A2.: Augmenting Transport Map with Metamodel Tools for Accurate and Efficient Bayesian Framework in 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 [1].

In this project, we propose a novel approach to address these challenges by augmenting the transport map framework [1] 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 [2]. On the other hand, Sliced Normal Distributions offer an efficient tool to describe the probability density functions of highly non-linear outputs [3].

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.

[1] Kitahara M, Song J, Wei P, et al (2022) A Distributionally Robust Approach for Mixed Aleatory and Epistemic Uncertainties Propagation. AIAA Journal 60:4471–4477. doi.org/10.2514/1.J061394

[2] Rubio P, Louf F, Chamoin L (2019) Transport Map sampling with PGD model reduction for fast dynamical Bayesian data assimilation. Int J Numer Methods Eng 120:447–472. doi.org/10.1002/nme.6143

[3] Brunton SL, Proctor JL, Kutz JN (2016) Sparse Identification of Nonlinear Dynamics with Control (SINDYc), IFAC-PapersOnLine 49:710–715. doi.org/10.1016/j.ifacol.2016.10.249

[4] Crespo LG, Colbert BK, Kenny SP, Giesy DP (2019) On the quantification of aleatory and epistemic uncertainty using Sliced-Normal distributions. Systems & Control Letters 134:104560. doi.org/10.1016/j.sysconle.2019.104560

Supervision: Prof. Dr.-Ing. Michael Beer (LUH), Dr. Ludovic Chamoin (ENS)