New Time Sampling Strategy for the Estimation of the Parameters in DRSM Models

Abstract

There are a substantial number of automated laboratory reactor systems available to run a reaction at different conditions in parallel. These systems are also able to collect a multitude of samples for analysis robotically. Such time-resolved information on the concentration of the present species can be effectively modeled by the newly proposed dynamic response surface methodology (DRSM) (Dong et al. 2019). Because of the power of this modeling methodology and the cost and effort needed to perform the chemical analysis on the collected samples, there is considerable motivation to reduce the number of samples and to select the most appropriate time instants to collect them. In this paper, we propose a new time sampling strategy used for the estimation of accurate DRSM models. The new time sampling strategy leads to a model with substantially reduced uncertainty and reduced correlation of parameters compared to the classical strategy of collecting samples at an equidistant interval of time. In the case study, a model of the same accuracy can be achieved with almost half of the measurements if the new sampling strategy is followed. Instead of sampling equidistantly in time, the new strategy has samples collected equidistantly in θ, an exponential transformation of time using the slowest dynamics of the process.