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In this paper we consider a novel componentwise coherence function, which is determined by the cross-spectral densities of stationary components of periodically nonstationary random processes i.e. stationary correlated random processes, which modulate their carrier harmonics. The properties of the introduced coherence function are specified for the amplitude- and phase-modulated signals. Its graphical frequency dependencies have been obtained for the specified signal parameters. The advantages of componentwise coherence function in comparison with previously suggested integral coherence function are shown. We present the method for the selection of stationary modulating components, which is based on the frequency shift and low-pass filtration. The properties of selected components for the cases of amplitude- and phase-modulated processes are analyzed. [ABSTRACT FROM AUTHOR]

A coherence function characterizing the correlation between harmonic components of two signals that are described by periodically correlated random processes has been proposed. Such function is shown to be invariant with regard to linear transformations of signals.Aformula for coherence function is concretized for the amplitude- and phase-modulated signals. [ABSTRACT FROM AUTHOR]

The development of an automatic system for the intelligent support of continuous cast billet production control processes is described. The motivation for the development of the system is that it should improve the efficiency of production facilities and minimize the possibility of producing inferior and unacceptable quality products. A theoretical analysis of the information relating to the quality control of the processes and the finished products is presented, enabling the identification of the sources of information, methods of information acquisition, and techniques for processing it to ensure improved product quality. The development of mathematical support is described for a program analyzer that automatically and reliably identifies the defects and quality of the continuously cast billets. The application of graphic information acquisition and processing techniques concerning the quality of the metal products is also presented. The development of mathematical and software support is described for the set point adjustment module operating in the automatic system for the intelligent support of the multistage continuous cast billet production control facility. This module makes use of adaptive fuzzy trees with dynamic structures to provide scientifically grounded analysis of factors causing billet defects. The introduction of the developed systems, including practical issues, into the operation of a production facility is explained. The study identifies the general lack of automatic systems that encompass and control the whole production chain on the basis of product quality. Typical savings resulting from quality improvements in a continuous cast billet production facility can approach a million rubles. [ABSTRACT FROM AUTHOR]

Properties of linear and quadratic invariants of correlation tensor-function of vectorial periodically non-stationary random processes are considered. We analyze the properties of their estimations, given in the form of trigonometric polynomials, whose Fourier coefficients can be obtained using averaging on time of realization parts. Formula for estimations bias and variance, which allow to calculate systematic and mean square errors of processing in dependence on processing parameters and process parameters, are derived. [ABSTRACT FROM AUTHOR]

Properties of cross-correlation components estimations of two periodically correlated random signals are analyzed. The conditions of absence of the first and the second genus aliasing effects are obtained. The formulas for estimations variance which allow to select a valid sampling step in dependences on realization length and signal properties are derived. The results are concretized for amplitude modulated signals. [ABSTRACT FROM AUTHOR]

Brief analysis of correlation and spectral characteristics that describe interconnections between two periodically correlated random processes is conducted. Properties of coherent estimates of signals' mutual correlation function and estimates of mutual correlation components are studied. Expressions for biases and dispersions of estimates are specified for amplitude modulated signals. [ABSTRACT FROM AUTHOR]

The coherent estimators of probabilistic characteristics of periodically correlated random processes with unknown period have been investigated. It is shown that these estimators are asymptotically unbiased and consistent. In a first approximation formulas were obtained for the bias and dispersion of estimators defining the impact of the preliminary determination of the period on the value of estimation error. [ABSTRACT FROM AUTHOR]