Comments on “Identification of Multi-Degree-of-Freedom Non-Linear Systems Under Random Excitations by the ‘Reverse Path’ Spectral Method”

Application of the Conditioned Reverse Path Method

“…However, when the number of excitations is smaller than the number of response locations and non-linearities are far from the locations of the excitations, the reverse path method can not be directly applied. To overcome this difficulty the 'Conditioned Reverse Path' formulation has been developed starting from the concepts explained in references [1,15,16].…”

Application of the Conditioned Reverse Path Method

“…As shown in reference [10], the relationships among the power spectral densities of displacements, forces and non-linear vectors can be expressed in terms of a linear system, involving the cross spectral density matrix between the ith and the jth non-linear vector fyðtÞg; namely ½G ij : If excitations are applied at every response location, parameter estimation is completed by solving an algebraic system (reverse path method). However, if the number of excitations is smaller than the number of response locations N; and non-linearities are away from the locations of the applied excitations, the 'conditioned reverse path' (CRP) formulation has been developed [10] by generalising the concepts by Bendat [11][12][13].…”