# Unsupervised Deep Anomaly Detection for Industrial Multivariate Time Series Data
## 3 Materials and Methods
### Inference
Specifically, we designed three configurations with different numbers of convolutional kernels: the first layer of the convolutional encoder had 32 kernels and the second layer had 16 kernels (denoted as \(AT-DCAEP_{A}\)); the first layer had 48 kernels and the second layer had 24 kernels (denoted as \(AT-DCAEP_{B}\)); the first layer had 64 kernels and the second layer had 32 kernels (denoted as \(AT-DCAEP_{C}\)). The convolutional decoder mirrored the hierarchical structure of the convolutional encoder. We compared the performance of these three configurations with different numbers of convolutional kernels, and the results are presented in Table 3. It is observed that, for the SWaT, SMD, and SMAP datasets, adopting a larger number of convolutional kernels did not enhance the performance of anomaly detection. In the MSDS, WADI, and MBA datasets, increasing the number of convolutional kernels even led to a decrease in performance. This indicates that augmenting the number of convolutional kernels does not always significantly improve performance; instead, it may increase computational costs. Therefore, careful consideration is required when choosing the stack depth of convolutional layers and the number of convolutional kernels, balancing performance and computational costs. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{\(AT-DCAEP_{A}\)} & \multicolumn{4}{c}{\(AT-DCAEP_{B}\)} & \multicolumn{4}{c}{\(AT-DCAEP_{C}\)} \\ \cline{2-13}  & \(P\) & \(R\) & \(AUC\) & \(F1\) & \(P\) & \(R\) & \(AUC\) & \(F1\) & \(P\) & \(R\) & \(AUC\) & \(F1\) \\ \hline MSDS & 0.9924 & 0.9406 & 0.9609 & 0.9658 & 0.8881 & 0.9956 & 0.8344 & 0.9387 & 0.8400 & 0.9983 & 0.7516 & 0.9123 \\ SWaT & 0.9977 & 0.6770 & 0.8383 & 0.8066 & 0.9977 & 0.6770 & 0.8383 & 0.8066 & 0.9977 & 0.6770 & 0.8383 & 0.8066 \\ SMD & 0.9940 & 0.9981 & 0.9987 & 0.9960 & 0.9940 & 0.9981 & 0.9987 & 0.9960 & 0.9940 & 0.9981 & 0.9987 & 0.9960 \\ WADI & 0.7880 & 0.8295 & 0.9121 & 0.8082 & 0.7421 & 0.8295 & 0.9113 & 0.7834 & 0.7438 & 0.8295 & 0.9114 & 0.7843 \\ SMAP & 0.8904 & 0.9999 & 0.9940 & 0.9420 & 0.8904 & 0.9999 & 0.9940 & 0.9420 & 0.8883 & 0.9999 & 0.9939 & 0.9408 \\ MBA & 0.9923 & 0.9999 & 0.9980 & 0.9961 & 0.9870 & 0.9999 & 0.9966 & 0.9934 & 0.9900 & 0.9999 & 0.9974 & 0.9950 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Impact of the number of convolutional kernels on performance. Figure 3: Impact of the number of convolutional layers on model performance. (**a**) The impact of the number of convolutional layers on \(AUC\). (**b**) The impact of the number of convolutional layers on \(F1\) score. The adjustment of parameters \(\alpha\) and \(\beta\) in the model is crucial, as they serve as tunable parameters with a significant impact on model effectiveness. A larger \(\alpha\) corresponds to a stronger emphasis on the reconstruction contribution of the convolutional autoencoder in anomaly scoring, while a larger \(\beta\) corresponds to a greater emphasis on the contribution of prediction. Adjusting these parameters without retraining the model is essential for tuning detection sensitivity. Table 4 reports the impact of different \(\alpha\) and \(\beta\) values on detection performance, including precision, recall, \(AUC\), and \(F1\) scores. It is observed that by increasing \(\alpha\) and decreasing \(\beta\), precision improved by 28.27% but recall decreased by 21.14%. The best \(AUC\) and \(F1\) scores were achieved at \(\alpha\) = 0.3 and \(\beta\) = 0.7. Therefore, by adjusting \(\alpha\) and \(\beta\), the sensitivity of anomaly detection in the AT-DCAEP model can be parameterized to meet the requirements of real production environments. This tuning allows a single model to achieve different levels of sensitivity, catering to various needs in different layers of real production environments.