Isolation enhanced principal component analysis

Principal component analysis (PCA) may reduce the dimensionality of plant models significantly by exposing linear dependences among the variables. While PCA is a popular tool in detecting faults in complex plants, it offers little support in its original form for fault isolation. However, by utilizing the equivalence between PCA and parity relations, all the powerful concepts of analytical redundancy may be transferred to PCA. Following this path, it is shown how structured residuals, which have the same isolation properties as analytical redundancy residuals, are obtained by PCA. The existence conditions of such residuals are demonstrated, as well as how disturbance decoupling is implied in the method. The effect of the presence of control constraints in the training data is analyzed. Statistical testing methods for structured PCA residuals are also outlined. The theoretical findings are fully supported by simulation studies performed on the Tennessee Eastman process.