An improved polynomial-based nonlinear variable importance measure and its application to degradation assessment for high-voltage transformer under imbalance data

Variable importance measures (VIM) are widely used in reliability engineering. Traditional nonlinear VIMs are difficult to simultaneously obtain both most important variable combination and an explanatory function. Variable combination is the variable set that fits better than redundant variables, but each of them may fits worse than redundant variables. In this paper, a practical and improved polynomial-based VIM is proposed for nonlinear variable relationships with an unknown functional form. Polynomial approximation, combined with a novel ensemble-based product selection, is applied to gain an explanatory linear model consisting of important product combination, which is selected accurately by the proposed product selection. The simulations show the effectiveness of the proposed method on nonlinear VIM. Furthermore, the approach is applied in long-term degradation assessment of high voltage transformer under large imbalance samples. In the experiment, the details of important relationships among input variables can be measured under a powerful and competitive assessment model. The proposed approach paves the way for VIM in complex nonlinear reliability systems with multiple dependent inputs.