Cyclic Linear Random Process As A Mathematical Model Of Cyclic Signals

In this study the cyclic linear random process is defined, that combines the properties of linear random process and cyclic random process. This expands the possibility describing cyclic signals and processes within the framework of linear random processes theory and generalizes their known mathematical model as a linear periodic random process. The conditions for the kernel are given and the probabilistic characteristics of generated process of linear random process in order to be a cyclic random process. The advantages of the cyclic linear random process are presented. It can be used as the mathematical model of the cyclic stochastic signals and processes in various fields of science and technology.

Segmentation and Statistical Processing of Geometric and Spatial Data on Self-Organized Surface Relief of Statically Deformed Aluminum Alloy

The methods of segmentation and statistical processing of the data on the relief formation on the self-organized surface of the statically deformed alloy D16chT are used. This allowed determining the signal parameters, segment structure and morphological peculiarities of self-organization as the data of the cyclic random process model. The mathematical methods are proposed, which allow increasing the accuracy, reliability and informative value of the profilometric data processing in diagnostic systems of control of the surface condition.