Modeling of complex dynamical behaviours using a state representation technique based on a vector ARMA approach

We present an original method for constructing linear stochastic models of state representation type able to describe the second-order random behaviour of complex mechanical systems submitted to random dynamical excitations. The situation is the following: the dynamical behaviour to investigate is fundamentally nonlinear and it expresses the dynamics of a system whose mechanical behaviour is complex, poorly known, and consequently hard, even impossible to model. The proposed method is based on the spectral linearization principle and on the use of a vector ARMA formulation. The application considered here concerns the two-dimensional nonlinear stationary dynamical response ξ=(ξ1, ξ2) of structural elements of a nuclear power plant. We observe a very good fitting between the target and the result obtained by the proposed method.