Dimensional reduction technique-based maximum entropy principle method for safety degree analysis under twofold random uncertainty双重随机不确定性下安全性分析的基于降维技术的最大熵方法
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Feng KX, Lu ZZ, Li HC, He PF, Dai Y, 2024. Dimensional reduction technique-based maximum entropy principle method for safety degree analysis under twofold random uncertainty. Probabilistic Engineering Mechanics, 76: 103628.DOI: 10.1016/j.probengmech.2024.103628
摘要 | Abstract
本文提出了一种改进的失效机会测度 (failure chance measure, FCM)，用于评估双重随机不确定性影响下的结构安全性。这种不确定性来源于具有随机分布参数的随机输入。本研究的目的是在此类条件下有效评估结构的安全性。本文引入了一种基于降维技术的最大熵方法来求解这一问题。该方法利用最大熵原理在分数阶矩约束下高效逼近最优概率密度特性。此外，采用降维策略估算分数矩，使得计算成本随维度线性增长。本文的主要贡献在于将用于估算失效机会测度的双重不确定性分析解耦为单层不确定性分析。该方法重复使用同一组积分网格点估算求解失效机会测度所需的不同分数阶矩。采用该方法在可接受精度下求解失效机会测度结果表明，当不确定性维度限制在 20 时，功能函数所需的评估次数可减少到 100 次以下。这验证了所提方法在求解失效机会测度方面的高效性。关键词: 双重随机不确定性, 失效机会测度, 降维技术, 最大熵原理, 单层不确定性分析A modified failure chance measure (FCM) was proposed to assess the safety degree of structures under the influence of twofold random uncertainty. This uncertainty arises from random inputs with random distribution parameters. The aim of this paper is to effectively evaluate the safety degree of structures in such conditions. This paper introduces a method named dimensional reduction technique-based maximum entropy principle to address the issue at hand. The proposed method utilizes maximum entropy principle method to efficiently approach optimal probability density characteristics while adhering to the constraints imposed by fractional moments. Additionally, the dimensional reduction strategy is employed to estimate fractional moments, resulting in a linear increase in computational cost with respect to the dimensionality. The primary contribution of this work involves the detailed decoupling of the double-uncertainty analysis used to estimate FCM into a single-uncertainty analysis. This approach allows for the innovative re-use of the same group integral grid points to estimate different fractional moments required for solving FCM. The results of applying the proposed method to solve FCM under acceptable accuracy demonstrate that the number of evaluations required for the performance function can be reduced to less than 100 when the uncertainty dimensionality is limited to 20. This finding confirms the high efficiency of the proposed method for solving FCM.Keywords: Twofold random uncertainty; Failure chance measure; Dimensional reduction technique; Maximum entropy principle; Single-uncertainty analysis![]()
Fig. 1. Visualization of evaluating the failure probabilities by repeatedly using the same samples
Fig. 2. Flowchart of the proposed method for estimating the FCM
Fig. 3. An automobile front axle structure
图 4: 汽车前轴结构在单随机分布参数下失效概率的概率分布函数Fig. 4. Cumulative distribution function of the failure probability of case 1 in example 1
图 5: 汽车前轴结构在单随机分布参数下关于置信水平的失效机会测度估计Fig. 5. FCM estimates with respect to the confidence level of case 1 in example 1
图 6: 汽车前轴结构在单随机分布参数下失效机会测度估计的相对误差Fig. 6. Relative errors of FCM estimates of case 1 in example 1
图 7: 汽车前轴结构在三个随机分布参数下关于置信水平的失效机会测度估计Fig. 7. FCM estimates with respect to the confidence level of case 2 in example 1
图 8: 汽车前轴结构在三个随机分布参数下失效机会测度估计的相对误差Fig. 8. Relative errors of FCM estimates of case 2 in example 1
图 9: 汽车前轴结构在三个随机分布参数下失效概率的概率分布函数Fig. 9. Cumulative distribution function of the failure probability of case 2 in example 1
Fig. 10. Geometry of two-bay six-storey frame
图 11: 两跨六层框架关于置信水平的失效机会测度估计Fig. 11. FCM estimates with respect to the confidence level of example 2
图 12: 两跨六层框架失效机会测度估计的相对误差Fig. 12. Relative errors of FCM estimates of example 2
Fig. 13. Cumulative distribution function of the failure probability of example 2
Fig. 14. A non-linear undamped single-degree of freedom system
图 15: 非线性无阻尼单自由度系统关于置信水平的失效机会测度估计Fig. 15. FCM estimates with respect to the confidence level of example 3
图 16: 非线性无阻尼单自由度系统失效机会测度估计的相对误差Fig. 16. Relative errors of FCM estimates of example 3
图 17: 非线性无阻尼单自由度系统失效概率的概率分布函数Fig. 17. Cumulative distribution function of the failure probability of example 3
Fig. 18. Turbine shaft structure
图 19: 涡轮轴结构在单随机分布参数下关于置信水平的失效机会测度估计Fig. 19. FCM estimates with respect to the confidence level of case 1 in example 4
图 20: 涡轮轴结构在单随机分布参数下失效机会测度估计的相对误差Fig. 20. Relative errors of FCM estimates of case 1 in example 4
图 21: 涡轮轴结构在两随机分布参数下关于置信水平的失效机会测度估计Fig. 21. FCM estimates with respect to the confidence level of case 2 in example 4
图 22: 涡轮轴结构在两随机分布参数下失效机会测度估计的相对误差Fig. 22. Relative errors of FCM estimates of case 2 in example 4
作者信息 | Authors
冯凯旋 Kai-Xuan Feng, 共同通讯作者 (Corresp.) 同济大学 (Tongji Universtiy) 航空航天与力学学院Email: 18392592026@163.com
西北工业大学 (Northwestern Polytechnical University) 航空学院
西北工业大学 (Northwestern Polytechnical University) 航空学院
贺鹏飞 Peng-Fei He, 共同通讯作者 (Corresp.) 同济大学 (Tongji Universtiy) 航空航天与力学学院Email: ph232@tongji.edu.cn
同济大学 (Tongji Universtiy) 航空航天与力学学院
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)
