变量加权型主元分析算法及其在故障检测中的应用

Variable weighted principal component analysis algorithm and its application in fault detection

传统主成分分析(PCA)算法旨在挖掘训练数据各变量间的相关性特征,已在数据驱动的故障检测领域得到了广泛的研究与应用。然而,传统PCA方法在建模过程中通常认为各个测量变量的重要性是一致的,因此不能有效而全面地描述出变量间相关性的差异。为此,提出一种变量加权型PCA(VWPCA)算法并将之应用于故障检测。首先,通过对训练数据进行加权处理,使处理后的数据能够充分体现出变量间相关性的差异。然后,在此基础上建立分布式的PCA故障检测模型。在线实施故障检测时,则通过贝叶斯准则将多组监测结果融合为一组概率指标。VWPCA方法通过相关性大小为各变量赋予不同的权值,从而将相关性差异考虑进了PCA的建模过程中,相应模型对训练数据特征的描述也就更全面。最后,通过在TE过程上的测试验证VWPCA方法用于故障检测的优越性。

Traditional principal component analysis （PCA） algorithm, targeting to explore correlations among measured variables in training dataset, has been intensively investigated and applied to data-driven fault detection. However, all variables are considered equally important in modeling process of traditional PCA-based methods, the difference between variable correlations cannot be comprehensively described. A variable weighted PCA （VWPCA） algorithm was proposed and applied to fault detection. Weight calculations were performed on the training dataset so correlation differences among measured variables were fully reflected in the processed data and a distributed PCA-based fault detection model was constructed. When implemented in online fault detection, the Bayesian inference was used to combine multiple monitoring results into an ensemble of probability indices. VWPCA approach assigned different weights to different variables according to the correlation difference, thus PCA modeling took correlation difference into account and the models could completely describe characteristics of the training dataset. Finally, superiority of the proposed VWPCA method was validated by well-known TE process.