Нигматуллин Р.Р., Тобоев В.А. «Неинвазивные методы выделения значимых информационных составляющих и кластеризация акустических шумов произвольной природы» Нелинейный мир, 7, № 5, с. 348-354 (2009)

Предложены неинвазивные методы исследований нестационарных акустических шумов, не вносящие неконтролируемые ошибки и обеспечивающее упрощение интерпретации на основе кластеризации выделенных фрагментов (участков) по статистически однородному признаку. New noninvasive methods for consideration of time-dependent (unstable) acoustic noises have been suggested. They do not add uncontrolled errors and provide the simplification of data interpretation based on clusterization of the chosen fragments (parts) with the usage of the statistically homogeneous indication (sign). For increasing the resolution of acoustic noises the recurrence integration of the chosen fragments is suggested. This procedure allows in finding of the statistically closed fragments and detects the internal (not imposed by researcher) diagnostic indications. For their indication it is suggested to consider the sequences of the ranged amplitudes (SRA) belonging to relative fluctuations and optimal trends (that are obtained by means of the procedure of the optimal linear smoothing (POLS) with the Gaussian kernel). This procedure is applied to the fragments of the integrated sequences. The selection of the lengths of the fragments is determined by means of the generalized Pearson correlation function (GPCF). The usage of the SRA allows to express quantitatively the behavior of the relative fluctuations in terms of a universal set of the reduced (fitting) parameters that enter to the fitting function describing the envelope of the SRA. These parameters are used for comparison of arbitrary fragments of the acoustic noise. The increasing of number of the fitting parameters one can detect the quantitative differences between two fragments compared. If these differences are not so important one can determine the confidence interval, where two fragments compared are becoming "indistinguishable". The generalized mean value function (GMV) and the GPCF give a possibility to find true correlations between two random fragments compared and obtain statistically homogeneous cluster of the quantitative parameters with respect to some external factor. This cluster (having minimal numbers of quantitative parameters equaled four) allows in determination of fragments with collective acoustic noise (phone), the hidden periodicities, marginal peculiarities and predict a possible development of the acoustic process considered. The SRA and the GMV function are completely free from any (a priori) model assumption related to the nature of the acoustic process considered and so they are used for analysis and treatment of a wide class of time-dependent acoustic processes.