基于马尔可夫链的钢箱梁正交异性板疲劳状态分析

为对正交异性板U肋的剩余强度退化规律进行研究，引入马尔可夫过程理论，以特大跨径钢箱梁悬索桥--西堠门大桥为工程背景展开研究。首先分析西堠门大桥钢箱梁长期应变监测数据的时频特征，应用小波分析分离出环境温度变化所引起的桥面板结构应力波动，再对小波变换系数在不同尺度上选择合适的阈值来消除由环境随机激励和测量噪声引起的低幅值应力变异；采用雨流计数法对车辆荷载作用下的应变监测数据进行统计分析，得到疲劳应力范围并设定6个疲劳应力区间；然后由U肋对接部位的典型S-N曲线计算得到其强度从初始状态至最终状态的转移概率，并根据Palmgren-Miner线性疲劳累积损伤理论构造出连接部位易损点区域强度演变的状态转移概率矩阵；最后利用初始状态的概率分布向量和状态转移概率矩阵，得出大桥运营阶段不同时刻对应的剩余强度值，给出U肋连接部位的强度退化轨迹。结果表明：所建立的疲劳状态分析模型可以考虑构件强度退化过程中各状态的相关性，能够根据车流量变化来预测正交异性板U肋疲劳状态随桥梁服役时间的变化规律，从而可实现钢箱梁正交异性板U肋的服役性能评估。

Fatigue state analysis of orthotropic plates of steel box girder based on Markov chain

 In order to study the residual strength degradation rule of the U-ribs of orthotropic plates, the Markov process theory was adopted to assess the state change in the very long-span steel box girder suspension bridge-Xihoumen Bridge. First, the time-frequency characteristics of the long-term strain monitoring data of the steel box girder of Xihoumen Bridge were analyzed. The wavelet analysis was used to separate the stress fluctuation of the bridge deck structure caused by the change of environmental temperature. To eliminate the low amplitude stress variation caused by environmental random excitation and measurement noise, the appropriate threshold was selected for the wavelet transform coefficient at different scales. The rain-flow counting method was used to statistically analyze the monitoring data of strain under vehicle load, so that the fatigue stress range was obtained, and six fatigue stress intervals were set. Furthermore, the transition probability of the strength from the initial state to the final state was calculated from the typical S-N curve of the rib-to-rib connection of U-ribs, and the state transition probability matrix of the strength evolution of the vulnerable portion of the connection was constructed according to the Palmgren-Miner linear fatigue cumulative damage theory. Finally, the probability distribution vector of the initial state and the state transition probability matrix were used to obtain the residual strength values at different service time of the bridge, and the strength degradation trajectory of the connection of U-ribs was fitted. The results show that the established fatigue state analysis model can consider the correlation of different states during the process of component strength degradation, and can predict the variation of the U-rib fatigue state of the orthotropic plate during the service time of the bridge according to the change of traffic flow-Hence, the service performance assessment of orthotropic plates of steel box girder can be realized and completed.