船舶结构腐蚀检测与腐蚀模型不确定性及其更新

针对经典的概率论不能有效地处理无损检测中检测概率的参数不确定性问题,提出了定量分析检测概率参数不确定性问题的贝叶斯方法,并以威布尔分布形式的检测概率为例,推导了量化参数不确定性的放大系数的计算公式.针对传统的数据分析法及专家判断法不能分析模型不确定性更新问题,本文基于无损检测信息,采用贝叶斯更新方法量化了检测概率分布函数的统计模型不确定性,得到了检测概率统计模型权重的后验概率及相应的分布参数的后验概率密度函数.最后提出了分析船体结构腐蚀多层次模型不确定性问题的全概率模型法,并用算例证明了文中所提方法的有效性.

Inspection Uncertainty and Model Uncertainty Updating for Ship Structures Subjected to Corrosion Deterioration

The classical probability theory cannot effectively quantify the parameter uncertainty in probability of detection.Furthermore,the conventional data analytic method and expert judgment method fail to handle the problem of model uncertainty updating with the information from nondestructive inspection.To overcome these disadvantages,a Bayesian approach was proposed to quantify the parameter uncertainty in probability of detection.Furthermore,the formulae of the multiplication factors to measure the statistical uncertainties in the probability of detection following the Weibull distribution were derived.A Bayesian updating method was applied to compute the posterior probabilities of model weights and the posterior probability density functions of distribution parameters of probability of detection.A total probability model method was proposed to analyze the problem of multi-layered model uncertainty updating.This method was then applied to the problem of multi-layered corrosion model uncertainty updating for ship structures.The results indicate that the proposed method is very effective in analyzing the problem of multi-layered model uncertainty upda-ting.