Attempts to enhance the differential coefficients method for reconstruction of transient emissions from heavy-duty vehicles

Abstract

Engine tailpipe emissions as measured by a sampling system and analyser do not clearly reflect the actual transient emissions from the engine at the tailpipe of the vehicle exhaust. With increasing demand for accurate emissions measurements, several research efforts are being made to compensate for the measurement distortions of the analyser system. The differential coefficients method is one such approach which reconstructs the input signal by approximating the analyser input as a linear combination of the output and the first two derivatives of the output. While the results with this approach were found to be acceptable, this paper focuses on the possibilities of improving the accuracy of the reconstruction by altering the ways in which the numerical derivatives are computed and by considering higher order derivatives in the linear combination. It was found that the use of backward differences in computing the numerical derivatives proved more effective than forward differences. Using higher order derivatives has shown improvement of about 10 per cent over using just the first two derivatives, but this margin may be important for model accuracy or for assessing pass/fail emissions criteria.

Keywords

differential coefficients method time delay time alignment cross-correlation instantaneous input dispersion reconstructed input dispersed output central/ forward/ backward differences

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