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Michael Muskulus

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Master thesis (2025) - F.O. Jersch, Qing Shen, J.O. (Oriol) Colomes Gene, Michael Muskulus, Eyal Taub, W. Yu, S.J. Watson
Floating Offshore Wind Turbine (FOWT) unlock far-offshore wind resources in deep waters that can’t be harvested under economic aspects using bottom-fixed wind turbines. Numerical modelling tools are employed to assess different FOWT designs under various environmental conditions. In order to be competitive and yet guarantee working designs, the numerical tools need to be reliable and computationally efficient. This justifies the need for assumptions simplifying the models.

One such simplification is the rigid floater assumption, where the FOWTs’ substructure is assumed rigid. This reduces the computational effort but at the same time alters the results, like the tower’s first natural frequency and corresponding mode shape.

Multiple approaches are used in literature to match the tower’s first natural frequency of flexible and rigid floaters. This involves adjusting the tower properties, such as length or Young’s modulus, or alternatively, implementing a flexible element between a rigid floater and a flexible tower. Siemens Gamesa currently makes use of the latter method by tuning the flexible elements’ properties to achieve a match in the models’ tower first bending natural frequency.

So far no studies have been conducted on the impact of the flexible element parameters on the tower first mode shape when tuning towards a matching tower first bending frequency. Additionally, the effect of differently correct mode shape variants on the tower dynamics is investigated. This leads to the goal of improving the tower dynamics for a FOWT with a rigid substructure.

The analysis was based on two versions of the U-Maine FOWT model. One fully flexible floater design served as a reference, whilst a fully rigid floater design was used to incorporate the different flexible element designs. Various flexible elements with distinct properties were evaluated to understand the sensitivity of the mode shape to these parameters. Subsequently, selected designs exhibiting varying degrees of accuracy of the mode shape were compared to the flexible floater design in time domain simulation. Furthermore, three separate methods of identifying the tower’s first bending mode are proposed.

In the course of modelling the flexible floater design, a modelling error was made that resulted in double counting of the heave motions. Despite this error, it was concluded that for constant and turbulent wind, all flexible element designs outperform the rigid floater design. Furthermore, a close mode shape match likewise results in an increased match of bending moment and tower top rotation for high and low wind speeds. In the range of rated wind speeds, the shortest flexible element design with the worst mode shape match performs best. Comparing the tower top acceleration also indicates an overall improvement of the results, but less significant. This is expected to result from tuning towards the first tower mode rather than higher-order modes.

Generally, using any flexible element design already results in an improved mode shape match with minor differences. The impact of these discrepancies on the tower dynamics is small. Therefore, it is concluded that any flexible element, even when only tuned to match the tower’s first natural frequency, is an improvement over the rigid floater design. ...
Master thesis (2019) - Jaehyeun Lee, Andrei Metrikine, Eliz-Mari Lourens, Michael Muskulus, Alexandros Iliopoulos, Hendrik Kramers
Fatigue is often a governing design factor for offshore wind turbines. Since the design of offshore wind turbines includes conservatism, the actual accumulated fatigue damage can be lower than what the turbine is designed for. In this case, the operator can make a decision on life time extension of existing wind turbines. Therefore, it is important to estimate the actual accumulated fatigue damage to support decision making on life time extension, and for optimization of support structure design. However, fatigue critical locations are located near mudline where it is unfeasible to install strain gauges to measure the accumulated fatigue damage. The first purpose of this thesis is to investigate if data-driven approaches (linear regression and feed-forward neural network) can be applied to estimate the accumulated fatigue damage both in individual turbines and farm-wide levels. The second purpose is to determine the minimum number of sensors and quantity of data required for accurate estimation. Towards this goal, real measurement data of two offshore turbines in the same wind farm have been used. Specifically, the data-driven approaches have been applied with real measurement data from the SCADA system, measurements at the top and bottom of the tower, and data from a wave measurement system. This data was used to estimate the accumulated fatigue damage at multiple locations (tower bottom, transition piece and two levels on the monopile) in the form of damage equivalent loads. Throughout the study, 10 min. statistical properties of the measurement data have been used as input to the learning algorithms. One remark is that the estimation has not been performed for the fatigue critical location near mudline itself, but it is expected that estimation with these approaches can be expanded to the fatigue critical location if accurate response estimation at multiple locations on the support structure is possible. The results of this thesis show that the data-driven approaches can give accurate estimates damage equivalent loads on individual turbine level at multiple locations on the support structure when moment or inclination signals at tower bottom is used. For farm-wide level load estimation as well, it has been proven that the data-driven approaches can give quite accurate estimates the damage equivalent load. However, it should be noted that the turbines used in this study have similar dynamic properties. Therefore, the farm-wide level load estimation with the data-driven approaches should be further investigated in the future. ...

