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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.
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