Model-Based Experimental Design in Process Engineering

Reliability and Cost

Reliability of model calibration comes generally comes a high cost. But the model contains helpful information for the experimenter:

• On the one hand, model parameter uncertainty and prediction error are directly proportional to measurement accuracy, i.e., higher sensor precision equals higher model reliability
• However, correlations in model sensitivity, in particular with respect to the model’s parameters, give hint to efficient experimental designs

This will be demonstrated by the following example.

Catalyst: Age Versus Temperature

In general, chemical reaction speed increases with temperature. For example, food often is cooled to extend its shelf life. Catalysts are a common building block to accelerate chemical reactions. However, as these catalysts mature, their efficiency reduces. Consequently, as the catalyst ages, reactor temperature needs to be increased in order to maintain product quality. While catalyst age and reactor temperature obviously are correlated, there is no rigorous calculation of these effects on the reactor product. Thus, the effects of catalyst age and reactor temperature need to be studied in laboratory experiments.

In model-based experimental design, model sensitivities with respect to the parameters are investigated, so an experimental plan is set given a certain laboratory capacity. On the catalyst aging example, model-based experimental design suggests performing measurements at high catalyst age for both, high and low reactor temperature, and low catalyst age at high reactor temperature. The data acquired by these experimental measurements allow for the quantification and separation of the effect of age and temperature on the final reactor product.

Industrial Applications

Together with our partners, we apply the concepts of model-based experimental design to their actual models and pilot plants. The application of optimal experimental design includes the calibration of models to experimental data, the analysis of model sensitivities, the estimation of prediction error uncertainty, and generation of experimental plans. These individual steps are usually conducted in a circular sequence, as illustrated in the below figure. These methods are packed into stable software tools and come with intuitive user interfaces.

Reducing the Number of Experiments

Within the scope of an industrial cooperation, we demonstrated that the application of model-based design of experiments can reduce the number of experiments required to achieve a certain prediction error by up to a third compared to legacy methods.

Robust Experimental Design Under Model Uncertainty

Models of real systems generally introduce simplifications and by that, some sort of uncertainty. The effect of such uncertainties can be incorporated into the model-based design of experiments algorithms. In an industrial cooperation, we provide our partner software tools that support the identification of robust experimental designs, which allows for reducing the effect of uncertainties on the success of model calibration.