Identifying static and dynamic prediction models for NOx emissions with evolving fuzzy systems

Abstract

ElsevierLughofer, E.; Macian Martinez, V.; Guardiola García, C.; Klement, EP. (2011) AbstractAntipollution legislation in automotive internal combustion engines requires active control of pollutant formation and emissions. In addition to new technologies, like selective catalyst systems or diesel particulate filters, predictive emission models are needed. These models are of great use in the system calibration phase, and also can be integrated for the engine control and on-board diagnosis tasks. In this paper, fuzzy modelling of the NOx emissions of a diesel engine is investigated, which overcomes some drawbacks of pure engine mapping or analytical physical-oriented models. For building up the fuzzy NOx prediction models, the FLEXFIS approach (short for FLEXible Fuzzy Inference Systems) is applied, which automatically extracts an appropriate number of rules and fuzzy sets by an evolving version of vector quantization (eVQ) and estimates the consequent parameters of Takagi-Sugeno fuzzy systems with the local learning approach in order to optimize the least squares functional. The predictive power of the fuzzy NOx prediction models is compared with that one achieved by physical-oriented models based on high-dimensional engine data recorded during steady-state and dynamic engine states.

ECU-oriented models for NOx prediction. Part 1: a mean value engine model for NOx prediction

“…Black box models rely on system identification [24] and their quality is linked to the quality of the data used for training the model: the Design of Experiments (DoE) is not an easy task. Some examples are: Hirsch et al [25] who present a gray box model for NO x and PM, Takagi-Sugeno fuzzy models [26,27], Hammerstein-Wiener (HW) [28], or Neural Networks (NN) [29,30,31,32].…”

“…intake volume is small and mixing is so fast that no heat is transferred to the walls. Therefore and assuming that the specific heat capacities are equal for all gases, m int T int =ṁ a T boost +ṁ egr T egr (27) and from (26), the productṁ int T int , which defines the intake enthalpy flow, can be inferred aṡ and rewriting the mass equilibrium at the intake junctioṅ…”

A computationally efficient Kalman filter based estimator for updating look-up tables applied to NOx estimation in diesel engines

“…Here, different possibilities can be found. For example, heuristic approaches can derive maps from complex models (Schilling, Amstutz, Onder, & Guzzella, 2006) or engine data (Lughofer et al, 2011), building a model that is easy to integrate into the engine ECU, but lacking of extrapolation capabilities. This needs some filtering for catching dynamics and if implemented online, drift can be corrected with observers (Payri et al, 2012) or feedback control.…”

“…NEDC is also used as application. For more details about experimental setup see Lughofer et al (2011). SOI steps are used for NO x sensor characterization; the interested reader can go to Galindo et al (2011) …”

“…Schilling, Amstutz, and Guzzella (2008) that develops a real time NO x model using maps, Winkler-Ebner, Hirsch, Del Re, Klinger, and Mistelberger (2010) that designs a virtual NO x sensor for selective catalyst reduction (SCR) control and diagnosis or other examples. Problem is highly non-linear and some examples for coping with this are Takagi-Sugeno fuzzy models (Lughofer, Macian, Guardiola, & Klement, 2011;Takagi & Sugeno, 1985), Hammerstein-Wiener (Falck et al, in press), or neural networks (Yen & Michel, 1991). Nevertheless, in commercial engine ECUs the prevailing approach is to use look-up tables to model nonlinear and operating point dependent behaviors because of the simple programming although it attaches a big calibration effort.…”