The nonlinear output frequency response functions (NOFRFs) are extensions of the frequency response function (FRF) in linear systems to weakly nonlinear systems, have been applied in nonlinear system analysis and structural damage detection. The NOFRFs of the nonlinear auto- regressive with exogenous input (NARX) model can be obtained by solving a series of difference equations in a method called generalized associated linear equations (GALEs). In the present study, an experimental study was carried out on a beam structure with cracks. The main method is to use a data-driven method to establish the NARX model of the beam under different damage states, and obtain the NOFRF of the beam under different damage states by computing the GALEs of the system. Finally, the beam structure in different damage states was evaluated based on the NOFRFs. And it was shown that the NOFRFs can be used to represent the dynamics of different systems. It is shown that NOFRFs can be used to represent the state characteristics of different system dynamics, which can be well applied to damage detection of engineering structures.