Statistical Simplex Method for Experimental Design in Process Optimization

Abstract

Experimental optimization with scarce and noisy process data is a key issue in laboratory automation for faster chemical process research and development, real-time process optimization, and the ability to embed a learning capability into the design of self-calibrating instruments and extremum-seeking controllers. To deal successfully with noise and uncontrollable factors in experimental design for process optimization, a statistical characterization of an optimum using process data is proposed. The Kendall?s tau statistic is used for identifying a minimum (maximum) in a data set as a cluster center of positively (negatively) correlated points. A new simplex search algorithm with a logic that resorts to correlation-based ranking of simplex vertices for reflection, expansion, contraction, and shrinking steps is proposed. The advantage of resorting to a data set that cumulatively provides a global perspective of the output landscape through Kendall?s tau calculations is a novel feature of the statistical simplex method. Encouraging results obtained for Rastringin?s multimodal function and in the optimization of the operating policy for a semibatch reactor are presented.