Soma Tayamon

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

This paper deals with the identification of the nitrogen oxide emissions (NOx) 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 NOx inlet concentration, injected urea, inlet temperature and exhaust flow are used as inputs to a detailed simulator. NOx 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 NOx emission with a fit of 68.93% and 38.92% for the identification and validation data, respectively.

Nonlinear black box identification of a selective catalytic reduction system

Abstract This paper discusses the identification of linear and non-linear black-box models for describing a diesel engine selective catalytic reduction (SCR) system. SCR aftertreatment systems form an important technology for reducing the NO x produced by diesel engines, and therefore good models are essential for the control of these systems. This paper compares a linear and a non-linear model for identification of the system. The output signals of the SCR were generated from 4 measured input signals, using a simulated 18 state model. The experiments with a recursive prediction error method, RPEM, with only 2 states show that the system can be accurately approximated with a much simpler model. The RPEM estimates 16 unknown parameters while the linear model uses 9 parameters. The results were compared based on the model fit and it was clear from the validation data set that the non-linear model gives better results and captures more of the system dynamics as compared to the linear model. A comparison of the RPEM using the midpoint integration method and the Euler method for discretisation was also made for the models. The results clearly show that the more accurate discretisation algorithm results in a better model fit.

Convergence analysis and experiments using an RPEM based on nonlinear ODEs and midpoint integration

A convergence analysis is performed for a recursive prediction error algorithm based on nonlinear ODEs and the midpoint integration algorithm. Several conditions are formulated such that the stability of an associated differential equation can be tied to the local and global convergence properties of the algorithm. This is used to show that the algorithm converges to a minimum point of the criterion function, which may or may not be unique. A consequence is that convergence to the true parameters is possible. As compared to previous work, complete system assumptions are integrated in the analysis, thereby generalising previous results. The theoretical analysis of this paper is complemented with numerical examples and with live data experiments.

Convergence analysis of a recursive prediction error method.

Abstract A convergence analysis is performed for a recursive prediction error algorithm discretised using the midpoint integration method. Several conditions are formulated such that the stability of an associated differential equation can be tied to the local and global convergence properties of the algorithm. This shows that convergence to the true parameters is possible. The theoretical analysis of this paper is complemented by numerical example.

Recursive prediction error identification and scaling of non-linear systems with midpoint numerical integration

A new recursive prediction error algorithm (RPEM) based on a non-linear ordinary differential equation (ODE) model of black-box state space form is presented. The selected model is discretised by a midpoint integration algorithm and compared to an Euler forward algorithm. When the algorithm is applied, scaling of the sampling time is used to improve performance further. This affects the state vector, the parameter vector and the Hessian. This impact is analysed and described in three Theorems. Numerical examples are provided to verify the theoretical results obtained.

Modelling of Selective Catalytic Reduction Systems Using Discrete-Time Linear Parameter Varying Models

In this work, a Linear Parameter Varying (LPV) model of the Selective Catalytic Reduction (SCR) system, used for NOx reduction placed as after-treatment systems in diesel engines is developed. The LPV model structure is formed utilising the physical properties of the system yielding only 7 unknown parameters for a third order model structure of the SCR, which is a significant reduction in number of parameters in comparison with other nonlinear models used in this paper. The states of the model however, do not possess any physical interpretation. The LPV model structure is validated using real measured data from cell tests at Scania AB with promising results. The proposed model is compared to previous global nonlinear models of the system, i.e. a nonlinear state space model and a Hammerstein-Wiener model of the system.