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.

中文翻译：

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基于改进核密度估计的类不平衡问题扰动设备脆弱性评估

由于收集某些效应水平的样本比较困难，类别不平衡问题是脆弱性评估中​​的一个具有挑战性的问题。类别不平衡问题会导致似然函数的偏差，从而导致脆弱性评估的结果出现偏差。传统的评估方法忽视它会导致高估或低估。在本文中，我们提出了改进的核密度估计（IKDE）来解决这个问题。该方法首先计算每个效应水平样本的概率密度函数。然后，在似然函数中引入空间特征，以减少类别不平衡问题的影响。 IKDE中的参数通过马尔可夫链蒙特卡罗确定，最后可以得到每个效应水平的概率。通过不同类不平衡程度和样本量的模拟，我们说明了所提出的 IKDE 的有效性。最后，通过案例研究评估纳秒电磁脉冲激励下的10 kV配电变压器的易损性。