MATHEMATICAL MODEL FOR DECISION MAKING SYSTEM BASED ON THREE-SEGMENTED LINEAR REGRESSION
DOI:
https://doi.org/10.15588/1607-3274-2022-3-4Keywords:
flight safety system, approximation, least squares method, three-segmented linear regression with jumps, abscissa optimization of the jump point, linearity test sample, fractal dimension, quality metric, cluster, sample formation.Abstract
Context. The problem of approximation of empirical data in the decision-making system in safety management.. The object of the study was to verify the adequate coefficients of the mathematical model for data approximation using information technology.
Objective. The goal of the work is the creation adequate math-ematical model using information technology on the bases analyze different approaches for approximating empirical data an that can be used to predict the current state of the operator in the flight safety system..
Method. A comparative analysis of the description of the transformation of information indicators with a non-standard structure. The following models of transformation of information indicators with similar visual representation are selected for comparison: parabolas of the second and third order, single regression and regression with jumps. It is proposed to use new approaches for approximation, based on the use of the criterion proposed by Kuzmin and the Heaviside function. The adequacy of the approximation was checked using these criteria, which allowed to choose an adequate mathematical model to describe the transformation of information indicators. The stages of obtaining a mathematical model were as follows: determining the minimum sum of squares of deviations for all information indicators simultaneously; use of the Heaviside function; optimization of the abscissa axis in certain areas; use of the linearity test. The obtained mathematical model adequately describes the process of transformation of information indicators, which will allow the process of forecasting changes in medical and biological indicators of operators in the performance of professional duties in aviation, as one of the methods of determining the human factor in a proactive approach in flight safety.
Results. The results of the study can be used during the construction of mathematical models to describe empirical data of this kind.
Conclusions. Experimental studies have suggested recommending the use of three-segment linear regression with jumps as an adequate mathematical model that can be used to formalize the description of empirical data with non-standard structure and can be used in practice to build models for predicting operator dysfunction as one of the causes of adverse events in aviation.
Prospects for further research may be the creation of a multiparameter mathematical model that will predict the violation of the functional state of the operator by informative parameters, as well as experimental study of proposed mathematical approaches for a wide range of practical problems of different nature and dimension.
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Copyright (c) 2022 V. M. Kuzmin, R. V. Khrashchevskyi, M. S. Kulik, O. B. Ivanets, M. Yu. Zaliskyi, Yu. V. Petrova
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