Augmenting transport maps with metamodel tools for an accurate and efficient Bayesian framework for dynamical systems

Real-time diagnostics of complex mechanical systems, such as aircraft engines or gas turbines in power plants, is one of the greatest current challenges in maintenance industry to control cost and time. Accurate online state and parameter estimation in uncertain non-linear dynamical systems have traditionally relied on non-linear Kalman Filters or particle filters. While Bayesian model updating has proven successful in enhancing the fidelity of models affected by hybrid uncertainties, algorithms based on Markov Chain Monte Carlo exhibit prohibitive computational costs, especially when hybrid uncertainties are involved.  

In this project, we propose a novel approach to address these challenges by augmenting the transport map framework with metamodel tools, specifically Sparse Identification of Nonlinear Dynamics (SINDy) and Sliced Normal Distributions. SINDy offers an explainable AI approach to handle dynamical systems, providing insights into their behaviour. On the other hand, Sliced Normal Distributions offer an efficient tool to describe the probability density functions of highly non-linear outputs.  

The integration of SINDy and Sliced Normal Distributions into the transport map framework aims to create a powerful and numerically efficient Bayesian framework. This hybrid methodology leverages the strengths of each component to improve the accuracy and computational efficiency of online state and parameter estimation in uncertain non-linear dynamical systems. The resulting framework holds promise for a wide range of applications, particularly in scenarios where traditional methods face challenges posed by computational intensity and model fidelity.

Doctoral Researcher: Lukas Fritsch

Scientific Advisors:  Micheal Beer, Ludovic Chamoin