## 2 Materials and Methods
### The Need for Online Machine Learning
#### 2.2.3 Real-World Application: Slitting Machines  
In the experiments discussed in this work, data were collected using a test setup for winding stations from \"Kampf Schneid- und Wickeltechnik GmbH & Co. KG\", Wiehl, Germany, a company that specializes in building machines for slitting and winding web-shaped materials such as paper, plastic films, or aluminum foil, as depicted in Figure 3. A paper core is secured between two winding stations, to wind the web into a roll, achieving a diameter of up to 1500 mm and weights of up to 6 tons. The necessary web tension for different materials is maintained by a drive, which adjusts to compensate for the increasing diameter. The test setup facilitated the evaluation of new concepts for winding stations and helped in determining the lifespan of various components, including bearings and belts. Additional sensors were installed to monitor temperatures and vibration levels at different points, enabling a more comprehensive analysis of their behavior. In one of the trials, a machine run to wind up a representative material was simulated under defined conditions, including parameters such as material thickness, material density, material width, induced tension, machine speed, and acceleration and deceleration times, in addition to core and finished diameters. For the current experimental setup, sensor data from the winding machine were collected locally and supplied by the company. Machine learning algorithms were executed on a separate device. In the future, the plan is to establish a bi-directional connection between the sensors and the computing device. The collected time-series data encapsulated information regarding motor temperature, revolutions, and torques, as well as data from external sensors monitoring temperature and vibration levels. For the experiments outlined in this article, only specific data were utilized: motor revolution [\(\frac{1}{\text{min}}\)], motor torque [Nm], and the vibration data at a particular point. The vibration data were measured in analog values between 0 and 27,648, related to a range between 0-25 [\(\frac{\text{mm}}{g^{2}}\)]. Motor revolution and torque were used as input features, while the vibration level was the prediction target. Data were logged every one hundredth  
Figure 2: Construction of the different training datasets, depending on the modeling approach chosen. of a second, with each timestamp recording the respective feature values. To simulate external influences, such as roll handling or other factory operations, further vibrations were introduced intermittently by gently hitting and shaking the winding stations. In our experiments, the data provided by Kampf Schneid-und Wickeltechnik GmbH & Co. KG were utilized, to predict the vibration of level station 1, using motor revolution and torque. A forecast horizon of t = 150 was defined. This horizon refers to the time when the models will be updated again. For instance, in this experiment, the models were updated after collecting 150 data points, although each approach employed a distinct strategy. The classic batch method did not update the model and only utilized training data. The batch approach with a landmark strategy included newly collected data in the training data and created a new model on the enlarged dataset. On the other hand, the batch model with a shifting window approach excluded the first 150 data points of the training set and appended each new 150 data points to the end of the training data. A new model was then produced based on this new dataset, ensuring that the length of the training dataset remained constant. Finally, in the OML approach, 150 data points were collected and sequentially passed to the model. In the batch approaches, a Decision Tree Regressor from the _sklearn_ package [14] was utilized, while the Hoeffding Tree Regressor (HTR) from the _River_ package [8] was used in the OML approach. Before passing data to the regressor, it was standardized. For the initial training of the models, 1,462,555 samples were used.