Defining the structure of DPCA models and its impact on process monitoring and prediction activities

Abstract

Dynamic Principal Component Analysis (DPCA) is an extension of Principal Component Analysis (PCA), developed in order to add the ability to capture the autocorrelative behavior of processes, to the existent and well-known PCA capability for modeling cross-correlation between variables. The simultaneous modeling of the dependencies along the “variable” and “time” modes, allows for a more compact and rigorous description of the normal behavior of processes, laying the ground for the development of, for instance, improved Statistical Process Monitoring (SPM) methodologies, able to robustly detect finer deviations from normal operation conditions. A key point in the application of DPCA is the definition of its structure, namely the selection of the number of time-shifted replicates for each variable to include, and the number of components to retain in the final model. In order to address the first of these two fundamental design aspects of DPCA, and arguably the most complex one, we propose two new lag selection methods.The first method estimates a single lag structure for all variables, whereas the second one refines this procedure, providing the specific number of lags to be used for each individual variable. The application of these two proposed methodologies to several case studies led to a more rigorous estimation of the number of lags really involved in the dynamical mechanisms of the processes under analysis. This feature can be explored for implementing improved system identification, process monitoring and process control tasks that rely upon a DPCA modeling framework.