IMPROVING THE ROBUSTNESS WITH MODIFIED BOUNDED HOMOTOPIES AND PROBLEM-TAILORED SOLVING PROCEDURES, ACTA UNIVERSITATIS OULUENSIS C Technica 377
|ISBN-13:||978-951-42-9337-5 || |
|Kustantaja:||Oulun yliopisto|| |
|Oppiaine:||Tekniikka, matematiikka|| |
|Sijainti:||Print Tietotalo|| |
|Tekijät:||MALINEN ILKKA || |
The aim of this work is to improve the overall robustness in equation-oriented chemicalengineering simulation work. Because the performance of locally convergent solving methods isstrongly dependent on a favourable initial guess, bounded homotopy methods were investigatedas a way to enlarge the domain of convergence. Bounded homotopies make it possible to keep thehomotopy path inside a feasible problem domain. Thus the fatal errors possibly caused byunfeasible variable values in thermodynamic subroutines can be avoided.
To enable the utilization of a narrow bounding zone, modifications were proposed for boundedhomotopies. The performance of the modifications was studied with simple test problems andseveral types of distillation systems in the MATLAB environment.
The findings illustrate that modified bounded homotopies with variables mapping make itpossible to bound the homotopy path strictly to run inside a feasible problem domain. Thehomotopy path can be tracked accurately and flexibly also inside a narrow bounding zone.
It was also noticed that by utilizing the concept of bounding the homotopy path with respect tothe homotopy parameter, the possibility of approaching starting point and solution multiplicitiesis increased in cases where the traditional problem-independent homotopy method fails. Theconcept aims to connect separate homotopy path branches thus offering a trackable path with realspace arithmetic.
Even though the modified bounded homotopies were found to overcome several challengesoften encountered with traditional problem-independent homotopy continuation methods, alonethey are not enough to guarantee that the solution is approached from an arbitrary starting point.Therefore, problem-tailored solving procedures were implemented in the consideration ofcomplex column configurations. Problem-tailored solving procedures aim to offer feasibleconsecutive sub-problems and thus direct the solving towards the state distribution that fulfilsexact product purity specifications.
As a whole, the modified bounded homotopies and problem-tailored solving procedures werefound to improve the overall robustness of an equation-oriented solving approach. Thus thethreshold for designing and implementing complex process systems such as complex distillationconfigurations for practical use could be lowered.