关键词: 故障重构, PCA(主元分析), 未重构方差(VRE), 主元数(PCs), 主元子空间(PCS), 残差子空间(RS)

Abstract: Based on the theory of fault reconstruction, the determination of the principal components in PCA (principal component analysis) model is studied, the performance of PCA model is analyzed. 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 PCV polymerization process.