Cumulative fatigue damage detection for used parts plays a key role in the process of remanufacturing engineering and is related to the service safety of the remanufactured parts. In light of the nonlinear properties of used parts caused by cumulative fatigue damage, the based nonlinear output frequency response functions detection approach offers a breakthrough to solve this key problem. First, a modified PSO-adaptive lasso algorithm is introduced to improve the accuracy of the NARMAX model under impulse hammer excitation, and then, an effective new algorithm is derived to estimate the nonlin...