Methodology for Determining the Parameters of a Mathematical Model of the Dynamics of the Psychophysiological State of a Metallurgical Equipment Operator

Abstract

Introduction. Mathematical modelling is effective in the analysis of industrial safety at metallurgical plants, in particular for tracking problems of the man — machine system. To introduce the time factor, recurrence relations (in a discrete model) and differential relations (in a continuous model) are used. However, it is also necessary to solve the problem of linking the model parameters to the real conditions of the production environment and to the human factor.The aim of this study is to create a method for determining the parameters of simulation mathematical models of the dynamics of the operator’s psychophysiological indicators affecting the work.Materials and Methods. The operator’s psychophysiological state (PPS) was assessed by performance, fatigue levels, and error rate. The data were collected by the Digital Correction Task (DCT) test. Based on the obtained results, the experimental values of the operator’s PPS indicators, which were reduced to the normalized scale [0, 1], were calculated. These indicators for a particular respondent, the mathematical model and the developed algorithm were used to determine the numerical values of the model parameters. In order to interpret the indicators of performance, fatigue and error rate, we introduced scales with five gradations.Results. The use of the authors’ modified version of the mathematical model showed a significant improvement in its prognostic properties. Out of 10 participants the best result was shown by respondent no. 7, the worst result was shown by respondent no. 8. During the first working hour (from 9.00 to 10.00) their performance increased almost equally, from 0.5–0.55 to almost 0.6. Then the score of respondent no. 7 increased and remained well above the “good” level until the end of the day. The score of respondent no. 8 dropped and was below average from 14.00 to 15.00. The difference was largely determined by the operators’ chronotypes. Their chronophysiological characteristics also affected fatigue and error rate. The model’s quality varied for different participants in the experiments. In one case it was excellent (mean relative error ≤5%), in three cases it was good (≤10%) and in four it was satisfactory (≤15%).Discussion and Conclusion. The proposed approach allows us to obtain the dynamic profiles of psychophysiological characteristics for every individual, to assess their interrelationships and to perform a prediction on the basis of a modified mathematical model. However, in order to extend the functionality of the models to the real working conditions of the metallurgical plant operator, it is necessary to increase the sample size, reduce the discrete time step and conduct studies for different working conditions, considering technological, climatic, environmental, psychological and other factors.