DCs & Workpackages

Within this track a scalable and
generic framework for the deployment of MOR within vibro-acoustic problems will be defined. Specifically, the recruited DC will start by evaluating and enhancing the scalability of existing MOR techniques for FE and BE vibro-acoustic problems, employing High-Performance-Computing.
Then, the DC will define a framework for the flexible interchange of those and will exploit the best performing techniques with respect to efficiency, memory usage, code intrusiveness, heuristically defined parameters, number of inputs and outputs to develop a technique for the efficient solution of strongly coupled vibro-acoustic problems. Further, enhancing modelling possibilities the DC will develop techniques that enable the reduction of additional multi-physical models, such as lumped parameter modeling and flexible multibody systems, aiming the efficient modelling of e.g. the acoustic emission of moving parts of a wind turbine model. The DC will explore MOR strategies involving Krylov subspaces, component mode synthesis, POD and reduced basis method. Finally, jointly with the other candidates involved in WP1 (DC 3,4,7,8), DC1 will lead the creation
of a handbook with the best practice rules for vibro-acoustic MOR. Innovations: Scalability of MOR in acoustics using HPC, framework for MOR within multi-physical problems, handbook of MOR for vibro-acoustic problems.

An important aspect towards the use of vibro-acoustic digital twins, is its possibility to adapt to several operational conditions and its applicability for a wide range of products that a manufacturer might have. Therefore, DC2 will develop novel deep learning approaches to obtain a digital twin that is trained using both physics based metamodels/insights and measurements on the physical asset. To accelerate the training of the machine learning architecture, reduced order models of vibro-acoustic
systems are expected to play a key role in data generation, due to their rapid evaluation as compared to their full order model counterpart. Besides the usage of physics based reduced order models, also the addition of physical constraints in the machine learning architecture through physics informed neural networks will be considered to speed up the training. Finally, the addition of measurement data in the reduced physical models will be explored with the aim to obtain a more representative parameter dependent digital twin. The approach will be validated by investigating the sound radiated from a car tyre before and during operation.

Innovations: Combining MOR with deep learning for vibro-acoustic digital twins, physics informed neural networks in vibro-acoustics, inclusion of relevant data in the surrogate model.

DC3 will examine the use of MOR to accelerate acoustic metamaterial simulations including viscous and thermal losses effects. As a first step, the DC will incorporate the viscous and thermal losses as an impedance-like boundary condition within a numerical solution of acoustic wave equation by the finite element method. Next, the full linearized Navier-Stokes equations are solved numerically by the boundary element method.
The DC will examine various reduced basis approaches for minimizing the complexity of the acoustic mode, including Krylov subspace methods30 and novel modal decomposition. In a final step, the DC will investigate whether the algebraic structures emerging from periodicity can be exploited for an efficient simulation of finite metamaterials. Finally, the developed approaches will be validated on subwavelength metamaterial applications, arising from acoustic absorbers for buildings and sound barriers.

Innovations: Visco-thermal losses modelling, efficient design of
acoustic metamaterials, porous media simulations.

Within this research track robust and efficient workflows for computing parametric reduced order models of vibro-acoustic are to be established. The dimension reduction of the numerical models is to be achieved by projection. A special focus is put on methods enabling the reduction of models with a large number of parameters. Since in such cases traditional parametric model order reduction methods suffer from the curse of
dimensionality, techniques involving efficient parameter sampling techniques as well as sampling-free approaches and data-driven methods to obtain parametric reduced models will be exploited. All methods will be compared and assessed in terms of applicability and effectivity regarding vibro-acoustic systems. The most promising and robust approaches are to be tested on benchmark cases arising from a double layer floor construction of a railway-wagon and the fuselage sidewall of an aircraft.

Innovations: Efficient generation of pMOR models, high dimensional
spaces, robust algorithms.

DC5 aims at setting up numerical models allowing to determine the mechanical parameters of porous materials based on a microstructural elementary cell approach. Such numerical models are expensive, obviously because of the number of elementary cells but also because the modeling of a single cell is resource intensive. In that context, DC5 will use two-level model reduction techniques to reduce their complexity. The first part of the work will consist in realizing a reduced model of an elementary cell by a condensation technique. This reduction will be done on the elementary beams of the elementary cell. A dispersion study will then be carried out to obtain the fundamental solutions (quasi-plane waves) propagating in the structure. An experimental validation phase, using existing test benches, will then be conducted on structures obtained by 3D printing. The second part will aim at setting up a reduced model for an assembly of many reduced elementary cells. Particularly Krylov recycling techniques will be considered. A dispersion study on the assembled structure will show if the reduced model modifies or not the wave properties of the material.

