Random Field Representation in a Biorthogonal Wavelet Basis

Abstract

This paper develops a new representation scheme for random fields, which can be used in a variety of mechanics applications, based upon the projection onto a biorthogonal wavelet basis. The merits of such a scheme can be shown to result from the relaxation of the condition of orthonormality, while still requiring compact support of the basis functions. Earlier methods have relied on the diagonalization properties of wavelets to demonstrate how the Daubechies family of orthonormal wavelets is effective in weakening the correlation across scales for a large class of random processes. It is shown that biorthogonal processes achieve better decorrelation owing to the fact that fewer filter coefficients are needed to maintain the same support of basis functions when compared to the Daubechies family. Numerical examples of fields encountered in earthquake engineering and other applications are given.