of sample entropy of a signal before and after the signal is denoised using wavelet transform. De-noising was performed using the Daubechies wavelet transform, which was implemented with Matlab wavelet function with the following parameter settings: threshold type is ''rigrsure"; number of decomposition levels is 4; mother wavelet is ''db4". (Cusido et al.,2010) have monitored motor current for fault diagnosis in induction machines. The power detail density (PDD) function resulting from a wavelet transformation has proven to be one of the best methods for motor fault estimation under variable load. Power detail density was calculated as the squares of the coefficients of one detail. (Wang and Jiang, 2010) utilized an adaptive wavelet de-noising scheme by combining advantages of both hard and soft thresholding, to de-noise vibration signals from the aircraft engine rotor experimental test rig by block to light rub-impact rotational plate. After the de-noising procedure, the correlation dimension of the vibration signal is computed, and is used as the characteristic feature for identifying the fault deterioration

(Ece and Basaran, 2011) applied wavelet packet decomposition (WPD) in supply-side current signals for the condition monitoring of induction motors with adjustable speed and load levels. In this work, acquired data, sampled at 20 kHz, is analyzed using 11 level WPD. This way, the coefficients of three nodes at the 11th level corresponding to 43.92–48.8 Hz, 48.8–53.68 Hz, and 53.68–58.56 Hz that cover the region of both side-bands as well as the 50 Hz fundamental, are obtained. Using the coefficients of each resulted node, 5 statistical features (i.e. mean, variance, standard deviation, skewness, and kurtosis) are calculated resulting 15 element feature vectors. (Konar and Chattopadhyay, 2011) employed a hybrid CWT–Support Vector Machine approach (CWT-SVM) to analyze the frame vibrations of healthy and faulty induction motors during start-up. Various mother wavelets were utilized in the implementation of CWT. 'Morlet' and 'db10' wavelets were found to be the best choice and used throughout the study. Three statistical features (i.e. root mean square (RMS), crest and kurtosis values) were calculated from the CWT coefficients for each loading condition and consisted of the input in the SVM to classify between healthy and faulty states. In (Anami et al., 2011), a methodology to determine the health condition of motorcycles, based on discrete wavelet transform (DWT) of sound measurements is proposed. The 1-D central contour moments and invariant contour moments, of approximation coefficients of DWT form the feature vectors corresponding to various health states. The sound samples are subjected to wavelet decomposition using Daubechies 'db4' wavelets. The decomposition into approximation and detailed coefficients is carried out for the first 14 levels. The feature vector comprises of four 1D central contour moments (l2;l3; l4 and l5) and their four invariants (F1; F2; F3 and F4) computed on approximation coefficients of a wavelet sub-band. A dynamic time warping (DTW) classifier along with Euclidean

distance measure is successfully used for the classification of the feature vectors.

mother wavelets with no clear advantage of one of them in the ANN performances.

grade.

Tool condition monitoring is a very interesting industrial application. (Velayudham et al., 2005) used wavelet packet transform to study the condition of the drill during drilling of glass/phenolic composite under acoustic emission (AE) monitoring. The energy of the wavelet packet is considered as criterion for the selection of feature packets. Thus, the AE signals were decomposed into four levels, that is, splitting into 16 wavelet packets. Each wavelet packet corresponds to a frequency band ranging from 0–156.25 to 2343.75–2500 kHz. Out of the 16 packets resulted, it is necessary to select the packets (feature packets) that contain useful information. Based on the energy in each packet those with the maximum energy were selected. The monitoring index extracted from wavelet coefficients of highest energy packets could reliably detect the condition of the tool. (Shao et al., 2011) utilized a modified blind sources separation (BSS) technique to separate source signals in milling process. A single-channel BSS method based on wavelet transform and independent component analysis (ICA) was developed, and source signals related to a milling cutter and spindle were separated from a single-channel power signal. The experiments with different tool conditions illustrate that the separation strategy is robust and promising for cutting process monitoring. In (Liao et al., 2007) a wavelet-based methodology for grinding wheel condition monitoring based on acoustic emission (AE) signals was presented. Features were then extracted from each raw AE signal segment using the DWT via "db1" and 12 levels of analysis. An adaptive genetic clustering algorithm was finally applied to the extracted features in order to distinguish between different states of grinding wheel condition. (Li et al., 2005) utilized the DWT to recognize the tool wear states in automatic machining processes. The wavelet coefficients *d*(*j*, *k*) of cutting force signals were calculated after the application of DWT. *d(5,k)* coefficients proved sensitive and able to identify the different tool wear states and different cutting conditions. (Velayudham et al., 2005) used the WPT in order to characterize the acoustic emission signals released from glass/phenolic polymeric composite during drilling. In their work, the energy of the wavelet packets was taken as criterion for the selection of feature packets, with those having the higher energy to contain the characteristic features of the signal. The results showed that the selected monitoring indices from the wavelet packet coefficients were capable of detecting the drill condition effectively.

