## 6 Discussion
Figure 9: Classification accuracy for the individual classes (1 to 5) for (a) linear wear-state classes and (b) non-linear wear-state classes, which corresponds to the diagonal of the confusion matrices in Figures 7 and 8, respectively. the MAE performance metric was used for analysis purposes to ascertain the severity of the misclassifications. Feature subset compression using the non-linear one-third octave-based filtered for both linear and non-linear wear-states performed very well in both cases. This can be attributed to placing a higher emphasis on the lower portion of the spectra for feature extraction. From a feature-engineering perspective, this was shown to offer more valuable diagnostic trend information for characterising the health condition of the bearings under test [11]. Importantly, this reduces the multivariate dimensionality [70; 71] of the feature space in a more optimal way compared with linear filtering as the results demonstrated by yielding superior classification performance. Moreover, using a non-linear wear-state model approach to classification is more suitable as the ageing mechanisms typically follow an non-linear exponential trend; hence, we can see significantly higher performances achieved. Clearly, a trade-off exists as if the size of class 1, is too large with respect to the others, then the suitability of the RUL framework for taking timely action, such as equipment maintenance and critical parts replacement diminishes. As the subsequent classes would therefore be too short in time, the severity of degradation between these classes would occur rapidly. Our non-linear exponential model described in Equation (6) strikes a suitable balance and was found to work extremely well in this proposed approach. The highest overall classification scores were achieved using the Cosine \(k\)-NN classifier. This was achieved across all seven bearing test-cases using the round robin framework and, hence, demonstrates how the proposed ML methodology performs on unseen raw vibration signals. However, these \(k\)-NN and SVM ML algorithms are heavily reliant on the depth of the training data, which is common in the field of supervised learning and hence makes these methods prone to producing over-fitted prediction models. While this paper introduced a valuable and robust approach for RUL estimation, future work might investigate applying this proposed method on larger data-sets. The dataset used here in this research was limited in terms of the total number specimens aged and captured using vibration signals In addition, the level of accelerated ageing is perhaps too rapid, which led to a high proportion of abrupt failure modes occurring approximately 43% of the time. These have a completely different degradation trend to the gradual ageing mechanisms; hence, this places limits on testing the true efficacy of the ML frameworks and recipes due to model over-fitting. If the datasets were significantly improved by increasing the number of specimens and reducing the level of accelerated ageing, this would offer the potential to explore ML approaches that employ advanced deep learning using neural networks. In testing the versatility and robustness of the proposed ML method recipes on different bearing types and sizes under different speed and load conditions, work could explore vibration data gathered from research testbeds where the shaft speed changes. This will require developing extensive experimental campaigns to create more advanced datasets that better reflect typical real-world operating conditions.