Downloaded from orbit.dtu.dk on: Oct 07, 2021 Optimal Experimental Design for Grey Box Models Davidescu, Florin Paul Publication date: 2008 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Davidescu, F. P. (2008). Optimal Experimental Design for Grey Box Models. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Optimal experimental design for grey-box models Ph.D. Thesis Florin Paul Davidescu CAPEC Department of Chemical Engineering Technical University of Denmark January 14, 2009 ii Copyright c Florin Paul Davidescu CAPEC Department of Chemical Engineering Technical University of Denmark, 2009 ISBN 87-91435-93-5 Printed by Book Partner, Nørhaven Digital, Copenhagen, Denmark Preface This thesis is submitted as partial fulfillment of the requirements for the Ph.D. degree at Technical University of Denmark. The work has been carried out at the Computer Aided Process Engineering Center research center (CAPEC), at Department of Chemical Engineering at Technical University of Denmark between January 1st 2005 and 31st of December 2007. The project has been funded by the European Union by the EUROBIOSYN project under the 6th Research Framework Program. I will take the opportunity to acknowledge the persons that directly or indi- rectly have contributed to the work presented in this thesis. First of all I would like to express my gratitude to the main supervisor, Professor Sten Bay Jørgensen from the Department of Chemical Engineering for the many discussions that we have had during this project. I would like to thank my co-supervisor, Professor Henrik Madsen from the Department of Informatics and Mathematical Modelling for his inputs all long the way. Secondly, I would like to express my gratitude to the European Union for funding this project through the EUROBIOSYN project under the 6th Re- search Framework Program. I would like to give thanks to all the colleagues from all the four research centers involved in this project and especially Mr. Michael Sch¨umperli for carrying out the necessary laboratory experiments. Thirdly, I would like to thank all the CAPEC co-workers and especially to Loic, Mauricio, Vipasha, Piotr, Jacob, Jan and Steen for creating a good social environment at the CAPEC and during the conferences. I'm sorry if I have not included all of you here. Fourthly, I would like to thank the Department of Chemical Engineering at the Technical University of Denmark for giving me the opportunity to do the study related to this PhD project. Furthermore I would like to acknowledge the computing services kindly offered by Danish High Performance Computing Center at the Department of Informatics and Mathematical Modelling. More- over, I would like to thank the workshop for their help and assistance even though their input did not enter directly into the work presented here but in my teaching assistance activities around the pilot plant of the department. Finally I would like to thank my parents and my brothers for their love and support during this project while being away from them and for trying to understand my work. København, Florin Paul Davidescu iv Preface Abstract In the recent years, chemical and biochemical process modelling has dominated the research and development. There are various targets of the developed mod- els such as steady-state and dynamic simulation in order to better investigate and understand the process, process design, process control, process optimiza- tion and even more recently fault monitoring and diagnosis. In this thesis the main reason to develop process models is to first better understand the behavior of the enzymatic reaction network and to possibly identify the bottle-necks and limitations. The secondary objective and equally important was and still is to optimize the operating conditions of the system of biotransformations (SBT) in order to maximize the yield. Moreover in order to move to the production on a larger scale the reactor design can become an important target. There is a need however for different tools that the end-user needs in order to advance faster in this very time consuming task of building dynamic process models. The contribution of this thesis is therefore twofold at least. The first way is toward the model development for the enzymatic reaction network in form of stochastic differential models. The second way is toward the necessary system- atic methodology and tools needed at various steps in this process. One important step is assessing the possibility of estimating the model param- eters from real life data once the a model has been formulated. In addressing this issues a systematic methodology has been set up. Given a model structure, a set of measured states and perturbed inputs this methodology provides the parameters which can be at least theoretically estimated. Another important step is represented by qualitative experimental design which aims at determining the optimal set of measured states and perturbed inputs. By optimal we mean either the case of minimum number of measured states and perturbed inputs rendering all model parameters estimable or at least as many parameters as possible. A related step is designing the experimental conditions, sometimes called quantitative experimental design, for the optimally selected set of measured states and perturbed inputs. Typically, the initial values of measured states, the optimal sampling points, the input profiles are searched for, within a dynamic optimization problem framework formulation. In terms of software, a computer program to determine the optimal quanti- tative experimental design for models described by stochastic differential equa- tions has been developed. The program called Continuous Time Stochastic Modelling (CTSM) Kristensen et al. (2004b) previously developed, has been vi Abstract further extended to be more flexible in handling experimental data obtained under different conditions and in estimating each of the the parameters either globally for all the experiments or locally for each experiment, allowing varying parameters. Resum´ep˚adansk I de seneste ˚arhar kemisk og biokemisk procesmodellering domineret forskn- ing og udvikling. Der er forskellige form˚almed de udviklede modeller s˚asom steady-state og dynamisk simulering af en given proces for bedre at kunne un- dersøge og forst˚aprocessen, procesdesign, procesregulering, procesoptimering samt overv˚agningog diagnose af procesfejl. I dette arbejde har det primære form˚almed udviklingen af procesmodeller været at øge forst˚aelsenaf det enzymatiske reaktionsnetværk og om muligt identificere flaskehalse og begrænsninger. Det sekundære form˚alaf lige s˚astor vigtighed har været og er stadig at optimere procesbetingelserne for systemet af biotransformationer (SBT) for at optimere udbyttet. Derudover, kan reak- tordesign blive en vigtig applikation af modellen ved opskalering af processen. Der er et behov for forskellige værktøjer, som kan hjælpe brugeren til hur- tigt at n˚afremskridt under den uhyre tidskrævende opgave det er at opbygge dynamiske procesmodeller. Bidraget i dette arbejde er derfor mindst tofoldigt. Dels i retning af model ud- vikling for det enzymatiske reaktionsnetværk i form af stokastiske differential- ligninger. Dels i retning af en nødvendig systematisk metodologi og værktøjer, der er behov for under de forskellige trin i processen. Et vigtigt trin er at vurdere muligheden af at estimere model parametre fra virkelige forsøg n˚aren model er blevet formuleret. For at h˚andteredette er en systematisk metodologi blevet sat op. Givet en modelstruktur, et sæt af m˚alte tilstande og pertuberede inputs giver denne metodologi de parametre, som i det mindste teoretisk kan blive estimeret. Et andet vigtigt trin og intet andet end et udvidet identificerbarhedsprob- lem er repræsenteret ved kvalitative eksperimentelle designs, som søger at bestemme det optimale sæt af m˚altetilstande og pertuberede inputs. Med op- timale menes enten det tilfælde hvor alle eller s˚amange parametre som muligt kan blive estimeret ud fra det mindste mulige antal m˚altetilstande og pertu- berede inputs. Et beslægtet trin omhandler design af de eksperimentelle betingelser, ofte benævnt kvantitativt eksperimentelt design, for det valgte sæt af m˚altetil- stande og pertuberede inputs. Typisk søges der efter begyndelsesværdierne af de m˚altetilstande, de optimale tidspunkter for prøveudtagning samt inputpro- filerne indenfor en dynamisk optimeringsproblem framework formulation. Vedrørende software er et computer program til bestemmelse af det opti- male kvantitative eksperimentelle design for modeller beskrevet ved stokastiske differentialligninger blevet udviklet. Dette tidligere udviklede (Kristensen et al. 2004b) program, Continuous Time Stocastic Modelling (CTSM) er blevet viii Resum´ep˚adansk videre