*4.3. Ludovic® Simulation*

Figure 9 compares the values obtained with Ludovic® simulation (*x*-axis) to the experimental measures (*y*-axis) for different process parameters. This representation involves that the closer the values are to the *x* = *y* line, the closer the predictions of Ludovic® are to the measures. These results are fully detailed in Table A2 of the Appendix A.

The die temperatures measured by the extruder thermocouple are all around 200 ◦C, while the output temperatures measured with a manual thermocouple are much higher and more scattered. It is often a problem with extruder thermocouples which, being placed on the walls of the die, are influenced by its temperature and do not measure the actual melt temperature.

Concerning the simulation results, the first thing to notice is that all temperatures seem to be overestimated by the software, which matches the fact that polyethylene degradation is not considered. The actual viscosity decreases along with the screws and causes less self-heating than what could be expected without degradation. The temperature is, in fact, closer to the one imposed by the extruder.

This viscosity error also causes an overvaluation of the pressure in the die, more accentuated for UHMWPE because of its high viscosity. Concerning the torque and the engine power, and in the case of HDPE, the experimental values match pretty well with the simulation. It can be surprising considering the error between simulated and experimental viscosities caused by degradation. However, as viscosity decreases along the extruder, we can think that the torque value is mainly ruled by the most viscous part, which is the raw polyethylene present in the first screw elements and not yet degraded. The torque is then

*Polymers* **2022**, *14*, x FOR PEER REVIEW 14 of 23

*4.3. Ludovic® Simulation* 

ruled by the viscosity of raw polyethylene, which is the one implemented in Ludovic® (SC-Consultants, Saint-Etienne, France) The ability of machine learning algorithms to make better predictions than classic simulation is studied in what follows. perimental measures (*y*-axis) for different process parameters. This representation involves that the closer the values are to the x = y line, the closer the predictions of Ludovic® are to the measures. These results are fully detailed in Table A2 of the Appendix A.

Figure 9 compares the values obtained with Ludovic® simulation (*x*-axis) to the ex-

**Figure 9.** Comparison of Ludovic® Simulation versus Experimental data for in-line measured parameters. **Figure 9.** Comparison of Ludovic® Simulation versus Experimental data for in-line measured parameters.
