Collecting and analyzing high frequency emission measurements has become very usual during the last decade as significantly more information with respect to formation conditions can be collected than from regulated bag measurements. A puzzling issue for researchers is the time-alignment betweentailpipe measurements and engine operating variables. An alignment procedure should take into account both the reaction time of the analyzers and the dynamics of gas transport in the exhaust and measurement systems. Although some alignment methods have been proposed, they appear to be rather tedious and expensive in their implementation. Thus, in practice the majority of studies that collect and analyze high frequency emission measurements, adopt a constant time delay and shift tailpipe data backwards using a time-lag that optimizes some criterion (e.g. maximizes cross-correlation). This paper displays a statistical modeling framework that compensates for variable exhaust transport delay while relating tailpipe measurements with engine operating covariates. Specifically it is shown that some variants of the Smooth Transition Regression model allow for transport delays that vary smoothly as functions of the exhaust flow rate. These functions are characterized by a pair of coefficients that can be estimated via a least-squares procedure. The proposed models can be adapted to encompass inherent nonlinearities that were implicit in previous instantaneous emissions modeling efforts. This article describes the methodology and presents an illustrative application which uses data collected from a diesel bus under real-world driving conditions.
Abstract