# Fault-Resilient Manufacturing Scheduling with Deep Learning and Constraint Solvers
## 4 Deep Learning-Based Fault Prediction
### Model Architecture  
The selected 1D-CNN model was designed to effectively capture temporal patterns in time series data of machine states, such as temperature, vibration, operating hours, and tool wear. The architecture balances prediction accuracy with computational efficiency, making it ideal for edge computing scenarios. The architecture details are outlined below:  
* Input Layer: The input to the model consists of sequences of machine state features with a shape of \((batch\_size,sequence\_length,features)\);the sequence length is set to 10, and the number of features is 4 (temperature, vibration, operating hours, and tool wear).
* Conv1: 32 filters, kernel size = 3, padding = 1, activation = ReLU.  
Figure 4: Comparison of model performance (RMSE, MAE, training time, epochs).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **RMSE** & **MAE** & **Training Time (s)** & **Epochs** \\ \hline
1D-CNN & 5.5204 \(\pm\) 0.5738 & 2.5557 \(\pm\) 1.0863 & 1.6556 & 22.30 \\ GRU & 5.4882 \(\pm\) 0.1063 & 2.1015 \(\pm\) 0.4075 & 3.5945 & 32.00 \\ LSTM & 5.4032 \(\pm\) 0.6431 & 2.2741 \(\pm\) 0.5513 & 5.5326 & 46.00 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of model performance metrics.  
Conv2: 32 filters, kernel size = 3, padding = 1, activation = ReLU.
* Pooling Layers: A pooling layer follows each convolutional layer to reduce dimensionality and emphasize the most critical features, preventing overfitting and improving computational efficiency.
* Flattening Layer: The multidimensional output from the convolutional layers is flattened into a one-dimensional vector in order to prepare it for the fully connected layer.
* Fully-Connected Layers: These layers combine the extracted temporal features to predict the fault probability for the next 10-min interval.
* Output Layer: This layer produces a single continuous value representing the fault probability (\(P(M_{i},J_{j},t+10)\)) for each machine-job pair.  
The proposed architecture offers several key advantages that make it particularly suitable for real-time fault prediction in dynamic production environments. By incorporating a rolling prediction mechanism, the model generates updated fault probabilities every minute, enabling the system to dynamically adapt and make proactive scheduling decisions based on the latest machine state information. This real-time adaptability ensures that the scheduling process remains responsive to changing conditions, thereby minimizing fault risks.  
In terms of computational efficiency, the use of convolutional layers allows the model to process input sequences in parallel, significantly reducing its training and inference times compared to traditional recurrent models. This efficiency is particularly beneficial in edge computing environments, where computational resources are often limited and low-latency predictions are critical. Furthermore, the architecture demonstrates strong scalability. Its design can easily accommodate variations in sequence length or the number of input features without requiring substantial modifications. This flexibility allows the model to be applied to a wide range of industrial scenarios, making it a robust solution for fault prediction in diverse manufacturing settings.