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Item type:Publication, Access status: with files , From internal resonance to kinking and stacking in the response of nonlinear oscillatorsIn nonlinear dynamical systems, internal resonance is a well known phenomenon. Natural frequencies may change with vibration amplitude, becoming commensurable or close at certain energy levels. Nonlinear modes then interact based on their participating oscillators. Here, we investigate effects on the response curve of a system as neighboring oscillators are modified. This provides new insights into the relation of internal resonance and the frequency response of coupled nonlinear systems. We use methods of Harmonic Balance and a continuation algorithm to compute nonlinear frequency response curves and nonlinear normal modes for a model system. It is arranged as a chain of Duffing oscillators with separated natural frequencies. We demonstrate a kinking effect in the response curve once internal resonance emerges in the system’s forced response. The kink is observed as a shift to higher response levels, stretching the response curve. We also show how this kinking effect is modified by adapting the nonlinearities of neighboring oscillators. The system’s response branches kink vertically as an oscillator in the chain is made linear, stacking on top of each other. Multiple stable solutions at a certain frequency may then be observed. We show that these solutions correspond to varying degrees of vibration localization in the system. We expect our results to be valuable in system design. It should be possible to exploit the observed kinking effect, shaping the response curve by adding suitable oscillators of various characteristics. The engineer may thus be able to reach a target system response level at a certain frequency.Publicationtype: Journal Article39 47 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A network‐based approach to identifying key components in structural vibrationsModeling the dynamics of systems with many interacting components, such as robots, wind turbines, and trusses, remains challenging today. These systems often display complex oscillatory responses to external inputs, and harmful vibrations might be excited along with the desired motion. Understanding the relative importance of individual components or systems aspects to the overall system dynamics could be a vital step towards focused design and maintenance efforts. This work proposes a network‐based approach to studying the dynamics of a mechanical system by representing the system as a network of coupled oscillators, where each node corresponds to a machine component and each link denotes a physical connection, such as a weld or bolt. Inspired by studies of dynamics in biological and social networks, we show how network measures can be used to predict the importance of a single oscillator, or component, for shaping the overall dynamics. We further demonstrate under which conditions these conclusions are possible, and where the metrics fail. This study hopes to contribute to the broader field of network‐based methods in engineering and yield insights that help focus design and maintenance efforts in the future.Publicationtype: Journal Article21 7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Data-driven, non-linear ship response prediction based on time series of irregular, long-crested sea states amidships(Elsevier, 2025-02-01); ; ; ; The accurate prediction of vessel responses in waves is crucial for decision-making and contribute to the operational safety and risk minimization. Short-term predictions can be carried out by estimating the vessel's motions and loads based on incident waves. Existing model-based approaches either require computationally intensive simulations that compromise real-time capability or use simplified models affecting the accuracy of the prediction. Therefore, this study explores the feasibility of using neural networks for mapping time signals of surface elevation data and a set of corresponding ship responses, i.e. the heave and pitch motions as well as the vertical bending moment. The approach followed here is built on the assumption that the wave profile amidships is known. A synthetic dataset was generated using a time-domain strip theory solver with considerations of non-linear effects on motions and loads due to large amplitude waves in a variety of irregular, long-crested sea state conditions. We propose two different neural network models, a multi-layer perceptron (MLP) and a fully convolutional neural network (FCNN), and compare their performances on measurement data obtained from model tests in a seakeeping basin. The evaluations also include the freak wave reproduction of the ‘new year wave’. The proposed networks are able to estimate the motions and bending moment accurately for a wide range of sea state conditions, surpassing current state-of-the-art models on the given data sets.Publicationtype: Journal Article79 99 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Building functional networks for complex response analysis in systems of coupled nonlinear oscillatorsSome aspects of engineering dynamics, such as nonlinearities and transient motion of many interconnected parts, remain difficult to handle today. To comply with increasing demands on resilience and safety, the dynamics of large machines need to be better understood. Complex network methods, already present in many scientific disciplines, provide a tool set complementary to conventional methods of system analysis. This work aims at providing a new, function-based view on mechanical systems by generating functional networks. To this end, a network algorithm is applied to sets of cyclically coupled Duffing oscillators as a common example of a complex nonlinear mechanical system. In the functional network, each node represents an oscillator while the direction of the network edges represents a functional coupling. Results show that the network method is capable of identifying dynamical transitions and synchronization between components, as well as determining the number of different states present within a system. Additionally, the time evolution of the component interactions, especially in response to a disturbance, is studied via a sliding-window approach. The results of this analysis might hopefully open new ways for a more efficient system analysis through optional sensor placement, and for effective countermeasures against unwanted dynamics through improved analysis of transient dynamics.Publicationtype: Journal Article20 60 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data(Elsevier, 2023-11-15); ; ; ; Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modelling assumptions that compromise the real-time capability or accuracy of the subsequent prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modelling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO demonstrates superior performance in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and output in Fourier space.Publicationtype: Journal Article28 96 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Towards neural network‐based numerical friction modelsFriction contacts can be found in almost all mechanical systems and are often of great technical importance. However, they are usually difficult to describe, and their behavior and influence on the whole system are hard to predict accurately. Modern product design and system operation strongly benefit from numerical simulation approaches today, but reliable friction models still represent a major challenge in this context. To tackle this problem, we employ neural network regression to capture the characteristics of frictional contacts and make them accessible for numerical methods in a minimal intrusive fashion. In particular, we test our approach using a Finite Element model of a 2D cantilever beam subject to stick-slip vibrations induced by a moving conveyor belt at its free end. As a reference solution, we perform a transient analysis based on a simple analytical friction model, where the kinetic friction force only depends on the normal load and the relative sliding velocity. We take the same friction model, add some artificial noise to mimic uncertainties coming with experimental measurements, and pick a limited set of data points to train a regression neural network. The machine learning friction model is then deployed in the Finite Element code to predict the kinetic friction force acting on the beam tip during the slip phases. The deflection curves obtained by the transient numerical analysis using the new neural network friction model agree well with the reference solution based on the underlying analytical model. The results indicate that data-driven approaches may also be capable of capturing more complex frictional contacts, including effects of temperature, humidity, and load history. The trained neural network friction models can then be employed in numerical simulations in a minimally intrusive manner. This approach opens up new possibilities to predict individual mechanical system behavior as accurately as possible.Publicationtype: Conference Paper43 240 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Machine learning-based state maps for complex dynamical systems: applications to friction-excited brake system vibrationsIn this work, a purely data-driven approach to mapping out the state of a dynamical system over a set of chosen parameters is presented and demonstrated along a case study using real-world experimental data from a friction brake system. Complex engineering systems often exhibit a rich bifurcation behavior with respect to one or several parameters, which is difficult to grasp using experimental approaches or numerical simulations. At the same time, the growing need for energy-efficient machines that can operate under varying or extreme environmental conditions also calls for a better understanding of these systems to avoid critical transitions. The proposed method combines machine learning techniques with synthetic data augmentation to create a complete state map for a dynamical system. First, a machine learning model is trained on experimental data, picking up hidden mechanisms and complex parametric relations of the underlying dynamical system. The model is then exploited to assess the state of the system for a set of synthetically generated data to obtain a state map over the complete space spanned by the chosen parameters. In addition, an extension of the concept to a probability state map is introduced. The results indicate that the proposed method can uncover hidden variables which drive dynamical transitions between different states of a system that were previously inaccessible.Publicationtype: Journal ArticleScopus© Citations 2 36 78 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , bSTAB: an open-source software for computing the basin stability of multi-stable dynamical systemsThe pervasiveness of multi-stability in nonlinear dynamical systems calls for novel concepts of stability and a consistent quantification of long-term behavior. The basin stability is a global stability metric that builds on estimating the basin of attraction volumes by Monte Carlo sampling. The computation involves extensive numerical time integrations, attractor characterization, and clustering of trajectories. We introduce bSTAB, an open-source software project that aims at enabling researchers to efficiently compute the basin stability of their dynamical systems with minimal efforts and in a highly automated manner. The source code, available at https://github.com/TUHH-DYN/bSTAB/, is available for the programming language Matlab featuring parallelization for distributed computing, automated sensitivity and bifurcation analysis as well as plotting functionalities. We illustrate the versatility and robustness of bSTAB for four canonical dynamical systems from several fields of nonlinear dynamics featuring periodic and chaotic dynamics, complicated multi-stability, non-smooth dynamics, and fractal basins of attraction. The bSTAB projects aims at fostering interdisciplinary scientific collaborations in the field of nonlinear dynamics and is driven by the interaction and contribution of the community to the software package.Publicationtype: Journal ArticleScopus© Citations 13 110 258 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Spatially localized vibrations in a rotor subjected to flutterThe current push toward lightweight structures in aerospace and aeronautical engineering is leading to slender design airfoils, which are more likely to undergo large deformation, hence experiencing geometrical nonlinearities. The problem of vibration localization in a rotor constituted by N coupled airfoils with plunge and pitch degrees of freedom subjected to flutter instability is considered. For a single airfoil, it is shown that depending on the system parameters, multiple static and dynamic equilibria coexist which may be a fixed point, a limit cycle, or irregular motion. By elastically coupling N airfoils, a simplified rotor model is obtained. The nonlinear dynamical response of the rotor is studied via time integration with particular attention to the emergence of localized vibrating solutions, which have been classified introducing a localization coefficient. Finally, the concept of basin stability is exploited to ascertain the likelihood of the system to converge to a certain localized state as a function of the airstream velocity. We found that homogeneous and slightly localized states are more likely to appear with respect to strongly localized states.Publicationtype: Journal ArticleScopus© Citations 6 201 170