基于分数阶微分的重叠伏安峰分离方法

Separation Method for Overlapping Voltammetric Peaks Based on the Fractional-order Differential

根据特定峰信号微分的极值和过零点随着微分阶数的变化而改变,建立了峰信号的极值和过零点与其相应微分阶数的关系式。利用这些关系式建立的估计器Ⅰ和估计器Ⅱ,可以用来估计Gaussian峰、Lorentzian峰和Tsallis峰信号的特征参数,为定量分析重叠峰信号提供了一种新的方法。首先,利用分数阶微分器获得特定峰信号的分数阶阶微分;然后,利用估计器Ⅰ和估计器Ⅱ提取这些特征峰信号的特征参数。对于未知重叠峰信号,采用Tsallis峰作为子峰模型进行重叠峰信号分离,仿真和实测重叠峰信号分离实验表明本方法简单高效。

Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders. Also, equations between the differential order and the zero-crossing of the fractional-order differential of the specified peak signals are proposed acording to the variation of the zero-crossing of the specified peak signals at different orders. Characteristic paramters of Gaussian peak, Lorentzian peak and Tsallis peak can be estimated using Estimator Ⅰ and Estimator Ⅱ which are obtained by the equations above. So that a new method is presented to separate the overlapped peak signal. Firstly, a fractional-order differential of the specified peak signals were obtained with the fractional-order differentiation filter. Then, characteristic paramters of the specified peak signals could be extracted using Estimator Ⅰ and Estimator Ⅱ . Finally, Tsallis peak was used as a model to assign the overlapping peak signals correctly. Experimental results show that the proposed method is efficient and effactive for the simulated overlapping peaks and detected overlapping voltammetric peak signals.