We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is \textit{apriori} unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.

翻译：我们建议为基于时间的可靠性分析建立一个新型模型数据驱动的可靠性分析框架。拟议方法 -- -- 称为Montrara -- -- 将可解释的机器学习、巴耶斯统计和确定随机动态方程结合起来,以评价物理原理不明的随机振荡刺激动态系统的可靠性。我们建议采取一个两阶段办法:在第一阶段,开发一个高效的变异巴耶斯方程发现算法,以确定从测量的产出数据中测出的基本随机差分方程(SDE)的物理原理。开发的算法是高效的,并说明了由于数据有限和繁琐,以及由于环境影响和外部引力而导致的显性不确定性。在第二阶段,发现SDE是使用随机集成集成计划解决的,概率失败是计算出来的。在三个数字实例中说明了拟议方法的功效。获得的结果表明,可能采用拟议的方法,从现场测量中可靠地分析现场和遗产结构。