Accelerating crack growth simulations through adaptive model order reduction

Rocha, I.B.C.M.; Meer, F.P. van der; Mororó, L.A.T.; Sluys, L.J.

doi:10.1002/nme.6303

Cited by 10 publications

(7 citation statements)

References 29 publications

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“…Techniques for basis enrichment in zones of strain localisation have also been combined with domain partitioning strategies to address crack propagation problems, where the subdomain in which the crack is located is solved in high-fidelity coordinates and is properly assembled to the reduced representation of the remaining structure. 45,46 Building upon these contributions, certain works have attempted to refine the projection basis, whenever necessary based on physics-based indicators, 44,47,48 whereas further extensions have reported frameworks that assemble the ROM without any offline model evaluations, 49,50 compromising though the high precision of the derived model.…”

Section: Introductionmentioning

confidence: 99%

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Agathos,

Vlachas,

Garland

et al. 2024

Numerical Meth Engineering

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In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection‐based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low‐dimensional spaces, in which solutions are represented. In the proposed approach, low‐dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

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Section: Introductionmentioning

confidence: 99%

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Agathos,

Vlachas,

Garland

et al. 2024

Numerical Meth Engineering

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“…In the online phase, a computationally efficient reduced-order model is constructed using reduced-order bases, and the model is used to accelerate predictive simulations. The POD method has been widely applied in conjunction with Galerkin projection to build reduced-order models for a wide range of engineering problems, such as thermal-visco-plastic deformation behavior [8], unsteady turbulent incompressible flow [9], contact problems [10], and crack propagation [11], among others.…”

Section: Introductionmentioning

confidence: 99%

POD-Galerkin FSI Analysis for Flapping Motion

Kaneko,

Yoshimura

2023

Biomimetics

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FSI simulations of flapping motions have been widely investigated to develop a flapping-wing micro air vehicle. Because an intensive parametric study is important for the product design, a computationally efficient model is required. The purpose of the present study was to develop a reduced-order model of flapping motion. Among the various methods available to solve FSI problems, we employed the Dirichlet–Neumann partitioned iterative method, in which three sub-systems (fluid mesh update, fluid analysis, and structural analysis) are executed. In the proposed analysis system, first, snapshot data of structural displacement, fluid velocity, fluid pressure, and displacement for the fluid mesh update were collected from a high-fidelity FSI analysis. Then, the snapshot data were used to create low-dimensional surrogate systems of the above three sub-systems based on the POD under Galerkin projection (i.e., the POD-Galerkin method). In numerical examples, we considered a two-dimensional FSI problem of simplified flapping motion. The problem was described via two parameters: frequency and amplitude of flapping motion. We demonstrated the effectiveness of the presented reduced-order model in significantly reducing computational time while preserving the desired accuracy.

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“…This notion of adaptivity in a ROM context has already been discussed, for example, in [1,2], where suitable error estimators are utilized in the input parameter space to assemble an adaptive basis construction scheme. Performance enrichment and basis update techniques during the online phase have also been suggested in [3] via low-rank matrix updates, in [4,5] by means of full-order simulations, or in [6,7] employing local refinements and vector sieving strategies.…”

Section: Introductionmentioning

confidence: 99%

A Physics-Based Reduction with Monitoring Data Assimilation for Adaptive Representations in Structural Systems

Vlachas

Tatsis

Martinez

et al. 2022

Model Validation and Uncertainty Quantification, Volume 3

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Digital twin representations have become an indispensable tool for delivering data-informed virtualizations of operating systems, especially in structural health monitoring applications. In this context, challenges arise when the response often shifts beyond regular operating conditions due to extreme events such as earthquakes or structural damage. Our work proposes a reduced order modeling for adaptive digital twins, for systems undergoing damage, condition deterioration or experiencing stochastic excitation. Our approach initiates by featuring a projection-based Reduced Order Model (ROM), relying on Proper Orthogonal Decomposition (POD) and local subspaces to form a low-cost surrogate of the parametrized high fidelity system that retains a physical connotation. However, extreme events induce loading conditions and model states that challenge the accuracy of such representations. To this end, we propose adopting the derived ROM as a forward simulator and adapt the projection basis on-the-fly during operation via a Gaussian Processes Regressor (GPR) scheme. During operation, the ROM framework receives response monitoring information from a sparse number of nodes. It employs a suitable condition indicator to highlight the potential low precision of the initial surrogate. Subsequently, the GPR-based scheme utilizes the monitoring input to reconstruct the current deformed configuration of the whole system in an online manner. In turn, this approximation serves as a damaged mode that enriches the projection-based ROM and enables online adaptivity. This coupling yields a ROM equipped with critical features for health monitoring applications such as (near) real-time basis refinement, signaling potentially irreversible consequences, and estimation of the uncertainty in the enrichment mode and the adapted ROM prediction.

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Accelerating crack growth simulations through adaptive model order reduction

Cited by 10 publications

References 29 publications

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

POD-Galerkin FSI Analysis for Flapping Motion

A Physics-Based Reduction with Monitoring Data Assimilation for Adaptive Representations in Structural Systems

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