D-S理论和Markov链组合的桥梁性能退化预测研究  

Research on Bridge Performance Degradation Prediction Based on Combination of the D-S Theory and the Markov Chain

作　　者：杨国俊[1,2] 田里 唐光武 毛建博[1] 杜永峰 YANG Guojun;TIAN Li;TANG Guangwu;MAO Jianbo;DU Yongfeng(School of Civil Engineering,Lanzhou University of Technology,Lanzhou 730050,P.R.China;State Key Laboratory of Bridge Engineering Structural Dynamics,China Merchants Chongqing Communications Technology Research&Design Institute Co.,Ltd.,Chongqing 400067,P.R.China)

机构地区：[1]兰州理工大学土木工程学院,兰州730050 [2]招商局重庆交通科研设计院有限公司桥梁工程结构动力学国家重点实验室,重庆400067

出　　处：《应用数学和力学》2024年第4期416-428,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(52168042);甘肃省科技计划(22JR5RA250);甘肃省优秀研究生“创新之星”项目(2023CXZX-460)。

摘　　要：为准确预测桥梁性能退化,考虑到数据随机性和微小扰动发生状态跳跃,提出了一种D-S(Dempster-Shafer)证据理论和Markov链组合的桥梁性能退化组合预测模型和性能退化率的概念.该模型基于指数平滑(exponential smoothing,ES)方法获得新的预测数据序列,并利用Markov链和D-S理论不断进行优化,从而实现桥梁性能退化的组合预测.实际工程的应用结果表明:性能退化率可以直观地表征在梁性能退化的速度.其次,该模型的平均相对误差为1.54%,较于回归、灰色和模糊加权Markov链模型,精度分别提高了1.11%,0.88%和2.8%,而后验差比值为0.242,小于0.35;模型的标准差为9.021,相比其他模型分别减小了3.978,3.405和7.500,而变异系数为0.109,均小于其他模型,验证了组合预测模型在精度和稳定性方面的优越性,可为在役桥梁结构性能退化预测与维护提供理论基础.To accurately predict bridge performance degradation,the inherent data randomness and the subtle perturbations leading to state transitions were considered.A combined prediction method for the bridge performance degradation based on the D-S theory and the Markov chain,and the performance degradation rate concept,were proposed.In this model,the exponential smoothing(ES) methodology was employed as the basis for generating new sequences of predictive data.It was continuously optimized through the utilization of the Markov chains and the Dempster-Shafer(D-S) evidence theory.The combined prediction of bridge performance degradation was achieved.The application results from practical engineering show that,the performance degradation rate serves as an intuitive indicator of the speed at which the bridge performance degrades.Subsequently,the combined model demonstrates an average relative error of 1.54%,improves by 1.11%,0.88%,and 2.8% in accuracy,respectively in comparison with other models of the regression,the grey system,and the fuzzy weighted Markov chain.Additionally,the calculated posterior difference ratio is 0.242,well below the established threshold of 0.35.In terms of stability,the standard deviation of the model is 9.021,reduces by 3.978,3.405 and 7.500,respectively compared with those of the other 3 models.The coefficient of variation is 0.109,indicating a significant reduction in comparison to those of the other models.The combined prediction model,with verified accuracy and stability,establishes a theoretical foundation for prediction and maintenance of in-service bridges' structural performance degradation.

关 键 词：桥梁工程 性能退化预测 D-S证据理论 MARKOV链 组合预测模型 桥梁性能退化率 

分 类 号：U448.33[建筑科学—桥梁与隧道工程] O29[交通运输工程—道路与铁道工程]