MODEL STANDARDIZATION AND FREQUENCY-DOMAIN ANALYSIS FOR NONLINEAR SYSTEMS WITH NON-ZERO EQUILIBRIUM POINTS

When evaluating structural damage by calculating the nonlinear output frequency response functions (NOFRFs) using nonlinear frequency-domain methods, it is usually necessary to identify a nonlinear auto-regressive with exogenous inputs (NARX) model. However, the constant term commonly present in this model, which indicates that the system is stabilized at a non-zero equilibrium point, severely interferes with the applicability of the traditional Volterra series method. This interference is specifically manifested in the calculation of the NOFRFs: the generalized associated linear equations (GALEs) method is the latest approach for solving the NOFRFs based on time-domain models such as nonlinear differential equation (NDE) or NARX models. This study aims to fundamentally address the theoretical obstacles and computational limitations caused by the constant term by establishing a universal model standardization method to characterize and evaluate the nonlinear intensity of complex damaged structures. Through rigorous mathematical derivation, this research establishes a standardized transformation theoretical framework for NDE models and NARX models stabilized at non-zero equilibrium points. The core innovation lies in the universality of this model standardization method for systems containing various complex nonlinear coupling terms. By systematically introducing a system offset parameter, a nonlinear system stabilized at a non-zero equilibrium point is transformed into an equivalent system stabilized at a zero equilibrium point. This method theoretically eliminates the interference of the constant term in subsequent nonlinear frequency-domain analysis, particularly in solving the NOFRFs using GALEs, thereby significantly expanding the applicability scope of the Volterra series method. To validate the effectiveness of the proposed method, this study takes a damaged aluminum plate containing cracks as the subject. A single-frequency harmonic excitation is applied, and the response signals are measured. The NARX model of the damaged aluminum plate system is successfully identified through data-driven methods, and the proposed standardization framework is applied for processing. Finally, the NOFRFs characteristics of the system are calculated. Physical experimental results indicate that the NOFRFs features extracted after the proposed standardization treatment can characterize the state of crack damage in the aluminum plate. This not only solves the problem of NARX model constant term interference in NOFRFs calculation but also greatly enhances the applicability of the Volterra series to actual complex damaged systems. It provides a reliable theoretical foundationand practical analytical tools for the quantitative detection of early structural damage based on nonlinear frequency-domain theory.