MAntRA: A framework for model agnostic reliability analysis

TL;DR

MAntRA is a novel, model-agnostic framework that combines machine learning and Bayesian methods to evaluate the reliability of complex dynamical systems with unknown physics, using limited and noisy data.

Contribution

It introduces a two-stage approach with an efficient variational Bayesian algorithm for physics discovery and stochastic analysis for reliability assessment, applicable to real-world structures.

Findings

Successfully applied to three numerical examples.

Accurately identifies governing stochastic differential equations.

Provides reliable failure probability estimates from limited data.

Abstract

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.