René Schenkendorf

Publications

• Parameter identification of time-delay systems: A flatness based approach

  R. Schenkendorf, U. Reichl, M. Mangold

  Mathmod 2012 - 7th Vienna International Conference on Mathematical Modelling; 02/2012

• Qualitative and Quantitative Optimal Experimental Design for Parameter Identification of a MAP Kinase Model

  R. Schenkendorf, M. Mangold

  18th IFAC World Congress; 09/2011
• 0.59

  Impact points

  Influence of non-linearity to the optimal experimental design demonstrated by a biological system

  R. Schenkendorf, A. Kremling, M. Mangold

  Mathematical and Computer Modelling of Dynamical Systems. 01/2011;

• Challenges of Parameter Identification for Nonlinear Biological and Chemical Systems

  R. Schenkendorf, M. Mangold

  SIAM Conference on Optimization; 01/2011

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• 2.38

  Impact points

  Optimal experimental design with the sigma point method.

  R Schenkendorf, A Kremling, M Mangold

  IET systems biology. 02/2009; 3(1):10.

  Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their v... [more] Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their variances. To obtain highly predictive models, very precise parameters are needed. The optimal experimental design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher information matrix. The application of this traditional method has at least two shortcomings for models that are nonlinear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, the authors show that by applying the sigma point (SP) method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the SP method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The SP method is demonstrated for the example of a widely used biological model.

• Optimal Experimental Design and Model Selection by a Sigma Point Approach

  Schenkendor, René, Kremling, Andreas, Michael, Mangold

  Mathmod 2009 - 6th Vienna International Conference on Mathematical Modelling, VIenna, Austria; 01/2009

  The identification of a model structure, i.e., the relationship of model components, and the usually unknown model parameters are essential to get meaningful deterministic models. Due to imperfect and limited measurement data to fulfil both requirements can be a challenging task. Therefore, the Opti... [more] The identification of a model structure, i.e., the relationship of model components, and the usually unknown model parameters are essential to get meaningful deterministic models. Due to imperfect and limited measurement data to fulfil both requirements can be a challenging task. Therefore, the Optimal Experimental Design (OED) was introduced to detect some optimal stimuli of the regarded system, that increase the information content of measurements. For models which are linear with respect to their parameters, the OED is well known to reduce the influence of measurement noise to the parameter estimation process and to find conditions that make the difference of competing model hypothesis more obvious. Unfortunately, in practise the most used models are non-linear with respect to their parameters. The established methods for the linear case, e.g. the Fisher Information matrix (FIM), can lead to a crude approximation of the non-linearity that results at best in a sub-optimal choice of the system stimuli. The usage of sample based approaches, e.g. Monte Carlo methods, seems to be more suitable to consider non-linear effects, but their inherent computational effort prohibits the application in the framework of Optimal Experimental Design. In this work, the Sigma Point method is used instead, because its advantages are at least threefold for OED: 1) a more reliable approximation of parameter uncertainties can be achieved, 2) a definition of a novel design criterion for OED becomes possible, and 3) it provides an efficient and elegant way to take the imperfection of parameter estimation in the field of model selection into account. All three aspects are demonstrated for the example of a biological substrate uptake model.
• 2.14

  Impact points

  Two State Estimation for the Barium Sulfat Precipitation in a Semi-Batch Reactor

  M. Mangold, A. Bück, R. Schenkendorf, C. Steyer, A. Voigt, K. Sundmacher

  Chemical Engineering Science. 01/2009; 64:646-660.

• A Sigma Point Method for Optimal Experimental Design

  R. Schenkendorf, A. Kremling, M. Mangold

  The 20th International Symposium on Chemical Reactor Engineering (ISCRE 20); 01/2008