基于贝叶斯更新的飞机结构腐蚀可靠度模型

民用飞机结构腐蚀发展的时变性和样本采集的局限性，给腐蚀检测数据分布函数的确定及参数的估计带来了很大的不确定性。针对这一问题，给出了基于贝叶斯公式的合理分布函数选取及参数估计方法。为满足在役飞机结构可靠性动态管理的需求，基于贝叶斯更新思路，将反映结构性能退化共性规律的预测模型视为先验模型，沿着具体结构生命周期不断挖掘利用新信息，建立具体飞机结构腐蚀失效概率和可靠度的动态预测模型。算例采用某型民用飞机地板梁结构腐蚀的无损检测数据，结果显示：腐蚀深度的合理分布为双参数威布尔分布，基于贝叶斯更新后的腐蚀失效概率计算得到的结构可靠度与未更新的显著不同。表明更新后的可靠度因为既考虑了模型参数的历史先验信息，又利用了当前数据实时更新了预测模型，从而有效地降低了有限样本带来的不确定性，使得预测值稳健且具有时变性，更符合工程实际。

Reliability Model of Aircraft Structure Corrosion Based on Bayesian Updated

The time-dependent nature in the development of civil aircraft structure corrosion and the limitations of sample collection have brought uncertainty to the distribution form and parameters of structure corrosion data. Therefore, an approach to select a reasonable distribution function and parameter estimation method is presented in this paper based on Bayesian formula. To meet the demands of the dynamic reliability management of aircraft structures in service, the dynamic forecast models are provided of the corrosion failure probability and the reliability of aircraft structures based on the Bayesian updating with the condition of new testing data being input constantly. The nondestructive testing data of floor beam structure corrosion in a civil aircraft are taken as an example, and the results show that the reasonable distribution of corrosion depth exhibits a Weibull distribution with two parameters, and the calculated reliability of the floor beam structure based on Bayesian updated corrosion failure probability is different from that without updating. It indicates that the updated reliability not only considers the priori information of the model parameters, but also uses the current data to update the forecast model timely, which can effectively reduce the uncertainty resulting from the limited number of samples. Therefore, the forecasts are steady, dynamic, and more in line with engineering practice.