This paper presents an investigation into sampling strategies for reducing the computational expense of creating error models for steady hypersonic flow surrogate models. The error model describes the quantity of interest error between a reduced-order model prediction and a full-order model solution. The sampling strategies are separated into three categories: distinct training sets, single training set, and augmented single training set for the reduced-order model and the error model. Using a distinct training set, three sampling strategies are investigated: latin hypercube sampling, latin hypercube sampling with a maximin criterion, and a D-Optimal design. It was found that using a D-Optimal design was the most effective at producing an accurate error model with the fewest number of training points. When using a single training set, the leave-one-out cross validation approach was used on the D-Optimal design training set. This produced an error model with an R2 value of greater than 0.8, but it had some outliers due to high nonlinearities in the space. Augmenting the training points of the error model helped improve its accuracy. Using a D-Optimal design with distinct training sets cut the computational cost of creating the error model by 15% and using the LOOCV approach with the D-Optimal design cut the cost by 64%.
High-fidelity hypersonic aerodynamic simulations require extensive computational resources, hindering their usage in hypersonic vehicle design and uncertainty quantification. Projectionbased reduced-order models (ROMs) are a computationally cheaper alternative to full-order simulations that can provide major speedup with marginal loss of accuracy when solving manyquery problems such as design optimization and uncertainty propagation. However, ROMs can present robustness and convergence issues, especially when trained over large ranges of input parameters and/or with few training samples. This paper presents the application of several different residual minimization-based ROMs to hypersonic flows around flight vehicles using less training data than in previous work. The ROM demonstrations are accompanied by a comparison to fully data-driven approaches including kriging and radial basis function interpolation. Results are presented for three test cases including one three-dimensional flight vehicle. We show that registration-based ROMs trained on grid-tailored solutions can compute quantities of interest more accurately than data driven approaches for a given sparse training set. We also find that the classic ℓ2 state error metric is not particularly useful when comparing different model reduction techniques on sparse training data sets.
Bayesian inference is used to calibrate a bottom-up home PLC network model with unknown loads and wires at frequencies up to 30 MHz. A network topology with over 50 parameters is calibrated using global sensitivity analysis and transitional Markov Chain Monte Carlo (TMCMC). The sensitivity-informed Bayesian inference computes Sobol indices for each network parameter and applies TMCMC to calibrate the most sensitive parameters for a given network topology. A greedy random search with TMCMC is used to refine the discrete random variables of the network. This results in a model that can accurately compute the transfer function despite noisy training data and a high dimensional parameter space. The model is able to infer some parameters of the network used to produce the training data, and accurately computes the transfer function under extrapolative scenarios.