基于贝叶斯统计推断的框架结构损伤诊断研究

DAMAGE ASSESSMENT RESEARCH ON FRAME STRUCTURE BASED ON BAYESIAN STATISTICAL INFERENCE

介绍了贝叶斯统计的基本理论,针对贝叶斯方程中分母由于维数较大难以积分的困难,引进了基于马尔可夫链的蒙特卡罗模拟方法,利用先验概率产生多维空间样本,得到的后验分布能诊断结构的损伤。在实验室的地基上进行了框架结构局部加强柱的损伤前后的模态实验,得到损伤前后的模态参数。利用非损伤状态下的模态参数经过贝叶斯估计得到后验分布的均值,作为第一步模型修正过程;第二步过程采用前次后验分布的均值先修正模型,再重新计算后验分布。利用第二步得到的均值能有效地识别损伤的位置。识别结果还发现地基对识别的结果有较大的影响。

Basic theory of Bayesian statistics is introduced in this paper, in order to solve the difficulties of the denominator hardly in integral due to the larger dimensions, the method of Markov chain＇s Monte Carlo （MCMC） simulation is introduced, the samples in multi-dimension space are produced by prior probability, the damage in structures can be deduced by posterior distribution. The modal experiments were done on a frame structure by enhancing the local column on soil foundation in the laboratory before damage and after damage, the modal parameters were obtained. The modal parameters in non-damage status are used to obtain the mean value of posterior distribution by Bayesian inference, and it is used as the first step of model updating. In the second step, the mean value of the former distribution has been used to update the model, and then the posterior distribution is recalculated. The mean value obtained in step two can identify the location of the damage. The identification results also show that the foundation has important influence on the identification results.