Multifractal approach to the description and wavelet analysis of the fatigue damage

Abstract

A phenomenological model for the multifractal description of the fatigue damage accumulation has been introduced. The multifractal approach gives probabilistic evidence for the existence of a constructive process hidden in the temporal pattern of damage accumulation. It is shown that a series of Bernoulli trials results in multiplicative bi- or polynomial process that recursively generates the multifractal probability measure. Connection between parameter of the Bernoulli trials and multifractal spectrum is considered. A technique for revealing the multifractal properties of the damage accumulation is proposed. For the approbation of the technique, a computer simulation study has been done. The wavelet transform has been used for revealing the intrinsic temporal structure of data sets obtained from numerical simulation, tests, empirical observations and measurements.