MAntRA: A framework for model agnostic reliability analysis

We propose a novel model-agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach - referred to as MAntRA - combines Bayesian inference and stochastic differential equations to evaluate the reliability of stochastically-driven dynamical systems for which the governing physics is a priori 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-only data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data and aleatoric uncertainty because of environmental effects and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme, and the probability of failure is computed. The efficacy of the proposed approach is illustrated in four 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.

Automated summary

We propose a novel model-agnostic data-driven reliability analysis framework, named MAntRA, for time-dependent reliability analysis. The framework combines Bayesian inference and stochastic differential equations to evaluate the reliability of stochastically-driven dynamical systems with unknown governing physics. The proposed approach adopts a two-stage method: an efficient variational Bayesian equation discovery algorithm is used to determine the governing physics from output-only data, and then the discovered equation is solved and the probability of failure is computed using a stochastic integration scheme. The efficacy of the approach is demonstrated through four numerical examples, indicating its potential application for reliability analysis of in-situ and heritage structures from on-site measurements.