## 3 Methodology and Overall Framework  
### System Architecture  
Our PM-based adaptive process scheduling pipeline is depicted in Figure 1. The architecture consists of a machinery system (in our case, a conveyor belt run by a servo motor), its digital twin, predictive maintenance mechanism, and adaptive control mechanism.  
A digital twin model of the conveyor system is developed using the specifications of the servo motor and the conveyor belt, which is then further approximated with the actual values collected from the real system (covered in Section 3.2). In order to reach better classification accuracy for the predictive maintenance, the twin generates normal operation data as well as data under abnormal conditions that are hard to observe and may be harmful for the real machine. The generated (synthetic) data, along with the real motor data, are used in PM classification model training. The data in our case includes speed, power and torque readings from the servo motor driving a conveyor belt. We refer to the collection of data generated under nominal operating conditions as the _\"fingerprint\"_ of the system. The training step for PM generates a nonlinear decision boundary over the fingerprint data, which is done initially offline and can be updated frequently. That  
Figure 1: The predictive maintenance (PM)-based adaptive process scheduling pipeline.  
is, with the newly collected data during run-time, our pipeline allows for continuously updating the fingerprint of the system in case the nominal operating conditions for the process changes. This then triggers the training to generate a new decision boundary model. This is a supervised and procedural step since our pipeline cannot automatically detect drastic changes in the nominal (boundary) conditions that may arise from various factors including manual updates in the process, for example, replaced components, changing requirements, carrying heavier loads on the conveyor.  
The real-time PM takes place in the _Anomaly Detection_ stage in Figure 1. It takes speed and power readings from the motor as input and uses the trained decision boundary to perform anomaly predictions on the new data in real-time (covered in Section 3.3). Our adaptive control contains two components. First, after an anomaly is detected, the _Maintenance Analysis_ (error calculation) block further analyzes the abnormal readings by calculating the error, that is, the deviation from an expected value under a requested operation (covered in Section 3.4). We call these expected values \"nominal values\". During run-time, we use the twin model to calculate the nominal values for the requested operation. After that, the _Operation Control_ block makes a decision by scheduling a new operation mode. We use a state-of-the-art genetic algorithm for this purpose. An operation mode is, in our case, an allowed speed interval to run the conveyor belt motor and it is selected with the optimization criteria of achieving maximum possible performance (speed) while ensuring a safe operation on the system. A user may adjust the optimization goal by giving more weight on more performance or on less power, that is, more protection (covered in Section 3.4.1).