# Latent Dimensions of Auto-Encoder as Robust Features for Inter-Conditional Bearing Fault Diagnosis
## 5 Experimental Validation
### Architecture of the Auto-Encoder  
Upon investigating the classification results of our methodology on the validation data (a part of the training dataset), we understood that the frequency features as inputs to the MLCAE are better at segregating appropriate classes than the raw data. Thus, the inputs to the MLCAE in further experiments will be the magnitude of the positive spectrum of the FFT data. In the case of the CWRU dataset, each observation consisted of 1024 sample points so that it approximately fits information of two rotations of the motor spindle. This means that considering only the positive spectrum of the FFT data will lead to an input size of (512,1) for the CWRU dataset. Similarly, to approximately fit the information of two spindle rotations, the samples in each observation for the Paderborn data were chosen as 4096. Thus, the input size of the architecture used for Paderborn will be of size (2048,1). Some of the parameters used in architectures for CWRU and Paderborn are similar, whereas some are not. Details of these parameters are also mentioned in Table 3.  
Such AE-based extractors are trained with the FFT data of each condition. During the process of training, it considers the loss of reconstruction and tries to minimize this loss while optimizing the whole network. Once the stop criteria (non-reducing loss or suggested epochs) are met, the training algorithm stops, and the encoder part of the so-trained AE is considered for further usage. When an observation from a different condition is inferred using this encoder, it produces a reduced number of features (values from the latent dimension), which will then be used as inputs to train the classifier. Numerically, the MLCAE (Multi Layer Convolutional AE) will train and bring sizes of (512,1) of CWRU and (2048,1) of Paderborn to (20,1) latent dimensions, which will then be used by the KNN classifier for further classification. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Reference** & **Source Only** \\ \hline SVM & [8] & Yes \\ CNN & [8] & Yes \\ CNN-MMD & [8] & No \\ MDDAN & [8] & No \\ MDIAN & [8] & No \\ CMD & [16] & No \\ MLCAE-KNN & Proposed & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Robust learning and domain adaptation methods from the literature are used to compare with the proposed method. We also discussed in the previous section that the choice of K value for the KNN may fall anywhere between 1 and 15. Upon further investigation for random transfer tasks, the classification results across conditions were inconsistent when the K values are small and was showing degraded performance across conditions when the value is high. The exact nearest number of observations to consider for predicting a new sample in case of both the datasets was thus found to be optimal at k = 5. The trained classifier from one condition was then tested against other conditions, and the experimental results for various transfer tasks were discussed accordingly. The training and testing process adopted in this article is as described in Algorithm 1.