Improving the robustness with modified bounded homotopies and problemtailored solving procedures 

Author:  Malinen, Ilkka 
Organizations:  University of Oulu, Faculty of Technology, Department of Process and Environmental Engineering, Chemical Process Engineering Laboratory 
Format:  eBook 
Online Access:  PDF Full Text (PDF, 1 MB) 
Persistent link:  http://urn.fi/urn:isbn:9789514293382 
Language:  English 
Published: 
Oulu : University of Oulu,
2010

Publish Date:  20110111 
Thesis type:  Doctoral Dissertation 
Defence Note:  Academic dissertation to be presented with the assent of the Faculty of Technology of the University of Oulu for public defence in Kuusamonsali (Auditorium YB210), Linnanmaa, on 21 January 2011, at 12 noon 
Tutor: 
Professor Juha Tanskanen 
Reviewer: 
Professor Ville Alopaeus Professor Eric S. Fraga 
Description: 
AbstractThe aim of this work is to improve the overall robustness in equationoriented chemical engineering simulation work. Because the performance of locally convergent solving methods is strongly dependent on a favourable initial guess, bounded homotopy methods were investigated as a way to enlarge the domain of convergence. Bounded homotopies make it possible to keep the homotopy path inside a feasible problem domain. Thus the fatal errors possibly caused by unfeasible variable values in thermodynamic subroutines can be avoided. To enable the utilization of a narrow bounding zone, modifications were proposed for bounded homotopies. The performance of the modifications was studied with simple test problems and several types of distillation systems in the MATLAB environment. The findings illustrate that modified bounded homotopies with variables mapping make it possible to bound the homotopy path strictly to run inside a feasible problem domain. The homotopy 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 to the homotopy parameter, the possibility of approaching starting point and solution multiplicities is increased in cases where the traditional problemindependent homotopy method fails. The concept aims to connect separate homotopy path branches thus offering a trackable path with real space arithmetic. Even though the modified bounded homotopies were found to overcome several challenges often encountered with traditional problemindependent homotopy continuation methods, alone they are not enough to guarantee that the solution is approached from an arbitrary starting point. Therefore, problemtailored solving procedures were implemented in the consideration of complex column configurations. Problemtailored solving procedures aim to offer feasible consecutive subproblems and thus direct the solving towards the state distribution that fulfils exact product purity specifications. As a whole, the modified bounded homotopies and problemtailored solving procedures were found to improve the overall robustness of an equationoriented solving approach. Thus the threshold for designing and implementing complex process systems such as complex distillation configurations for practical use could be lowered. 
Series: 
Acta Universitatis Ouluensis. C, Technica 
ISSN:  03553213 
ISSNE:  17962226 
ISSNL:  03553213 
ISBN:  9789514293382 
ISBN Print:  9789514293375 
Issue:  377 
Subjects:  
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