Development in Surrogate-Based Polynomial Chaos with Adaptive Sobol Sensitivity Analysis for Uncertainty Quantification and Offshore 15 MW Wind Turbine Performance Prediction: Comparative, Icing, and Wind Farm Optimization Studies

Accurate performance prediction for large offshore wind turbines requires a principled treatment of uncertainty in both the wind resource and the rotor design parameters. In the present work, we develop a surrogate-based, multi-level uncertainty quantification (UQ) framework coupling a physics-based Blade Element Momentum (BEM) solver with a spectral Polynomial Chaos Expansion (PCE) surrogate that replaces the expensive Monte Carlo loop and apply it to the IEA 15 MW offshore reference wind turbine. The framework is completed by Sobol variance-based global sensitivity analysis. The contribution is methodological rather than algorithmic: although each individual ingredient (PCE, Sobol, BEM, and Jensen) is well established, their joint deployment in a single, internally consistent, end-to-end probabilistic workflow that simultaneously delivers (i) aerodynamic–structural UQ with analytical Sobol ranking, (ii) a like-for-like cross-comparison of three reference turbines, (iii) a quantitative leading-edge icing degradation study, and (iv) a farm-level wake-steering optimization on the same IEA 15 MW reference rotor yields a unified probabilistic envelope from which manufacturing tolerances, cold-climate investment thresholds, and farm-layout/control trade-offs can be read off consistently. Five input parameters are treated as random variables: hub-height wind speed (Weibull, k = 2.2, c = 9.8 m/s), air density, blade chord length, twist angle, and rotor speed. A degree-4 sparse PCE is built by non-intrusive spectral projection using N = 5000 Sobol quasi-random realizations, which allows the Sobol indices to be recovered analytically from the expansion coefficients at essentially no extra cost. Three parallel engineering studies complement the core UQ analysis: (A) a head-to-head comparison of the NREL 5 MW, DTU 10 MW, and IEA 15 MW reference turbines; (B) a quantitative assessment of leading-edge ice accretion at four severity levels; and (C) a Jensen-based wake optimization for a 25-turbine offshore array with static wake steering. The main results are as follows: the turbine reaches Cp,max = 0.480 at λopt = 8.51, and an annual energy production (AEP) of 71,261 MWh/year (PCE: 70,840 ± 2,140 MWh/year, 95% CI). Wind speed emerges as the dominant driver of Cp variance (S1 = 0.412), followed by blade twist (0.198) and chord (0.143). Severe icing (30 kg/m) reduces Cp by 18.2% and increases the blade-root Damage Equivalent Load (DEL) by 18.5%. For the array, the optimal spacing (sx = 8D, sy = 6D) gives a farm efficiency of 89.6% and 1296 GWh/year, and a 15° wake-steering offset adds a further +3.2% to farm AEP. Compared with plain Monte Carlo, the sparse PCE delivers the same statistics with about 36% fewer model evaluations and a relative error below 0.8%.