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Accurate online state and parameter estimation of uncertain non‐linear dynamical systems is a demanding task that has been traditionally handled by adopting non‐linear Kalman Filters or particle filters. However, in case of Kalman filters the system needs to be linearised and for particle filters the computational demand can be high. Recent advances in optimal transport theory and the application to Bayesian model updating pave the way for other approaches to system and parameter identification. They also provide a way of formulating the problem in such a way that efficient online estimation for complex systems is possible. In this work, we investigate the properties of the transport map approach when compared to standard Markov Chain Monte Carlo in an off‐line setting as a first step towards on‐line parameter estimation. We apply both approaches to an analytical exponential model and a dynamical system with seven unknown parameters subjected to ground displacement. Details on the theory of transport maps and on the used MCMC algorithm are also given. [ABSTRACT FROM AUTHOR]

In this paper, an alternative to solving Bayesian inverse problems for structural health monitoring based on a variational formulation with so-called transport maps is examined. The Bayesian inverse formulation is a widely used tool in structural health monitoring applications. While Markov Chain Monte Carlo (MCMC) methods are often implemented in these settings, they come with the problem of using many model evaluations, which in turn can become quite costly. We focus here on recent developments in the field of transport theory, where the problem is formulated as finding a deterministic, invertible mapping between some easy to evaluate reference density and the posterior. The resulting variational formulation can be solved with integration and optimization methods. We develop a general formulation for the application of transport maps to vibration-based structural health monitoring. Further, we study influences of different integration approaches on the efficiency and accuracy of the transport map approach and compare it to the Transitional MCMC algorithm, a widely used method for structural identification. Both methods are applied to a lower-dimensional dynamic model with uni- and multi-modal properties, as well as to a higher-dimensional neural network surrogate system of an airplane structure. We find that transport maps have a significant increase in accuracy and efficiency, when used in the right circumstances. [ABSTRACT FROM AUTHOR]