Advanced Modeling and Simulation in Engineering Sciences最新文献_第2页

Large-scale graph-machine-learning surrogate models for 3D-flowfield prediction in external aerodynamics 用于外部空气动力学三维流场预测的大规模图机器学习代用模型

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-03-23 DOI: 10.1186/s40323-024-00259-1

Davide Roznowicz, Giovanni Stabile, Nicola Demo, Davide Fransos, Gianluigi Rozza

The article presents the application of inductive graph machine learning surrogate models for accurate and efficient prediction of 3D flow for industrial geometries, explicitly focusing here on external aerodynamics for a motorsport case. The final aim is to build a surrogate model that can provide quick predictions, bypassing in this way the unfeasible computational burden of traditional computational fluid dynamics (CFD) simulations. We investigate in this contribution the usage of graph neural networks, given their ability to smoothly deal with unstructured data, which is the typical context for industrial simulations. We integrate an efficient subgraph-sampling approach with our model, specifically tailored for large dataset training. REV-GNN is the chosen graph machine learning model, that stands out for its capacity to extract deeper insights from neighboring graph regions. Additionally, its unique feature lies in its reversible architecture, which allows keeping the memory usage constant while increasing the number of network layers. We tested the methodology by applying it to a parametric Navier–Stokes problem, where the parameters control the surface shape of the industrial artifact at hand, here a motorbike.

文章介绍了归纳图机器学习代用模型在准确、高效地预测工业几何形状的三维流动方面的应用，并明确将重点放在赛车运动的外部空气动力学方面。最终目的是建立一个能提供快速预测的代用模型，从而避免传统计算流体动力学（CFD）模拟所带来的不可行的计算负担。鉴于图神经网络能够流畅地处理非结构化数据，而这正是工业仿真的典型环境，因此我们在本文中研究了图神经网络的使用。我们将一种高效的子图抽样方法与我们的模型相结合，专门用于大型数据集的训练。REV-GNN 是我们选择的图机器学习模型，它能够从相邻图区域中提取更深入的见解。此外，它的独特之处还在于其可逆架构，可以在增加网络层数的同时保持内存用量不变。我们将该方法应用于参数化 Navier-Stokes 问题，对其进行了测试，在该问题中，参数控制着手头工业产品（此处为摩托车）的表面形状。

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引用次数: 0

A posteriori error estimation for model order reduction of parametric systems 减少参数系统模型阶次的后验误差估计

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-03-11 DOI: 10.1186/s40323-024-00260-8

Lihong Feng, Sridhar Chellappa, Peter Benner

This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the vector space $${mathbb {C}}^n$$ and provide the corresponding proofs in $$mathbb C^n$$ . Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for three examples show the robustness of the new error estimator.

本研究讨论参数系统（包括线性和非线性、时变和稳定系统）模型阶次降低的后验误差估计。我们将重点介绍我们在过去几年中提出的误差估计方法，并将它们与文献中最相关的误差估计方法进行比较。为了更清晰地进行比较，我们将函数空间中提出的一些现有误差边界转换为向量空间 $${mathbb {C}}^n$ 并在 $$mathbb C^n$ 中提供了相应的证明。我们还探讨了我们提出的误差估计器的一些新见解。此外，我们还回顾了新提出的非线性时间演化系统误差估计器，它适用于由任意时间积分求解器求解的降阶模型。我们最近在多保真度误差估计方面的工作也得到了简要讨论。最后，我们为非线性时间演化系统推导了一个新的无下限常数输出误差估计器。三个实例的数值结果显示了新误差估计器的鲁棒性。

引用次数: 0

The displacement mechanism of the cracked rock – a seismic design and prediction study using XFEM and ANNs 开裂岩石的位移机理--利用 XFEM 和 ANNs 进行的抗震设计和预测研究

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-02-28 DOI: 10.1186/s40323-024-00261-7

Omer Mughieda, Lijie Guo, Yunchao Tang, Nader M. Okasha, Sayed Javid Azimi, Abdoullah Namdar, Falak Azhar

