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For more complex reactive distillation processes, rigorous dynamic modeling from an initially cold and empty state is necessary. 4 CONTROL AND OPTIMIZATION In process control, linearized Laplace-transformed models are often used. The advantages and disadvantages of such models are discussed elsewhere [46, 47]. 16 Trend models: different models classes to characterize the response of process variables. , Proc. American Control Conference, Albuquerque, 1997; MC Kindsmüller, L Urbas, Situation Awareness in der Fahrzeug- und Prozessführung.
A single neuron is depicted on the left. fm Page 15 Tuesday, April 26, 2005 2:11 PM Process Modeling 15 input data (stimuli) to output data (response), using sets of multivariate data of known system inputs and outputs. , data not included in the training set). Kell and Sonnleitner  describe common pitfalls in applying and training ANNs and give recommendations for good modeling practice. Recommendations include ensuring the network is trained with a consistent set of data to guarantee the applicability of the model and not using the model on data outside the range of the training data.
578, Düsseldorf: VDI Verlag, ISBN 3-18-358703-3, 1998. 58. L Urbas. Entwicklung und Realisierung einer Trainings- und Ausbildungsumgebung zur Schulung der Prozessdynamik und des Anlagenbetriebs im Internet. Fortschritt-Berichte VDI, Reihe 10, Nr. 614, Düsseldorf: VDI Verlag, ISBN 3-18-361410-3, 1998. , systems that do not rely on mathematical reconstruction to form an image). We begin by considering the fundamental characteristics of laser and white light sources, then describe the basic properties and structure of twodimensional image sensors, image intensifiers, and thermal sensors.