Adapting multivariate analysis for monitoring and modeling of dynamic systems.

摘要

This work considers the application of several related multivariate data analysis techniques to the monitoring the modeling of dynamic processes. Included are the method of Principal Components Analysis (PCA), and the regression technique Continuum Regression (CR), which encompasses Principal Components Regression (PCR), Partial Least Squares (PLS) and Multiple Linear Regression (MLR), all of which are based on eigenvector decompositions.; It is shown that proper application of PCA to the measurements from multivariate processes can facilitate the detection of failed sensors and process upsets. The relationship between PCA and the state-space process model form is shown, providing a theoretical basis for the use of PCA in dynamic systems. For processes with more measurements than states, the deterministic variation in the output data is redundant and PCA modeling can be applied. Under these conditions are residuals of the PCA model re related only to the process measurement noise; the state of the process does not affect the residuals. Statistical limits, which define the normal amount of process noise, can be calculated for the process residuals. Failed sensors or process upsets manifest themselves as changes in the PCA residuals and can be detected through the application of statistical tests.; Collections of PLS models are used in a manner analogous to PCA for the failure detection problem. This technique can be more effective than PCA monitoring. However, the method suffers because, unlike PCA models, it maps state information into the residuals. Statistical limits on the residuals must account for this. Changes in the process inputs invalidates the calculated limits.; CR is applied to the identification of Finite Impulse Response (FIR) and Auto-Regressive eXtensive variable (ARX) dynamic models. In FIR identification, the frequency domain effects of CR, and in particular PCR, are investigated from a theoretical perspective. This results in a fundamental understanding of the effects of CR on FIR identification. Observed trends in CR identification are consistent with the theoretical understanding. CR appears to be a great advantage over existing methods for the identification of FIR models, but offers only moderate improvements for ARX models.