Materials with sufficient strength and stiffness can transfer nonlinear design loads without damage. The present study compares crack propagation speed and shape in rock-like material and sandstone when subjected to seismic acceleration. The nonlinear extended finite element method (NXFEM) has been used in numerical simulation. It assumes the model has a pre-existing crack at 0° from the horizontal. The mechanical properties of the model, crack propagation shape, and crack speed were selected as the main parameters. The nonlinear stress and strain along the crack have been compared in two simulated models. NXFEM and Artificial Neural Networks (ANNs) were used to predict the displacement. The simulation results illustrate that the materials’ crack propagation mechanism and mechanical properties control the stress, strain, and displacement at the selected points in the model. In addition, crack propagation in materials is related to elastic-plastic stresses and strains along the crack path. The speed and shape of the crack are associated with the mechanical properties of the materials. The prediction of crack paths helps to understand failure patterns. Comparison of the seismic response of the rock-like material with sandstone helps to assess the stress, strain, and displacement levels during cracking. This study’s findings agree with the literature report and field observations.

具有足够强度和刚度的材料可以传递非线性设计荷载而不会损坏。本研究比较了类岩石材料和砂岩在地震加速度作用下的裂纹扩展速度和形状。数值模拟采用了非线性扩展有限元法（NXFEM）。它假定模型在与水平面成 0°的位置有一条预先存在的裂缝。模型的力学性能、裂缝扩展形状和裂缝速度被选为主要参数。比较了两种模拟模型沿裂缝的非线性应力和应变。使用 NXFEM 和人工神经网络 (ANN) 预测位移。模拟结果表明，材料的裂纹扩展机制和机械性能控制着模型中选定点的应力、应变和位移。此外，材料中的裂纹扩展与裂纹路径上的弹塑性应力和应变有关。裂纹的速度和形状与材料的机械特性有关。对裂缝路径的预测有助于了解破坏模式。比较类岩石材料与砂岩的地震响应有助于评估开裂过程中的应力、应变和位移水平。本研究的结果与文献报告和现场观察结果一致。

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引用次数: 0

A hybrid twin based on machine learning enhanced reduced order model for real-time simulation of magnetic bearings 基于机器学习增强型减阶模型的混合孪生系统，用于磁悬浮轴承的实时仿真

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-02-03 DOI: 10.1186/s40323-024-00258-2

Chady Ghnatios, Sebastian Rodriguez, Jerome Tomezyk, Yves Dupuis, Joel Mouterde, Joaquim Da Silva, Francisco Chinesta

The simulation of magnetic bearings involves highly non-linear physics, with high dependency on the input variation. Moreover, such a simulation is time consuming and can’t run, within realistic computation time for control purposes, when using classical computation methods. On the other hand, classical model reduction techniques fail to achieve the required precision within the allowed computation window. To address this complexity, this work proposes a combination of physics-based computing methods, model reduction techniques and machine learning algorithms, to tackle the requirements. The physical model used to represent the magnetic bearing is the classical Cauer Ladder Network method, while the model reduction technique is applied on the error of the physical model’s solution. Later on, in the latent space a machine learning algorithm is used to predict the evolution of the correction in the latent space. The results show an improvement of the solution without scarifying the computation time. The solution is computed in almost real-time (few milliseconds), and compared to the finite element reference solution.

磁悬浮轴承的模拟涉及高度非线性物理，对输入变化有很高的依赖性。此外，这种模拟非常耗时，使用传统计算方法无法在实际计算时间内完成控制目的。另一方面，经典的模型缩减技术无法在允许的计算窗口内达到所需的精度。为了解决这一复杂问题，这项工作提出了一种基于物理的计算方法、模型还原技术和机器学习算法的组合，以满足要求。用于表示磁轴承的物理模型是经典的考尔梯形网络法，而模型还原技术则应用于物理模型解的误差。随后，在潜空间中使用机器学习算法来预测修正在潜空间中的演变。结果表明，在不增加计算时间的情况下，解法得到了改进。解法几乎是实时计算的（几毫秒），并与有限元参考解法进行了比较。

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引用次数: 0

Fast rapidly convergent penetrable scattering computations 快速收敛的可穿透散射计算

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-01-20 DOI: 10.1186/s40323-023-00255-x

Jagabandhu Paul, Ambuj Pandey, B. V. Rathish Kumar, Akash Anand

We present a fast high-order scheme for the numerical solution of a volume-surface integro-differential equation. Such equations arise in problems of scattering of time-harmonic acoustic and electromagnetic waves by inhomogeneous media with variable density wherein the material properties jump across the medium interface. The method uses a partition of unity to segregate the interior and the boundary regions of the scattering obstacle, enabling us to make use of specially designed quadratures to deal with the material discontinuities in a high-order manner. In particular, the method uses suitable changes of variables to resolve the singularities present in the integrals in conjunction with a decomposition of Green’s function via the addition theorem. To achieve a reduced computational cost, the method employs a Fast Fourier Transform (FFT) based acceleration strategy to compute the integrals over the boundary region. Moreover, the necessary offgrid evaluation of the density and the inter-grid transfer of data is achieved by applying an FFT-based refined-grid interpolation strategy. We validate the performance of the method through multiple scattering simulations. In particular, the numerical experiments demonstrate that the proposed method can handle high-contrast material properties without any adverse effect on the number of GMRES iterations.

