Improving Convergence of Derivative-Based Parameter Estimation with Multistart Parameter Clustering Based on DAE Decomposition

Atya Elsheikh
Research Center Jülich, Institute of Biotechnology, Germany

Katharina Nöh
Research Center Jülich, Institute of Biotechnology, Germany

Eric von Lieres
Research Center Jülich, Institute of Biotechnology, Germany

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp09430039

Ingår i: Proceedings of the 7th International Modelica Conference; Como; Italy; 20-22 September 2009

Linköping Electronic Conference Proceedings 43:6, s. 47-55

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Publicerad: 2009-12-29

ISBN: 978-91-7393-513-5

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


Derivative-based optimization methods for parameter estimation require good start values in order to converge to the global optimum. A conventional multistart strategy is often not practical for identifying such start values; especially for high dimensional problems. Moreover; the computational efforts for each iteration of the optimizer are significantly increased by the computation of parameter sensitivities. We hence present a multistart recursive clustering strategy that utilizes DAE decomposition algorithms; in particular Tarjan’s and tearing algorithms. These algorithms are also used by standard Modelica compilers for improving the performance of solving large DAE systems. Our key concept is to provide a natural decomposition of the parameter estimation problem into smaller clusters (i.e. subproblems); each of which requires fewer start values and less computation. The resulting local minima are taken as start values for enlarged subproblems; and so forth until good start values for the original problem are found. This approach serves to improve global convergence and computational speed of multistart derivative-based optimization strategies for large sparse DAE systems.


Parameter estimation; global optimization; cluster methods; DAE decomposition algorithms


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