In this study, we establish a foundational framework for controlling flexible floating structures by integrating state-of-the-art Model Predictive Control (MPC) with a high-fidelity Finite Element model representing these structures. Our specific objective is to enhance the stability of floating structures in offshore engineering applications. We commence with a comprehensive literature review to identify potential challenges, which informs the development of a well-structured research plan that addresses these challenges comprehensively.

From the insights gained during the literature review, we formulate a theoretical framework that serves as the basis for our methodology. We subsequently examine two distinct control scenarios—regular and irregular wave conditions—serving as a Proof of Concept, and we discuss the significant observations derived from these experiments. In conclusion, we summarize our findings and provide recommendations for future research directions.

We utilize a two-way monolithic Finite Element formulation of the flexible floating structure as a representation of the real-world system we aim to control. For our control strategy, we implement Model Predictive Control, which facilitates the incorporation of advanced functionalities, including the application of constraints. To enhance computational efficiency, we employ a Reduced Order Model (ROM) through Dynamic Mode Decomposition with Control (DMDc), trained using open-loop data derived from the Finite Element model. Additionally, we implement a Kalman filter to reconstruct the system's state from sparse and noisy measurements obtained from the floating structure.

We design two Reduced Order Models specifically for controlling the floating structure under the aforementioned conditions. Prior to executing the control strategies in these distinct scenarios, we conduct an in-depth investigation of DMDc, exploring its relationship with Koopman theory. We generate open-loop data free from pollution using the Finite Element model, which is subsequently utilized to derive the Reduced Order Model. A convergence study is performed by analyzing the eigenvalues and amplitudes of the DMDc, following methodologies established in prior research. We validate the DMDc models against validation datasets, allowing us to select the model exhibiting the smallest validation error. Furthermore, we ensure that the training datasets inherently encompass the wet modes by employing Proper Orthogonal Decomposition.

Our initial control scenario involves managing the floating structure under regular wave conditions. This case is pivotal for acquiring fundamental insights into the control mechanisms. We observe that the frequency of the control input aligns precisely with the excitation frequency. Subsequently, we extend our study to encompass the control of the floating structure in irregular wave conditions, characterized by a sea state defined by the JONSWAP spectrum. Consistent with our findings from the regular wave scenario, we discover that the control mechanism exploits the natural frequencies of the floating structure, which closely correspond to the energy-dense region of the sea state's spectrum. This is achieved by amplifying the reflected wave, thereby counteracting the incoming wave and reducing energy input into the system.

In conclusion, we advocate for further research to bolster the proposed method by examining various structural properties and wave environments, thereby providing robust evidence to validate the approach presented in this study. Our findings indicate that the integration of advanced control strategies, such as MPC and DMDc, holds significant promise for optimizing the performance and stability of flexible floating structures in dynamic offshore conditions.

In this study the contribution of the low-frequency residuals to the sea-level variability has been examined. This is done using 106-year old sea-level record obtained at Hoek van Holland. Computing the mean sea-level per season each year and the corresponding standard deviation one finds an increase in both these features of the sea-level record. The rise of the mean sea-level implies the effect of climate change. Moreover, it is found that the standard deviation in the sea-level, thus the intensity of variation, is the highest during fall and winter. This implies that the sea-level variability has a seasonal dependency. Furthermore, one finds an increase in the standard deviation on the long term. However, since a big part of the mean sea-level is influenced by tidal events, the increase in standard deviation is possibly linked to climate change in meteorological factors as has been found is in the study carried out by Gerkema and Duran-Matute(2017). With the use of the computational algorithms such as the Fast Fourier Transformation and the Wavelet Transformation one can extract the low-frequency residuals from the sea-level record. Inspired by the study of Gerkema and Duran-Matute(2017) a correlation between the wind speed and the low-frequency residuals have been found. Using the Wavelet Transformation it is found that the low-frequency residuals obtain the most energy during fall and winter, this empowers the finding that these low-frequency residuals are seasonal dependent. Moreover, when studying the low-frequency residuals closely it is found that the frequencies below 0.60 1 day obtain the most energy during fall and winter, especially the frequencies near 0.10 1 day . With these findings one can say that the contribution of the low-frequency signals, thus the low-frequency residuals, is correlated to meteorological events, such as the wind. Moreover, it is found that the variation in the low-frequency residuals is much smaller during spring and summer compared to the case during winter and fall. This seems not to be the case for the sea-level variability due to the tidal constituents and the high-frequency waves. Therefore, one may conclude that these low-frequency residuals contribute to a great extent in the standard deviation of the sea-level.