Regression-Based Oxides of Nitrogen Predictors for Three Diesel Engine Technologies

Abstract

Models of diesel engine emissions such as oxides of nitrogen (NO x ) are valuable when they can predict instantaneous values because they can be incorporated into whole vehicle models, support inventory predictions, and assist in developing superior engine and aftertreatment control strategies. Recent model-year diesel engines using multiple injection strategies, exhaust gas recirculation, and variable geometry turbocharging may have more transient sensitivity and demand more sophisticated modeling than for legacy engines. Emissions data from 1992, 1999, and 2004 model-year U.S. truck engines were modeled separately using a linear approach (with transient terms) and multivariate adaptive regression splines (MARS), an adaptive piece-wise regression approach that has limited prior use for emissions prediction. Six input variables based on torque, speed, power, and their derivatives were used for MARS. Emissions time delay was considered for both models. Manifold air temperature (MAT) and manifold air pressure (MAP) were further used in NO x modeling to build a plug-in model. The predictive performance for instantaneous NO x on part of the certification transient test procedure (Federal Test Procedure [FTP]) of the 2004 engine MARS was lower (R 2 ϭ 0.949) than the performance for the 1992 (R 2 ϭ 0.981) and 1999 (R 2 ϭ 0.988) engines. Linear regression performed similarly for the 1992 and 1999 engines but performed poorly (R 2 ϭ 0.896) for the 2004 engine. The MARS performance varied substantially when data from different cycles were used. Overall, the MAP and MAT plug-in model trained by MARS was the best, but the performance differences between LR and MARS were not substantial.

Modeling Heavy/Medium-Duty Fuel Consumption Based on Drive Cycle Properties

“…It has the ability to model complex and highdimensional data dependencies and has been used for diverse applications in predicting and data mining in recent years [24][25]. Additional information on the use of MARS is to predict engine emissions illustrated by Chen [26].…”