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Integration of Optimization Algorithms With Sensitivity Analysis, With Application to Volcanic Regions

Tiede, Carola (2005)
Integration of Optimization Algorithms With Sensitivity Analysis, With Application to Volcanic Regions.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung

Kurzbeschreibung (Abstract)

The purpose of this thesis is the generation of improved optimization approaches, applied to a volcanic modeling. Neither local nor global optimization algorithms can guarantee the generation of a global optimization solution. Furthermore, the generated models have to be integrated into the physical context of other available observations and models in the specific volcanic region. A reliable optimization result can only be given by a model with significant determined parameters which can be seen on small dispersion if the optimization is carried out several times as well as considering the results of statistical tests about the model fit. In addition, this model has to be validated by additional information from other observation techniques and models. Different improvements of the optimization have been analyzed within this thesis: (1) The first approach is given by the definition of physical constraints, which are implemented into the optimization approach by penalty terms. This approach shall lead to a decrease of possible solutions so the dispersion of the unknown parameters is decreased, which is equal to an increase of significance of these unknown parameters. (2) Another approach of improvement is given by the implementation of the results from a global sensitivity analysis. A re-weighting factor is implemented into the optimization approach, so the weight of the observations is varied with respect to their sensitivity against changes in a specific unknown parameter. (3) The last improvement approach is described by the implementation of a fuzzy logic model. This model fuses physical plausibility checks as well as available density data of the volcanic region. The fuzzy logic model results in a physical reliability value for the model. This approach is implemented actively into the optimization approach by an addend to the objective function. The generated models without any implementation improvements serve as reference. Data collected at the high risk volcano Merapi at Central Java, Indonesia serve as a case study. The modeling is based on a non-linear inversion of gravity changes and three-dimensional displacements which were measured between the years 2000 and 2002 at Merapi. The physical based mathematical model is described by the generalized static Navier equations which are solved for the mathematical half-space where elastic and gravitational effects are coupled. The parameters which have to be determined are given by the point mass of source, its position, and an energy value, described by the product of pressure and cubed radius. The different improvement approaches have been implemented into two different optimization algorithms: A downhill simplex and a genetic algorithm. The best optimization approach has been determined by comparing the different optimization configurations. The comparison results in the definition of a recommended optimization approach concerning the model's significance and physical reliability. The approach given by the implementation of the sensitivity analysis results into the genetic algorithm could determine the best elastic-gravitational source model concerning the dispersion of the unknown parameters and the fitness value of the result. Finally, the application of the fuzzy logic is used to validate these results with respect to the physical reliability of the elastic-gravitational source's position. So the quality of the model can be described statistically as well as physically. Nevertheless, all optimization configurations showed that a model which is solely based on a magmatic source is not feasible. All optimization results showed very shallow sources with small mass components and large energy values. These properties as well as the lack of ability to model the deformations lead to the assumption that another influence is acting. This effect is modelled by superposition of a local fault zone to the assumed magmatic source. This final model results in statistical significant and physical reliable parameters for a volcanic source superimposed with the effects of a fault zone. The model is statistically significant with a larger significance level than the models which are based on a solely elastic-gravitational source. In addition, this combined model also fits into the prior anticipations about the structure of Merapi given in the literature.

Typ des Eintrags: Dissertation
Erschienen: 2005
Autor(en): Tiede, Carola
Art des Eintrags: Erstveröffentlichung
Titel: Integration of Optimization Algorithms With Sensitivity Analysis, With Application to Volcanic Regions
Sprache: Englisch
Referenten: Göpfert, Prof. Dr. Wolfgang ; Ostrowski, Prof. Dr. Manfred
Berater: Gerstenecker, Prof. Dr. Carl ; Tiampo, Prof. Dr. Kristy
Publikationsjahr: 11 Juli 2005
Ort: Darmstadt
Verlag: Technische Universität
Datum der mündlichen Prüfung: 3 Juni 2005
URL / URN: urn:nbn:de:tuda-tuprints-5814
Kurzbeschreibung (Abstract):

