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Uncertainty evaluation of semi-active load redistribution in a mechanical load-bearing structure

Gehb, Christopher Maximilian (2019)
Uncertainty evaluation of semi-active load redistribution in a mechanical load-bearing structure.
Technische Universität Darmstadt
doi: 10.25534/tuprints-00009712
Ph.D. Thesis, Primary publication

Abstract

Load-bearing structures in mechanical engineering applications typically face the challenge of withstanding and transmitting external loads. In most cases, the load path through the load-bearing structure is predetermined by the design. However, if parts of the load-bearing structure become weak or suffer damage, e.g. due to deterioration or overload, the load capacity becomes uncertain. In this thesis, the semi-active load redistribution to bypass a portion of the loading away from damaged parts of the structure is used in order to prevent the structure from failure or malfunction. So far, studies on semi-active or active measures to adapt or manipulate the dynamic behavior of a structure have primarily investigated damping or vibration control and not load redistribution. The proposed semi-active load redistribution provides a technological possibility to influence the load path during operation via augmenting already existing parts of the load-bearing structure with actuators. Furthermore, for accurate numerical predictions of the load redistribution capability, an adequate mathematical model is needed. Therefore, the accuracy of the load-bearing structure’s mathematical model predictions is evaluated and increased methodologically by model parameter uncertainty quantification and reduction.

The structure to numerically and experimentally investigate load Redistribution in this thesis is based on a load-bearing structure developed within the SFB 805 and consists of a translational moving mass connected to a beam by a spring-damper system and two newly developed semi-active augmented guidance elements for load redistribution. The beam is supported at its ends by two supports. The stiffness characteristic of the supports can be adjusted to simulate structural damage. The structural damage, in turn, causes misalignment of the beam, which is defined as malfunction. A mathematical model of the load-bearing structure is derived for numerical investigations of the load redistribution capability and for controller design. A BAYESIAN inference based calibration procedure is applied to reduce and simultaneously quantify the model parameter uncertainty. Thus, the model is adjusted to the present conditions and the model prediction accuracy is increased. Clipped-optimal LQR and PID controllers are introduced for the semi-active load redistribution and designed based on the calibrated model.

With the presented procedure, the model prediction variation due to Parameter uncertainty is reduced by up to 85%. Comparing the passive and semi-active load-bearing structure, the malfunction is reduced by up to 53% numerically and by up to 51% experimentally. The evaluation of the load paths shows that a redistribution of the load between the two supports is achieved by means of the semi-active guidance elements. The results of this thesis contribute to the methodological parameter uncertainty quantification and reduction as well as the technological application of semi-active load redistribution.

Item Type: Ph.D. Thesis
Erschienen: 2019
Creators: Gehb, Christopher Maximilian
Type of entry: Primary publication
Title: Uncertainty evaluation of semi-active load redistribution in a mechanical load-bearing structure
Language: English
Referees: Melz, Prof. Dr. Tobias ; Kirchner, Prof. Dr. Eckhard
Date: 17 December 2019
Place of Publication: Darmstadt
Refereed: 9 July 2019
DOI: 10.25534/tuprints-00009712
URL / URN: https://tuprints.ulb.tu-darmstadt.de/9712
Abstract:

Load-bearing structures in mechanical engineering applications typically face the challenge of withstanding and transmitting external loads. In most cases, the load path through the load-bearing structure is predetermined by the design. However, if parts of the load-bearing structure become weak or suffer damage, e.g. due to deterioration or overload, the load capacity becomes uncertain. In this thesis, the semi-active load redistribution to bypass a portion of the loading away from damaged parts of the structure is used in order to prevent the structure from failure or malfunction. So far, studies on semi-active or active measures to adapt or manipulate the dynamic behavior of a structure have primarily investigated damping or vibration control and not load redistribution. The proposed semi-active load redistribution provides a technological possibility to influence the load path during operation via augmenting already existing parts of the load-bearing structure with actuators. Furthermore, for accurate numerical predictions of the load redistribution capability, an adequate mathematical model is needed. Therefore, the accuracy of the load-bearing structure’s mathematical model predictions is evaluated and increased methodologically by model parameter uncertainty quantification and reduction.

The structure to numerically and experimentally investigate load Redistribution in this thesis is based on a load-bearing structure developed within the SFB 805 and consists of a translational moving mass connected to a beam by a spring-damper system and two newly developed semi-active augmented guidance elements for load redistribution. The beam is supported at its ends by two supports. The stiffness characteristic of the supports can be adjusted to simulate structural damage. The structural damage, in turn, causes misalignment of the beam, which is defined as malfunction. A mathematical model of the load-bearing structure is derived for numerical investigations of the load redistribution capability and for controller design. A BAYESIAN inference based calibration procedure is applied to reduce and simultaneously quantify the model parameter uncertainty. Thus, the model is adjusted to the present conditions and the model prediction accuracy is increased. Clipped-optimal LQR and PID controllers are introduced for the semi-active load redistribution and designed based on the calibrated model.

