## 5 Discussion  
This work extends on our previous research [11] to investigate the performance of our proposed models utilizing an adaptive wide-kernel in the first convolutional layer in fault detection and condition monitoring tasks. This adaptive layer is able to scale towards varying dimensionalities of time series data, while maintaining its core task for extracting valuable features without representation loss. With this adaptive layer we optimized our previous proposed models as described in [11] resulting in two models, respectively _A-WCNN_ and _Ada-WMCNN_. The first model initializes the adaptive wide-kernel layer followed by small kernel layers, similar to the previous proposed WDTCNN model. The _Ada-WMCNN_ is able to process multivariate time series in a univariate way in the first wide-kernel layer. This model has a similar principle as the WDMTCNN model proposed in [11], but is more computationally efficient due to the lower number of trainable parameters and higher computation speed, as can be seen in Table 7. We compared the models with many traditional machine learning applications (optimized with a grid search) as well as with the original WDCNN proposed by [10] and our completely separate multichannel CNN (_A-WMCNN_). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Experiment** & **Parameters** & **Ms/step** \\ \hline
**WDCNN** & CWRU & 54.804 & 15.50 \\  & Paderborn & 55.828 & 16.25 \\ \hline
**A-WCNN** & CWRU & 58.468 & 15.88 \\  & Paderborn & 65.204 & 16.50 \\ \hline
**A-WMCNN** & CWRU & 107.460 & 23 \\  & Paderborn & 161.140 & 29.25 \\ \hline
**Ada-WMCNN** & CWRU & 56.420 & 17 \\  & Paderborn & 59.060 & 18.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Number of parameters and computation speed, expressed in milliseconds per epoch (Ms/step) using GPU acceleration, for the CNN models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experiment** & **K-NN** & **RF** & **SVM** & **WDCNN** & **A-WCNN** & **A-WMCNN** & **Ada-WMCNN** \\ \hline
**CWRU** & 62.34 & 81.57 & 76.63 & 78.24 & 85.07 & **89.39** & 88.16 \\  & (12.34) & (9.09) & (11.32) & (20.54) & (15.85) & (10.99) & (12.49) \\ \hline
**Paderborn** & 88.13 & 91.84 & 80.00 & 94.94 & **99.00** & 93.54 & 98.13 \\  & (5.65) & (3.78) & (5.58) & (5.31) & (1.07) & (4.06) & (1.49) \\ \hline
**Overall** & 74.06 & 86.24 & 78.16 & 85.83 & 91.40 & 91.27 & **92.69** \\  & (16.26) & (8.79) & (9.23) & (17.58) & (13.57) & (8.73) & (10.47) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Averaged test accuracy scores (%) for both datasets (with standard deviation). The proposed models are tested in a wide range of experiments on two well-known bearing fault datasets; the CWRU Bearing dataset, a dataset with few samples and many different fault and machine conditions and the Paderborn Bearing dataset, a large-scale dataset with a vast number of samples and fewer fault conditions. Compared to the ML models and the original WDCNN, our optimized models demonstrated a better performance; therefore, concluding that an adaptive wide-kernel layer is a valuable addition to existing 1D CNN architectures. However, between the different settings for the adaptive models, it seems that highest performance depends on the properties of the dataset, e.g., the best performing model deviates per dataset. Overall, we can conclude that the _Ada-WMCNN_ model performs best throughout all experiments suggesting that a separate multichannel in the first wide-kernel layer is effective and adaptable to changing environments. Furthermore, both models handle raw signals directly and are quite good in detecting faults and distinguish between machine conditions, even in cases with minimal training data. On another note, in this research our models are only trained on experimental data that are carefully recorded and annotated, which is usually difficult to obtain in real-world settings. Thus, generalization of the trained models in real-world settings is difficult to assess, also due to scarcity of available data.