A physically based averaging procedure is applied to a general form of a nonlinear single-degree-of-freedom equation, with nonwhite random excitation, leading to a one-dimensional continuous Markov model for the energy envelope. It is demonstrated that, in combination with an energy-based technique for estimating the potential energy function, the Markov model can be used as the basis of a stochastic identification method for estimating the spectrum of the excitation, the static nonlinear restoring characteristic, and the nonlinear damping function, from measurements of the response alone. Moreover it is shown that, by combining results for two levels of stochastic excitation, it is possible to obtain good estimates of damping and stiffness parameters, both linear and nonlinear. [S0021-8936(00)02304-7]

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