Bayesian Inference for Complex and Large-Scale Engineering Systems

The process of blending observational data in numerical models can be formulated using the Bayesian estimation method. The Bayesian statistical framework strives to find the best state and/or parameter estimates using (a) the stochastic computational model and (b) the noisy observational data. In sequential Bayesian estimation techniques, the data assimilation is performed at each time instant as data arrives. A number of extensions to the linear Kalman filter (e.g. extended Kalman filter, unscented Kalman filter and ensemble Kalman filter) have become popular tools for sequential data assimilation problems applicable to nonlinear systems. In the Bayesian setting, the most general nonlinear filtering algorithm is the so-called particle filter which can handle general form of nonlinearities and non-Gaussian noises in the model and measurement operators. The problem of static (time-invariant) parameter estimation problem is formulated using the aforementioned filtering techniques in combination with the Markov Chain Monte Carlo sampling method. In this thesis, the usefulness of these methods is demonstrated through novel applications in structural dynamics and aeroelasticity.;The following statements summarize the findings from the investigations undertaken in this thesis: (1) the proposed probabilistic flutter margin method applied to a two-degrees-of-freedom numerical model provides more accurate (unbiased) and precise (low variance) estimates for the flutter speed in comparison to the conventional method; (2) for the estimation of time-invariant parameters of a nonlinear system exhibiting noisy oscillation, Markov Chain Monte Carlo sampling, ensemble Kalman filter and particle filter provide parameter estimates which are comparable in accuracy for the case of dense observational data and weak measurement noise whereas for the cases of strong measurement noise and sparse observational data, the Markov Chain Monte Carlo sampling-based algorithm and particle filters outperform the ensemble Kalman filter; (3) For static parameter estimation problem of a non-linear aeroelastic system using wind tunnel data, numerical predictions of the limit cycle oscillation match the experimental observations from wind tunnel tests with reasonable accuracy; (4) the developed parallel data assimilation algorithm that integrates the polynomial chaos-based Kalman filter and domain decomposition solver shows scalable performance for stochastic diffusion and advection-diffusion problems with spatially varying non-Gaussian random parameters; (5) A new parallel solver for non-symmetric stochastic systems based on the preconditioned biconjugate gradient stabilized method is developed to tackle the steady-state stochastic advection-diffusion equation with spatially varying non-Gaussian diffusivity coefficient.;For large-scale computational models, the parallel filtering algorithms aim to estimate the state of the system by exploiting high performance computing platforms. A significant research initiative has recently been focused on the parallelization of the ensemble Kalman filter due to its relatively low computational requirements. A major limitation of the ensemble Kalman filter to tackle the data assimilation problem for large-scale systems is the necessity of a large ensemble size which is often computationally impractical or infeasible. By avoiding Monte Carlo sampling, a novel filter has been recently proposed in the literature to address this issue by using a functional series (i.e. polynomial chaos series) representation of the stochastic state vector. This representation is more efficient in capturing the model state statistics for accurate forecast and analysis of observations leading to the Polynomial Chaos-based Kalman filter. In this thesis, a parallel assimilation (update) algorithm is developed with a scalable implementation using the Polynomial Chaos-based Kalman filter that exploits a previously developed polynomial chaos based scalable domain decomposition solver. Numerical investigations involve the two-dimensional stationary stochastic diffusion and advection-diffusion problems. The scalability of the parallel Polynomial Chaos-based Kalman filter algorithm is investigated in a Linux cluster.