摘要
贝叶斯模型更新是一种基于先验分布和观测数据来预测和校准模型的有效方法。在工程试验中,仪器精度、人为误差和环境干扰等不确定因素都会引起观测数据的不准确,进而导致后验分布参数也具有不确定性,给贝叶斯更新带来了新的挑战。为准确得到观测不确定性下后验样本的分布,通过将观测不确定性下的贝叶斯更新问题等价转化为区间和随机变量共同作用下的可靠性分析问题,建立观测不确定性下的贝叶斯更新模型,并提出了模型求解的双层和单层Kriging算法,高效地实现了观测不确定性下贝叶斯模型更新的量化求解。所建模型和方法在机翼等结构中的应用表明,所建模型能够准确度量观测不确定性对后验分布参数的影响,实现观测不确定性下输入变量分布参数的完整更新,有效地降低输入变量分布参数的不确定性;所建的单层Kriging算法可以高效地给出后验样本的平均估计,双层Kriging算法能够精确地给出后验样本分布参数的完整取值区间。相比于蒙特卡洛方法,所提2种方法在保证精度的同时,大幅减少了原始模型的调用次数,提高了观测不确定性下贝叶斯更新的计算效率。
Bayesian model updating is an effective method to predict and calibrate models based on prior distribution and observation data.Uncertainties in engineering experiments,such as instrumental accuracy,human errors and environmental interference,can cause inaccuracy of observation data,which in turn result in uncertainty of posterior distribution parameters,bringing new challenges to Bayesian updating.To obtain the accurate posterior sample distri⁃bution under the observation uncertainty,the Bayesian updating problem under the observation uncertainty is studied.By equivalently transforming the Bayesian updating problem under the observation uncertainty into a reliability analysis problem involving interval and random variables,a new Bayesian updating model is established.A single-layer and a double-layer Kriging algorithms for estimating the established model are proposed,which can efficiently achieve quan⁃titative Bayesian model updating under the observation uncertainty.The application of the proposed model and method in wing and other structures shows that the established model can accurately measure the influence of obser⁃vation uncertainty on posterior distribution parameters,achieve the complete update of input variable distribution pa⁃rameters under observation uncertainty,and effectively reduce the uncertainty of input variable distribution param⁃eters.The single-layer Kriging algorithm can efficiently provide the average estimates of the posterior sample distribu⁃tion,while the double-layer Kriging algorithm can accurately provide the complete value interval of posterior sample distribution parameters.Compared with the Monte Carlo method,the two proposed algorithms significantly reduce the number of calls to the original model while ensuring the accuracy,enhancing the computational efficiency of Bayesian updating under observation uncertainty.
作者
于汀
李璐祎
刘昱杉
常泽明
YU Ting;LI Luyi;LIU Yushan;CHANG Zeming(School of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China)
出处
《航空学报》
EI
CAS
CSCD
北大核心
2023年第24期112-129,共18页
Acta Aeronautica et Astronautica Sinica
基金
国家自然科学基金(52375156)。
