A two-step method to locate multiple local nonlinearities

Nonlinear localization is an important component of structural nonlinear identification. Its accuracy is of great significance for damage localization, health monitoring, and performance prediction of structural systems. In this paper, a two-step localization method is proposed for the nonlinear localization of multi-degree-of-freedom (MDOF) systems with multiple local nonlinearities. The approach achieves accurate nonlinear localization in two steps. In the first step, subset nonlinearity detection is performed to initially narrow down the nonlinear localization range. This effectively reduces the dimensionality of the candidate nonlinear basis functions in the second step. In the second step, candidate nonlinear basis functions are used to further confirm the doubtful connections. The accuracy and effectiveness of the method are verified by two numerical examples of a one-dimensional chain-type structure and a two-dimensional structure. In addition, an experimental study is conducted on a floor structure with two local nonlinearities to verify the effectiveness of the proposed method. Results show that the proposed method has good accuracy in a noisy environment and it requires only the input and output data of the system under a wide-band excitation.