Keywords

Shape Optimization, Optimal Control, Adjoint, Sensitivity Analysis, Plastics Processing, Extrusion

Summary

In the extrusion of plastics, both the die design and the identification of the optimal operating point represent an iterative process. While computational fluid dynamics are increasingly being used in the flow channel design, only few simulation models take into account the occurring process fluctuations. These can be calculated using uncertainty analyses and sensitivity analyses (SA), but the most widely used methods are so computationally intensive that they are not feasible for practical application. In addition, simulation-based optimization is often performed using methods that require the evaluation of a large number of design points. Adjoint-based methods can be used for both efficient SA and optimization. With the cost of only two calls of the flow solver, the sensitivities for application-specific objective functions can be calculated deterministically. In addition to SA, the sensitivities can also be used for optimization. With two additional solver calls, the second-order sensitivities can even be used to map the interaction between the considered input variables. However, a systematic comparison of adjoint-based sensitivities and sensitivities from global, statistical sensitivity analyses has never been performed for this application. In particular, there are no known studies in which adjoint-based second-order sensitivities have been used to analyze this application. Furthermore, the potential of combining shape optimization of the extrusion die’s flow channel with optimal control of the operating point for the simulation-based design of extrusion processes has hardly been investigated to date.

The first objective of the research project is therefore to investigate adjoint-based first- and second-order sensitivities to test their suitability as a substitute for cost-intensive global statistical sensitivity analyses. For this purpose, both adjoint-based first- and second-order sensitivities and sensitivities from various local and global statistical methods are calculated and compared for a profile extrusion die with a complex exit cross-section. The second objective of the research project is to develop an adjoint-based algorithm for the optimization of extrusion processes, using both geometric sensitivities for shape optimization and non-geometric sensitivities for optimal control of the operating point. The combined optimization algorithm is validated using a use case with available laboratory data, thus testing its suitability for a more efficient design and optimization process.

The research project thus makes a valuable contribution to the analysis and optimization of extrusion processes, taking uncertainties into account.

Acknowledgment

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 586063853.