Normalization of Higher Order Spectrum and Analysis of Quadratic Phase Coupling

고차스펙트럼의 정규화 방법과 이차 위상결합 해석

This thesis is concerned with the development of useful engineering techniques to detect and analyze nonlinearities in mechanical systems. The methods developed are based on the concepts of higher order spectra, in particular the bispectrum. The study of higher order statistics has been dominated by work on the bispectrum. The bispectrum can be viewed as a decomposition of the third moment(skewness) of a signal over frequency and as such is blind to symmetric nonlinearities. Initially auto higher order spectra are studied in detail with particular attention being paid to normalization method. Traditional method based on the bicoherence are studied. Under certain conditions, notably narrow band signals, the above normalization method is shown to fail and so a new technique based on prewhitening the signal in the time domain is developed.