This study focuses upon the development of accurate prediction methods of non-linear, multi-degree of freedom (MDOF) structural systems subject to external and parametric random vibration. A formulation based upon Markov methods, which combines stochastic averaging, white noise shaping filters and moment closure techniques is presented. The analysis yields a system of algebraic equations which can be used to provide non-Gaussian response information. To illustrate this general analytical approach, a series of examples focused on the response of deep water compliant offshore platforms subjected to realistic surface wave spectrum are presented. In order to represent the random sea environment, dimensionless shaping filters are developed to modify the white noise input and provide the surface elevation and fluid kinematic data needed for the response simulation. The implications of this approach on MDOF system response and reliability estimates is explored and discussed.
