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Statistische Versuchsplanung pp 231–323Cite as

Metamodelle

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Zusammenfassung

Die direkte Analyse und Optimierung komplexer Systeme ist schwierig und zeitaufwendig, so dass diese immer häufiger mit der Unterstützung von Metamodellen durchgeführt wird. Metamodelle bilden das zu untersuchende System auf Basis von Mess- oder Simulationsdaten mathematisch ab und können Systemantworten im Bereich von Millisekunden oder Sekunden vorhersagen. Der Einsatz von linearen Modellen oder Polynomen mit starrer Vorgabe der maximal abzubildenden Komplexität oder der Grundform von Zusammenhängen ist nicht zielführend. Gerade bei unbekannter und gleichzeitig hoher Komplexität des abzubildenden Systems führt dies zu falschen Folgerungen. Daher sind verschiedenste Modellverfahren entwickelt worden, die ohne feste Vorgabe von Systemzusammenhängen komplexe Systeme auf Basis von raumfüllenden Mess- oder Simulationsdaten abbilden. Dieses Kapitel stellt Grundlagen und Algorithmen verschiedener Verfahren sowie Methoden zur Qualitätskontrolle vor. Dabei startet es bei alt bekannten Verfahren, wie Regression oder Splines und entwickelt sich über verbreitete Verfahren, wie Kriging, Radiale Basisfunktionen oder Künstliche Neuronale Netze hin zu Support Vector Regression oder Gauß Prozess Modellen. Die Aufbereitung der Algorithmen ermöglicht eine gezielte Auswahl und den sicheren Einsatz der Verfahren in kommerziellen Softwarepaketen oder eine erste grundlegende Implementierung.

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    Karl Siebertz

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    David van Bebber

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    Thomas Hochkirchen

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Siebertz, K., Bebber, D.v., Hochkirchen, T. (2017). Metamodelle. In: Statistische Versuchsplanung. VDI-Buch. Springer Vieweg, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55743-3_9

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