Accessible Unlicensed Requires Authentication Published by De Gruyter November 16, 2021

Predicting the Non-Linear Conveying Behavior in Single-Screw Extrusion: A Comparison of Various Data-Based Modeling Approaches used with CFD Simulations

W. Roland, C. Marschik, M. Kommenda, A. Haghofer, S. Dorl and S. Winkler

Abstract

The traditional approach to modeling the polymer melt flow in single-screw extruders is based on analytical and numerical analyses. Due to increasing computational power, data-driven modeling has grown significantly in popularity in recent years. In this study, we compared and evaluated databased modeling approaches (i. e., gradient-boosted trees, artificial neural networks, and symbolic regression models based on genetic programming) in terms of their ability to predict – within a hybrid modeling framework – the three-dimensional non-linear throughput-pressure relationship of metering channels in single-screw extruders. By applying the theory of similarity to the governing flow equations, we identified the characteristic dimensionless influencing parameters, which we then varied to create a large dataset covering a wide range of possible applications. For each single design point we conducted numerical simulations and obtained the dimensionless flow rate. The large dataset was divided into three independent sets for training, interpolation, and extrapolation, the first being used to generate and the remaining two to evaluate the models. Further, we added two features derived from expert knowledge to the models and analyzed their influence on predictive power. In addition to prediction accuracy and interpolation and extrapolation capabilities, we evaluated model complexity, interpretability, and time required to learn the models. This study provides a rigorous analysis of various data-based modeling approaches applied to simulation data in extrusion.


Wolfgang Roland, Institute of Polymer Extrusion and Compounding, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria

Acknowledgements

This research was funded by the Austrian Science Fund (FWF), grant number: I 4872-N. The authors additionally acknowledge support from the Christian Doppler Research Association and the Federal Ministry for Digital and Economic Affairs under the aegis of the Josef Ressel Center for Symbolic Regression.

The computational results presented were achieved in part by using the Vienna Scientific Cluster (VSC).

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Appendix

The best performing symbolic regression model is given by:

(34) ΠV(Πp,Z,n,t/Db,h/w)=a00+a01ea02F1+A1(A2+A3)+A4A5.

with the sub-functions:

(35) A1=a03ea04h/w+a05Πp,za06( e a07F2+a08h/w+a09n+a10Πp,z )n,
(36) A2=a11(ea12Πp,z+a13n)(a14h/w+Πp,z)+a21h/w+a22n+a23Πp,z,
(37) A3=ea14F2ea16h/wea17ea18t/Db+a19F1+a20Πp,2n
(38) A4=a24e(ea25h/w+a26Πp,z)(a27F1+a28Πp,z)+a29Πp,z
(39) A5=a30+ea31t/Db(ea32h/w+a33Πp,znA6+a34t/Db),
(40) A6=a35+eea36t/Db(a37h/w+a38Πp,2)+a39F1+a40n+a41t/Db.

The derived features F1 and F2 are according to Eqs. 31 and 32, respectively. The model coefficients are given by Table 8.

Received: 2021-02-02
Accepted: 2021-04-24
Published Online: 2021-11-16

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