我们提出了一种用于体积-表面积分微分方程数值求解的快速高阶方案。这种方程出现在时谐声波和电磁波被密度可变的非均质介质散射的问题中，其中材料特性在介质界面上跳跃。该方法使用统一分区来隔离散射障碍物的内部和边界区域，使我们能够利用专门设计的四元数以高阶方式处理材料的不连续性。特别是，该方法利用适当的变量变化来解决积分中存在的奇异点，并通过加法定理对格林函数进行分解。为了降低计算成本，该方法采用了基于快速傅立叶变换（FFT）的加速策略来计算边界区域的积分。此外，通过应用基于快速傅立叶变换的细化网格插值策略，实现了必要的密度离网格评估和网格间数据传输。我们通过多次散射模拟验证了该方法的性能。特别是，数值实验证明，所提出的方法可以处理高对比度的材料特性，而不会对 GMRES 的迭代次数产生任何不利影响。

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引用次数: 0

Dimension independent data sets approximation and applications to classification 独立维度数据集近似及在分类中的应用

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-01-03 DOI: 10.1186/s40323-023-00256-w

Patrick Guidotti

We revisit the classical kernel method of approximation/interpolation theory in a very specific context from the particular point of view of partial differential equations. The goal is to highlight the role of regularization by casting it in terms of actual smoothness of the interpolant obtained by the procedure. The latter will be merely continuous on the data set but smooth otherwise. While the method obtained fits into the category of RKHS methods and hence shares their main features, it explicitly uses smoothness, via a dimension dependent (pseudo-)differential operator, to obtain a flexible and robust interpolant, which can adapt to the shape of the data while quickly transitioning away from it and maintaining continuous dependence on them. The latter means that a perturbation or pollution of the data set, small in size, leads to comparable results in classification applications. The method is applied to both low dimensional examples and a standard high dimensioal benchmark problem (MNIST digit classification).

我们从偏微分方程的特殊视角出发，在非常具体的背景下重温了近似/插值理论的经典核方法。我们的目标是，通过将正则化与程序所得到的插值的实际平滑度联系起来，突出正则化的作用。后者在数据集上是连续的，但在其他方面是平滑的。虽然所获得的方法属于 RKHS 方法的范畴，因此也具有它们的主要特征，但它通过一个与维度相关的（伪）微分算子，明确地利用平滑性来获得一个灵活而稳健的插值器，该插值器可以适应数据的形状，同时又能迅速脱离数据，并保持对数据的连续依赖。后者意味着对数据集进行小规模的扰动或污染，就能在分类应用中获得相似的结果。该方法同时适用于低维示例和标准高维基准问题（MNIST 数字分类）。

引用次数: 0

An efficient PGD solver for structural dynamics applications. 结构动力学应用的高效 PGD 求解器

IF 2 Q3 MECHANICS

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-01-01 Epub Date: 2024-07-23 DOI: 10.1186/s40323-024-00269-z

Clément Vella, Pierre Gosselet, Serge Prudhomme

We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based on the Hamiltonian formalism. The novelty of this work lies in the implementation of a solver that is halfway between Modal Decomposition and the conventional PGD framework, so as to accelerate the fixed-point iteration algorithm. Additional procedures such that Aitken's delta-squared process and mode-orthogonalization are incorporated to ensure convergence and stability of the algorithm. Numerical results regarding the ROM accuracy, time complexity, and scalability are provided to demonstrate the performance of the new solver when applied to dynamic simulation of a three-dimensional structure.

