基于同伦分析方法的梁结构静力随机损伤识别  

Static stochastic damage identification of beam structures based on homotopy analysis method

作　　者：黄斌[1] 刘雨欣 吴志峰 李烨君 HUANG Bin;LIU Yuxin;WU Zhifeng;Li Yejun(School of Civil Engineering and Architecture,Wuhan University of Technology,Wuhan 430070,China;School of Civil and Hydraulic Engineering,Huazhong University Science and Technology,Wuhan 430074,China;School of Civil Engineering and Architecture,Hubei Polytechnic University,Huangshi 435003,Hubei China)

机构地区：[1]武汉理工大学土木工程与建筑学院,湖北武汉430070 [2]华中科技大学土木与水利工程学院,湖北武汉430074 [3]湖北理工学院土木建筑工程学院,湖北黄石435003

出　　处：《华中科技大学学报（自然科学版）》2023年第7期69-76,共8页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51978545);湖北理工学院人才引进项目(18xjz12R);湖北省教育厅中青年人才项目(Q20194503).

摘　　要：针对测量误差变异性较大时梁结构损伤识别效果不佳的情况,提出了一种基于同伦分析方法的静力随机损伤识别方法.首先,建立了关于损伤系数的随机损伤识别方程;然后,采用同伦分析方法求解随机损伤识别方程,在求解过程中,分别通过静力凝聚技术和L1正则化方法解决有限的测量信息和随机控制方程不适定性的问题;最后,根据定义的损伤概率指标,评估损伤存在的概率.变截面简支梁的数值算例和混凝土梁静载试验的识别结果表明:该方法具有较高的识别精度和效率,在测量误差和初始模型误差较大的情况下,能保证较好的损伤识别效果.A static random damage identification method based on homotopy analysis was proposed to address the poor performance of beam structure damage identification when the variability of measurement errors is large.At first,the stochastic damage identification equations corresponding to the damage indexes were established.Then a new homotopy analysis method was used to solve the stochastic damage identification equations.During the computational process,the static condensation technique and the L1 regularization method were employed to address the limited measurement data and ill-posed problems,respectively.Finally,according to the defined damage probability index,the probability of existing damages was evaluated.The numerical example of the various senction simply supported beam and the static loading test of the concrete beam showed that the new damage identification method has relatively high accuracy and efficiency,can ensure a higher accuracy at the relatively large measurement error and the initial modelling error.

关 键 词：随机损伤识别 同伦分析方法 模型误差 测量误差 静力凝聚 L1正则化 

分 类 号：TU312.3[建筑科学—结构工程]