# Model Predictive Evolutionary Temperature Control via Neural-Network-Based Digital Twins
## 2 Materials and Methods  
### Experimental Setup  
This case study is motivated by the significant impact that high-temperature technical processes can have on the degradation of components. Accordingly, the proposed approach seeks to develop an intelligent controller using machine learning techniques to enable predictive cooling. The main objective is to generate control laws that facilitate a uniform temperature distribution, thereby minimizing the stresses and deformations arising from the formation of hot spots in the presence of unknown disturbances, or sudden changes in the thermal load.  
The physical setup is designed as a multi-mode cooling problem. It consists of the following components (Figure 1):  
* A copper plate--selected due to its high thermal conductivity in order to reduce the duration of the experiments;
* The copper plate is coated with a high-emissivity black paint (Nextel Velvet Coating 811-21) for improved signal-to-noise ratio;
* Three heating strips on the backside of the plate arranged in a \"Z\"-like pattern--310 mm \(\times\) 17 mm, 24 V, 36 W;
* Three fans located on the perimeter of the plate--SUNON, 12 V, 1.62 W;* A data acquisition module (myDAQ, NI) with an in-house built control unit;
* A mid-wave infrared camera--FLIR SC5000, (512 \(\times\) 640) pixels;
* A LabVIEW interface for the real-time control of the system.  
The infrared camera detects thermal radiation emitted by the copper plate and other components. The detected radiation is dependent on the plate surface temperature only for constant ambient conditions. This is achieved by conducting the tests in an air-conditioned room. This way, changes in the camera signal can be directly attributed to changes in the plate surface temperature.  
A single experiment begins from an initial steady state \(s_{0}\). A heating disturbance is then introduced through the strips and the fan loads are adjusted. The experiment lasts until a new steady state \(s_{1}\) is reached. Figure 2 depicts the recordings of two experiments (top row and bottom row) from the training dataset. The first six frames show the steady-state temperature distribution reached at the end of the previous operating point, while the final two frames illustrate the new steady state under the new thermal loads and cooling configuration. There are two options for \(s_{0}\). We either start with the system completely shut down (no heating or cooling), or we carry on with the steady state reached in the previous operating point.  
Figure 1: The physical setup is devised as a multi-mode cooling problem, depicted in the upper section. The arrangement of fans around the copper plate is illustrated in the lower left corner, while the configuration of heating strips at the back of the plate, along with randomly placed thermal insulators, is shown in the lower right corner.  
The following conditions are used to define the second steady state \(s_{1}\) (Figure 3):  
1. The per pixel percentage difference of consecutive frames after 16 \(\times\) 16 max filter is less than 1.5%. The application of this max filter is required for two reasons. First, due to thermal inertia, the difference between consecutive frames can be small, and thus we increase the rigidity of the steady-state condition. Second, we reduce the impact of objects that have the same temperature in all frames (e.g., the frame around the plate).
2. The pixels with a 3% deviation in consecutive frames are less than 1% of the total pixels in a frame after a 16 \(\times\) 16 max filter.  
It is important to highlight that thermal insulation is absent at the slab edges as well as behind the resistance heating strips. The experimental configuration, illustrated in Figure 1, was executed in this manner. Once the system attains a steady state, it does so due to the interplay of forced and natural convection, conduction, and radiative heat transfer processes. In other words, the system was deliberately rendered more susceptible to environmental disturbances and fluctuations.