基于故障重构的PCA模型主元数的确定  

Determination of Principal Components in PCA Model on Basis of Fault Reconstruction

作　　者：李元[1] 谢植[1] 王纲[2] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004 [2]沈阳化工学院信息工程学院,辽宁沈阳110142

出　　处：《东北大学学报（自然科学版）》2004年第1期20-23,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(50174021).

摘　　要：基于故障重构理论研究了PCA模型主元数的确定方法,应用累积方差贡献率以及复相关系数对主元模型性能进行分析·在基于PCA理论进行故障诊断中,故障变量可根据故障的方向向量进行重构,未重构方差(VRE)可分别投影于主元子空间(PCS)和残差子空间(RS)·确定最优重构是使两空间的VRE之和达到最小,与此相对应的主元数即为最优主元数(PCs)·应用累积方差贡献率以及复相关系数对主元模型性能进行评价,结果表明确定的PCA模型PCs保证了PCS中的信息存量·对于工业PVC聚合反应过程的故障诊断说明了上述方法的合理性与有效性·Based on the theory of fault reconstruction, the determination of the principal components in PCA (principal component analysis) model is studied, thus analyzing the performance of PCA model. In the fault diagnosis based on PCA theory, the faulty variables can be reconstructed in the direction of vectorized faults data, with the variance of reconstruction error (VRE) projected separately onto principal component sub-space (PCS) and residual sub-space (RS). An optimal reconstruction is convincing only if the sum of all VREs in both PCS and RS come to minimum, among which the corresponding principal components are referred to as optimum principal components. An evaluation is carried out for the performance of PCA model by virtue of cumulative percent variance (CPV) and multi-correlation coefficients. The results show that the principal components determined as above in PCA model can ensure enough information in PCS. The reasonableness and effectiveness of the determination method is proved through a fault diagnosis for industrial PVC polymerization process.

关 键 词：故障重构 PCA模型 主元分析 未重构方差 VRE 主元数 PCS 主元子空间 残差子空间 数据分析 数据处理 

分 类 号：TP274[自动化与计算机技术—检测技术与自动化装置]