针对非高斯振动信号的幅值概率密度函数难以用数学模型表述的问题,提出了基于高斯混合模型的非高斯概率密度函数表示方法。首先,基于时域样本信号得到非高斯振动信号的高阶矩估计值。其次,基于高斯随机过程偶次高阶矩之间的定量关系,结合二阶高斯混合模型建立方程组,求解得到混合模型中每个高斯分量的方差和权值。然后,将各高斯分量的权值和方差代入高斯混合模型,得到适用于对称非高斯振动信号的幅值概率密度函数。最后,通过仿真信号和实测振动信号,验证了该方法的有效性和适用性。

Aiming at the difficulty in deriving mathematical expressions of amplitude probability density functions of non-Gaussian vibrations,a Gaussian mixture model-based probability density function (PDF ) was proposed for non-Gaussian vibration signals.The estimation of higher-order moments of a non-Gaussian vibration process was obtained with sample time histories.Based on the quantitative relations between the even order moments of a given Gaussian process, combining with a secorld order Gaussian mixture model,an equation set for achieving the parameters of each Gaussian component in the Gaussian mixture model was established.Based on the obtained weighting factors and variances of Gaussian components,the mathematical model of non-Gaussian probability density function was then achieved.The examples of simulated signals and measured signals verified the validity of the presented method.

构造了非高斯修正系数的多项式响应面模型,提出了一种基于高斯近似的非高斯随机振动疲劳寿命估计方法。采用Winterstein传递函数法将非高斯随机应力转化成高斯随机应力,并联合雨流计数和Miner损伤准则分别估算两种随机应力下的累计损伤和谱矩,对多个样本进行最小二乘拟合之后构建一个关于应力谱矩和非高斯修正系数的多项式响应面模型。利用高斯近似法估算非高斯随机振动疲劳损伤量,并与经过雨流计数和Miner损伤准则估算的非高斯随机过程下疲劳损伤对比,结果表明：高斯近似法具有较好的精度。

Here,a non-Gaussian correction coefficient’s polynomial response surface model was constructed,and a new method for fatigue life estimation under non-Gaussian random vibration was proposed.Non-Gaussian random stress was transformed into Gaussian random stress using Winterstein transfer function method.The cumulative damages and spectral moments for the two types of stresses were estimated using the rain-flow counting and Miner damage criterion.A polynomial response surface model for stress spectral moments and non-Gaussian correction coefficient was constructed by applying the least square method to many samples.Contrasting non-Gaussian random vibration damages estimated with Gaussian approximation method and those estimated with the rain-flow counting and Miner damage criterion,the results showed that Gaussian approximation method has a better accuracy.

对低温加热工艺生产的以AlN为主抑制剂的高磁感取向硅钢高温退火过程进行中断实验,借助电子背散射衍射技术对高温退火过程中高斯晶粒的演变进行了研究.在升温过程中高斯晶粒平均尺寸先减小再增大.800℃时取向分布函数图出现高斯织构组分,但强度很弱,高斯晶粒偏离角在10°以上;900℃时高斯晶粒平均生长速率超过其他晶粒;950~1000℃时高斯晶粒异常长大,偏离角3°~6°;在1000℃之前高斯取向晶粒相比于其他晶粒没有尺寸优势.

The high-temperature annealing process of high permeability grain-oriented silicon steel with AlN as an inhibitor was studied by interrupting test. The evolution of Goss texture in this process was analyzed by electron back-scattered diffraction. It is found that the Goss grain size first decreases and then increases with the rise of temperature. Goss texture appears in the orientation distribu-tion function at 800℃, but the intensity is very weak and the deviation angle is more than 10o. The average growth rate of Goss grains is faster than other grains at 900℃. Goss grains grow abnormally from 950 to 1000℃, and the deviation angle ranges from 3o to 6o. Before 1000℃, in comparison with other grains, Goss grains have no size advantage.

针对单高斯模型对道路背景提取的不足,提出一种基于混合高斯模型的道路背景提取方法。利用多个高斯分布组成混合高斯模型来表示道路背景图像中的各个像素点,并且针对该算法利用MATLAB进行仿真实验,实验结果验证了基于混合高斯模型的道路背景提取方法的实用性和有效性。

Aiming at the shortcomings of the road background extraction method based on the single Gaussian model,this article proposes a road background extraction method based on the Gaussian mixture model.It adopts the Gaussian mixture model made up of the multiple Gaussian distributions to represent the each pixel point of the road background image,and conducts simulation experiments for the algorithm by using MATLAB. The experimental results certify the practicality and effectiveness of the road background extraction method based on the Gaussian mixture model.

在高斯投影复变函数的基础上,引入复变等角纬度的概念,避免等量纬度在极点的奇异性。其次,在复变等角纬度的基础上引入复变等角余纬度,并将极点作为高斯投影的坐标原点,建立了极区非奇异高斯投影复变函数表示形式。最后,与传统高斯投影幂级数及以往复变函数表示式相比较,验证了该公式的准确性。新的极区高斯投影表达式克服了传统高斯投影分带的缺陷,使得高斯投影在极区有一个统一的完整的"一体化表示形式"。

Based on expressions of Gauss projection by complex numbers , the conformal latitude by complex numbers was introduced to solve the singularity problem of isometric latitude in polar regions . Secondly ,conformal colatitude by complex numbers was introduced on the basis of conformal latitude by complex numbers ,with the polar point taken as the origin of coordinates in Gauss projection ,the non-singular formula of Gauss projection in polar regions by complex numbers was set up .Finally ,compared with traditional power series and expressions by complex numbers of Gauss projection ,the non-singular formula proved to be highly accurate .The new expression of Gauss projection in polar regions could overcome imperfection of zonation of traditional Gauss projection ,which makes Gauss projection a uniform integrated form in pol ar regions .