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Abstract
This paper reports a study into the errors of process forecasting under the conditions of uncertainty in the dynamics and observation noise using a self-adjusting Brown's zero-order model. The dynamics test models have been built for predicted processes and observation noises, which make it possible to investigate forecasting errors for the self-adjusting and adaptive models. The test process dynamics were determined in the form of a rectangular video pulse with a fixed unit amplitude, a radio pulse of the harmonic process with an amplitude attenuated exponentially, as well as a video pulse with amplitude increasing exponentially. As a model of observation noise, an additive discrete Gaussian process with zero mean and variable value of the mean square deviation was considered. It was established that for small values of the mean square deviation of observation noise, a self-adjusting model under the conditions of dynamics uncertainty produces a smaller error in the process forecast. For the test jump-like dynamics of the process, the variance of the forecast error was less than 1 %. At the same time, for the adaptive model, with an adaptation parameter from the classical and beyond-the-limit sets, the variance of the error was about 20 % and 5 %, respectively. With significant observation noises, the variance of the error in the forecast of the test process dynamics for the self-adjusting and adaptive models with a parameter from the classical set was in the range from 1 % to 20 %. However, for the adaptive model, with a parameter from the beyond-the-limit set, the variance of the prediction error was close to 100 % for all test models. It was established that with an increase in the mean square deviation of observation noise, there is greater masking of the predicted test process dynamics, leading to an increase in the variance of the forecast error when using a self-adjusting model. This is the price for predicting processes with uncertain dynamics and observation noises.
Highlights
Forecasting the processes in the socio-economic area is considered one of the most important tasks related to resolving the issues of ensuring the sustainable development of society
The need to address this task is exacerbated by the fact that most actual processes [1] that disrupt the sustainable development of mankind belong to this very type of process
Our results show that for small values of the observation noise standard deviation (SD) (0.005) under the conditions of uncertainty in the dynamics of processes in comparison with known adaptive models for the adaptation parameter from the classical and beyond-the-limit set, a more accurate forecast is produced by the self-adjusting model
Summary
Forecasting the processes in the socio-economic area is considered one of the most important tasks related to resolving the issues of ensuring the sustainable development of society. Due to the high uncertainty in the dynamics of the specified processes and the conditions for their observation, it is possible to resolve this issue based on self-adjusting models and forecasting methods. The most dangerous are those fires that occur on the premises (FaP) [6] This is because FaP is a massive phenomenon for all countries that cause significant damage to human life [7], objects [8], and the environment [9]. In this regard, studying the self-adjusting models for forecasting processes with uncertain dynamics and unknown observation noises becomes a relevant task
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