# Whitening CNN-Based Rotor System Fault Diagnosis Model Features
## 5 Discussion  
Based on the results, ND seems like a competitive solution for BN in CNN-based machine fault diagnosis from vibration data. In Section 4.1, the modified models with ND were compared to the baseline models with a well-established benchmark dataset for bearing fault diagnosis. In this multi-categorical bearing fault recognition task, the modified models with ND mostly outperformed the baseline models with BN in terms of the average accuracy of all experiments. Whitening seemed to especially improve WDCNN performance. The average accuracy of modified WDCNN was 5.18 pp and 11.73 pp higher than the baseline in results shown in Figures 7 and 8, respectively. Furthermore, the modified WDCNN and modified SRDCNN outperformed remarkably the corresponding baselines in experiments with training data drawn from the vibration data sampled at a 3 hp motor load.  
In Section 4.2, the modified models and the baseline models were compared by using a real world dataset consisting of ship thrusters in diverse environments. In these thruster fault detection tasks, all models achieved relatively high accuracies of over 84%. However, there were no significant differences between the fault detection accuracies of the compared models. Based on these thruster fault detection tasks, ND can be considered as good as BN for normalising the activations of CNN-based fault detection models.  
Although ND is a promising technique for whitening the features between CNN layers, it introduces a few extra hyperparameters for fault diagnosis model training. Moreover, the models relying on ND can be very sensitive toward these hyperparameters. That is, the sampling stride, the number of coupled Newton-Schulz iterations and the regularisation  
Figure 11: Mean and standard deviation of accuracies of the baseline models with BN (**red**) and the modified models with ND (**green**) on both binary fault detection problems over 10 trial runs. Datasets were randomly drawn for each trial separately. Every model was tested with the same randomly drawn set of samples.  
term \(\epsilon\), for example, may affect optimisation results and require careful tuning. For convenience, Appendix D shows accuracies at different subsampling strides and batch sizes. Furthermore, Appendix E provides some examples of the deconvolution matrix **D** after a different number of coupled Newton-Schulz iterations. Fortunately, similar ND hyperparameters seemed to perform well in both model validation case studies, even though the data was significantly different due to the measurement circumstances and due to the health state spaces. Therefore, the values searched in this work for ND hyperparameters are likely suitable for other vibration diagnosis tasks.  
Overall, whitening the layer inputs seems to consistently provide high test performance for CNN-based fault diagnosis models. By whitening the layer inputs, the model learns uncorrelated features containing less redundant information than correlated features. With uncorrelated features, the domain adaptation of the model improves on average, as shown in Section 4.1. The difference in domain adaptation between whitened features and batch normalised features is significant, especially when shifting from the higher load domains to lower load domains. Furthermore, decor-related features seem to significantly increase the accuracies of the diagnosis models compared to the baseline models when data from two sensors were employed, as Figure 8 shows. This indicates that decorrelating CNN-based model features may increase fault diagnosis accuracy of condition monitoring systems with many sensors.