本文提出了一种用于线性弹性力学问题降阶建模的适当广义分解（PGD）求解器。它主要侧重于提高之前推出的基于哈密顿形式主义的 PGD 求解器的计算效率。这项工作的新颖之处在于实现了介于模态分解和传统 PGD 框架之间的求解器，从而加速了定点迭代算法。为了确保算法的收敛性和稳定性，还采用了艾特肯三角平方过程和模式正交化等附加程序。本文提供了有关 ROM 精度、时间复杂性和可扩展性的数值结果，以证明新求解器在三维结构动态模拟中的性能。

引用次数: 0

Improved accuracy of continuum surface flux models for metal additive manufacturing melt pool simulations. 提高用于金属添加剂制造熔池模拟的连续表面通量模型的精度。

IF 2 Q3 MECHANICS

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2024-01-01 Epub Date: 2024-08-22 DOI: 10.1186/s40323-024-00270-6

Nils Much, Magdalena Schreter-Fleischhacker, Peter Munch, Martin Kronbichler, Wolfgang A Wall, Christoph Meier

Computational modeling of the melt pool dynamics in laser-based powder bed fusion metal additive manufacturing (PBF-LB/M) promises to shed light on fundamental mechanisms of defect generation. These processes are accompanied by rapid evaporation so that the evaporation-induced recoil pressure and cooling arise as major driving forces for fluid dynamics and temperature evolution. The magnitude of these interface fluxes depends exponentially on the melt pool surface temperature, which, therefore, has to be predicted with high accuracy. The present work utilizes a diffuse interface finite element model based on a continuum surface flux (CSF) description of interface fluxes to study dimensionally reduced thermal two-phase problems representative for PBF-LB/M in a finite element framework. It is demonstrated that the extreme temperature gradients combined with the high ratios of material properties between metal and ambient gas lead to significant errors in the interface temperatures and fluxes when classical CSF approaches, along with typical interface thicknesses and discretizations, are applied. It is expected that this finding is also relevant for other types of diffuse interface PBF-LB/M melt pool models. A novel parameter-scaled CSF approach is proposed, which is constructed to yield a smoother temperature field in the diffuse interface region, significantly increasing the solution accuracy. The interface thickness required to predict the temperature field with a given level of accuracy is less restrictive by at least one order of magnitude for the proposed parameter-scaled approach compared to classical CSF, drastically reducing computational costs. Finally, we showcase the general applicability of the parameter-scaled CSF to a 3D simulation of stationary laser melting of PBF-LB/M considering the fully coupled thermo-hydrodynamic multi-phase problem, including phase change.

对基于激光的粉末床熔融金属增材制造（PBF-LB/M）过程中的熔池动力学进行计算建模，有望揭示缺陷产生的基本机制。这些过程伴随着快速蒸发，因此蒸发引起的反冲压力和冷却成为流体动力学和温度演变的主要驱动力。这些界面通量的大小与熔池表面温度成指数关系，因此必须对其进行高精度预测。本研究利用基于界面通量连续面通量（CSF）描述的扩散界面有限元模型，在有限元框架内研究了 PBF-LB/M 的代表性降维热两相问题。研究表明，当采用经典的 CSF 方法以及典型的界面厚度和离散度时，极端的温度梯度加上金属和环境气体之间材料属性的高比率会导致界面温度和通量的显著误差。预计这一发现也适用于其他类型的扩散界面 PBF-LB/M 熔池模型。本文提出了一种新颖的参数缩放 CSF 方法，该方法可在扩散界面区域产生更平滑的温度场，从而显著提高求解精度。与经典的 CSF 相比，所提出的参数缩放方法在一定精度水平上预测温度场所需的界面厚度至少减少了一个数量级，从而大大降低了计算成本。最后，我们展示了参数缩放 CSF 对 PBF-LB/M 固定激光熔化三维模拟的普遍适用性，考虑了包括相变在内的全耦合热流体力学多相问题。

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引用次数: 0

Real-world application of a discrete feedback control system for flexible biogas production 离散反馈控制系统在柔性沼气生产中的实际应用

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2023-11-27 DOI: 10.1186/s40323-023-00251-1

