基于高斯混合模型的非高斯振动疲劳频域求解方法

朱帅康1,董龙雷1,官威1,王珺2,李斌潮2

振动与冲击 ›› 2022, Vol. 41 ›› Issue (16) : 93-99.

PDF(1320 KB)
PDF(1320 KB)
振动与冲击 ›› 2022, Vol. 41 ›› Issue (16) : 93-99.
论文

基于高斯混合模型的非高斯振动疲劳频域求解方法

  • 朱帅康1,董龙雷1,官威1,王珺2,李斌潮2
作者信息 +

A frequency method for fatigue life estimation under non-Gaussian random loading based on a Gaussian mixture model

  • ZHU Shuaikang1,DONG Longlei1,GUAN Wei1,WANG Jun2,LI Binchao2
Author information +
文章历史 +

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

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

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

Key words

non-Gaussian load / Gaussian mixture model / EM algorithm / frequency domain fatigue life

引用本文

导出引用
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[J]. Journal of Vibration and Shock, 2022, 41(16): 93-99

参考文献

[1] Miner MA. Cumulative damage in fatigue. Applied  Mechanics Transactions (ASME) 1945; 12(3):A159–A164.
[2] Wirsching P H, Light M C. Fatigue under Wide Band  Random Stresses[J]. Journal of the Structural Division, 1980,  106(7):1593-1607.
[3] Dirlik,T. Application of computers in fatigue analysis. Ph.D.   Coventry:The University of Warwick, 1985.
[4] Zhao W, Baker M J. A new stress range distribution model  for fatigue analysis under wave loading[C] // Environmental  Forces on Offshore Structures and Their Predictions. London,  UK: Society of Underwater Technology, 1990: 271-291.
[5] D Benasciutti, Tovo R. Cycle distribution and fatigue  damage assessment in broad-band non-Gaussian random  processes[J]. Probabilistic Engineering Mechanics, 2005,  20(2):115-127.
[6] 刘杨,张海萍,邓扬,等. 公路桥梁车辆荷载建模方法及 疲劳寿命评估[J]. 应用力学学报, 2016, 33(4): 652-658.
LIU Yang, ZHANG Hai-ping, DENG Yang, et al. Highway  bridge vehicle load modeling method and fatigue life  assessment[J]. Chinese Journal of Applied Mechanics, 2016,  33(4): 652-658.
[7] Braccesi C , Cianetti F , Lori G , et al. The frequency domain  approach in virtual fatigue estimation of non-linear systems:  The problem of non-Gaussian states of stress[J]. International  Journal of Fatigue, 2009, 31(4):766-775.
[8] Cianetti F , Palmieri M , Morettini G , et al. Correction  formula approach to evaluate fatigue damage induced by  non-Gaussian stress state[C]// AIAS International Conference  on Stress Analysis. 2017.
[9] Winerstein, Steven R. Nonlinear Vibration Models for  Extremes and Fatigue[J]. Journal of Engineering Mechanics,  1988, 114(10):1772-1790.
[10] Wolfsteiner, P. Fatigue assessment of non-stationary random  vibrations by using decomposition in Gaussian portions[J].  International Journal of Mechanical Sciences, 2017, 127,  10–22.
[11] Wolfsteiner P , Breuer W . Fatigue assessment of vibrating  rail vehicle bogie components under non-Gaussian random  excitations using power spectral densities[J]. Journal of  Sound & Vibration, 2013, 332(22):5867-5882.
[12] Steinwolf A, Rizzi S A. Non-Gaussian analysis of turbulent  boundary layer fluctuating pressure on aircraft skin panels[J].  Journal of Aircraft, 2006, 43(6) : 1662-1675.
[13] 梅刚, 秦权, 林道锦. 公路桥梁车辆荷载的双峰分布概率 模型[J]. 清华大学学报(自然科学版), 2003,  43(010):1394-1396,1404.
MEI Gang, QIN Quan, LIN Dao-jin. Bi-modal probabilistic  model of highway and bridge vehicle loads[J]. Journal of  Tinghua University: Science and Technology, 2003, 43(10):  1394-1397.
[14] 程红伟, 陶俊勇, 蒋瑜,等. 基于高斯混合模型的非高斯随 机振动幅值概率密度函数[J]. 振动与冲击, 2014,  33(5):115-119.
CHENG Hong-wei, TAO Jun-yong, JIANG Yu, CHEN Xun.  Amplitude probability density functions for non-Gaussian  random vibrations based on a Gaussian mixture model[J].  Journal of vibration and shock, 2014, 35(5):115-119.
[15] Benasciutti D , Tovo R . Comparison of spectral methods for  fatigue analysis of broad-band Gaussian random processes[J].  Probabil Engineering Mechanics, 2006, 21(4):287-299.
[16] Benasciutti D, Tovo R. Spectral methods for lifetime  prediction under wideband stationary random processes[J]. 
International Journal of Fatigue, 2005;27(8):867-77.
[17] Matjaž Mršnik, Janko Slavič, Miha Boltežar.  Frequency-domain methods for a vibration fatigue life  estimation-Application to real data [J]. International Journal  of Fatigue, 2013,47:8-17.
[18] Smallwood D O. Generating non-Gaussian vibration for  testing purposes[J]. Sound & Vibration, 2005, 39(10):18-24.
[19] Amzallag C , Gerey J P , Robert J L , et al. Standardization of  the rainflow counting method for fatigue analysis[J].  International Journal of Fatigue, 1994, 16(4):287-293.
 

PDF(1320 KB)

Accesses

Citation

Detail

段落导航
相关文章

/