Resolution of overlapping signals in spectrometry using a wavelet packet transform and an Elman recurrent neural network

A novel method named a wavelet packet transform based Elman recurrent neural network (WPTERNN) was proposed for the simultaneous UV–visible spectrometric determination of Cu(II), Cd(II) and Zn(II). This method combined wavelet packet denoising with an Elman recurrent neural network. A wavelet packet transform was applied to perform data compression, to extract relevant information, and to eliminate noise and collinearity. An Elman recurrent network was applied for nonlinear multivariate calibration. In this case, using trials, the kind of wavelet function, the decomposition level, and the number of hidden nodes for the WPTERNN method were selected as Daubechies 14, 3, and 8, respectively. A program (PWPTERNN) was designed that could perform the simultaneous determination of Cu(II), Cd(II) and Zn(II). The relative standard errors of prediction (RSEP) obtained for all components using WPTERNN, a Elman recurrent neural network (ERNN), partial least squares (PLS), principal component regression (PCR), Fourier transform based PCR (FTPCR), and multivariate linear regression (MLR) were compared. Experimental results demonstrated that the WPTERRN method was successful even where there was severe overlap of spectra. The results obtained from an additional test case also demonstrated that the WPTERNN method performed very well. Figure The part of WP coefficients obtained by wavelet packet transforms