In this paper an original method based on the link between a piecewise identifiability analysis and a piecewise numerical estimation is presented for estimating parameters of a phenomenological diesel engine combustion model. This model is used for design, validation and pre-tuning of engine control laws. A cascade algebro-differential elimination method is used for studying identifiability. This investigation is done by using input-output-parameter relationship. Then these relations are transformed by using iterated integration. They are combined with an original numerical derivative estimation based on distribution theory which gives explicit point-wise derivative estimation formulas for each given order. Then new approximate relations, linking block of parameters and outputs (without derivative) are obtained. These relations are linear relatively to the blocks of parameters and yield a first estimation of parameters which is used as initial guess for a local optimization method (least square method and a local search genetic algorithm).
Denis-Vidal, L. and Joly-Blanchard, G. (2004) Equivalence and Identifiability Analysis of Uncontrolled Nonlinear Dynamical Systems. Automatica, 40, 287-292. http://dx.doi.org/10.1016/j.automatica.2003.09.013
Verdière, N., Denis-Vidal, L. and Joly-Blanchard, G. (2012) A New Method for Estimating Derivatives Based on a Distribution Approach. Numerical Algorithms, 61, 163-186. http://dx.doi.org/10.1007/s11075-012-9535-4
Fliess, M., Mboup, M., Mounier, H. and Sira-Ramirez, H. (2005) Questioning Some Paradigms of Signal Processing via Concrete Examples. Proc. Summer School: Fast Estimation Method in Automatic Control and Signal Processing, Paris.