**5. Conclusions**

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

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-

(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

(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

(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

cases considered, the technique was able to detect incipient faults.

Markov models.

systems.

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 monitoring the following years.

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