﻿ 非高斯随机振动的模拟方法
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Simulation of non-Gaussian random vibration
Xu Fei, Li Chuanri, Jiang Tongmin, Rong Shuanglong
School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:Traditionally, only Gaussian signal can be produced by random vibration controller using power spectral density (PSD). However, actual vibration is usually non-Gaussian, which makes random vibration testing unable to simulate the failure mode that products will experience. Simulation of non-Gaussian random vibration with constant root mean square (RMS) and running RMS was performed respectively using two case studies. Case study 1 uses Hermite polynomial to transform Gaussian signal to non-Gaussian signal. The synthesized non-Gaussian signal has constant RMS, desired kurtosis and the same PSD with original Gaussian signal. Case study 2 uses a new method to simulate measured non-Gaussian random vibration which has running RMS. The synthesized non-Gaussian signal has the same PSD, kurtosis and probability density function with the field data.
Key words: non-Gaussian     random vibration     power spectral density(PSD)     kurtosis     probability density function

 图 1 高斯振动信号 Fig. 1 Gaussian signal

Winterstein[20]首次提出了利用Hermite多项式将一个平稳高斯信号x转换成平稳非高斯信号y:

 图 2 高斯和转换后的非高斯振动信号 Fig. 2 Gaussian and synthesized non-Gaussian signal

 图 3 100组转换后的非高斯信号的峭度 Fig. 3 Kurtosis for 100 synthesized non-Gaussian signal
 图 4 高斯和非高斯信号的功率谱密度 Fig. 4 PSD of Gaussian and non-Gaussian signal

 图 5 高斯和非高斯信号的概率密度函数 Fig. 5 PDF of Gaussian and non-Gaussian signal
 图 6 输入不同峭度下得到的实际信号的峭度 Fig. 6 Real kurtosis calculated from given kurtosis

 图 7 实测加速度随机振动信号 Fig. 7 Field acceleration random signal
 图 8 实验对象和实验装置 Fig. 8 Test item and setup

 图 9 实测信号及合成的高斯信号的功率谱密度 Fig. 9 PSD of field data and synthesized Gaussian signal

 图 10 利用功率谱密度合成的高斯信号 Fig. 10 Synthesized Gaussian signal from PSD
 图 11 实测信号及合成高斯信号的概率密度函数 Fig. 11 PDF of field data and synthesized Gaussian signal

 图 12 时域信号和均方根值 Fig. 12 Time history and running RMS
 图 13 RMS的概率密度函数 Fig. 13 PDF of running RMS

 图 14 实测信号及合成的非高斯信号 Fig. 14 Field data and synthesized non-Gaussian signal
 图 15 实测信号及合成的非高斯信号的功率谱密度 Fig. 15 PSD of field data and synthesized non-Gaussian signal
 图 16 实测信号及合成的高斯和非高斯信号的概率密度函数 Fig. 16 PDF of field data,synthesized Gaussian and non-Gaussian signal
3 结 论

1) Hermite多项式法可以在保证功率谱密度不变的同时得到具有指定峭度的RMS不随时间变化的非高斯信号,但该方法对于输入的峭度有限制:当输入峭度大于10时,误差达到了20%.

2) 提出的新方法利用实测信号的RMS的分布函数构造一个幅值调制信号与利用功率谱密度合成的高斯信号相乘,可以得到和实测信号具有相同PSD、峭度和概率密度函数的非高斯信号.

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#### 文章信息

Xu Fei, Li Chuanri, Jiang Tongmin, Rong Shuanglong

Simulation of non-Gaussian random vibration

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(9): 1239-1244.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0579