The purpose of this thesis is the generation of improved optimization approaches, applied to a volcanic modeling. Neither local nor global optimization algorithms can guarantee the generation of a global optimization solution. Furthermore, the generated models have to be integrated into the physical context of other available observations and models in the specific volcanic region. A reliable optimization result can only be given by a model with significant determined parameters which can be seen on small dispersion if the optimization is carried out several times as well as considering the results of statistical tests about the model fit. In addition, this model has to be validated by additional information from other observation techniques and models. Different improvements of the optimization have been analyzed within this thesis: (1) The first approach is given by the definition of physical constraints, which are implemented into the optimization approach by penalty terms. This approach shall lead to a decrease of possible solutions so the dispersion of the unknown parameters is decreased, which is equal to an increase of significance of these unknown parameters. (2) Another approach of improvement is given by the implementation of the results from a global sensitivity analysis. A re-weighting factor is implemented into the optimization approach, so the weight of the observations is varied with respect to their sensitivity against changes in a specific unknown parameter. (3) The last improvement approach is described by the implementation of a fuzzy logic model. This model fuses physical plausibility checks as well as available density data of the volcanic region. The fuzzy logic model results in a physical reliability value for the model. This approach is implemented actively into the optimization approach by an addend to the objective function. The generated models without any implementation improvements serve as reference. Data collected at the high risk volcano Merapi at Central Java, Indonesia serve as a case study. The modeling is based on a non-linear inversion of gravity changes and three-dimensional displacements which were measured between the years 2000 and 2002 at Merapi. The physical based mathematical model is described by the generalized static Navier equations which are solved for the mathematical half-space where elastic and gravitational effects are coupled. The parameters which have to be determined are given by the point mass of source, its position, and an energy value, described by the product of pressure and cubed radius. The different improvement approaches have been implemented into two different optimization algorithms: A downhill simplex and a genetic algorithm. The best optimization approach has been determined by comparing the different optimization configurations. The comparison results in the definition of a recommended optimization approach concerning the model's significance and physical reliability. The approach given by the implementation of the sensitivity analysis results into the genetic algorithm could determine the best elastic-gravitational source model concerning the dispersion of the unknown parameters and the fitness value of the result. Finally, the application of the fuzzy logic is used to validate these results with respect to the physical reliability of the elastic-gravitational source's position. So the quality of the model can be described statistically as well as physically. Nevertheless, all optimization configurations showed that a model which is solely based on a magmatic source is not feasible. All optimization results showed very shallow sources with small mass components and large energy values. These properties as well as the lack of ability to model the deformations lead to the assumption that another influence is acting. This effect is modelled by superposition of a local fault zone to the assumed magmatic source. This final model results in statistical significant and physical reliable parameters for a volcanic source superimposed with the effects of a fault zone. The model is statistically significant with a larger significance level than the models which are based on a solely elastic-gravitational source. In addition, this combined model also fits into the prior anticipations about the structure of Merapi given in the literature.