Comparison of structures with circular and rectangular cross-section subjected to the frequency lock-in regime

Master thesis (2017) - Cody Owen, Andrei Metrikine, Hayo Hendrikse, Marnix van den Berg, Michael Muskulus, Wojciech Popko, Gesa Ziemer, Philipp Hinse
Offshore wind energy has very recently begun expanding into subarctic regions with seasonally ice-infested waters like the Baltic Sea. For offshore wind turbines with conventional support structures such as monopiles and jackets that are typically flexible and vertically sided, the phenomenon known as ice-induced vibrations can develop. In response to the growing interest in offshore wind in the Baltic Sea and in further validating a state-of-the-art numerical model for ice-structure interaction, the Ice-induced Vibrations of Offshore Structures
(IVOS) project has been coordinated with the Hamburg Ship Model Basin (HSVA) and many academic and industry partners—including TU Delft and NTNU—in order to enhance understanding of the topic via a comprehensive laboratory testing campaign.
In this thesis, specific data are selected fromthe extensive IVOS Phase 2 tests such that a comparative analysis is performed between two different model-scale structures, one with circular cross-section and another with rectangular cross-section, that were subjected to ice-induced vibrations in the frequency lock-in regime. Preceding the comparative analysis, the data from the IVOS Phase 2 tests are organized into a database and post-processing tools are developed to facilitate further research by supplying analysis-ready data sets. Included in the post-processing tools is an attempt to determine ice-induced global loads from uncalibrated tactile sensor data, which offers insight into the relationship between the relative pressure distributions along the ice-structure interface and the ice-induced global forces on the model structure.
The comparative analysis garnered qualitative information about the frequency lock-in regime and buckling failure of ice. It is observed that frequency lock-in vibrations usually persisted regardless of buckling events. For the frequency lock-in regime, the ice-induced global loads on the circular cross-section structure are generally lower than those for the rectangular cross-section structure. It is unclear whether the difference in global loads between the structures is caused by the difference in cross-sectional shape, other structural properties, ice properties, or combinations thereof. The analysis of the energy of the system is intriguing but does not offer lucid conclusions. However, the quasi-figure-eight pattern from the x-direction and derived y-direction structural displacements is an enlightening discovery that may explain inconsistencies in the energy of the system. Based on the general configuration of the test apparatus from the IVOS Phase 2 tests and the results from the comparative analysis, it can be concluded that ice-induced vibrations of the model-scale structures in the frequency lock-in regime should be regarded as a two-dimensional problem. ...
Master thesis (2017) - Matthieu Rhomberg, Andrei Metrikine, Michael Muskulus, Eliz-Mari Lourens, Lisa Ziegler
Optimization of structures in a domain with large uncertainties is rather difficult. This also applies for the offshore wind energy sector. For current offshore wind energy development locations with monopile-based support structures the fatigue limit state is the driving design criteria. These analyses are connected with long time domain evaluations to cover non-linearities. Model, statistical and data uncertainties lead to a combined fatigue damage prediction uncertainty. The former are either covered by a design fatigue factor or a material factor, which are stated in certification standards, e.g. DNVGL-ST-0126. The influence of mass changes regarding different lifetimes and the impact of this design fatigue factor has not been published yet.

