Conference Agenda

Thermal drills have become an important tool for the exploration of the cryosphere. In particular, cryobots are employed to access icy environments and retrieve (geo-)physical data, e.g., in Antarctica. In view of future missions to the icy moons of our Solar System, we have to extrapolate the performance of melting probes to extreme conditions that cannot be tested for with experiments on Earth. Thus, digital twins and virtual testbeds will help to develop and improve cryobots for such future missions. In our contribution, we present a testbed that includes environmental data, physics-based forward models for the performance of the cryobots, as well as data-driven approaches based on experimental cryobot data.

First, we need to provide data that can be employed by simulation software. Crysophere measurement data often lack simulation readiness as their (meta)data is inconsistent and incomplete [1]. We developed a tool, named Ice Data Hub, that flexibly stores cryosphere data in a reusable manner and provides interfaces to simulation software. It comes with a GUI to enter, edit, analyze, interpret and export the data. The interface to simulation tools ensures consistent data supply and reproducible preprocessing.

From a modeling perspective, cryobots offer an extremely challenging problem. We have to consider, in fact, a physical object melting its way through a static environment, for which a high-fidelity mathematical model that reflects the probe’s dynamic response to the ambient conditions does not exist as of now. Instead, we build upon a model hierarchy of increasing complexity for different simulation purposes. Starting from the energy balance in the microscale melt film, the melting velocity can be derived and integrated into a global trajectory prediction [2]. Alternatively, we can examine the transient ramp-up of the melting process by neglecting equilibrium assumptions. Finally, the evolution of the melt channel around the probe can be modeled by considering the evolving phase-change interface. The aforementioned problems require advanced numerical techniques, such as mesh-update and level-set methods [3].

In this work, we present our simulation models and tools and their integration with the Ice Data Hub. Furthermore, we show test cases of increasing complexity in view of realistic physical scenarios and discuss future extensions.

[1] A. Simson et al., Enriched metadata for hybrid data compilations with applications to cryosphere research, Helmholtz Metadata Collaboration Conference, online, October 5-6, doi: 10.5281/ZENODO.7185422 (2022).

[2] M. S. Boxberg et al., Ice Transit and Performance Analysis for Cryorobotic Subglacial Access Missions on Earth and Europa, Astrobiology, doi: 10.1089/ast.2021.0071 (2023).

[3] L. Boledi et al., A level-set based space-time finite element approach to the modelling of solidification and melting processes, Journal of Computational Physics 457 (2022) 111047.

The ever-increasing demand for the integration of high fidelity multidisciplinary simulations in other processes such as optimization and machine learning requires cutting computational costs of each task comprising an analysis, while also ensuring their desired accuracy. Exploiting the inherently different spatial scales that the physical phenomena act on is a proven approach [1] toward achieving this goal. However, such problems often evolve over vastly different time scales as well, but methods taking advantage of this fact [2, 3] are much less mature and lack generalization.

A prime example of diverse spatial and temporal scales is coupling meteorological analyses that have hour-long time steps with local fluid simulations focusing on specific regions, that require temporal resolutions on the scale of seconds, to better capture the influence of local flow effects. Another one is accurately predicting the damage evolution of coupled chemical-mechanical degradation processes, such as the interaction between physical salt attack and dynamic loading on concrete structures.

Partly due to the diversity of the involved phenomena and the wide range of temporal scales, existing multiscale time integration approaches lack a unified structure, greatly limiting their applicability to problems other than what they were designed for. We propose a generic framework for temporal multiscale analyses that incrementally introduce specializations to exact problems in order to help the interchangeability of methods between disciplines. Furthermore, we demonstrate specific applications focusing on meteorology, fluid-structure interaction, and chemical-physical degradation.

[1] E. Weinan, B. Engquist, X. Li, W. Ren, and E. Vanden-Eijnden. Heterogeneous multiscale methods: A review. Communications in Computational Physics, 2(3):367–450, 2007.

