In
a recent publication (Ind. Eng. Chem. Res. 2013, 52 (35), 12369) we generalized the
classic design of experiments (DoE) methodology by introducing the
Design of Dynamic Experiments (DoDE), allowing for the systematic
design of experiments involving time-varying inputs. Here, we expand
the response surface model (RSM) methodology, used in DoE and DoDE
problems, so that it describes the time-evolution of the process,
not just the results at the end of the experiment. We apply this generalized
type of RSM model, to be denoted by DRSM, to three example processes;
a nonisothermal batch reactor with a simple reaction, an isothermal
semibatch reactor with several reactions, and a semibatch penicillin
fermentation process. Using a limited number of online measurements
at prespecified equidistant time instants, we are able to quickly
and accurately represent the time evolution of the process output
through these simple interpolative data-driven models. The ever-increasing
availability of time-resolved measurements is expected to make the
proposed approach widely useful.