Controlled spectral parameter synthesis based on an adaptive informative subset

Abstract

The relevance of the study is due to the increasing complexity of inverse spectroscopy problems arising in materials science, optoelectronics and related fields, as well as the limitations of classical methods of spectral synthesis of parameters, which are based on the use of the full spectrum. This leads to high computational costs, reduced numerical stability and deterioration of the identifiability of parameters in the presence of noise. In this regard, it is relevant to develop methods that provide a controlled reduction in the dimensionality of spectral data without losing the physical correctness and accuracy of parameter synthesis. The aim of the work is to develop a method of controlled spectral synthesis of parameters, in which the inverse spectral problem is solved on an adaptively formed informative subset of the spectrum. To achieve the set goal, the following tasks were solved: the concept of spectral informativeness was formalized based on the sensitivity analysis of parameters; a mechanism for adaptive formation of an informative spectral subset was developed; A controlled computational cycle of parameter synthesis using a physically based model was constructed; criteria for stability and stopping the synthesis process were determined. The work applied methods of mathematical modeling of spectral characteristics, variational optimization methods, sensitivity analysis, regularization of inverse problems, and principles of controlled computational processes. In the developed method, spectral synthesis of parameters is considered not as a one-time optimization procedure, but as a closed controlled cycle with dynamic adaptation of the spectral region of analysis. The results obtained demonstrate that the use of an adaptive informative subset of the spectrum allows to significantly reduce the amount of spectral data while maintaining an admissibly small relative error in parameter estimation. It is shown that in the process of iterative controlled synthesis, weakly informative spectral sections are automatically excluded, for which the sensitivity of the model to parameter variations is low or degenerate, which directly leads to an improvement in the conditionality of the inverse problem. The reduction of spectral redundancy and the concentration of analysis on informative areas ensure the reduction of the influence of noise disturbances on the identification results and the stabilization of the functional minimization process. As a result of numerical testing, the existence of a compromise between the accuracy of parameter synthesis and the volume of spectral information used was confirmed, which within the framework of the developed method is implemented in a controlled, reproducible and without loss of physical interpretability of the results. The method was tested on experimental spectral data of a nanosecond discharge plasma, which confirmed its suitability for the identification of Zn, N2 and N II concentrations. The practical significance of the results obtained lies in the possibility of increasing the efficiency and stability of inverse spectroscopic calculations in applied information systems.