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Method of Determination of the Stationary Segments Based on the Statistics of the Fractional Moments

Keywords:

R.R. Nigmatullin, V.A. Toboev


For detection of the stationary segments in the processes analyzed the generalized dynamical criterion is suggested. The detection of these segments is related (a) to calculation of the nonstationary function (t,) in sliding window (it is determined as a fragment of a temporal series that shifts along the time axis or (b) it is based on comparison in different temporal windows (fragments). The new peculiarities of this function are based on the total set of the moments (redundant information). Thanks to this fact it reflects the intermittent dynamics that passes across quasi-stationary segments. It helps to find the statistically close fragments, compare them with the usage of the generalized Pearson correlation function and detect the internal (not imposed by researcher) the diagnosis indications. The analysis of the dynamics of the function (t,) allows in finding the characteristic nonstationary times and to give a possibility for more accurate detection of changing of the intermittent dynamical regimes of the process analyzed. Based on the relationships found between parameters of clustering calculated from statistically homogeneous fragments of the temporal series analyzed one can find the stationary segments, hidden periodicities and marginal peculiarities. The application of the statistics of the fractional moments opens wide possibilities for interclustering classification of the diagnostic features of the process analyzed. This classification is based on the reference – test clusters. The acoustic noise of a campfire was analyzed. The obtained results confirmed the basic positions of the (t,)-theory developed.
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