Abstract: Objectives Propulsion excitation information is an important input parameter for predicting and controlling ship acoustic vibrations. Therefore, this paper proposes an OU Gaussian generalized characterization model for turbulence induced unsteady broadband excitation of propellers. Methods An approximate analytical model for the power spectrum of broadband excitation in pump-jet rotors is derived based on the Ornstein-Uhlenbeck stochastic process theory and blade element theory. Sobol global sensitivity analysis is used to identify the operating frequency ranges and influence patterns of model parameters, and CFD results validate the model’s rationality and generality. Results The proposed generalized characterization model accurately captures the broadband attenuation characteristics and hump features in the power spectrum of non-stationary excitation. The model parameters exhibit strong frequency dependence; parameters characterizing the OU process operate over a wide frequency range, while parameters determining the Gaussian functions focus on frequencies near the hump. The generalized characterization model shows consistency with CFD results in describing the thrust power spectrum of a pump-jet thruster, and its rationality and generality are validated from a statistical confidence interval perspective. Conclusions The proposed generalized characterization model provides a simple and reliable empirical spectrum input for the acoustic and vibration control of ships. It also offers prior information constraints for the inversion and identification of non-stationary excitation in thrusters, mitigating the ill-posedness of inverse problems and improving identification accuracy.