A practical determination of an optimal order of state probability distribution expression with hierarchical expansion form observed in the actual sound and vibration environments

Abstract

The probability distribution of state variables for the stochastic systems has been very often used so far in the generalized expression form of an infinite orthonormal series expansion.However, in the case of applying this expansion expression to actual random phenomena, it is impossible to employ infinite expansion terms and only the finite sampled level data are available to estimate the expansion coefficients.In this study, a new trial for determining the optimal order of expansion terms for the state probability distribution is proposed.Furthermore, a part of the effectiveness of the proposed method is experimentally confirmed by applying it to the actually observed data in the sound environment.