necessitating its active management. A reliable method for noise reduction in the time domain is the application of Finite Impulse Response (FIR) moving average and standard deviation filters. These filters are not only simple and fast but also provide remarkable results by eliminating noise while retaining essential information and sharp step responses, as demonstrated in Figure 2 Figure 3 - Euclidean distance calculation (where p and q are two points) The process of developing a virtual health index commences with the calculation of the Euclidean distance between the signal's quiet value of each bearing and that of the signal at time t, as depicted in Figure 3, for each filtered component of the relative vibration channel signal. Multiple features become available for each time t, as shown in Figure 4. Following the methodology described in the
Figure 6 - Resulting threshold based on failure case. Red arrow = moment of bearing failure; yellow/orange arrow = signal pattern change. Yellow/Orange threshold defined as warning and alarm stage division. remarkable. In addition to the case used for generalization, three more bearing cases were available, and all were correctly identified by the developed methodology without any false positives or false negatives (see Figure 7). To ensure correct fitting, the method was also tested on the remaining two machines without recalibration.
Figure 4 - Features for VHI developed by raw signal filter and Euclidean distance calculation Health Indicator construction chapter [39] [40] [41] [42], which incorporates the use of a non-linear minimum function, the data can be aggregated to create a virtual Health Index, as illustrated in Figure 5.
Figure 7 - Prediction result on development paper machine The results, as depicted in Figure 8, were equally remarkable, with no false positives or false negatives identified, even in instances when no failure cases were observed on the machine.
Figure 5 - Virtual Health Index for a single bearing as derived by signal displayed in Figure 5 The final step involves dividing the Health Index into various health stages. As described in Chapter 4, a semi-supervised approach is implemented due to the scarcity of labelled data available in the dataset, which is limited by the practical run-to- failure cases, as discussed in section 4.1. The threshold for health stage division is determined based on the patterns observed in the failure case depicted in Figure 5, and explained in Figure 6. The availability of data from multiple paper machines allows for cross-validation to assess the extent to which the developed methodology can be generalized. The performance of the methodology on the machine used for method development was
Figure 8 - Methodology testing on unseen/unbiased data
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