Abstract
The article presents the definition of linear random processes of many of their stochastic characteristics such as moments, correlation functions, characteristic functions. Linear AR and ARMA processes are also considered. Kernels and characteristic functions of the random processes are represented for the processes. Not only stationary linear random processes are considered. Linear random processes with periodic structures are also discussed. The properties of kernels and the characteristic functions of such processes are shown. Cases of both non-stationary random processes with continuous time and random processes with discrete time are considered. Random processes with discrete time and periodic structures are linear AR and ARMA processes with periodic kernels and periodic generating processes. The properties of the kernels of linear AR and ARMA which are important for the practical use of such models are also presented. Method of forecasting the time of failure using statistical spline-function is considered. The estimation of random signals stationarity with practical examples of the estimation stationarity of vibration signals of rolling bearings is also discussed. A procedure of decision-making rule development for the vibration signals is represented.
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Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M. (2020). Methods and Models for Information Data Analysis. In: Diagnostic Systems For Energy Equipments. Studies in Systems, Decision and Control, vol 281. Springer, Cham. https://doi.org/10.1007/978-3-030-44443-3_2
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