## 6 A CWT Fault Prediction System  
Many researchers have applied a CWT scalogram to identify the fault features in signals, and some of them have achieved promising results. However, there still exist problems when dealing with transient changes in the signals, especially the whole data set of CWT. Useful information may disappear because of energy leakage or poor frequency resolution happened during CWT of the whole data set.  
The proposed data processing method cuts the whole data set into segments. By choosing the right scale for small segments, transient and unnoticeable information can be extracted when CWT is applied to the whole data set over a number of time segments. Since each data set contains 2000 more points as mentioned (about 20 min), the question is: how many smaller time segments within these 20 min should be used to detect the changing machine conditions. After numerous trials of dividing the data set in different ways, it was found that the most effective length was around 300 to 350 points when the frequency information could be explicitly observed on the scalograms. To create continuity as the detection process moves between time segments, 50 data points are duplicated between every 350 points, resulting in a total of more than 2400 points. Hence, each data set was divided into seven sub-time segments, that is 1-351 to 2101-2451. The sampling frequency was two points per second. Thirty-one scalogram images were generated for each 350-point length segment.  
Figure 6 shows four of the 31 scalograms in one sub-time segment. The absolute coefficient value represents the colour in the scalogram changing from below 0.5 to above 3.5. The values are indicated by the colour scale bar at the right-hand side of Figure 6. Each high value region (yellow regions) represents one single pulse.  
Figure 6: Four of the 31 CWT scalograms in one semi-time segment: **(a)** fuzzy pulses in frequency ranges 0.4–0.5 Hz and others, **(b)** fuzzy pulses in frequency ranges 0.4–0.5 Hz, 0.8–0.9 Hz, 0.9–1.0 Hz and others, **(c)** fuzzy pulses in frequency ranges 0.9–1.0 Hz and others, **(d)** fuzzy pulses in frequency ranges 0.8–0.9 Hz, 0.9–1.0 Hz and others.  
The scalograms in Figure 6 are typical CWT scalograms obtained from the trampoline machine. When a yellow colour bar appears, it means that the shape of the wavelet matches the shape of the signal in this time segment, thus creating a larger value of coefficient and brighter colours. However, the scalogram pattern changes over the 20 min operation duration. Therefore, it is still necessary to find how the pulses in the frequency range trigger the faults that occur in the real world by analysing further the information presented in the scalograms.  
It is hypothesized that there was a relationship between the number of pulses and the frequency ranges that these pulses were found to have. Changes in the number of pulses over time for these frequency ranges could provide an indication of the trend to onset of a fault. However, counting pulses in the scalogram depicted in Figure 6 is difficult because the high coefficient values are not focused. A more precise distinguished frequency indicator at different times is required to provide a clearer recognition of fault trend. In this case, a synchrosqueezed scalogram is introduced to further improve the readibility of the scalogram and the efficiency of the pulse counting process in different special frequency ranges.