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摘要:
传统的环境振动试验常将随机振动信号假设服从高斯分布，且利用功率谱密度（PSD）来作为试验条件。然而实际环境中结构所受到的振动激励很多呈现非高斯性，且PSD只能描述信号的低阶统计量，无法描述非高斯信号的峭度和偏度等高阶统计量。针对此情况，研究了在窗函数幅值调制法（AMT）基础上利用自PSD和峭度生成非高斯信号的方法。针对调制信号的生成，提出了近似模拟方法。通过Weibull和Beta 2种分布构造调制信号，研究分布参数与目标峭度值之间的关系，并分析2种分布合成目标峭度值的范围。案例验证了仿真生成的非高斯信号与实测外场数据具有相同的PSD、概率密度函数（PDF）和峭度值，进而证明了方法的正确性。
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关键词:
- 幅值调制法(AMT) /
- 近似模拟方法 /
- 峭度 /
- Weibull分布 /
- Beta分布
Abstract:The traditional environmental vibration tests usually assume that the random vibration signal follows Gaussian distribution and power spectral density (PSD) is used as the test conditions, while in practice, lots of vibration excitations to the structure are non-Gaussian distribution and PSD can only describe the low-order statistics of signals but not for the high-order statistics of the non-Gaussian signals such as the kurtosis and skewness. So a method based on amplitude modulation technique (AMT) of window function to generate the non-Gaussian signal with PSD and kurtosis is developed. An approximated simulation method is provided to generate the modulation signal. Two kinds of statistical distribution, Beta and Weibull, are used to construct modulation signal, the relation between target kurtosis and modulation signal distribution parameters is explored, and the suitable kurtosis range of two distributions is discussed. A case study is presented to show that the synthesized non-Gaussian signal has the same PSD, probability density function (PDF), and kurtosis as outfield measured data, which verifies the correctness of the method.
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图 2 参数β为[0.2，10.2]时对应调制信号的PDF
Figure 2. PDF of modulation signal when β is [0.2, 10.2]
图 4 形状参数r为[1.28，1.88]时对应调制信号的PDF
Figure 4. PDF of modulation signal when shape parameter r is [1.28, 1.88]
图 8 实测外场数据RMS的自相关函数
Figure 8. Auto correlation function of RMS of measured outfield data
图 10 实测外场数据和仿真的高斯信号的PSD
Figure 10. PSD of measured outfield data and simulated Gaussian signal
图 12 实测外场数据RMS和Weibull信号的自相关函数
Figure 12. Auto correlation function of measured outfield data RMS and Weibull signal
图 14 实测外场数据和仿真非高斯信号的PSD
Figure 14. PSD of measured outfield data and simulated non-Gaussian signal
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