Identification of a discrete-time nonlinear Hammerstein-Wiener model for a selective catalytic reduction system

Abstract

This paper deals with the identification of the nitrogen oxide emissions (NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ) from vehicles using the selective catalyst as an after treatment system for its reduction. The process is nonlinear, since the chemical reactions involved are highly depending on the operating point. The operating point is defined by the driving profile of the vehicle, which includes for example, cold and hot engine starts, highway, and urban driving. The experimental data used in this paper are based on a standard transient test developed for Euro VI testing. Real measurements of NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> inlet concentration, injected urea, inlet temperature and exhaust flow are used as inputs to a detailed simulator. NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> output concentration from the simulator is used as output, so there is no interference from the ammonia concentration in the NOχ output concentration due to cross-sensitivity. Experimental data are properly divided into identification and validation data sets. A Hammerstein-Wiener model is identified and it represents the dynamics very well. The best fits achieved with this model are 78.64% and 68.05% for the identification and validation data, respectively. Nonlinear static functions are selected from the knowledge and analysis of a selective catalytic reduction first principles based model. Identified linear models are able to represent the NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> emission with a fit of 68.93% and 38.92% for the identification and validation data, respectively.