Sparsity-enabled signal decomposition using tunable Q-factor wavelet transform for fault feature extraction of gearbox

Instantaneous Frequency Estimation of Multi-Component Non- Stationary Signals using Tunable-Q Wavelet Transform and Time-Varying Auto Regressive Model

“…The redundancy parameter is the total number of wavelet coefficients divided by the length of the input signal to which the TQWT is applied .If the two channel filter bank is iterated with infinitely many levels, the wavelet transform is over sampled by a factor r which is given by the following equation [6]: (10) It can be interpreted as a measure of how much spectral overlap exists between adjacent band-pass filters. It controls the excessive ringing in order to localize the wavelet in time without affecting its shape.…”

“…The parameter r does not affect the general shape of the wavelet of frequency spectrum (they are controlled by Q). With larger r, the number of levels J should be increased in order to cover the same frequency range because of the increased overlap .The specified value of r must be greater than 1, and a value of 3 (or) greater is generally recommended [7][8][9][10][11][12][13][14][15].…”

“…From Figure 5. Three aspects of information can be summarized as follows [10][11][12][13][14] a)First, for a certain Q-factor, the waveforms of the wavelet embedded in different sub bands are different, though they are with the same Q-factor, with the increase of the decomposition level, the time duration of the wavelet becomes wider, and the oscillation period of the wavelet increases as shown in Figure 5.b, and Figure 5.d. A specific basis associated with specific Q consists of J wavelets which are translated and/or scaled versions of each other but all have the same degree of oscillation, due to the same Qfactor.…”

Extraction of Fundamental Component in Power Quality Application using Tunable-Q Wavelet Transform

“…Meanwhile, it can be interpreted as a measure of how much spectral overlap exists between adjacent band-pass filters. Increasing r has the effect on increasing overlapping in the frequency domain of band-pass filters constituting the TQWT [12][13].…”

Fault Detection of High-Speed Train Wheelset Bearing Based on Impulse-Envelope Manifold

“…Both continuous wavelet transform (CWT) and discrete wavelet transform (DWT) have been successfully applied for fault detection of rotational machines with multiresolution [25,26]. The huge computational costs and redundant coefficients of CWT limit its wide application as compared to DWT which has a faster algorithm [27]. Wavelet packet transform (WPT) is proposed to improve the decomposition performance of WT on highfrequency band which contains useful information for fault detection [28].…”