Optimal determination of frequencies in the spectral representation of stochastic processes

A family of criteria based on the concept of standard deviation spectrum is proposed and rigorously proved for optimal determination of the number and frequency of the harmonic components in the representation of stochastic processes. The stochastic processes composed of harmonic components with deterministic and/or randomized frequencies are discussed. The Clough-Penzien spectrum is taken to illustrate the proposed method. The results show that the number of the harmonic components can be reduced considerably. Response analyses of linear and nonlinear MDOF systems validate the proposed criteria and algorithms.