ESTIMATION OF THE NUMBER OF REAL HARMONIC COMPONENTS OF OBSERVATIONS WITHIN A LIMITED TIME INTERVAL

Abstract

The first stage of providing selectivity of devices for analyzing the spectrum of polyharmonic signals observed against the background of parametrically uncertain Gaussian noise is considered: detection, measurement of the number of discrete components of the spectrum of the real process. Model representations and requirements formulated in the set part of the problem to be solved correspond to the concepts and problems of the current state of diagnostic practice, which is associated with the study of the characteristics of vibration processes of various units. In particular, information on the number and levels of harmonics in operating conditions is a sign of defects in the work and the degree of their development. In the framework of the statistical theory of many alternative solutions using the criterion of the likelihood ratio proposed method for solving the problem of detection and estimating the number of harmonic components of the spectrum of a time-limited real process. On the basis of the developed methodology, the rule of making decisions with a given degree of reliability in favor of any of the hypotheses put forward about the number of harmonic components of the spectrum of the real signal observed against the background of parametrically uncertain Gaussian noise is synthesized. It is proved that in the considered model representations in solving this type of statistical problems it is advisable to focus on the analysis in the interference subspace of the correlation matrix of observations. A distinctive feature of the synthesized decision-making rule: meets the methodology of maximum likelihood, critical statistics is formed on the basis of the characteristic value of the correlation matrix of observation, standard computational operations are applied for implementation. The distribution density of critical statistics is tabulated. This makes it possible to "a priori" to set the required value of the significance level. Certification of the synthesized test-decision-making rules in favor of the proposed hypothesis about the prevailing number of harmonic components in the spectrum of the process is carried out at the level of digital statistical modeling. As the initial data were given: q – the value of the significance level (0.05; 01); P – noise power; the number of harmonic components N=2. In experimental studies, the amplitude of the second harmonic varied from 0 to the amplitude of the first harmonic. The results of the modeling analysis of the relationship between the number of correct decisions (made hypotheses) from changes power the second harmonic at a given ratio of signal/noise. The obtained performance characteristics of the algorithm confirmed the theoretical conclusions of the research.

Keywords

• критерий логарифма отношения правдоподобия
• число сигналов
• спектральный анализ
• уровень значимости