Surface Charge Inversion for Wind Turbine Blade Coatings with Uncertain Erosion Geometry

Rain erosion changes the surface profile and dielectric interfaces of wind turbine blade protection coatings, introducing geometry-dependent bias into surface charge reconstruction. A constrained inversion method combines a finite library of erosion profiles with continuous radial charge parameterization in a three-dimensional laminate model. Candidate-specific responses and variable projection jointly estimate geometry and charge, while the square specimen’s D4 symmetry reduces the computational domain to one eighth. Continuous-source finite-element potentials provide the numerical observations. With matched generating and inverse discretizations, median global errors over 24 inputs are 0.172% and 1.039% at single-reading noise standard deviations of 0.003 and 0.1 V, respectively. At 0.003 V, 21 inputs have global errors at or below 20%; three broad-charge realizations reach 65.69–70.01%. Across six out-of-library cases, candidate selection reduces the median pit-interior error from 10.264% to 4.821%, while the median pit-edge error increases. Joint ±10% permittivity shifts give global errors of 9.660% and 8.027% in one representative case. Representative finite-aperture simulations and controlled mesh refinement further reveal the sensitivity of fine-scale recovery. The method relates the estimated charge distribution to erosion geometry, providing a numerical approach to local electrical characterization of damaged coatings.