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Parameter Identifiability and Parameter Estimation of a Diesel Engine Combustion Model

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http://www.scirp.org/journal/PaperInformation.aspx?PaperID=45287#.VL30BCzQrzE

ABSTRACT
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).
 
Cite this paper
Denis-Vidal, L. , Cherfi, Z. , Talon, V. and Brahmi, E. (2014) Parameter Identifiability and Parameter Estimation of a Diesel Engine Combustion Model. Journal of Applied Mathematics and Physics, 2, 131-137. doi: 10.4236/jamp.2014.25017.
 
References
[1]Talon, V. (2004) Modélisation 0-1D des moteurs à allumage commandé. Ph.D Thesis, Orléan University, Orléan.
 
[2]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
 
[3]Vajda, S., Godfrey, K.R. and Rabitz, H. (1987) Similarity Transformation Approach to Identifiability Analysis of Non-linear Compartmental-Models. Mathematical Biosciences, 93, 217-248. http://dx.doi.org/10.1016/0025-5564(89)90024-2
 
[4]Pohjanpalo, H. (1978) System Identifiability Based on the Power Series Expansion of the Solution. Mathematical Biosciences, 41, 21-33.
 
[5]Ollivier, M. (1990) Le problème de l'identifiabilité structurelle globale: Approche théorique, méthodes effectives et bornes de complexité. Ph.D Thesis, Ecole Polytechnique, Paris.
 
[6]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
 
[7]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.
 
[8]Deb, K. and Agrawal, R.W. (1995) Simulated Binary Crossover for Continuous Search Space. Complex Systems, 9, 115-148                                                                                                              eww150120lx
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