A new Bayesian inference method has been developed and applied to Furan shock tube experimental data for efficient statistical inferences of the Arrhenius parameters of two OH radical consumption reactions. The collected experimental data, which consist of time series signals of OH radical concentrations of 14 shock tube experiments, may require several days for MCMC computations even with the support of a fast surrogate of the combustion simulation model, while the new method reduces it to several hours by splitting the process into two steps of MCMC: the first inference of rate constants and the second inference of the Arrhenius parameters. Each step has low dimensional parameter spaces and the second step does not need the executions of the combustion simulation. Furthermore, the new approach has more flexibility in choosing the ranges of the inference parameters, and the higher speed and flexibility enable the more accurate inferences and the analyses of the propagation of errors in the measured temperatures and the alignment of the experimental time to the inference results.

We carry out the design of experiments for the identification of the reaction parameters in Furan combustion. The lacks of information on the true value of the control parameters, specifically, the initial temperature and the initial TBHP concentration, are considered in the design procedure by errors-invariables models. We use two types of observables. The first is a scaler observable, i.e., half decay time of the [TBHP]. The second is the time history of the concentration.

A Bayesian optimal experimental design methodology has been developed and applied to refine the rate coefficients of elementary reactions in Furan combustion. Furans are considered as potential renewable fuels. We focus on the Arrhenius rates of Furan + OH ↔ Furyl-2 + H2O and Furan ↔ OH Furyl-3 + H2O, and rely on the OH consumption rate as experimental observable. A polynomial chaos surrogate is first constructed using an adaptive pseudo-spectral projection algorithm. The PC surrogate is then exploited in conjunction with a fast estimation of the expected information gain in order to determine the optimal design in the space of initial temperatures and OH concentrations.

An ensemble-based approach is developed to conduct time-optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where a set deterministic predictions is used to model and quantify uncertainty in the predictions. In the operational setting, much about dynamics, topography and forcing of the ocean environment is uncertain, and as a result a single path produced by a model simulation has limited utility. To overcome this limitation, we rely on a finitesize ensemble of deterministic forecasts to quantify the impact of variability in the dynamics. The uncertainty of flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each the resulting realizations of the uncertain current field, we predict the optimal path by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of sampling strategy, and develop insight into extensions dealing with regional or general circulation models. In particular, the ensemble method enables us to perform a statistical analysis of travel times, and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.

We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Center. The unknown parameters are the pre-exponential parameters and the activation energies in the reaction rate functions. The control parameters are the initial hydrogen concentration and the temperature. First, we build a polynomial based surrogate model for the observable related to the reactions in the shock tube. Second, we use a novel MAP based approach to estimate the expected information gain in the proposed experiments and select the best experimental set-ups corresponding to the optimal expected information gains. Third, we use the synthetic data to carry out virtual validation of our methodology.