基于贝叶斯理论评估轴力作用下带损伤段梁

Assessment of Axially Loaded Beam with Damage Section Using Bayesian Estimation Theory

提出利用半幅函数求得带损伤段梁在轴力作用下自由振动的近似解。考虑模型误差和量测噪声的影响,在基于动力响应的损伤识别中引入了贝叶斯估计理论。通过构造基于前两阶自振频率的损伤位置指标和损伤程度指标,分别获取了损伤段参数的后验概率分布表达式。考虑到贝叶斯公式中多维函数积分困难的问题,采用马尔科夫链蒙特卡罗抽样技术获取了损伤段参数的样本序列,得到了相应的数值统计特征值。数值算例表明提出的方法可以成功识别概率意义上的损伤位置和损伤程度。

Approximate solution for free vibration of axially loaded beam with damage section is obtained using half-range function. Bayesian estimate theory was introduced in damage identification utilizing dynamic response consideration of model error and measurement noise. Damage location indexes and damage level ones are construc- ted based on the first two natural frequencies. The posterior distribution expressions for damage section parameters are realized. Consideration of integral difficulties in multi dimension function of Bayesian formula, Markov chain Monte Carlo sampling technology is used to obtain the sampling chain, and the conresponding numerical statistical characteristic value are obtained too. The methodology presente successfully identified damage location and extent in probability framework in the numerical case study.