Influence of uncertainties on dynamic properties and responses of human-structure coupled system under bouncing excitations人致振动激励下不确定性对人—结构耦合系统动力特性与响应的影响
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Zeng DJ, Wang HQ, Chen J, 2024. Influence of uncertainties on dynamic properties and responses of human-structure coupled system under bouncing excitations. Probabilistic Engineering Mechanics, 75: 103593.DOI: 10.1016/j.probengmech.2024.103593
摘要 | Abstract
近年来，在服役性能评估中考虑人—结构耦合系统的固有不确定性已成为共识。来自人体和结构的不确定性通过人—结构相互作用 (human-structure interaction, HSI) 效应耦合并共同传播。然而，目前尚不清楚每个随机源在有节奏运动下如何影响系统输出，且缺乏相关研究。本文介绍了在人群屈伸运动下大跨楼板的不确定性量化和全局灵敏度分析方法。通过建立人—结构相互作用模型，同时考虑了结构和人体的不确定性。采用 Kullback–Leibler 散度指标和概率密度演化方法 (probability density evolution method, PDEM) 进行不确定性分析。研究了具有不同特征的四种结构的动力特性和振动响应。对结构模态质量、阻尼比和自振频率进行了参数分析，以获得通用结论，并提出了一种快速识别重要变量的方法。还研究了忽略不重要变量对动力可靠性的影响。结果发现，无论结构特性如何，进行屈伸运动的人群对结构频率的影响有限，但可能显著增加结构阻尼比及其变异性。在大多数情形下，人体阻尼比和频率是影响结构阻尼比的主要参数。人群屈伸运动下结构加速度响应具有较大的变异性，需要在计算中考虑。人体的质量、频率、阻尼比以及结构的质量和阻尼比在大多数情形下对加速度响应不重要，而屈伸运动的频率和结构频率在大多数情形下很重要。生物力动载因子的重要性在很大程度上取决于结构频率和阻尼比。仅考虑建议重要变量的可靠性结果对于实际工程已精度足够。关键词: 全局灵敏度分析; 不确定性量化; 概率服役性能评估; 人群跳动; 人—结构相互作用The consideration of inherent uncertainties of the human-structure coupled system during serviceability assessment has become a consensus in recent years. The uncertainties from human body and structures are coupled and propagate together through the human-structure interaction (HSI) effect. However, how each random source affects the system output under rhythmic motion remains unclear and lacks investigation. In this paper, a method for uncertainty quantification and global sensitivity analysis for large-span floors under crowd bouncing is introduced. Both the uncertainties from the structure and the human body are considered through an HSI analytical model. The Kullback–Leibler (K-L) divergence indices and probability density evolution method (PDEM) are adopted for the uncertainty analysis. Dynamic properties and vibration responses of four structures with different characteristics are investigated. Parametric analysis of structural modal mass, damping ratio, and natural frequency is carried out for general insights and a quick method identifying the important variables is proposed. The influence on dynamic reliability after eliminating unimportant variables is investigated. It is found that a bouncing crowd has limited influence on structural frequency regardless of the structural characteristics but may significantly increase the structural damping ratio and its variability. The human body damping ratio and the human body frequency are the main influential parameters for the structural damping ratio in most cases. The structural acceleration responses under crowd bouncing are with large variability, which needs to be considered during the calculation. The mass, frequency, damping ratio of human body, the mass, and the damping ratio of structure are unimportant for acceleration responses in most cases, while the frequency of bouncing activity and structure are important in most cases. The importance of biomechanical load factors heavily depends on the structural frequency and the structural damping ratio. The reliability results only considering the suggested important variables are accurate enough for the engineering practice.Keywords: Global sensitivity analysis; Uncertainty quantification; Probabilistic serviceability assessment; Crowd bouncing; Human-structure interaction![]()
Fig. 1. Diagram of analytical model
Fig. 2. Overview of the structures
图 3: 人群—结构耦合系统自振频率与阻尼比的统计特性Fig. 3. Statistical characteristics of the natural frequency and damping ratio of the crowd-structure coupled systems
Fig. 4. TSI results of the natural frequency and the damping ratio
图 5: 结构 I 动力特性原概率密度函数与固定某一变量下概率密度函数的对比Fig. 5. Comparison between the original PDF and PDF with one variable set fixed of dynamic properties of structure I
Fig. 6. Statistical characteristics of acceleration responses
Fig. 7. TSI results of acceleration responses
图 8: 结构 I 加速度响应原概率密度函数与固定某一变量下概率密度函数的对比Fig. 8. Comparison of original PDF and PDF with one variable set fixed of acceleration response of structure I
Fig. 9. Change of TSI values with the mean value of structural damping ratios
图 10: 3% 平均阻尼比下人群频率、人致激励频率与结构频率的总灵敏度指标值随自振频率与模态质量均值的变化Fig. 10. Change of TSI values for f_h, f_b, and f_s with mean values of natural frequency and modal mass at 3% mean damping ratio
图 11: 3% 平均阻尼比下生物力动载因子的总灵敏度指标值随自振频率与模态质量均值的变化Fig. 11. Change of TSI values for β_1, β_2, and β_3 with mean values of natural frequency and modal mass at 3% damping ratio
图 12: 17 t 模态质量下生物力动载因子的总灵敏度指标值随自振频率与阻尼比均值的变化Fig. 12. Change of TSI values for β_1, β_2, and β_3 with mean values of natural frequency and damping ratio at 17t modal mass
图 13: 加速度响应的原概率密度函数与仅考虑建议重要性变量不确定性的概率密度函数对比Fig. 13. Comparison of original PDF of acceleration response and PDF only considering the uncertainties of the suggested important variables
图 14: 加速度响应的原可靠度与仅考虑建议重要性变量不确定性的可靠度对比Fig. 14. Comparison of original reliability and the reliability only considering the uncertainties of the suggested important variables
作者信息 | Authors
同济大学 (Tongji University) 土木工程学院
王浩祺 Hao-Qi Wang, 通讯作者 (Corresp.) 同济大学 (Tongji University) 土木工程学院Email: 12wanghaoqi@tongji.edu.cn
同济大学 (Tongji University) 土木工程学院
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)
