Damage Detection in Beam Structures Based on Frequency-Domain Analysis Methods for Nonlinear Systems

Structural damage detection is crucial for ensuring the safety and durability of engineering systems. Conventional detection methods based on the frequency response function (FRF) in linear systems tend to fail when small early damage occurs in engineered structures. Nonlinear output frequency response functions (NOFRFs), which are extensions of the FRF in linear systems to weak nonlinear systems, have been applied in nonlinear system analysis. In this study, we extended the structural damage detection method based on NOFRFs to multi-degree-of-freedom systems and beam structures. Due to the presence of multiple modal frequencies in these structures, the nonlinear characteristic frequencies exhibited by the system are often more complex than those of typical rotor systems, significantly increasing the difficulty of system identification and the feasibility of frequency-domain analysis. To improve the accuracy of the Nonlinear Auto-Regressive with eXogenous inputs (NARX) model and reduce the impact of noise interference, we proposed a Multi-input Multi-output Forward Regression Orthogonal Least Squares (MFROLS) algorithm for processing multi-input multi-output data to identify the NARX model of the same structural system. Next, a numerical simulation study was conducted using the combined NARX model and Generalized Associated Linear Equations (GALEs) method, taking a one-dimensional multi-degree-of-freedom (MDOF) system as an example. Nonlinear stiffness terms were introduced into the MDOF system to simulate structural damage, and a comparative study was performed with a least squares method (LSM). The results show that the proposed method can capture the trends of dynamic characteristic changes in the one-dimensional MDOF system under the influence of different nonlinear stiffnesses, whereas the LSM fails to do so. Finally, experimental research was carried out on simply supported beams with varying degrees of damage. The results demonstrate that the frequency-domain analysis method based on nonlinear systems can detect differences in damage levels in beam structures, providing a new approach for structural damage detection.