The identification of many phenomena, processes and objects is based on the study of stochastic noise signals created by these phenomena and processes, or during the functioning or testing of objects. The monograph investigates the issue of object-oriented identification of stochastic noise signals, that is, the process of establishing the correspondence of recognized processes or objects or their states to specific representations based on the determination of their informational features and coincidence with the corresponding representations. Provided that the input signal of the research object is a stochastic process of white noise, a color noise signal is formed at its output. This makes it possible to implement the identification process by evaluating sets of informational features selected for the corresponding model of noise signals. The monograph describes in detail the constructive mathematical model of a stochastic noise process – a linear random process and its characteristics. The theoretical argumentation of the relationship between random processes with independent increments and random processes with independent values – random processes of white noise – is given. The model of a linear random process (LRP) is a mathematical model of colored noises of different colors. The characteristic functions of both non-stationary and stationary LRP are given. Their ergodic properties have been proven to be important for the practical use of LRP. The case of a vector linear random process is considered as a model of multi-channel noise signals. A new result in the theory of random functions is the creation of a constructive model of a conditional linear random process, determination of its distribution laws in the form of a characteristic function and corresponding statistical characteristics. These characteristics can be used as potential signs of identification of stochastic noise processes. The results of research on periodic stochastic models are considered. Cyclic, rhythmic, natural and man-made phenomena, processes and signals of the functioning of objects are the subject of a wide range of research using periodic, almost periodic and stochastically periodic mathematical models. A detailed analysis of the linear periodic random process was carried out, and the characteristics of the identification of periodic models of stochastic noise signals were considered. Considerable attention is paid to the application of contour and phase methods as a theoretical basis for solving the problems of narrow-band noise signal identification. Obtaining the amplitude, phase, and frequency characteristics of such signals as functions of time through their Hilbert transformation is considered. The analysis of the random vector model with independent Gaussian components in the polar coordinate system is performed, the probability distributions of the modulus and argument of the random vector are given, and the possibility of approximating the latter by the Mises distribution is indicated. The application of the phase characteristic of narrow-band noisy random signals to determine circular statistics, which can be used as identifiers of such signals, is considered. The methodology of using phase characteristics for the identification of narrow-band noise signals is proposed. The monograph also presents the task of identifying vibration noise signals of electric power facilities in order to evaluate their actual condition. The mathematical model of the vibration noise signal of the bearing unit of the electric machine in the form of a linear random process – stationary RLC-multi-resonance noise is substantiated. The issue of identifying the empirical laws of the distribution of vibration noise signals based on the Pearson curve system is considered. Algorithmic software for statistical evaluation of empirical distribution laws of stationary vibration noise signals using smoothing curves from the Pearson curve system is presented. Examples of the identification of stochastic noise signals are given, which are based on the obtained theoretical results. In particular, this is the assessment of the characteristics of the identification of vibration noise signals of bearing assemblies, the assessment of the characteristics of electroencephalographic noise signals that are studied in biomedical technical systems, the determination of the characteristics of stochastic narrow-band signals in ultrasonic flaw detection systems, etc. The monograph is intended for researchers, engineers, as well as graduate students and students of higher educational institutions dealing with the problems of identification of technical and physiological objects.
