Computer-based process monitoring/fault detection using principal component analysis

Principal component analysis or PCA, determines the combinations of variables, or factors, that describe major trends in data which is being analyzed. Mathematically, PCA is a decomposition of the data matrix consisting of the process variables where the rows pertain to the samples or observations at different times during a process and the columns represent process variables. During analysis, the data matrix is decomposed into the outer product of the score vectors and loading vectors, where the score vector is made of linear combinations of the original data defined by the loading vectors and the loading vector contains the eigenvectors of the covariance matrix. This results in a reduction of the variables needed to describe the process.; In this research, the problem of using PCA to aid in process control and fault detection is addressed. Attempts to utilize the confidence limits on the residuals of each variable for fault detection are made. This will be referred to as an enhancement to PCA. This is in contrast to just using the confidence limits on the residuals for an overall residual. A new, graphical approach to display and identify each variables contribution to the faulty behavior of the process was developed to aid in assimilating results. This approach was tested on two different data sets from chemical processes operating in normal and faulty modes. The results show that using confidence limits on the residuals of individual variables can reduce the amount of time required to detect a fault. Therefore, with this enhancement principal component analysis can be used to increase the productivity of an industry process and decrease the amount of waste in materials and labor.