Uncertainties quantification for damage localization in concrete based on Bayesian method基于 Bayes 方法的混凝土损伤定位不确定性量化
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Zhang MH, Zhou DY, Yang X, Sun XT, Kong QZ, 2024. Uncertainties quantification for damage localization in concrete based on Bayesian method. Probabilistic Engineering Mechanics, 77: 103660.DOI: 10.1016/j.probengmech.2024.103660
混凝土中的缺陷会削弱结构承载力，产生安全性和耐久性的潜在问题。因此，迫切需要一种可提高损伤定位灵敏度、分辨率和鲁棒性的方法，以评估混凝土结构状态。本研究提出了一种基于 Bayes 概率融合的损伤定位方法，考虑并量化了测量和识别过程中的不确定性。该方法基于双曲线损伤定位方法构建似然函数，并结合测量数据的 Bayes 定理计算未知参数的后验分布。此外，建立了细观层次的有限元模型，其中混凝土介质视为多边形骨料、砂浆基体和界面过渡区组成的三相复合材料。通过细观层次建模，可更好地表征混凝土内部应力波的传播行为及应力波与混凝土内部结构的复杂相互作用。最后，从响应信号中提取损伤信息 (到达时间差)，并数值验证了所提方法的有效性。数值结果表明，所提概率融合方法在空间分辨率和损伤定位的鲁棒性方面优于传统双曲线方法。关键词: Bayes 方法, 损伤定位, 细观层次混凝土数值模型, 结构健康监测The presence of defects in concrete can diminish load-bearing capacity of structures, giving rise to potential concerns regarding safety and durability. Thus, a method that enhances the sensitivity, resolution and robustness of damage localization is critically necessary to assess the condition of concrete structures. This research presents a damage localization method based on Bayesian probabilistic fusion, and uncertainties from measurement and identification process are considered and quantified. The likelihood function is constructed based on the hyperbola-based damage localization method, and the posterior distributions of unknown parameters are calculated via Bayesian theorem combined with measurement data. Furthermore, a meso-level finite element model is established, wherein the concrete medium is considered as a three-phase composite material consisting of polygonal aggregates, mortar matrix and interface transition zones. Owing to the meso-level modeling, the propagation behavior of stress waves within concrete and complicated interactions between stress waves and concrete internal structures can be better characterized. Finally, the damage information, time-difference-of arrival, is extracted from the response signals and the efficiency of the proposed method is verified numerically. The numerical results demonstrate that the proposed probabilistic fusion method outperforms the conventional hyperbola-based method in terms of achieving high spatial resolution and resilience in damage localization.
Keywords: Bayesian method; Damage localization; Meso-level concrete numerical model; Structural health monitoring.![]()
Fig. 1. Schematic of hyperbola-based damage localization method
Fig. 2. Flow chart of proposed probabilistic fusion methodology
图 3: 含随机多边形骨料的介观混凝土模型: (a) 模型 I; (b) 模型 II; (c) 模型 IIIFig. 3. Meso-level concrete model with random polygonal aggregates: (a) Model I; (b) Model II; (c) Model III
图 4: 二维混凝土模型的数值研究示意图: (a) 宏观模型; (b) 介观模型Fig. 4. Schematic diagram of two-dimensional concrete model in numerical studies: (a) Macro-level model; (b) Meso-level model
图 5: 正常与缺陷条件下应力波的传播: (a) 宏观层面; (b) 介观层面Fig. 5. Propagation of stress wave in both healthy and defective conditions: (a) Macro-level; (b) Meso-level
图 6: 四种不同条件下应力波的介观传播: (a) 正常状态; (b-d) 含三种不同直径损伤的缺陷状态: 10, 20, 30 mmFig. 6. Stress wave propagation at meso-level with four different conditions: (a) Healthy condition; (b-d) Defective conditions with three different damage diameters: 10 mm, 20 mm, and 30 mm
图 7: 案例 I 中以 P1 为执行器从宏观和介观模型获得的响应信号: (a,d) 正常状态; (b,e) 缺陷状态; (c,f) 传感路径下正常信号与缺陷信号的对比Fig. 7. Response signals obtained from macro-level and meso-level models with 'P1' as actuator in Case I: (a,d) Healthy condition; (b,e) Defective condition; (c,f) Comparison of healthy signal and defective signal of sensing path 'P1-8' (denoting the 'P1' is actuator and 'P8' is receiver)
图 8: 案例 I 中未知参数的 Markov 链蒙特卡罗样本直方图: (a) x 坐标; (b) y 坐标Fig. 8. Histograms of MCMC samples for the unknown parameters in Case I: (a) x-coordinate (x_d); (b) y-coordinate (y_d)
图 9: 案例 I 采用所提方法的损伤定位结果: (a) 全局图; (b) 局部放大图Fig. 9. Damage localization result using proposed method in Case I: (a) Global diagram (the black symbol “ο” indicates transducer location); (b) Local zoomed-in diagram (the black pentagram symbol “☆” indicates estimated damage location, and the black symbol “ο” indicates actual damage location)
图 10: 案例 I 采用传统方法的损伤定位结果: (a) 全局图; (b) 局部放大图Fig. 10. Damage localization result using conventional method in Case I: (a) Global diagram (the black symbol “ο” indicates transducer location); (b) Local zoomed-in diagram (the blue pentagram symbol “☆” indicates estimated damage location, the blue symbol “ο” indicates actual damage location)
图 11: 案例 II 中未知参数的 Markov 链蒙特卡罗样本直方图: (a) x 坐标; (b) y 坐标Fig. 11. Histograms of MCMC samples for the unknown parameters in Case II: (a) x-coordinate (x_d); (b) y-coordinate (y_d)
图 12: 案例 II 采用所提方法的损伤定位结果: (a) 全局图; (b) 局部放大图Fig. 12. Damage localization result using proposed method in Case II: (a) Global diagram; (b) Local zoomed-in diagram
图 13: 案例 II 采用传统方法的损伤定位结果: (a) 全局图; (b) 局部放大图Fig. 13. Damage localization result using conventional method in Case II: (a) Global diagram; (b) Local zoomed-in diagram
作者信息 | Authors
同济大学 (Tongji University) 结构防灾减灾工程系
同济大学 (Tongji University) 结构防灾减灾工程系
同济大学 (Tongji University) 结构防灾减灾工程系
同济大学 (Tongji University) 结构防灾减灾工程系
孔庆钊 Qing-Zhao Kong, 通讯作者 (Corresp.)同济大学 (Tongji University) 结构防灾减灾工程系Email: qkong@tongji.edu.cn
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)