Lingga Aksara Putra, Bernhard Huber, Matthias Gaderer

Using renewable energy is increasingly prevalent as part of a global effort to safeguard the environment, with a reduction in $${mathrm{CO}}_{2}$$ being one of the primary objectives. A biogas plant provides an opportunity to produce green energy, but its profitability prevents it from being utilized more frequently. A suitable response to this economic issue would be flexible biogas production to exploit fluctuating energy prices. Nevertheless, the complex nature of the anaerobic digestion process that proceeds within the biogas plant and the wide range of substrates that may be utilized as the plant’s feeds make it challenging to achieve flexible biogas production truly. Most plant operators will rely on their experience and intuition to run the plant without knowing exactly how much biogas they will produce with the feed substrate. This work combines a system model estimation and feedback controller to provide an intuitive yet precise feedback control system. The system model estimation represents the biogas plant mathematically, and a total of six distinct approaches have been compared and evaluated. A PT1 model most accurately approximated the step-down and the step-up by the time percentage method, with the Akaike Information Criterion as the primary evaluation criterion for selecting the best model. The downward model was controlled by a discrete PI controller modified with the Root Locus Method and an Anti-Windup scheme, and the upward model was controlled by a state space controller. The quality of the controller was evaluated in both simulation and at the actual biogas plant in Grub, and the controller was able to reduce the biogas production rate approaching the setpoint in the expected period. Furthermore, the developed feedback control system is effortless enough to be installed in many biogas plants.

作为全球保护环境努力的一部分，使用可再生能源越来越普遍，减少$${mathrm{CO}}_{2}$$是主要目标之一。沼气厂提供了生产绿色能源的机会，但其盈利能力使其无法更频繁地利用。对这一经济问题的适当回应是灵活的沼气生产，以利用波动的能源价格。然而，在沼气厂内进行的厌氧消化过程的复杂性，以及可以用作植物饲料的各种底物，使得真正实现灵活的沼气生产具有挑战性。大多数工厂操作员将依靠他们的经验和直觉来运行工厂，而不知道他们将用饲料基质产生多少沼气。这项工作结合了系统模型估计和反馈控制器，提供了一个直观而精确的反馈控制系统。系统模型估计在数学上代表了沼气厂，并对总共六种不同的方法进行了比较和评价。PT1模型以时间百分比法最准确地逼近降压和升压，并以赤池信息准则作为选择最佳模型的主要评价准则。向下模型由根轨迹法改进的离散PI控制器和Anti-Windup方案控制，向上模型由状态空间控制器控制。在模拟和实际沼气厂中对控制器的质量进行了评估，控制器能够在预期时间内将沼气产率降低到接近设定值。此外，所开发的反馈控制系统可以毫不费力地安装在许多沼气厂。

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引用次数: 0

Classification and analysis of common simplifications in part-scale thermal modelling of metal additive manufacturing processes 金属增材制造过程局部热建模中常见简化方法的分类与分析

Q1 Mathematics

Advanced Modeling and Simulation in Engineering Sciences

Pub Date : 2023-11-08 DOI: 10.1186/s40323-023-00253-z

Rajit Ranjan, Matthijs Langelaar, Fred Van Keulen, Can Ayas

Abstract Computational process modelling of metal additive manufacturing has gained significant research attention in recent past. The cornerstone of many process models is the transient thermal response during the AM process. Since deposition-scale modelling of the thermal conditions in AM is computationally expensive, spatial and temporal simplifications, such as simulating deposition of an entire layer or multiple layers, and extending the laser exposure times, are commonly employed in the literature. Although beneficial in reducing computational costs, the influence of these simplifications on the accuracy of temperature history is reported on a case-by-case basis. In this paper, the simplifications from the existing literature are first classified in a normalised simplification space based on assumptions made in spatial and temporal domains. Subsequently, all types of simplifications are investigated with numerical examples and compared with a high-fidelity reference model. The required numerical discretisation for each simplification is established, leading to a fair comparison of computational times. The holistic approach to the suitability of different modelling simplifications for capturing thermal history provides guidelines for the suitability of simplifications while setting up a thermal AM model.

近年来，金属增材制造的计算过程建模受到了广泛的关注。许多过程模型的基础是增材制造过程中的瞬态热响应。由于AM中热条件的沉积尺度建模在计算上是昂贵的，因此空间和时间简化，例如模拟整个层或多层的沉积，以及延长激光曝光时间，在文献中通常采用。虽然有利于降低计算成本，但这些简化对温度历史准确性的影响是逐案报告的。在本文中，现有文献中的简化首先在一个标准化的简化空间中进行分类，该简化空间基于空间和时间域的假设。随后，通过数值算例对各种简化形式进行了研究，并与高保真参考模型进行了比较。建立了每个简化所需的数值离散化，导致计算时间的公平比较。在建立热AM模型时，对捕获热历史的不同建模简化的适用性的整体方法为简化的适用性提供了指导。

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引用次数: 0