Identification of Nonlinearity Using Transfer Entropy Combined with Surrogate Data Algorithm

Abstract

A numerical time-delayed transfer entropy method combined with a surrogate data algorithm is proposed to identify the nonlinearities in the vibration data of structures with damages without the use of baseline data. Semianalytical methods based on the Galerkin method are used to precisely predict the linear and nonlinear response of structures. The proposed method can identify nonlinearities in vibration data well. A new nonlinearity index is also proposed. Computation results for different loads indicate that the nonlinearity index increases as load increases. Subsequently, a new discreteness degree index for transfer entropy is additionally proposed. The responses of a plate with different loads are calculated and linear relationships between the discreteness degree index and the nonlinearity index are obtained. Numerical examples with different geometries but similar nonlinearity indexes are also carried out. It is shown that the discreteness degree index for transfer entropy can quantitatively measure nonlinearity degree. As verified, the proposed methodology can be used for structure nonlinearity identification in areas such as civil engineering, mechanical engineering, and ocean engineering.