MS20.8 - UQ and Probabilistic Learning in Computational Dynamics

Modelling the dynamic response of civil structures is vital for many applications, including structural health monitoring, reliability analysis and design optimization. These systems often feature responses governed by highly uncertain exogenous excitations, for example, ground motions, wind, or wave loads. To quantify the effects of this uncertainty, many evaluations of the underlying numerical models are usually required. Therefore, in the presence of expensive simulations, surrogate models become necessary as a fast-to-evaluate proxy. However, for many time-dependent systems it is difficult to build surrogates that provide precise and stable predictions. Additional non-linearity is introduced by controllers that actively change the system properties depending on multiple state variables. One approach to surrogate such systems is to use non-linear auto-regressive with exogenous input (NARX) models, which exploit the temporal coherence of the system response and its strong dependence on the exogenous excitations. Constructing a stable and accurate NARX model, however, is often unattainable when the system response is highly non-linear, the dimensionality of the exogenous input is high, or when data is scarce. In this work, we present a novel approach called manifold NARX (mNARX) to tackle this class of problems. mNARX takes advantage of prior knowledge about the physics of the system to incrementally build an input manifold suitable for efficiently surrogating the dynamic system response. We showcase its efficiency on an aero-servo-elastic (ASE) wind turbine simulation benchmark. ASE simulators take turbulent wind as input, and model selected time-dependent quantities of interest (QoIs), such as power output or blade and tower loads. The exogenous input wind field is a spatio-temporal random field with high spatial dimensionality. Furthermore, most QoIs are affected by both the control system and rotor orientation, making the mapping from the exogenous inputs to the QoIs even more complex. Within the mNARX framework, we first predict physically meaningful auxiliary quantities, such as control and state variables, based on a NARX model built on a truncated set of time-dependent spectral coefficients of the wind input. We then use these predictions in conjunction with the spectral coefficients to form an exogenous input manifold onto which the final QoI NARX model is constructed. We demonstrate that this sequential approach leads to accurate predictions over a long time horizon, even in the presence of complex localized spectral features. Finally, we show that the training of this chain of surrogate models and its evaluation are computationally inexpensive, up to multiple orders of magnitude cheaper than its original ASE simulator counterpart.

Vortex-induced vibrations (VIV) of floating structures play an essential role in offshore engineering design. The accurate prediction of structural response is critical as vortex shedding behind bluff bodies may lead to continuous degradation of structural performance or even catastrophic failure. Typically, the description of vortex-induced vibrations requires a high-fidelity fluid-structure interaction model, coupling the structure's nonlinear dynamics (large displacements) with turbulent flows of the surrounding fluid. The last typically involves Computational Fluid Dynamics (CFD) approaches based on solving Navier-Stokes with a fine mesh that has to be frequently adapted to the structure motion. Unfortunately, the resulting model tends to be quite expensive in terms of computational costs, especially considering extensive multi-query analysis, like optimization, real-time response, or Uncertainty quantification. Such time-consuming tasks often hamper the use of high-fidelity codes constructed upon physics-based models. A good alternative to overcome such limitations is the construction of surrogate models that have become popular within many research fields due to their success in being efficient proxies for high-fidelity models. Such models have become essential tools to simplify the analysis and can be very useful in broad industrial applications, obtaining predictions with a much lower computational cost than CFD. In such a context, data-driven machine learning (ML) models, with the potential to combine field or experimental data with high-fidelity simulations, have gained prominence due to the potential to enhance the capability of computational simulations to describe complex physical systems. Several works have been dedicated to constructing predictive data-driven machine learning models to return accurate predictions at a low cost. Recently, transformer models built on self-attention were applied to model dynamical systems that can replace otherwise expensive computational models. Such a model has been proven able to accurately predict various dynamical systems and outperforms classical methods commonly used in the scientific machine learning literature. In this work, we propose a machine-learning approach based on the self-attention transformers to act as a surrogate model for VIV dynamics. We show through numerical experimentation that the surrogate model can yield accurate predictions of the VIV dynamics. More importantly, it amplifies the ability to investigate critical aspects of frequently used wake oscillator models.

Metamaterials have recently emerged in the search for lightweight noise and vibration solutions. One of their appealing properties for noise control engineering is the ability to create stop bands, which are frequency ranges without free wave propagation. These stop bands arise from the sub-wavelength addition of identically tuned resonators in or on a host structure and result in strong vibration attenuation. However, when manufacturing metamaterials, variability in material properties and geometry is inevitably introduced. On the one hand, the metamaterial attenuation performance can deteriorate due to variability, while on the other hand, variability can even broaden their typically narrowband performance. In this work, variability is exploited in view of broadening the vibration attenuation band of metamaterial beams. To this end, the design parameters of the metamaterial beam’s resonators are optimized in an allowed design space around their nominal, identical values to obtain a wider frequency range of vibration attenuation. To account for uncertainties early in the design phase, when often little information concerning the inherent variability is available, the resonator design parameters are defined as interval uncertain variables and vibration attenuation performance bounds are computed. By formulating a fitness function which allows trading-off vibration attenuation performance and performance robustness in terms of these performance bounds, optimal resonator design parameters are sought which enable robust vibration attenuation band broadening. To solve the above optimization problem, a global search approach can be followed. However, as the required amount of model evaluations for optimizing the performance and finding the performance bounds rapidly grow, using a global search approach can become prohibitively expensive especially for large models. Instead, this work explores the use of a recently proposed machine learning based non-intrusive uncertainty propagation approach to efficiently evaluate upper and lower performance bounds with a limited amount of model evaluations. Moreover, as the approach is based on a Gaussian Process regression model and Acquisition Functions, additional metrics can be introduced to assess if the obtained bounds are satisfactory. The robust optimization approach is applied to a simplified metamaterial beam with periodic mass-spring-damper resonators to investigate the importance of accounting for the robustness against design parameter variations in metamaterial performance broadening.