Alternatives oder übersetztes Abstract:
Alternatives AbstractSprache

Das Ziel der vorliegenden Arbeit besteht in der Generierung von verbesserten Optimierungsansätzen, die im Rahmen vulkanologischer Studien benutzt werden. Weder lokale noch globale Optimierungsverfahren köonnen das Auffinden der globalen Lösung eines Optimierungsproblemes garantieren. Weiterhin müssen Modelle physikalischen Randbedingungen genügen sowie in den physikalischen Kontext anderer Messverfahren und die daraus resultierenden Modellierungen gebracht werden. Erst ein Modell, dessen Modellparameter statistisch signifikant bestimmt werden konnten, sowie die Validierung dieses Modelles durch Ergebnisse anderer Messverfahren, führt zu einem vertrauenswürdigen Optimierungsresultat. Es werden drei Verbesserungsansätze der Optimierung untersucht: (1) Der erste Ansatz wird durch die Definition physikalischer Bedingungen beschrieben, die durch Penalty-Terme in die Optimierungen einfliessen. Dieser Ansatz hat zum Ziel, den Lösungsraum einzuschränken und somit die Signifikanz einzelner Unbekannten zu steigern. (2) Mittels einer globalen Sensitivitätsanalyse werden die Beobachtungen regewichtet. Hierbei wird ein Regewichtungsansatz verfolgt, mit Hilfe dessen die Gewichtung von Beobachtungen in Abhängigkeit ihrer Sensitivität auf Änderungen eines unbekannten Parameters variiert wird. (3) In einem letzten Ansatz wird ein Fuzzy Logic Regler entworfen. Dieser fusioniert physikalische Plausibilitätstests mit Dichtedaten, die für das Untersuchungsgebiet zur Verfügung stehen und liefert ein physikalisches Vertrautheitsmass für das Modell. Dieser Ansatz wird aktiv als Additionsterm in die zu maximierende Zielfunktion eingefügt. Die Modelle, die mit dem Optimierungsalgorithmus ohne jegliche Implementation von Verbesserungen generiert worden sind, werden als Referenzergebnisse genutzt. Als Anwendungsfall dient der Hochrisikovulkan Merapi auf Java, Indonesien. Die Modellierung gründet sich hierbei auf die nicht lineare Inversion von Schwereänderungen sowie dreidimensionalen Deformationen, die zwischen den Jahren 2000 und 2002 gemessen worden sind. Das zugrundeliegende mathematische Modell basiert auf den generalisierten, statischen Navier Gleichungen, die für den mathematischen Halbraum gelöst sind und Elastizitäts- und Gravitationseffekte koppeln. Die zu modellierenden Parameter der Quelle sind durch Punktmasse, dessen Position sowie einer Energieform gegeben. Die verschiedenen Ansätze werden in einen downhill simplex und einem genetischen Algorithmus implementiert und bezüglich der Streuung und des physikalischen Vertrautheitsmasses der Ergebnisse getestet. Die beste Konfiguration wird durch den Einsatz des genetischen Algorithmus mit der Implementation der Resultate, die aus der globalen Sensitivitätsanalyse gewonnen wurden, erreicht. Die Ergebnisse werden letztendlich durch den Fuzzy Logic Regler mit einem physikalischen Vertrautheitsmass versehen, so dass die Qualität der Ergebnisse sowohl statistisch als auch physikalisch definiert ist. Optimierungsansätze, die nur eine magmatische Quelle betrachten, lieferten für den Vulkan Merapi keine plausiblen Ergebnisse. Die Teststatitik zeigte, dass diese Modelle zwar statistisch signifikant sind, jedoch die Modellanpassung an die Daten sehr gering ist. Alle Ansätze zeigten oberflächennahe Quellen mit sehr kleinen Massen jedoch zu grossen Energiewerten. Diese Eigenschaften und die schlechte Modellierbarkeit der Deformationen durch das physikalische Modell lassen einen weiteren Einfluss vermuten, der hauptverantwortlich für die grossen Deformationen, vor allem im Kraterbereich, ist. Dieser Einfluss wird durch Superposition einer Störzone und dem elastisch-gravitativen Modell erfasst. Die entgültige Modellierung liefert statistisch signifikante und physikalisch plausible Ergebnisse. Verglichen mit den Modellierungen, die sich einzig auf eine elastisch-gravitative Quelle stützen, zeichnet sich dieses Modell durch eine höhere statistische Signifikanz aus und ist konform zu publizierten Annahmen über die Struktur des Merapis im Kraterbereich.

Deutsch
Freie Schlagworte: genetic algorithm, elastic-gravitational model, volcanic modeling
Sachgruppe der Dewey Dezimalklassifikatin (DDC): 500 Naturwissenschaften und Mathematik > 550 Geowissenschaften
Fachbereich(e)/-gebiet(e): 13 Fachbereich Bau- und Umweltingenieurwissenschaften
Hinterlegungsdatum: 17 Okt 2008 09:22
Letzte Änderung: 26 Aug 2018 21:25
PPN:
Referenten: Göpfert, Prof. Dr. Wolfgang ; Ostrowski, Prof. Dr. Manfred
Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: 3 Juni 2005
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