中文摘要：

基于三参数功率谱曲线（Ecs）模型和自回归（AR）模型的螺旋桨噪声建模方法已经在工程中得到广泛的应用.然而,噪声模型输出的稳定性条件缺乏严格的证明,同时缺乏实测噪声到模型参数的一个有效提取方法,给噪声模型的实际应用带来困难.本文详细讨论了Ecs模型曲线的性质及其与螺旋桨辐射噪声统计特性的一致性.讨论了噪声模型中的AR模型稳定性条件.首先,利用Schur-Cohn准则将AR模型的稳定性等价为Levinson-Durbin递归计算中所有反射系数绝对值小于1的问题.其次,证明了Yule-Walker方程中的自相关矩阵合同于以各阶建模误差为对角元素的对角阵.根据Sylvester惯性定理,将对反射系数的约束条件等价为自相关矩阵的正定性条件.最后证明了在Ecs模型曲线非负条件下AR模型输出具有稳定性,给出了一种稳定Ecs模型中三个参数的约束条件.此外,本文给出了一种利用实测数据估计Ecs模型参数的方法.首先通过噪声功率谱峰值估计Ecs参数f0,设计Ecs曲线和测量噪声的功率谱曲线的误差函数联合估计fm和λ,最后修正信号的方差.采用缩比四叶螺旋桨模型,设计并开展了一次螺旋桨噪声水池实验,采集了多种转速条件下的螺旋桨辐射噪声.实验数据分析表明,在不同转速条件下,Ecs模型曲线均能较好的逼近实测螺旋桨噪声数据的功率谱谱形.实测数据估计的模型参数与螺旋桨的空化状态表现出较好相关性,可以作为噪声特征参数.

英文摘要：

The propeller radiated noise modeling method based on the three-parameter power spectrum curve（Ecs） model and the AutoRegressive（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 are also discussed in the propeller radiated noise modeling.The stability of the noise model depends on the stability of the AR model,which parameters are 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 are less than 1.Next,the autocorrelation matrix of Yule-Walker equation is proved to be contract with a diagonal matrix with diagonal element 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