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.

Novel technique to reconstruct instantaneous heavy-duty emissions

“…The results with the DCM have been presented comprehensively elsewhere [8, 10]. Trials were made to improve the DCM by adding more derivatives, and by trying different numerical ways to compute the derivatives, improvements were possible [9].…”

Accounting for Exhaust Gas Transport Dynamics in Instantaneous Emission Models via Smooth Transition Regression

“…To compensate for emission signal distortions, Weilenmann et al , Ajtay and Weilenmann and Ajtay described the emission transport process in the exhaust and dilution systems via ordinary differential equations after dividing the dynamics into two parts: a perfect time delay, corresponding to a piston like transport of the exhaust gas and a dynamic part, corresponding to the mixing of gases by turbulence along their way in the exhaust and dilution systems. Recently, Geivanidis and Samaras and Madireddy and Clark investigated variants of the so-called differential coefficients method of Ajtay and Weilenmann aiming to improve its accuracy. Sensitivity analyses performed in refs , indicate that this method displays satisfactory performance in reconstructing original emission signals, even in the presence of moderate contamination (e.g., noise) in the original data.…”

Implications of Sampling Methods on Geospatial Mapping of Methane Sources

“…where t is the time step in the signal. Madireddy and Clark compared the results of using more than two differentials and determined that for vehicle emissions more than three differentials did not contribute significantly to a better solution [92]. DCM of multiple differentials is:…”

“…Madireddy and Clark's analysis of the DCM was performed by observing the differential effects and initial constants [92]. Madireddy and Clark did not implement a coefficient for the constant which reduced the effect of the initial output signal.…”