Figure 6.60. Comparison of fault detection performances. Original data (upper figure) and approximation coefficients of thirds scale (lower figure). Dashed line represents 99% control limit in both figures.
proposed [437]. This algorithm can be summarized as:
1. Decompose data in a window of dyadic length
2. Reconstruct the signal after applying thresholding to the wavelet coefficients
3. Retain only the last point of the reconstructed signal
4. Shift the window in time when new data are available and keep the window length constant
Initial window length selection is critical. If the window length is chosen too small, there may not be enough data points to decompose in coarser scales. On the other hand, if the initial window length is too large, by the time process data reaches the chosen window length, the process might have already gone out of control. The window length is kept constant to reduce the computational burden. Another difference compared to off-line algorithm is the adjustment of detection limits for each scale as for the relation:
Figure 6.60. Comparison of fault detection performances. Original data (upper figure) and approximation coefficients of thirds scale (lower figure). Dashed line represents 99% control limit in both figures.
Measurements
Measurements
200 400 600 800 Measurement number
0 200 400 600 800 Measurement number
200 400 600 800 Measurement number
0 200 400 600 800 Measurement number
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