Based on this, within this graduation project, the monopile support structure is optimized for different lifetimes in order to identify mass changes and influences of the design fatigue factor. Literature shows that automatized optimization using genetic algorithms in offshore wind energy is possible but limited, due to the algorithm methodology including a large number of design evaluations. This graduation project shows the applicability of Importance Sampling for load case reduction in a genetic algorithm optimization for offshore wind. Compared to previous approaches Importance Sampling assists to use a full certification procedure for fatigue limit state computations in a feasible amount of time with high fatigue life estimation accuracies. Subsequently, the fatigue limit state load case table is reduced by 93%. By optimizing the monopile with this reduced amount of load cases the algorithm is computationally feasible for the industry.

Rambøll simulation software for offshore wind turbine support structure design is used in combination with the genetic algorithm function in Matlab®. The combination of the software leads to the optimization of monopile based offshore wind support structures for different lifetimes. The algorithm runs with a reduced amount of load cases. Resulting critical fatigue damage values of converged designs are showing deviations from actual fatigue damage values using full fatigue limit state load case tables at maximum 6.6% and minimum 1.7%. This high accuracy leads to an optimization of monopile structures for desired lifetimes and consequently to the mass versus lifetime curve. A mass increase of approximately 22% is observed from 25 to 100 years lifetime. After reaching 75 years lifetime the curve shows a flattening behavior. Besides, parameter evolutions of optimized monopile designs are discussed in terms of different fatigue life. The design variables are embedment depth, cone angle, and corresponding wall thicknesses of monopile sections.

Summarized, this thesis proved the implementation of a full state of the art fatigue limit state computation in the genetic algorithm by Importance Sampling with reduced load cases and also visualized the impact of mass changes for different projected lifetimes. As a conclusive remark, the application of Importance Sampling for load case reduction in the design process opens new possibilities of optimization in the offshore wind energy sector.
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Master thesis (2017) - Jorge Mendoza Espinosa, Andrei Metrikine, Michael Muskulus, Marc Vossbeck, Eliz-Mari Lourens
Jacket support structures are a preferred solution for offshore wind turbines in deeper waters. Extensive knowledge exists in relation to its construction technique as well as its crucial components, but due to considerable cost pressure, continued optimization is essential for the future competitiveness of the concept in the offshore wind business. Their joints along with their complex welds are of special interest in terms of cost reduction. The design of tubular joints is generally driven by fatigue resistance. Due to the size, complexity and cost of these joints, this is assessed by using detailed FE models.
Several aspects that have an impact on the results of the models are found to require further research and are investigated within this project: (1) influence of using solid versus shell elements in the modelling of the joint members; (2) degree of accuracy of the Efthymiou equations; (3) influence of the carry-over effect in multiplanar KK-joints; (4) differences in the fatigue life predictions between the hot-spot and the effective notch stress methods.
Guidelines recommend the use of both solid and shell theories for the definition of the FE models used in the hot-spot fatigue assessment. Both options are compared in terms of accuracy of the results and computational time. Generally speaking, significant differences are found between both models. The background of the differences is studied.
The employment of the Efthymiou formulae is common in practice. These equations provide the SCF at the locations around the weld where they are found to be maximum. The output of this approach is compared with the results of numerical models. The validity of its use is quantified.
Offshore wind jacket joints are mainly multiplanar KK-joints. Loading in the braces of one face of the jacket may yield significant carry-over effects on the out-of-plane braces connected to the same joint. A parametric comparison is carried out to study the accuracy of modelling the joint as a planar K-joint. In general, it is found that the carry-over effect cannot be neglected and the assumption is not accurate.
The fatigue assessment of tubular joints by means of the hot-spot method is subjected to several assumptions that limit the optimization of the members. The notch concept is a more realistic method that is presented as an alternative. However, this method is not widely used in engineering practice due to the difficulties in building the numerical model and the high computational requisites. An algorithm to carry out the effective notch stress assessment, based on the sub-modelling technique, is proposed. A comparison of the fatigue life prediction, between the hot-spot and the effective notch methods, is presented. The latter method is found to predict a higher fatigue life for many of the situations tested. Furthermore, since this method allows for a more detailed modelling, the weld profile can also be designed in order to optimize the fatigue resistance. The weld slope is found to have a significant impact on the results. ...