S. A. Burikov, S. A. Dolenko, T. A. Dolenko, I. G. Persiantsev

The paper contains comparative analysis of approaches connected with use of neural network algorithms for efficient solution of image recognition problem (inverse problem with discrete output) jointly with solution of inverse problem (IP) with continuous output. The analysis is performed at the example of the problem of identification and determination of concentrations of inorganic salts in multi-component water solutions by Raman scattering spectra. The first approach studied is connected with solution of both problems (classification and determination of concentrations) with the help of a single neural network (in a single stage), on experimental data and on quasi-model data obtained on the base of experimental data. The second approach studied provides solution of the classification problem with subsequent solution of the problem of determination of concentrations for each class separately. In this study, unique experimental material, having no analogues in the world, has been obtained. This is an array of Raman spectra (in the frequency range from 200 cm-1 to 4000 cm-1) of water solutions of inorganic salts (NaCl, NH4Br, Li2SO4, KNO3, CsI) in the range of total concentrations from 0 to 2.5 M (mole per liter of solution). The array consists of 8695 spectra for 4268 different solutions. The complex IP of identification of salts and of determination of their partial concentrations in 5-component water solution has been solved in one stage (Method 1), within the framework of the 'experiment-base» approach based on both bands of Raman spectrum (low-frequency and valence ones) and based on water Raman band only, and also within the framework of «quasi-model» approach based on both spectral bands. When the spectra used as input data were experimental Raman spectra, including, besides the water Raman valence band (2700-3900 cm-1), also the low-frequency part of the Raman spectrum of water and of the molecules of dissolved salts (280-1830 cm-1), sufficiently low values of the error of determination of concentrations on the experimental data set have been obtained: mean absolute error was from 0.019 to 0.029 M in the concentration range from 0 to 2.5 M. These results significantly outperform those obtained with the same experimental data by water Raman valence band only, and they are several fold better than the results obtained before for three-component solutions in narrower concentra-tion range. Quasi-models calculated by experimental spectra, based on perceptrons, GRNN, and GMDH, have been built. It has been obtained that the best approximation of the sought dependence was provided by the perceptron-based quasi-model. However, the quasi-model approach was a disappointment compared to the experiment-based approach. In all cases, the results obtained on the experimental examination data set within the framework of the quasi-model approach, were worse or significantly worse than the initial results obtained within the experiment-based approach. This is an evidence of the necessity to elaborate more complex quasi-models adequate to the complexity of the direct problem solved by them. The results obtained by Method 2 (solution of classification problem separately of the solution of the concentrations determination problem), were somewhat different from what was expected. The quality of solution of the classification problem even by a relatively simple method, was very high, while solving the problem of determination of salts concentrations separately in each combination class did not bring any improvement compared to Method 1. Thus, a bottleneck for Method 2 was not the solution of the classification problem, as it was expected initially, but the solution of the problem of determination of salts concentrations at unfavorable ratio of the number of samples in each separate class and the number of input features. Therefore, further work on perfec-tion of Method 2 should be focused on improvement of the results of the second stage. The main direction of further work should be data pre-processing aimed for reduction of the input dimension of the problem.