A High Robustness Surface Charge Inversion Method Based on B-spline Basis Functions

In recent years, surface flashover faults have occurred frequently in the core of the converter transformer valve side bushing, and the surface charge distribution at the gas-solid interface directly affects the insulation performance along the surface of the core. High-precision surface charge inversion algorithms are essential for studying the accumulation characteristics of charge at the gas-solid interface. This paper establishes a method that uses B-spline basis functions as the basis for surface charge inversion. Through geometric mapping, normalized nearly uniform B-spline curves and cyclic B-spline curves are mapped onto the surface of the object under test. The basis functions representing the surface charge distribution of the object are constructed by the product of the B-spline curves in the height direction of the sample and those in the circumferential direction. A simulation is conducted to construct the overdetermined equations relating potential and charge, achieving efficient and stable solutions using the LSMR iterative algorithm and the GCV regularization parameter selection method. This paper demonstrates the advantages of B-spline basis functions in characterizing the continuous distribution of surface charges at the gas-solid interface through fitting examples of two-dimensional continuous functions using both B-spline and binary rectangular window basis functions. It is verified that B-spline basis functions can achieve better inversion results with fewer basis functions in the surface charge inversion process, thus reducing computational complexity. Finally, the reliability of using B-spline basis functions as the basis for inversion is validated through dust pattern experiments and inversion of measured data.