[2] M. Brun, A. Gravouil, A. Combescure, and A. Limam. Two feti-based heterogeneous time step coupling methods for newmark and alpha-schemes derived from the energy method. Computer Methods in Applied Mechanics and Engineering, 283:130–176, 2015.

[3] M. Pasetto, H. Waisman, and J. S. Chen. A waveform relaxation newmark method for structural dynamics problems. Computational Mechanics, 63:1223–1242, 2019.

Digital twins of structures have a wide range of useful applications in fields such as structural health monitoring or predictive maintenance. Furthermore, they enable new methods based on the precise digital representation of a building.

During the lifetime of a building, its condition and state changes. This could be due to a planned change of the structure, damages as a result of use, and/or the degradation of materials. One of the crucial factors for the digital twin concept is that those changes must be reflected in the digital model. Therefore, an automated and robust way to calibrate the structural analysis model so that it meets the necessary criteria to be considered a digital twin is of high importance.

To measure how accurate the digital model is, real world measurements are compared with their corresponding simulation results. These simulations are often driven by high fidelity models (typically based on FEM) with a larger dimensional parameter space. This research aims to directly operate in such high dimensional parameter spaces without reducing is complexity – and thus also keeping the potential richness in information to be adjusted. Using such high fidelity parameter models allows for efficient workflows, a better capture of physical phenomena and a better representation of the real structure, even in complex scenarios.

The resulting inverse problem from such high fidelity models is in most cases highly underdetermined. Hence, to solve such ill posed problems efficiently, an approach based on adjoint sensitivity analysis is selected and different stabilization and regularization techniques are applied. The capabilities and limitations of this approach are demonstrated with illustrative examples.

Digital twins are models that map real physical objects and processes into the digital environment. As the world leans more towards digitalization, digital twins can potentially assist directly in monitoring and protecting critical infrastructure (e.g., bridges), where digital twins can have an essential role in structural health monitoring (SHM) [1]. Hybrid digital twins (HDTs) combine physics-based simulations (virtual twin) with data-based analysis (digital twin), providing a simulation tool with predictive capabilities for damage detection, conditional simulations, and trends identification. In this work, we explore hybrid digital twinning of steel-reinforced concrete beams, and analyse it with experimental data from a real-life structure.

Our virtual twin is based on finite element methods with a consistent beam-to-solid volume coupling approach [2]. A model for steel-reinforced concrete structures is created using embedded 1D beam finite elements that enable physics-based modeling to capture the interaction between the reinforcement components and the concrete matrix of the investigated structure. Our digital twin employs physics-informed neural networks (PINNs). The PINNs are trained by optimizing the network weights and biases to reduce the residuals of the partial differential equation, boundary, and initial conditions of a given initial boundary value problem. The network is additionally trained with sensor data to simulate reliable digital representations and provide predictions [3].

The digital and virtual twins can be combined in different approaches, including enriching the digital twin training with the physics-based model and using data-based analysis to enhance the virtual twin. The combination methods of the data-based techniques with physics-based modeling and simulation are studied and contrasted. The model predictions are also compared to the results of physical experiments and sensor data to provide real leverage of the benefits of each twin.

REFERENCES

[1] Thomas Braml, Johannes Wimmer, Yauhen Varabei, Stefan Maack, Stefan Küttenbaum, Thomas Kuhn, Maximilian Reingruber, Alexander Gordt and Jürgen Hamm. Digitaler Zwilling: Verwaltungsschale BBox als Datenablage über den Lebenszyklus einer Brücke. Bautechnik, 99, 2021.

[2] Ivo Steinbrecher, Matthias Mayr, Maximilian J. Grill, Johannes Kremheller, Christoph Meier, Alexander Popp. A mortar-type finite element approach for embedding 1D beams into 3D solid volumes Computational Mechanics, 66:1377-1398, 2020.

[3] Max von Danwitz, Thank Thank Kochmann, Tarik Sahin, Johannes Wimmer, Thomas Braml, and Alexander Popp. Hybrid Digital Twins: A Proof of Concept for Reinforced Concrete Beams. Accepted in Proceedings in Applied Mathematics and Mechanics, 2022.