基于海林格距离加权关键主元的流程工业故障检测研究

在采用主成分分析（principal component analysis，PCA）算法进行故障检测时，主元的选取及处理直接影响其故障检测的表现。对此，提出一种基于全变量表达（full variable expression，FVE）和海林格距离（Hellinger distance，HD）的故障检测方法。首先，利用FVE得到所有关键主元，即保留所有变量信息；然后考虑到与故障相关主元的重要性，定义基于海林格距离的变化率，用来衡量正常工况下主元与异常工况下主元的差异；对与故障发生更相关的主元进行加权，以突出与故障相关主元对于后续故障检测的影响；最后，考虑到降维后数据通常服从非高斯分布，利用改进的局部离群因子（local outlier factor，LOF）构建统计量，其相应控制限通过核密度估计（kernel density estimation，KDE）确定。数值实例及带钢热连轧实际生产数据验证了所提方法的有效性与优越性。

A fault detection method based on Hellinger distance-weighted key principal components for the process industry

When a principal components analysis (PCA) algorithm is used for fault detection, the selection of principal components and how to manage them directly affects the efficacy of fault detection. A new fault detection method based on full variable expression(FVE) and Hellinger distance(HD) is proposed in this work. All the key principal components are first obtained by FVE, and all the variable information is retained. The change rate based on Hellinger distance is then defined, considering the importance of fault-relevant principal components. This is used to measure the difference between the principal components under normal operation and abnormal operation. The principal components which are more relevant to the occurrence of faults are weighted in order to highlight the effect of fault-relevant principal components in subsequent fault detection. Finally, considering that the dimensionality reduction data often follow a non-Gaussian distribution, the improved local outlier factor (LOF) is used to construct the statistics and the corresponding control limit is determined by kernel density estimation(KDE). Finally, a numerical case and the actual data for a hot strip mill process have been used to verify the effectiveness and superiority of the proposed method in fault detection.