Abstract: Under random excitation, the behavior of SDOF nonlinear system is investigated. Nonlinear damping and nonlinear siffness are considered respectively. Equivalent linear damping and equivalent linear stiffness of nonlinear system are caculated by combining FPK transform and equivalent principle method. Results of equivalent linear FRF (Frequency Response Function) and Nyquist show that the FRF and Nyquist will change with the variation of excitation level. Moreover, it is observed that different nonlinear type shows different features. Thus the type of nonlinear can be charactered, and the hardening or softening characrteristic of the system can be deduced too.The result provides a theoretical foundation for choosing the model of the nonlinear dynamic system. The method can be used to identify the random test data of an aluminum honeycomb sandwich board to character the the type of nonlinear.