#### **4.6 Other applications**

(Borghetti et al., 2006) proposed a methodology based on the continuous-wavelet transform (CWT) for the analysis of voltage transients due to line faults, and discussed its application to fault location in power distribution systems. The analysis showed that correlation exists between typical frequencies of the CWT-transformed signals and specific paths in the network covered by the traveling waves originated by the fault. (Belotti et al., 2006) presented a diagnostic tool, based on the DWT, for the detection of wheel-flat defect of a test train at different speeds. DWT was applied on the rail acceleration signals via "db4" wavelet and 10-level decomposition. The results, achieved after an exhaustive experimental campaign, allowed the validation of the effectiveness of the diagnostic tool.

(Xu and Li, 2007) utilized oil spectrometric data from air-compressors. In the first stage denoising of the original signals through WPT (db4", 3 levels) and "*rigsure"* threshoding

Utilising the Wavelet Transform in Condition-Based Maintenance: A Review with Applications 305

test on a methane compressor and trend features were extracted. Then features were normalized and sent into neural network for feature-level fusion. Next, data de-noising was achieved by smoothing with moving average and then wavelet decomposition was applied ('db5', 5 levels of decomposition) to reduce the fluctuation and pick out the trend information. In (Eristi et al.,2010) a novel scheme composed of feature extraction and feature selection procedures for obtaining robust and adequate features of power system disturbances was presented. Firstly, features were obtained by different extraction techniques to the wavelet coefficients of all decomposition levels of the disturbance signal utilizing DWT and 'db4' wavelet. Then, by using sequential forward selection (SFS) technique, robust and adequate features were selected in the feature set resulted from the first stage. The detail coefficients and approximation coefficients were not directly used as the classifier inputs. Reduction of the feature vector dimension was first conducted. In this study, mean, standard deviation, skewness, kurtosis, RMS, form factor, crest-factor, energy, Shannon-entropy, log-energy entropy and interquartile range of the ten level coefficients were used as features. Finally the classification of the power system disturbances using

(Jiang et al, 2011) introduced a new de-noising method based on adaptive Morlet wavelet and singular value decomposition (SVD) for feature extraction of vibration signals from wind turbine gearbox. Modified Shannon wavelet entropy was utilized to optimize central frequency and bandwidth parameter of the Morlet wavelet so as to achieve optimal match with the impulsive components. The proposed method was applied to extract the outer-race fault in a rolling bearing and the fault diagnosis of a planetary gearbox in a wind turbine. The results show that the proposed method based on adaptive Morlet wavelet and SVD performed much better than the Donoho's "soft-thresholding de-noising", the de-noising method based on CWT and SVD, and the de-noising method based on Morlet wavelet. Thus, it provides an effective tool for fault diagnosis to extract the fault features submerged

Tremendous progress has been made the last 15 years in the evolution of WT theory as well as their applications in engineering and especially condition monitoring. WT literally gave a boost to the signal processing of engineering signals opening a wide full-of-options field. WT is now more mature than ever constituting one of the most powerful weapons in the signal analyst's arsenal. In this review, classical as well as second generation wavelet transforms were presented. The issue of mother wavelet choice and a variety of applications in wavelet-based condition monitoring were discussed. Some concepts on the beyond the state-of-the-art in WT were finally discussed. Despite the rapid evolution of WT there are still unresolved theoretical issues such as the optimum mother wavelet choice, the number of decomposition levels in DWT, WPT, SGWT and the number of analyzing scales in CWT. A solution by the mathematicians is expected there in the future. In the engineering field and especially in the condition monitoring, WT is expected to support (directly or indirectly) the developments in the fast evolving field of forecasting and prognostics. Wavelet-based utilization of schemes such as Hidden Markov Models, Particle Filters, Remaining Useful Life PDF, Trend extrapolation etc. are expected to dominate in the literature of condition

support vector machines (SVMs) was achieved.

in the background noise.

monitoring the following years.

