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Item type:Publication, Access status: without files , Bridging ocean wave physics and deep learning: physics-informed neural operators for nonlinear wavefield reconstruction in real-time(American Institute of Physics (AIP), 2025-10-07); ; Accurate real-time reconstruction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for obtaining initial conditions from sparse or indirect wave measurements. While recent advances in supervised deep learning have shown potential for this purpose, they require large labeled datasets of ground truth wave data, which are infeasible to obtain in real-world scenarios. To overcome this limitation, we propose a physics-informed neural operator (PINO) framework for reconstructing spatially and temporally phase-resolved, nonlinear ocean wave fields from sparse measurements, without the need for ground truth data during training. This is achieved by embedding residuals of the free surface boundary conditions of ocean gravity waves into the loss function, constraining the solution space in a soft manner. In the current implementation, the framework is demonstrated for long-crested, unidirectional wave surfaces, where the wave propagation direction is aligned with the radar scanning direction. Within this setting, we validate our approach using highly realistic synthetic wave measurements by demonstrating the accurate reconstruction of nonlinear wave fields from both buoy time series and radar snapshots. Our results indicate that PINOs enable accurate, real-time reconstruction and generalize robustly across a wide range of wave conditions, thereby paving the way for future extensions of this framework toward multidirectional sea states and thus operational wave reconstruction in realistic marine environments.Publicationtype: Journal Article28 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Physics-informed neural networks for phase-resolved data assimilation and prediction of nonlinear ocean waves(American Physical Society (APS), 2025-09-02); ; ; ; Cao, RuiThe assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave prediction. However, traditional wave prediction methods are often limited. For example, most simplified wave models have a limited ability to capture strong wave nonlinearity, while fully nonlinear PFT solvers often fail to meet the speed requirements of engineering applications. This computational inefficiency also hinders the development of effective data assimilation techniques, which are required to reconstruct spatial wave information from sparse measurements to initialize the wave prediction. To address these challenges, we propose a solver method that leverages physics-informed neural networks (PINNs) that parametrize PFT solutions as neural networks. This provides a computationally inexpensive way to assimilate and predict wave data. The proposed PINN framework is validated through comparisons with analytical linear PFT solutions and experimental data collected in a laboratory wave flume. The results demonstrate that our approach accurately captures and predicts irregular, nonlinear, and dispersive wave surface dynamics. Moreover, the PINN can infer the fully nonlinear velocity potential throughout the entire fluid volume solely from surface elevation measurements, enabling the calculation of fluid velocities that are difficult to measure experimentally.Publicationtype: Journal Article15 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Exploring localization in nonlinear oscillator systems through network-based predictionsLocalized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure due to fatigue. During operation, the emergence of localization is difficult to predict, partly because of changing parameters over the life cycle of a system. This work proposes a novel, network-based approach to detect an imminent localized vibration. Synthetic measurement data are used to generate a functional network, which captures the dynamic interplay of the machine parts, complementary to their geometric coupling. Analysis of these functional networks reveals an impending localized vibration and its location. The method is demonstrated using a model system for a bladed disk, a ring composed of coupled nonlinear Duffing oscillators. Results indicate that the proposed method is robust against small parameter uncertainties, added measurement noise, and the length of the measurement data samples. The source code for this work is available at C. Geier [(2024). “Code for paper Exploring localization in nonlinear oscillator systems through network-based predictions,” Zenodo. https://doi.org/10.5281/zenodo.12611988].Publicationtype: Journal Article19 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Data-driven generation of tailored wave sequences(American Society of Mechanical Engineers (ASME), 2024-06); ; ; ; This paper explores the applicability of machine learning techniques for the generation of tailored wave sequences. For this purpose, a fully convolutional neural network was implemented for relating the target wave sequence at the target location in time domain to the respective control signal of the wave board. The database was generated by means of extensive wave tank tests. The experimental campaign focused on the generation of very steep wave groups including wave breaking which cannot be covered by the simplified wave generation methods. The extensive experimental campaign was performed in a small wave tank with an fully automated approach including determination and control of the wave maker motion as well as data measurement. The training data set features wave groups of short duration based on JONSWAP spectra, where the parameters wave steepness, peak wave period and enhancement factor were systematically varied. At the end of the training process, the trained models are able to predict the wave maker control signal based on time series of the target wave defined for a specific target location in the wave tank. The accuracy of the trained models are evaluated by means of unseen validation data. In addition, the predictive accuracy of the trained models is compared with the classical linear transformation approach.Publicationtype: Conference Paper56 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , The role of damping in complex structural dynamics: Data-driven approachesThe Dynamics Group at Hamburg University of Technology has been working on two consecutive research projects supervised by Prof. Norbert Hoffmann within the Priority Programme SPP 1897. The first project ‘Understanding and improving energy dissipation and damping in structures subject to self-excited irregular vibrations’ focused on the chaotic nature of friction-excited dynamics and how properties of those complex vibrations can