Neural Network Method for Forecasting Time Series Discretized with Violation of the Kotelnikov-Shannon Theorem Requirements

The problem of restoring a continuous signal from a limited set of discrete values is in demand in automated digital production of Industry 4.0, controlled by artificial intelligence systems. When fulfilling the requirements of the Kotelnikov-Shannon theorem a continuous signal from discrete signal values is possible to be accurately reconstructed, however, in practice, situations, where there is a gap in discrete signal values or the discretization interval is random, often arise. The presented research results apply an engineering approach to the problem of reconstructing a continuous signal from its discrete signal values, which is not based on complex mathematical apparatus. The novelty of the research results lies in the proposed method of forecasting and restoring a continuous signal from a limited set of discrete values (time series) taken at random time moments, the mathematical expectation of which exceeds the value of the discretization interval specified by the Kotelnikov-Shannon theorem. The method is based on the use of an artificial neural network to obtain discrete signal values with a higher frequency than in the original set of discrete signal values of the time series. For this purpose, a stack of training data is formed for the neural network, including discrete signal values, interval discretization values, and the first and second differences of the time series values. The conducted model experiments with the program implementing the proposed method demonstrated its efficiency and high accuracy of the time series values obtained with its help with a regular discretization frequency satisfying the Kotelnikov-Shannon theorem.