A Quadratic-move Transitional Ensemble Markov Chain Monte Carlo strategy for the Physics-guided Stochastic Reliability Analysis under Limited Data

The paper presents a novel Quadratic-Move Transitional Ensemble Markov Chain Monte Carlo sampling strategy designed to improve mixing performance in high-dimensional sampling spaces. The core contribution lies in leveraging a quadratic-move proposal mechanism, which demonstrates superior exploration capabilities in confined and highly-skewed sample spaces compared to traditional stretch-move and random-walk strategies. To empirically assess its mixing performance, the proposed sampler is first implemented on a two-dimensional Rosenbrock function which provides a confined and highly-skewed sampling space. Following which, to demonstrate the practical relevance and performance of the proposed sampling strategy in a high-dimensional setting, a case study is conducted on a jet engine turbine blade whose reliability analysis is done on its thermal stress response. A physics-guided Bayesian reliability analysis is carried out using sparse data on the Young's modulus, Poisson's ratio, and the pressure loads from both the pressure and suction sides of the blade, whose respective aleatory variability is to be characterised. Comparative assessments against the stretch-move Transitional Ensemble Markov Chain Monte Carlo sampler in both case studies show that the quadratic-move variant significantly enhances the sample mixing performance. The results affirm the potential of the proposed strategy to improve inference robustness and reliability predictions in high-stakes engineering systems under limited data.

Keywords: Bayesian updating, Approximate Bayesian Computation, Transitional Ensemble Markov Chain Monte Carlo, Quadratic-move, Reliability analysis, Physics-enhanced Machine Learning.