be leveraged for understanding damping and stability. Within the second project ’Understanding and improving energy dissipation and vibration damping in structures subject to self-excited irregular vibrations - linking data driven approaches with modelling’, data-driven techniques were linked with conventional modeling approaches to arrive at hybrid simulation and identification approaches for damping in complex structural dynamics. The work at hand summarizes central findings and novel approaches that have been published in a number of peer-reviewed journal articles, poses new research questions, and gives an outlook.Publicationtype: Book part18 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves(Cambridge University Press (CUP), 2023-11-10); ; ; ; Algorithms for reconstructing and predicting nonlinear ocean wave fields from remote measurements are presented. Three types of synthetic observations are used to quantify the influence of remote measurement modulation mechanisms on the algorithms' performance. First, the observations correspond to randomly distributed surface elevations. Then, they are related to a marine radar model - the second type takes the wave shadowing modulation into account whereas the third one also includes the tilt modulation. The observations are numerically generated based on unidirectional waves of various steepness values. Linear and weakly nonlinear prediction algorithms based on analytical models are considered, as well as a highly nonlinear algorithm relying on the high-order spectral (HOS) method. Reconstructing surfaces from shadowed observations is found to have an impact limited to the non-visible regions, while tilt modulation affects the reconstruction more generally due to the indirect, more complex extraction of wave information. It is shown that the accuracy of the surface reconstruction mainly depends on the correct modelling of the wave shape nonlinearities. Modelling the nonlinear correction of the dispersion relation, in particular the frequency-dependent wave phase effects in the case of irregular waves, substantially improves the prediction. The suitability of the algorithms for severe wave conditions in finite depth and using non-perfect observations is assessed through wave tank experiments. It shows that only the third-order HOS solution predicts the right amplitude and phase of an emerging extreme wave, emphasizing the relevance of the corresponding physical modelling.Publicationtype: Journal Article12 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Machine learning simulation of one-dimensional deterministic water wave propagation(2023-09-15); ; ; Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.Publicationtype: Journal Article22 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Extreme wave excitation from localized phase-shift perturbations(2022-10); ; ; ; The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection of sidebands, which translate into an amplitude modulation of the wave field. The nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear Schrödinger equation (NLSE). In that case, the amplitude modulation of such coherent extreme wave structures is connected to a particular phase-shift seed in the carrier wave. In this Letter, we show that phase-shift localization applied to the background, excluding any amplitude modulation excitation, can indeed trigger extreme events. Such rogue waves can be for instance generated by considering the parametrization of fundamental breathers, and thus by seeding only the local phase-shift information to the regular carrier wave. Our wave tank experiments show an excellent agreement with the expected NLSE hydrodynamics and confirm that even though delayed in their evolution, breather-type extreme waves can be generated from a purely regular wave train. Such a focusing mechanism awaits experimental confirmation in other nonlinear media, such optics, plasma, and Bose-Einstein condensates.Publicationtype: Journal Article39 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A Novel Approach for the Frequency Shift of a Single Component Eigenmode through Mass Addition in the Context of Brake Squeal Reduction(2022-09-23); ; ; Brake squeal reduces comfort for the vehicle occupants, damages the reputation of the respective manufacturer, and can lead to financial losses due to cost-intensive repair measures. Mode coupling is mainly held responsible for brake squeal today. Two adjacent eigenfrequencies converge and coalesce due to a changing bifurcation parameter. Several approaches have been developed to suppress brake squeal through structural changes. The main objective is to increase the distance of coupling eigenfrequencies. This work proposes a novel approach to structural modifications and sizing optimization aiming for a start at shifting a single component eigenfrequency. Locations suitable for structural changes are derived such that surrounding modes do not significantly change under the modifications. The positions of modifications are determined through a novel sensitivity calculation of the eigenmode to be shifted in frequency. In the present work, the structural changes are carried out on a beam and a brake caliper. Selected eigenfrequencies are shifted while the frequencies of the other eigenmodes are simultaneously fixed. Experimental investigations for the brake caliper validate the numerical findings and the applicability as well as efficiency of the proposed methods.Publicationtype: Journal Article27 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Hydroelastic potential flow solver suited for nonlinear wave dynamics in ice-covered watersThe aim of this paper is to introduce a fully nonlinear numerical finite element solver for the simulation of nonlinear wave processes in the presence of a solid ice sheet. In this study, solid ice cover referred to the size of the ice sheet and denoted that the length of the ice sheet was many times larger than the longest relevant wavelength. The complexity of the ice sheet characteristics was assumed to be homogeneous, isotropic and in the linear elastic plate regime so that the deformation process could be modeled by the Kirchhoff–Love plate ansatz. The method presented was verified and validated for different ice dimensions and wave scenarios. At the beginning, the implementation of the flexural rigidity to the free surface boundary condition was verified by comparing the analytical wave-ice dispersion relation to simulation results with small amplitude regular waves and varying ice dimensions. Afterwards, the general applicability was validated by means of wave-ice experiments. The experiments were performed in the ice tank at Hamburg Ship Model Basin HSVA comprising regular waves and transient wave groups.Publicationtype: Journal Article50