Some remarks on equivalent linearization of stochastic dynamic systems

The relationship between statistical equivalent and true linearization techniques for nonlinear dynamic systems under Gaussian white noise excitations is discussed in this paper. It is shown that coefficients of the linearization depend on the averaging operation used in the mean-square criteria of linearization. New definitions of input and output linearization techniques are introduced. Detailed studies have been conducted for a one-dimensional input-output system and for the Duffing oscillator. The obtained results are illustrated with numerical examples.