基于高斯混合模型的非高斯振动疲劳频域求解方法

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摘要很多机械结构在工作环境下经受的随机载荷有着较强的非高斯性，按照传统的高斯假设对这些结构进行疲劳计算会带来很大误差。针对非高斯载荷下结构疲劳寿命难以预测的问题，提出了一种非高斯随机载荷下对结构进行疲劳计算的频域方法。首先引入高斯混合模型（Gaussian mixture model ,GMM）对载荷进行描述,并使用期望最大（EM）算法对模型参数进行求解，建立的模型可以准确描述单峰及多峰非高斯载荷。在此基础上结合Tovo-Benasciutti方法推导出一种多峰非高斯载荷下的频域疲劳计算方法。为了对该方法进行验证，对一个双峰分布的非高斯载荷信号进行了疲劳分析，以雨流计数法作为参考，结果表明在双峰非高斯载荷下，对多种材料，文中方法与直接使用传统频域疲劳计算方法相比计算精度提升明显，验证了该方法的精确性及较广的适用性。
关键词：非高斯载荷；高斯混合模型；EM算法；频域疲劳寿命计算

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	朱帅康1
	董龙雷1
	官威1
	王珺2
	李斌潮2

关键词 ：非高斯载荷, 高斯混合模型, EM算法, 频域疲劳寿命计算

Abstract：The random load of many mechanical structures in the working environment has obvious non Gaussian characteristics. According to the Gaussian hypothesis, the fatigue calculation of these structures will bring great error. Aiming at this problem, a frequency domain method for fatigue life estimation under non-Gaussian random loading is established in this paper. The Gaussian mixture model(GMM) was introduced for describing the non-Gaussian load, and the EM algorithm was used to estimate the parameters of the model. Based on the obtained model, the uni-modal and muti-modal non-Gaussian load can be described accurately. Then combined with Tovo-Benasciutti method, a vibration fatigue life estimation method was raised. A bi-modal load example was analyzed to test the accuracy of this method. Taking the rainflow counting method as a reference, the results showed that under bimodal non-Gaussian loads, for a variety of materials, compared with the traditional frequency domain fatigue calculation method, the calculation accuracy is significantly improved, which verifies the accuracy and wide applicability of the method.
Key words: non-Gaussian load; Gaussian mixture model; EM algorithm; frequency domain fatigue life

Key words： non-Gaussian load Gaussian mixture model EM algorithm frequency domain fatigue life

收稿日期: 2021-04-08 出版日期: 2022-08-28

引用本文:

朱帅康1，董龙雷1，官威1，王珺2，李斌潮2. 基于高斯混合模型的非高斯振动疲劳频域求解方法[J]. 振动与冲击, 2022, 41(16): 93-99.
ZHU Shuaikang1，DONG Longlei1，GUAN Wei1，WANG Jun2，LI Binchao2. A frequency method for fatigue life estimation under non-Gaussian random loading based on a Gaussian mixture model. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(16): 93-99.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I16/93

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