**5. Conclusions** 

strategy was conducted. Then decomposition of the de-noised signal through DWT (with "db1") followed. The variance of approximation coefficients and detail coefficients at level 1 were calculated. In the last stage the improved three-line method was adopted to ascertain decisive criteria for wear condition. The ability of the proposed method for classifying and recognizing wear patterns was verified. (Monsef and Lotfifard, 2007) presented a novel approach for differential protection of power transformers. DWT ("db9, 7 levels) and adaptive network-based fuzzy inference system (ANFIS) were utilized to discriminate internal faults from inrush currents. The proposed method has been designed based on the differences between amplitudes of wavelet transform coefficients in a specific frequency band generated by faults and inrush currents. The ability of the new method was demonstrated by simulating various cases on a typical power system. The algorithm is also tested off-line using data collected from a prototype laboratory three-phase power transformer. The test results confirm the effectiveness and reliability of the proposed algorithm. (Dong and He, 2007) proposed a methodology for the condition monitoring of hydraulic pumps. The collected vibration signals were processed using wavelet packet with "db10" wavelet and five decomposition levels. The wavelet coefficients obtained by the wavelet packet decomposition were used as the inputs to the hidden Markov and semi-Markov models for the classification of the various fault signals. The performance of the two methods was assessed resulting in higher classification rates in the case of hidden semi-Markov models.

(Carneiro et al., 2008) presented an approach for incipient fault detection of motor-operated valves (MOVs) using DWT with "db4" wavelet and six decomposition levels chosen. The motor power signature was acquired through three-phase current and voltage measurements at the motor control center. The results demonstrated the effectiveness of DWT-based methodology on incipient fault detection of motor-operated valves. In the two cases considered, the technique was able to detect incipient faults.

(Gketsis et al., 2009) applied the Wavelet Transform (WT) analysis along with Artificial Neural Networks (ANN) for the diagnosis of electrical machines winding faults. After an optimum wavelet selection procedure they utilized "db2" for the decomposition via DWT of the admittance, current and voltage curves. Level 7 (D7) detail is utilized for feature extraction. The Fourier Transform is employed to derive measures of amplitude and displacement (shift) of D7 details. Motor-operated valves are used in almost all nuclear power plant fluid systems. The purpose of motor-operated valves (MOVs) is to control the fluid flow in a system by opening, closing, or partially obstructing the passage through itself. The readiness of nuclear power plants depends strongly on the operational readiness of valves, especially MOVs. They are applied extensively in control and safety-related systems.

(Tang et al., 2010) employed continuous wavelet transformation (CWT) to filter useless noise in raw vibration signals from gearboxes in wind turbines, and auto terms window (ATW) function was used to suppress the cross terms in Wigner Ville Distribution. In the CWT de-noising process, the Morlet wavelet (similar to the mechanical impulse signal) is chosen to perform CWT on the raw vibration signals. The appropriate scale parameter for CWT is optimized by the cross validation method (CVM). (Niu and Yang, 2010) proposed an intelligent condition monitoring and prognostics system in condition-based maintenance architecture based on data-fusion strategy. They collected vibration signals from a whole

test on a methane compressor and trend features were extracted. Then features were normalized and sent into neural network for feature-level fusion. Next, data de-noising was achieved by smoothing with moving average and then wavelet decomposition was applied ('db5', 5 levels of decomposition) to reduce the fluctuation and pick out the trend information. In (Eristi et al.,2010) a novel scheme composed of feature extraction and feature selection procedures for obtaining robust and adequate features of power system disturbances was presented. Firstly, features were obtained by different extraction techniques to the wavelet coefficients of all decomposition levels of the disturbance signal utilizing DWT and 'db4' wavelet. Then, by using sequential forward selection (SFS) technique, robust and adequate features were selected in the feature set resulted from the first stage. The detail coefficients and approximation coefficients were not directly used as the classifier inputs. Reduction of the feature vector dimension was first conducted. In this study, mean, standard deviation, skewness, kurtosis, RMS, form factor, crest-factor, energy, Shannon-entropy, log-energy entropy and interquartile range of the ten level coefficients were used as features. Finally the classification of the power system disturbances using support vector machines (SVMs) was achieved.

(Jiang et al, 2011) introduced a new de-noising method based on adaptive Morlet wavelet and singular value decomposition (SVD) for feature extraction of vibration signals from wind turbine gearbox. Modified Shannon wavelet entropy was utilized to optimize central frequency and bandwidth parameter of the Morlet wavelet so as to achieve optimal match with the impulsive components. The proposed method was applied to extract the outer-race fault in a rolling bearing and the fault diagnosis of a planetary gearbox in a wind turbine. The results show that the proposed method based on adaptive Morlet wavelet and SVD performed much better than the Donoho's "soft-thresholding de-noising", the de-noising method based on CWT and SVD, and the de-noising method based on Morlet wavelet. Thus, it provides an effective tool for fault diagnosis to extract the fault features submerged in the background noise.
