• Developed the PaLiTra algorithm , which iteratively refines surrogate training data by maximizing pathline-based distances in both input and response spaces, enabling efficient uncertainty quantification within a surrogate-based framework compared with direct Monte Carlo simulation (MCS) and Latin Hypercube Sampling (LHS). • Validation on benchmark functions (Ackley, Rosenbrock, Six-hump Camel, and Sine) demonstrated faster convergence of statistical moments and higher prediction accuracy than traditional LHS-based surrogate models. • The method was successfully applied to multi-dimensional problems, including the Short Column and Borehole models, achieving close agreement with reference Monte Carlo results. • The proposed approach was applied to high-altitude drone rotor design and performance analysis under uncertainty, demonstrating that increased rotor size and rotor count improve energy consumption efficiency and system robustness. Uncertainty Quantification (UQ) is the process of analyzing how uncertain input parameters influence system responses. A commonly used technique for this is Monte Carlo Simulation (MCS), which relies on probabilistic random sampling. However, due to the high computational cost of MCS,especially for complex systems, machine learning based surrogate models are often employed to approximate system behavior efficiently. While classical Latin Hypercube Sampling (LHS) lacks adaptivity and often requires large datasets. The proposed PaLiTra algorithm refines surrogate training data iteratively by maximizing pathline-based distances in both input and response spaces, enabling the surrogate model to focus on regions exhibiting strong nonlinearities or high sensitivity. Integrated with a Radial Basis Function (RBF) surrogate framework, PaLiTra retains previously acquired data and incrementally improves surrogate fidelity while reducing the number of required high-fidelity evaluations. The method was validated across nonlinear benchmark functions, multi-dimensional engineering models including the Short Column and Borehole problems, and a real engineering application involving high-altitude multirotor UAVs analyzed via Blade Element Momentum Theory (BEMT). Across all cases, PaLiTra achieved faster convergence of statistical moments, improved reproduction of probability density functions, and higher prediction accuracy compared with LHS-based surrogates. In the UAVs case study, PaLiTra successfully quantified the effects of air-density uncertainty and thrust variability, demonstrating clear trends in power and speed sensitivity with respect to rotor radius and rotor count. Overall, the results confirm that PaLiTra provides a data-efficient adaptive framework for surrogate-based UQ in complex engineering systems, offering significant advantages in accuracy, stability, and computational efficiency.
Boksawat et al. (Fri,) studied this question.