Sequential inversion technique and differential coefficient approach for accurate instantaneous emissions measurement

Abstract

The need for accurate emissions measurements has coerced researchers into trying to reconstruct the true transient emission signal from that measured by the analyser. This paper discusses two such methods and examines the validity of those methods by testing them with real-time emissions data. The first method is the sequential inversion technique, which tries to reconstruct the input second by second, based on the measured response at each second and the dispersion characteristics of the analyser. The reconstruction was found to be accurate, but there were some constraints associated with the dispersion characteristics and the reconstruction failed if there was signal noise. The second method, the differential coefficients method (DCM) of Ajtay and Weilenmann, reconstructs the input signal by approximating the analyser input as a linear combination of the output and the output derivatives. When tested with real-time data, the DCM predicted the emission signal even when there was noise imposed on the signal. While the DCM is clearly a better prediction technique, the accuracy of the DCM is reduced when noise is added to the analyser input. The DCM, when coupled with cross-correlation techniques, can be a powerful tool in retrieving ‘lost’ information associated with the measurement delays and dispersion characteristics of the analyser.

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