The identification and characterization of nonlinear behavior for the purpose of fault detection—particularly those associated with cracks or structural damage—constitutes a significant area of research in engineering. This study investigates a novel and systematic methodology for characterizing nonlinearity through nonlinear output decomposition and regulation. It is demonstrated that the proposed approach enables effective assessment of both even-order nonlinearities and those induced by cracks, which exhibit more complex behavior than simple even-order responses, even in their early stages. Specifically, the magnitude of the second-order harmonic response, which is shown to vary linearly with crack severity, serves as a reliable indicator and can be accurately quantified using the proposed technique. Theoretical derivations, illustrative examples, finite element simulations, and experimental validations are presented to substantiate the efficacy and advantages of the method in capturing nonlinear dynamic characteristics associated with incipient damage. The framework introduced in this work offers a valuable alternative for frequency-domain nonlinear signal processing, with broad applicability in the detection and evaluation of structural faults across diverse engineering domains.