Abstract:  The propeller radiated noise modeling method based on the threrparameter power spectrum curve (Ecs) model and the AutoRegressivc(AR) model is widely applied in engineering recently. By adjusting three parameters, the model can produce noise with specified power spectra shape similar with
the actual propeller radiated noise. But there is a lack of rigorous theoretical proof of the stability conditions of the noise model. And there is also a lack of the effective extraction method of the Ecs curve parameters based on the measured propeller radiated noise.The two factors bring difficulties to the
practical application of the noise model, In this paper, several basic nature of Ecs curve is discussed in detail，including the symmetry, the curve peak position and the decay rate with the frequency. This nature is consistent with the characteristics of the propeller radiated noise spectrum statistically. The
stability conditions arc also discussed in the propeller radiated noise modeling. The stability of the noise model depends on the stability of the AR model，which parameters arc calculated based on the Ecs curve and Levinson-Durbin recursion algorithm. First，using the Schur-Cohn criteria, the stability condition of
the AR model is proved to be equivalent to the condition that the absolute values of reflection coefficients in Levinson-Durbin recursion algorithm arc less than 1. Next, the autocorrclation matrix of Yule-Walker equation is proved to be contract with a diagonal matrix with diagonal clement of each order modeling
errors of Levinson-Durbin recursion algorithm.Then, according Sylvester’s law of inertia, the stability condition of the AR model is equivalent to the positive of the autocorrelation matrix. At last，the stability of the AR model is proved under the conditions of the non-negative of the Ecs curve. A constraint of
parameters of Ecs curve is given. In addition, this paper presents a method to estimate the Ecs model parameters using measured data. First，Ecs parameters f₀ is estimated by the frequency value of the peak point of noise power spectrum curve. An error function between the Ecs curve and the measurement noise
power spectral curve is designed and used in estimating fm and λ of Ecs curve model jointly. Finally, the vanance of the signal is estimated. An experiment is designed and carried out using a scaled model of four-blade underwater propeller in an open pool.The experim ental propeller radiated noise at different
rotation speed was recorded using hydrophone and analyzed.The experiment result shows that, in different rotation speed condition of the propeller, 1)the parameters of the Ecs curve is effectively estimated. 2)The Ecs model with estimated parameters could be approximate to real underwater
propeller noise data well in the characters of power spectrum.The experiment also shows that the estimated parameters of the Ecs model have a good correlation with the propeller cavitations status, and can be used as features of the propeller radiated noise.