Modifying the method for forecasting hazardous processes with unknown dynamics in the presence of noise

Boris Pospelov,Kostiantyn Karpets,Svitlana Hryshko,Vladimir Andronov,Olekcii Krainiukov,Yuliia Bezuhla,Svyatoslav Manzhura,Olga Mukhina,Valentyna Ivanova,Kostiantyn Fisun

doi:10.15587/1729-4061.2022.252076

Abstract

This paper has substantiated a modified method that, within the framework of the adaptive zero-order Brown’s model, provides for increased accuracy in predicting processes with unknown dynamics masked by the noise of various levels. The forecasting method modification essentially involves an adaptive technique for determining the weight of the correction of the previous forecast, taking into consideration the recurrent state of the predicted process in time. To investigate the accuracy of the forecasting method, a test model of the process dynamics was determined in the form of a rectangular pulse with unit amplitude. In addition, a model of additive masking noise was defined in the form of a discrete Gaussian process with a zero mean and a variable value of the mean square deviation. Based on determining the exponentially smoothed values of current absolute forecasting errors, the dynamics of forecast accuracy were examined for the modified and self-adjusting methods. It was found that for the mean quadratic deviation of the masking noise equal to 0.9, the smoothed absolute prediction error for the modified method does not exceed 23 %; for the self-adjusting method – 42 %. This means that the prediction accuracy for the modified method is about twice as high. In the case of an average square deviation of masking noise of 0.1, the smoothed absolute prediction error for the modified and self-adjusting methods is approximately the same and does not exceed 10 %. That means that at a low level of masking noise, both prediction methods provide approximately the same accuracy. However, with an increase in the level of masking noise, the self-adjusting method significantly loses the accuracy of the forecast to the proposed modified method.

Highlights

Forecasting the state of complex objects in various fields [1] operating in unstable environments (UE) is the basis for solving the common problem of improving the efficiency of management of such objects [2]
Within the framework of the adaptive zero-order Brown’s model, a modified method for predicting hazardous processes with unknown and non-stationary dynamics masked by the noise of various levels, providing increased forecast accuracy, was substantiated
The essence of the proposed modification of the method is a technique for determining the weight of correction of the previous forecast based on the recurrent state for the measured data in real-time observation

Summary

Introduction

Forecasting the state of complex objects in various fields [1] operating in unstable environments (UE) is the basis for solving the common problem of improving the efficiency of management of such objects [2]. To describe the HP, a mathematical apparatus based on the application of systems of differential equations and the gener al theory of the state space is used [13] Existing models make it possible to describe the average dynamics of HP forecasting, characteristic of a limited number of objects and UE. Decisions on the operational management of non-stationary complex objects are often reactive in nature and are aimed at compensating for the already occurred emergency deviation of the dynamics of HP [14] Such an approach inevitably reduces the effectiveness of emergency management and requires a transition to proactive management, which provides a proactive response to a possible set of non-stationary conditions that arise in UE. The technology of HP STF with non-stationary and UD, MN, should be considered as an urgent issue

Literature review and problem statement

The aim and objectives of the study

The study materials and methods

A0i 1 Ai

Findings

Conclusions