A method to reduce the sampling variability of time-domain fatigue life by optimizing parameters in Monte Carlo simulations降低时域疲劳寿命采样变异性的蒙特卡罗模拟参数优化方法
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Sun H, Qiu YY, Li J, Bai J, Peng M, 2024. A method to reduce the sampling variability of time-domain fatigue life by optimizing parameters in Monte Carlo simulations. Probabilistic Engineering Mechanics, 75: 103591.DOI: 10.1016/j.probengmech.2024.103591
摘要 | Abstract
蒙特卡罗数值模拟用于生成平稳 Gauss 随机时域信号样本，在随机疲劳寿命预测中起着重要作用。随机种子、采样频率和数值模拟中的采样点数等控制参数对时域随机疲劳寿命有显著影响。本文采用常用的功率谱样本和工程材料系统地研究了这些影响，并提出了一种优化控制参数的新方法。该方法解决了许多论文中发现的一个关键问题，即频域疲劳寿命与时域疲劳寿命之间的相对误差随着 S-N 曲线的斜率 K 增加而增加。此外，它显著减少了斜率 K 很大的时域疲劳寿命的采样变异性，这将帮助相关研究人员通过使用时域疲劳寿命作为标准数据来建立更好的频域模型进行疲劳寿命预测。关键词: 随机疲劳寿命, 采样变异性控制, 蒙特卡罗模拟, 控制参数优化Monte Carlo numerical simulations for generating stationary Gaussian random time-domain signal samples fulfil an important role in random fatigue life prediction. Control parameters such as the random seed, the sampling frequency and the number of sampling points in the numerical simulations have significant effects on the time-domain random fatigue life. In this paper, the effects are investigated systematically by utilizing commonly used power spectrum samples and engineering materials, and so a new method for optimizing the control parameter values is proposed. The proposed method solves the critical problem found in many papers that the relative error between the frequency-domain fatigue life and the time-domain fatigue life increases with the slope K of the S–N curve. Furthermore, it observably reduces the sampling variability of time-domain fatigue life for the large slope K, which will help the related researchers to establish better frequency-domain models for fatigue life prediction by using the time-domain fatigue life values as standard data.Keywords: Random fatigue life; Sampling variability control; Monte Carlo simulations; Control parameters optimizing创新点 | Highlights
- A method for parameters optimizing in Monte Carlo simulations is developed
- The relative error between frequency and time domain life predictions is reduced
- The method reduces the sampling variability of time-domain random fatigue life
- The method contributes to establish better frequency-domain models
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Fig. 1. Two common PSD patterns
图 2: 不同斜率下不规则因子为 0.1071 时矩形谱样本疲劳损伤随采样点数对数、采样因子与随机种子的变化Fig. 2. Fatigue damages against lgN, η, and the random seed for a rectangle spectrum sample with α_2 of 0.1071 for different K
图 3: 不同斜率下不规则因子为 0.9293 时光滑谱样本疲劳损伤随采样点数对数、采样因子与随机种子的变化Fig. 3. Fatigue damages against lgN, η, and the random seed for a smooth spectrum sample with α_2 of 0.9293 for different K
图 4: 斜率为 3.624、不规则因子为 0.9293 时光滑谱样本在不同采样因子与随机种子下疲劳损伤随采样点数对数的变化Fig. 4. Fatigue damages against lgN for different η and different random seeds for a smooth spectrum sample with α_2 of 0.9293 for K = 3.624
图 5: 斜率为 3.624、不规则因子为 0.9293 时光滑谱样本在不同采样因子下的时域信号样本峰谷Fig. 5. Peaks and valleys of time-domain signal samples for different η values for a smooth spectrum sample with α_2 of 0.9293 for K = 3.624
图 6: 不同频率分辨率下功率谱密度样本的离散过程Fig. 6. Discretization process of a PSD sample with different frequency resolutions
Fig. 7. Range of the sampling factor η and the number of sampling points N for the maximum fluctuation δ_max
Fig. 8. Overall flowchart of the Method III proposed in this paper
图 9: 子流程图 A: 保持采样因子为常数而增加采样点数Fig. 9. Sub-flowchart A: Keep the sampling factor η constant and increase the number of sampling points N
图 10: 子流程图 B: 保持频率分辨率为常数而增大采样因子Fig. 10. Sub-flowchart B: Keep the frequency resolution Δf constant and increase the sampling factor η
Fig. 11. Sub-flowchart C: perform additional stability tests
图 12: 不规则因子为 0.1071 时三类不同方法下材料 M4 (斜率 17.75) 矩形谱样本的 100 组频域与时域疲劳寿命相对误差直方图Fig. 12. Histograms of 100 relative errors between frequency-domain fatigue life ζ_F and time-domain fatigue life ζ_T for a rectangle spectrum sample with α_2 = 0.1071 for material M4 (K = 17.75) for three different methods
图 13: 不规则因子为 0.9293 时三类不同方法下材料 M3 (斜率 11.76) 矩形谱样本的 100 组频域与时域疲劳寿命相对误差直方图Fig. 13. Histograms of 100 relative errors between frequency-domain fatigue life ζ_F and time-domain fatigue life ζ_T for a smooth spectrum sample with α_2 = 0.9293 for material M3 (K = 11.76) for three different methods
作者信息 | Authors
西安电子科技大学 (Xidian University) 机电工程学院
仇原鹰 Yuan-Ying Qiu, 共同通讯作者 (Corresp.) 西安电子科技大学 (Xidian University) 机电工程学院Email: yyqiu@mail.xidian.edu.cn
李静 Jing Li, 共同通讯作者 (Corresp.) 西安电子科技大学 (Xidian University) 机电工程学院Email: lijing02010303@163.com
中国航天推进技术研究院 (Xi'an Aerospace Propulsion Test Technology Institute)
湖南省汽车技师学院 (Hunan Province Motor Vehicle Technician College)
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
