MAntRA: A framework for model agnostic reliability analysis
This work addresses reliability analysis for engineers dealing with structures where physics is unknown, offering a novel framework, though it appears incremental as it builds on existing methods like Bayesian equation discovery.
The authors tackled the problem of reliability analysis for stochastically-excited dynamical systems with unknown governing physics by proposing MAntRA, a model-agnostic framework that combines interpretable machine learning and Bayesian statistics, achieving results demonstrated on three numerical examples with potential applications for in-situ and heritage structures.
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.