Dyes are organic compounds capable of transmitting their color to materials, which is why they are widely used, for example, in textile fibers, leather, paper, plastic, and the food industry. In the dying process, measuring the dye’s content is extremely important to evaluate the process efficiency and minimize the dye’s discharge in wastewater, but most of the time, dyes are present in multi-component mixtures; hence, quantification by spectrophotometric methods presents a great challenge because the signal obtained in the measurement overlaps the components in the mixture. In order to overcome this issue, the use of the high-performance liquid chromatography (HPLC) method is recommended; however, it has the disadvantage of being an expensive technique, complex, and requiring excessive sample preparation. In recent years, some direct spectrophotometric methods based on multivariate regression algorithms for the quantification of dyes in bicomponent mixtures have been reported. This study presents a new framework that uses a combined ANN and principal component analysis (PCA) model for the determination of the concentration of three dyes in aqueous mixtures: Tartrazine (TZ), Amaranth Red (AR), and Blue 1 CFC (B1) dyes. The PCA–ANN model was trained and validated with ternary mixture samples of TZ, AR, and B1, and with known different compositions, spectra absorbance samples were measured in a UV-Vis spectrophotometer at wavelengths between 350–700 nm with intervals of 1 nm. The PCA–ANN model showed a mean absolute prediction error and correlation coefficient (r²) of less than 1% and greater than 0.99, respectively. The results demonstrate that the PCA–ANN model is a quick and highly accurate alternative in the simultaneous determination of dyes in ternary aqueous mixtures.

Adsorption is a complex process since it is affected by multiple variables related to the physicochemical properties of the adsorbate, the adsorbent and the interface; therefore, to understand the adsorption process in batch systems, kinetics, isotherms empiric models are commonly used. On the other hand, artificial neural networks (ANNs) have proven to be useful in solving a wide variety of complex problems in science and engineering due to their combination of computational efficiency and precision in the results; for this reason, in recent years, ANNs have begun to be used for describing adsorption processes. In this work, we present an ANN model of the adsorption of fluoride ions in water with layered double hydroxides (LDHs) and its comparison with empirical kinetic adsorption models. LHD was synthesized and characterized using X-Ray diffraction, FT-Infrared spectroscopy, BET analyses and zero point of charge. Fluoride ion adsorption was evaluated under different experimental conditions, including contact time, initial pH and initial fluoride ion concentration. A total of 262 experiments were conducted, and the resulting data were used for training and testing the ANN model. The results indicate that the ANN can accurately forecast the adsorption conditions with a determination coefficient $R^2$ of 0.9918.