A new method based on artificial neural networks (ANN) for the processing of spectrophotometric data is proposed and illustrated on the example of the simultaneous quantification of ternary mixtures of zinc, cadmium, and mercury cations in aqueous solutions. Three types of commercially available metallochromic indicators were used as a simple model setup to create spectral data analogous to those normally received from an optical sensor array. In conventional ANN training methods for chemical sensors based on spectrophotometric data, a calibration is established by mathematically correlating the measured optical signal as network input with the concentration of the calibration sample as network output. In several situations, however, especially when dealing with mixed sample solutions, the relationship between a measured absorption spectrum and the corresponding ion concentrations is ambiguous, resulting in an "ill-posed problem". On the other hand, if the training direction is reversed by correlating known sample concentrations with measured optical signals, the relationship becomes reasonable for the ANN to obtain its structure. The proposed model illustrated in this paper is based on a more reasonable direct mapping and estimation by artificial neural network inversion (ANNI). In the training step, sample mixtures of known concentrations are optically measured to construct networks correlating the input data (ion concentrations) and the output data (absorption spectra). In the estimation step, the ion concentrations of unknown samples are estimated using the constructed ANN. The measured spectra of the unknown samples are fed to the output layer, and the appropriate input concentrations are determined by ANNI. When training the ANN system with 143 ternary mixtures of Zn2+, Cd2+, and Hg2+ in a concentration range from 1 to 100 μM, root-mean-square errors of prediction (RMSEP) of 0.45 (Zn2+), 0.96 (Cd2+), and 0.32 μM (Hg2+) were observed for the estimation of concentrations in 30 test samples, using the ANNI procedure. This newly proposed model, which involves the construction of an ANN based on direct mapping and estimation by ANNI, opens up one way to overcome the limitations of nonselective sensors, allowing the use of more easily accessible semiselective receptors to realize smart chemical sensing systems.
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