Rapid resolving algorithm of gas chromatographic overlapping peaks based on the asymptotic expansion of integration

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A novel algorithm, called asymptotic expansion of integration, is suggested to resolve gas chromatographic overlapping peaks. There are three steps for the algorithm. First, a valley peak or a shoulder peak is separated into two domains, and an integral equation on a subdivision and an algebraic equation on the overlapping peak domain are listed. Secondly, areas needed in two equations, are computed by a numerical integral method, then the integral equation is expended to an algebraic equation by the asymptotic formula of integration. At last, combing two equations with constraint equations of peak heights, we got a nonlinear algebraic set. The equation set can be solved rapidly by Gauss-Seidel iteration, and the maximum number of iterations is not more than 20 times. The simulation and experimental results showed that height and area errors of resolving peaks are quite small, the maximum error of area is less than 6.44%, and that of the height is about 6.80%. Because of the high accuracy and computational efficiency, the algorithm can be used in decomposition of gas chromatographic overlapping peaks and online real-time processing of general chromatographic overlapping peaks.