DIC Measurement of the Kinematics of a Friction Damper for Turbine Applications

International audienceHigh cycle fatigue (HCF) caused by large resonant stresses is a common cause for turbine blades failure. Passive damping systems, such as friction dampers are often used by aero-engine manufacturers to reduce the resonant stresses and mitigate the risk of HCF. The presence of friction dampers makes the dynamics of the system highly nonlinear, due to the complex stick-slip and separation phenomena taking place at the contact interface. Due to this nonlinear behaviour, an accurate understanding of the operating deflection shapes is needed for an accurate stress prediction. In this study, digital image correlation (DIC) in combination with a high speed camera is used to provide insights into the kinematics of the damper in a recently developed test rig. The in-phase and out-of-phase first bending modes of the blades were investigated leading to a full field measurement of the global ODS of the blades, and the local motion of the damper against its platforms. A significant change in the blades operational deflection shape could be observed due to the damper, and the sliding and rolling motion of the damper during a vibration cycle was accurately visualised

Multiple spatially localized dynamical states in friction-excited oscillator chains

International audienceFriction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity v d while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a "snaking-like" bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity

Up-Net: a generic deep learning-based time stepper for parameterized spatio-temporal dynamics

In the age of big data availability, data-driven techniques have been proposed recently to compute the time evolution of spatio-temporal dynamics. Depending on the required a priori knowledge about the underlying processes, a spectrum of black-box end-to-end learning approaches, physics-informed neural networks, and data-informed discrepancy modeling approaches can be identified. In this work, we propose a purely data-driven approach that uses fully convolutional neural networks to learn spatio-temporal dynamics directly from parameterized datasets of linear spatio-temporal processes. The parameterization allows for data fusion of field quantities, domain shapes, and boundary conditions in the proposed Up-Net architecture. Multi-domain Up-Net models, therefore, can generalize to different scenes, initial conditions, domain shapes, and domain sizes without requiring re-training or physical priors. Numerical experiments conducted on a universal and two-dimensional wave equation and the transient heat equation for validation purposes show that the proposed Up-Net outperforms classical U-Net and conventional encoder–decoder architectures of the same complexity. Owing to the scene parameterization, the Up-Net models learn to predict refraction and reflections arising from domain inhomogeneities and boundaries. Generalization properties of the model outside the physical training parameter distributions and for unseen domain shapes are analyzed. The deep learning flow map models are employed for long-term predictions in a recursive time-stepping scheme, indicating the potential for data-driven forecasting tasks. This work is accompanied by an open-sourced code

Recovery of differential equations from impulse response time series data for model identification and feature extraction

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics

The Basin Stability of Bi-Stable Friction-Excited Oscillators

Stability considerations play a central role in structural dynamics to determine states that are robust against perturbations during the operation. Linear stability concepts, such as the complex eigenvalue analysis, constitute the core of analysis approaches in engineering reality. However, most stability concepts are limited to local perturbations, i.e., they can only measure a state’s stability against small perturbations. Recently, the concept of basin stability was proposed as a global stability concept for multi-stable systems. As multi-stability is a well-known property of a range of nonlinear dynamical systems, this work studies the basin stability of bi-stable mechanical oscillators that are affected and self-excited by dry friction. The results indicate how the basin stability complements the classical binary stability concepts for quantifying how stable a state is given a set of permissible perturbations

Exploring the application of reinforcement learning to wind farm control

Optimal control of wind farms to maximize power is a challenging task since the wake interaction between the turbines is a highly nonlinear phenomenon. In recent years the field of Reinforcement Learning has made great contributions to nonlinear control problems and has been successfully applied to control and optimization in 2D laminar flows. In this work, Reinforcement Learning is applied to wind farm control for the first time to the authors' best knowledge. To demonstrate the optimization abilities of the newly developed framework, parameters of an already existing control strategy, the helix approach, are tuned to optimize the total power production of a small wind farm. This also includes an extension of the helix approach to multiple turbines. Furthermore, it is attempted to develop novel control strategies based on the control of the generator torque. The results are analysed and difficulties in the setup in regards to Reinforcement Learning are discussed. The tuned helix approach yields a total power increase of 6.8 % on average for the investigated case, while the generator torque controller does not yield an increase in total power. Finally, an alternative setup is proposed to improve the design of the problem

Limit cycle computation of self‐excited dynamic systems using nonlinear modes

A self-excited dynamic system is able to oscillate periodically by itself. Corresponding solutions of the autonomous differential equation are called limit cycles or periodic attractors. To find these solutions, a simple approach would be brute-force search for the corresponding basins of attraction. However, grid searching might become unfeasible with increasing number of degrees of freedom. Instead, solution path continuation techniques are often used to keep computational costs low. As the continuation of solution branches and their bifurcations provides only solutions which are connected to each other, isolas and detached branches are missed out. We present a method for fast limit cycle detection of self-excited systems with isolas based on nonlinear modes. A nonlinear mode, often referred to as nonlinear normal mode, is defined as a periodic motion of the undamped and unforced mechanical system. For nonconservative systems however, e.g. with friction nonlinearity, damping cannot be neglected as it is characteristic for the oscillators nonlinear dynamics. Therefore, the Extended Periodic Motion Concept (E-PMC) was proposed recently to find periodic solutions of nonconservative nonlinear systems. In this work, the E-PMC is applied to self-excited dynamic systems in order to find periodic attractors along its nonlinear modes. Zero crossings of the nonlinear damping curve indicate autonomous solutions which can be used as starting points for single parameter continuation. Thus, solutions corresponding to the main branch and detached curves in the solution space are connected by nonlinear modes. The proposed method is applied to a frictional oscillator with cubic stiffness and proves to be robust in the search for isolated periodic solutions that are already known from literature

Machine learning simulation of one-dimensional deterministic water wave propagation

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