Prediction error analysis for intelligent management and predictive diagnostics systems

Abstract

Random signal prediction is efficient for intelligent management and predictive diagnostics systems. Aim. The paper aims to analyse the error of random signal prediction. To develop recommendations for the selection of random signal extrapolator parameters. Methods. The paper uses the mathematics of the theory of random functions, formalization adopted in the theory of pulse systems, mathematical description of extrapolators with Chebyshev polynomials orthogonal over a set of equally spaced points. The coefficients of the predicting polynomial are selected according to the minimal least squares. Results. The paper describes the mathematical model of the extrapolator. Design ratios were obtained for prediction error assessments. The maximum and prediction interval-averaged relative mean square error of extrapolation were defined. The authors analyse the error of extrapolation of random processes defined by the sum of a centred stationary random process and a deterministic time function. Based on diverse calculations, recommendations were defined that allow selecting the parameters of the extrapolator (degree of the extrapolating polynomial, number of test points that precede the prediction interval, discretisation interval of the predicting function) under the specified input signal models. Conclusion. The use of extrapolators based on Chebyshev polynomials orthogonal on a set of equally spaced points and the least square method allows implementing a procedure for calculating predicted values of a random process with the required accuracy. Under the specified models of the predicting signal, a method was developed that allows selecting the extrapolator’s parameters (order, number of points involved in the generation of the prediction, sample spacing) for the purpose of ensuring the required accuracy.