Vulnerability Assessment of Equipment Excited by Disturbances for Class Imbalance Problem Based on Improved Kernel Density Estimation

Due to the difficulty in collecting samples of certain effect levels, the class imbalance problem is a challenging issue in vulnerability assessment. The class imbalance problem would cause deviation of likelihood function and thus deviate the result of vulnerability assessment. Conventional assessment method ignoring it would lead to over- or under-estimation. In this article, we propose the improved kernel density estimation (IKDE) to address this issue. The proposed method first calculates the probability density function of each effect level sample. Then, the spatial characteristics are introduced in the likelihood function to reduce the impact of the class imbalance problem. The parameters in IKDE are determined by Markov Chain Monte Carlo and the probabilities of each effect level can be obtained at last. Through simulations with different class imbalance degrees and sample sizes, we illustrate the effectiveness of the proposed IKDE. Finally, a case study is carried out to assess the vulnerability of 10 kV distribution transformer excited by nanosecond electromagnetic pulse.