Optimization of Chemical Plant Simulation Using Double Collocation
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Inhaltsangabe: Problemstellung: Für die Lösung einer breiten Klasse der chemischen Betriebssimulationsmodelle, einschlie lich Differentialgleichungen und Optimierung ist eine Methode konstruiert worden: Die doppelte orthogonale Kollokation und die Finite Elemente Methode werden angewendet, um das Modell in ein NLP Problem zu konvertieren. Das NLP Problem wird dann entweder durch den nichtlinearen Optimierungscode VF13AD, der auf der sukzessiven quadratischer Programmierung basiert oder durch den nichtlinearen Optimierungscode GRG2, der auf dem generalisierten Gradientenverfahren basiert, gelöst. Dieses Verfahren wird simultane Optimierung und Lösungsstrategie genannt. Das Zielfunktional kann dabei Integralterme enthalten und die Zustandsvariablen sowie die Entscheidungsvariablen können zeitliche Verzögerung haben. Das Modell kann Zustandsvariablen und Entscheidungsvariablen enthaltende Gleichungen, algebraische Gleichungen und Ungleichungen enthalten. Die Höchstzahl der unabhängigen Veränderlichen in den partiellen Differentialgleichungen ist zwei. Die Probleme, die drei unabhängige Veränderliche enthalten, können mit der Differenzenmethode in zwei unabhängige Veränderliche enthaltende Probleme konvertiert werden. Die Höchstzahl der NLP Variablen sowie die der Nebenbedingungen beträgt 1500. Die Methode ist auch für das Lösen der gewöhnlichen und partiellen Differentialgleichungen verwendbar. Die Zustandsfunktionen werden durch eine lineare Kombination der Lagrange Interpolationspolynomen approximiert. Die Kontrollfunktion kann entweder durch eine lineare Kombination der Lagrange Interpolationspolynomen oder durch eine Funktion, die stückweise konstant ist, approximiert werden. Der Wert der Funktion und die Zahl der inneren Kollokationspunkte kann je nach dem finiten Element variieren. Der residuale Fehler wird an äquidistanten Knotenpunkten ausgewertet und ermöglicht so die Genauigkeit der Lösung zwischen Kollokationspunkten zu überprüfen. Die Lösungsfunktio
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