With the presented procedure, the model prediction variation due to Parameter uncertainty is reduced by up to 85%. Comparing the passive and semi-active load-bearing structure, the malfunction is reduced by up to 53% numerically and by up to 51% experimentally. The evaluation of the load paths shows that a redistribution of the load between the two supports is achieved by means of the semi-active guidance elements. The results of this thesis contribute to the methodological parameter uncertainty quantification and reduction as well as the technological application of semi-active load redistribution.

Alternative Abstract:
Alternative abstract Language

Lasttragende Strukturen im Maschinenbau stehen typischerweise vor der Herausforderung, äußeren Belastungen standzuhalten und diese über einen Lastpfad zu übertragen. In den meisten Fällen ist der Lastpfad durch die lasttragende Struktur konstruktionsbedingt vorgegeben. Wenn jedoch Teile der lasttragenden Struktur geschwächt oder geschädigt werden, z. B. aufgrund von Verschleiß oder Überlastung, wird ihre Tragfähigkeit unsicher. In dieser Arbeit wird die semi-aktive Lastumverteilung verwendet, um einen Teil der Last um geschädigte Teile der Struktur herumzuleiten und so ein Versagen oder eine Fehlfunktion der Struktur zu verhindern. Bisherige Studien zu semi-aktiven oder aktiven Maßnahmen zur Anpassung oder Beeinflussung des dynamischen Verhaltens einer Struktur untersuchten hauptsächlich die Regelung von Dämpfungseigenschaften oder die Schwingungskontrolle und adressierten nicht die Lastumverteilung. Die vorgeschlagene semi-aktive Lastumverteilung bietet eine technologische Möglichkeit, den Lastpfad während des Betriebs anzupassen indem bereits vorhandene Teile der lasttragenden Struktur mit Aktuatoren erweitert werden. Darüber hinaus ist für genaue numerische Vorhersagen des Lastumverteilungsvermögens ein geeignetes mathematisches Modell erforderlich. Dafür wird die Genauigkeit der Vorhersage des abgeleiteten mathematischen Modells bewertet und methodisch durch die Quantifizierung und Reduktion der Parameterunsicherheit erhöht.

Die Struktur zur numerischen und experimentellen Untersuchung der Lastumverteilung in dieser Arbeit basiert auf einer im SFB 805 entwickelten lasttragenden Struktur und besteht aus einer translatorisch beweglichen Masse, die über ein Feder-Dämpfer-System mit einem Balken verbunden ist, und zwei neuentwickelte, semi-aktive Gelenkmodule für die Lastumverteilung. Der Balken ist beidseitig näherungsweise gelenkig gelagert. Die Steifigkeitscharakteristik der Lager kann angepasst werden, um strukturelle Schäden zu simulieren. Die strukturelle Beschädigung verursacht wiederum eine Schrägstellung des Balkens, die als Fehlfunktion definiert wird. Für numerische Untersuchungen des Lastumverteilungsvermögens und des Reglerentwurfs wird ein mathematisches Modell der lasttragenden Struktur gebildet. Ein auf Bayes‘scher Statistik basierendes Kalibrierungsverfahren wird angewendet, um die Modellparameterunsicherheit zu verringern und gleichzeitig zu quantifizieren. Dadurch wird das Modell an die gegenwärtigen Bedingungen angepasst und die Modellvorhersagegenauigkeit erhöht. Auf Basis des kalibrierten Modells werden für die Lastumverteilung ein clipped-optimal LQR- und ein PID-Regler entworfen.

Mit dem vorgeschlagenen Verfahren wird die Variation der Modellvorhersage aufgrund von Parameterunsicherheit um bis zu 85 % reduziert. Im Vergleich der passiven und semi-aktiven lasttragenden Struktur lässt sich die definierte Fehlfunktion numerisch um bis zu 53 % und experimentell um bis zu 51 % reduzieren. Die Auswertung der Lastpfade über die Lagerkräfte zeigt, dass mittels der semi-aktiven Gelenkmodule eine Umverteilung der Last zwischen den beiden Lagern erreicht wird. Zusammenfassend tragen die Ergebnisse dieser Arbeit zur methodischen Quantifizierung und Reduktion der Parameterunsicherheit sowie zur technologischen Anwendung der Lastumverteilung bei.

German
URN: urn:nbn:de:tuda-tuprints-97120
Classification DDC: 500 Science and mathematics > 500 Science
600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Research group System Reliability, Adaptive Structures, and Machine Acoustics (SAM)
DFG-Collaborative Research Centres (incl. Transregio)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 805: Control of Uncertainty in Load-Carrying Structures in Mechanical Engineering
Date Deposited: 22 Dec 2019 20:55
Last Modified: 09 Mar 2020 14:14
PPN:
Referees: Melz, Prof. Dr. Tobias ; Kirchner, Prof. Dr. Eckhard
Refereed / Verteidigung / mdl. Prüfung: 9 July 2019
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