Applied Hamiltonian Monte Carlo for multi-fidelity kriging modelling in experiment optimization

Surrogate modelling with multi-fidelity data brings significant improvements for experiments and simulations. A multi-fidelity kriging modelling method is proposed with the help of Hamilton Monte Carlo (HMC) to speed up the modelling process. The multi-fidelity Hamiltonian kriging (MHK) algorithm builds the initial model with the original value and gradient responses. The weight parameters are adaptively calculated based on HMC with a no-U-turn sampler (NUTS) strategy. The modelling process continues until the stopping criterion brought by probability improvement with NUTS is satisfied. MHK is demonstrated with two numerical examples, and applied to a validation case of low-speed flow analysis of the NACA 0012 aerofoil and an application example on the reliability modelling verification of a tethered satellite semi-physical system. The engineering applications show that the proposed MHK can perform precisely in complex experiments. The MHK can be useful for any other reliability engineering problems involving sampling from multi-fidelity models.