An orthogonal Hilbert-Huang transform and its application in the spectral representation of earthquake accelerograms
Abstract This paper first discusses the limitation that the intrinsic mode functions (IMFs) decomposed by the empirical mode decomposition (EMD) in Hilbert-Huang transform (HHT) are not orthogonal. As an improvement to the HHT method, three orthogonal techniques (the forward, backward and arbitrary sequence orthogonalization algorithms) based on the Gram-Schmidt method are then proposed to obtain the completely orthogonal IMFs. According to the orthogonal index and the energy index, the effectiveness of the proposed technique and algorithms is validated through a synthetic signal generated by the combination of three sinusoidal waves with different frequencies and the El Centro (1940, N-S) earthquake accelerogram. By taking the El Centro (1940, N-S) earthquake accelerogram as an example, the problem that whether the orthogonal IMFs satisfy the requirements of IMF is discussed, then the backward and the arbitrary sequence orthogonalization algorithms are recommended. Three historic earthquake accelerograms are analyzed by using the recommended orthogonalization algorithms combined with the Hilbert spectral analysis. The results show that the orthogonal Hilbert spectrum and the orthogonal Hilbert marginal spectrum can produce more faithful representation of earthquake accelerograms than the Hilbert spectrum and the Hilbert marginal spectrum, and they can be used to quantitatively characterize the energy distribution of earthquake accelerograms at different frequency regions.