基于模糊贝叶斯理论更新概率可靠性模型

UPDATING PROBABILITY RELIABILITY MODEL BASED ON FUZZY BAYESIAN THEORY

贝叶斯理论是基于无损检测结果对海洋工程结构可靠性进行更新研究的有力工具。针对传统贝叶斯理论无法有效地处理海洋结构无损检测中存在的大量模糊不确定性问题 ,根据模糊集合论的基本原理 ,在海洋结构可靠性概率模型更新研究中引入了模糊贝叶斯理论和模糊综合评判方法 ,对模型不确定性和检测结果中的模糊不确定性进行了定量评估。对基于检测结果的更新可靠性模型的参数分布和模型权值进行了探讨 ,并采用模糊综合评判方法确定了模型权值的先验概率。算例结果表明 ,此方法是可行的 ,检测结果的模糊性对可靠性概率模型更新具有重要影响 ,考虑模糊不确定性可以得到更为合理的结果。对于参数的概率密度函数而言 ,考虑多个模型和只考虑一个模型可得到相同的结果 ,但参数的不确定性对模型权值的更新有一定的影响。在工程实际应用中 ,对于有关海洋工程结构经检测和维修后的可靠性更新问题 。

Bayesian theory is an effective tool for updating prior failure probabilities based on the information from non-destructive inspection (NDI) of offshore structures. However, the preceding theorem failed to adequately deal with the uncertainties of the subjective parameters associated with NDI. Based on the basic principles of fuzzy set theory, a fuzzy Bayesian procedure was introduced to quantify the modeling uncertainty, including the uncertainty of model selection, the uncertainty of distribution parameter, and the fuzzy uncertainties in NDI. An algorithm to compute the weights of posterior probability model was presented, and the posterior probability and distribution of parameters were analyzed with the fuzzy Bayesian theorem. The prior probabilities of model weights were determined by the use of fuzzy synthetic evaluation. Some examples were investigated to illustrate the validation of the proposed method. The result shows that the effects of fuzzy uncertainties can be very significant to updating the reliability modeling.