Data-based Identification of nonlinear restoring force under spatially incomplete excitations with power series polynomial model

One of the present barriers to the realization of structural health monitoring is the lack of efficient and general identification methodologies for dealing with nonlinearity, because a priori knowledge of the nature and mathematical form of the nonlinearities of typical engineering structures are usually unknown. The studies on the identification of restoring force, which can be considered as a direct indicator of the extent of the nonlinearity, have received increasing attention in recent years. In this paper, the nonlinear restoring force (NRF) was estimated by using a power series polynomial, and each coefficient of the polynomial was identified by means of standard least-square techniques. No information about the system was needed, and only the applied excitations and the corresponding response time series were used for the identification. Two different cases, in which the system was under complete and incomplete excitations, were investigated. Moreover, the effect of noise level was also taken into consideration. The feasibility and robustness of the proposed approach were verified via a 2-degree-of-freedom (DOF) lumped-mass numerical model, and experimental tests on a 4-story shear building with magneto-rheological (MR) dampers which served to simulate nonlinear behavior. The results show that the proposed data-based method is capable of identifying the NRF in a chain-like multi-degree-of-freedom engineering structures without any assumptions on the structural parameters, and provides a promising way for damage detection in the presence of structural nonlinearities.