Innovations: Determination of mechanical parameters of porous
materials, microstructural elementary cell approach, two level MOR, condensation MOR, Recycling based solvers.

The objective of this research track is to optimize acoustic metamaterials of finite size with machine learning algorithms. While simple plate springs or C-shaped Helmholtz resonators are well-suited to study the basic principles, more complex unit cell realizations are required for a broadband, low-frequency attenuation. Although periodicity of the structure implies infinite structures, this is not the case for practical applications with the edges inducing a considerable effect. To effectively deal with the associated increased computational effort of modelling the cell multiple times, the DC will undertake MOR approaches in combination with machine learning strategies to result into performant numerical models that can be utilized in an optimization scheme. This research aims at incorporating MOR techniques into machine learning based optimization for a concurrent design of a host structure and a tailored metamaterial, aiming at automotive applications. An experimental validation (absorption coefficient in an impedance tube) of the designed structure (poroelastic core with the optimized inner resonator) will be done to validate the approach.

Innovations: Incorporation of MOR with machine learning, novel acoustic metamaterials design, acceleration of finite size periodic models.

The proposed doctoral project aims at investigating efficient strategies for the solution of large problems by domain decomposition methods (DDM) in the case of subdomains modelled with different strategies. Hence,
the coupling of subdomains handled with a range of different MOR techniques is in focus. The choice of MOR may be guided by a diversity of constraints and objectives (e.g., desire to extract specific physical features, geometrical properties, relative size and complexity of the subdomains,
interface-related complexity, …). The proposed project therefore seeks to combine several of these techniques, taking full advantage of their respective features in adequation with the nature of typical dynamics problems, to propose a physically- and computationally relevant decomposition of the full-order model, and to implement a cost-effective, accurate description of the resulting interfaces. An example of test case to be considered during the secondment at SG Ecophon may be found in
the acoustic treatment of large architectural office spaces, where not only the mismatch in characteristic lengths poses challenges, but also the distribution and intrinsic properties of these acoustic treatments (multi-phase materials, presence of thin films, partial anisotropic behaviour, ...).

Innovations: Efficient modelling of interfaces in DDM, scalable MOR algorithms, flexible framework for MOR techniques.

In this research track, novel MOR methods for vibro-acoustic systems modelling free radiation, initially focused on PML based modelling49, are to be established. The sought MOR solutions are aiming to overcome the
space and frequency dependency of the associated formulations, by exploiting previously documented solutions to be applicable in the most general configurations (e.g., not limited to cartesian formulations). The outcome of the proposed research is thus anticipated to bridge the gap
leading to an efficient FE modelling of noise radiation from a diversity of complex vibro-acoustic systems. The developed methods will be benchmarked on the basis of the sound radiation induced by vehicles with respect to existing methodologies related to alternative noise radiation modelling schemes, e.g., infinite elements, boundary elements and will yield a set of best practice rules.

Innovations: MOR for perfectly matched layers, best practice rules for radiation MOR.

This research track will investigate the use of model order reduction techniques to accelerate broadband vibroacoustic gradient-based shape optimization. The first step of the DC is to incorporate model order reduction methods into a vibroacoustic finite element and boundary element framework. As a second step, an adjoint gradient estimation method is developed based on the reduced vibroacoustic framework. The gradient estimation method will be utilized by the DC to perform shape optimization of broadband vibroacoustic applications, starting with single loudspeaker components (suspension, diaphragm, electrical/magnetic, etc.) and continuing with complete loudspeaker drivers where attention will
devoted to new objective functions which will allow for sound quality criteria. As an ultimate step, the developed shape optimization framework is evaluated and compared to the more traditional non-reduced vibroacoustic shape optimization approach where frequencies are treated individually.

Innovations: parametric MOR, shape optimization, broadband acoustic performance.

The goal of this track is to propose an innovative approach for the inverse identification of the acoustic and mechanical properties of acoustic materials. It consists in combining multi-fidelity approaches and reduced-order models to develop efficient surrogate models that will be used in a global optimization framework. The first step is to determine the most appropriate material models and reduced-order models for the low-fidelity and high-fidelity models with the aim of efficiently evaluating the vibro-acoustic response. The second step is to test this approach on well-known test cases to estimate its robustness and the speed-up as compared to other inverse techniques. Finally, the proposed methodology will be applied to more challenging inverse problem identification: stochastic inverse identification, simultaneous identification of acoustic and/or elastic and/or viscoelastic properties of foams/composites/multilayer structures, or the multilevel optimization of material parameters. The developed techniques will be deployed to identify the properties of degraded material on existing structures, such as the acoustic treatment of operating vehicles.

Innovations: MOR for inverse identification, stochastic inverse identification, global optimization framework.