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Computational method for solving weakly singular Fredholm integral equations of the second kind using an advanced barycentric Lagrange interpolation formula 利用先进的重心拉格朗日插值公式求解第二类弱奇异Fredholm积分方程的计算方法
Q3 MECHANICS Pub Date : 2021-12-01 DOI: 10.1186/s40323-021-00212-6
E. S. Shoukralla, Nermin Saber, A. Y. Sayed
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引用次数: 2
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework 在适当广义分解框架内涉及多个时间尺度的分离表示
Q3 MECHANICS Pub Date : 2021-11-26 DOI: 10.1186/s40323-021-00211-7
A. Pasquale, A. Ammar, A. Falcó, S. Perotto, E. Cueto, J. Duval, F. Chinesta
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引用次数: 6
Evaluation of POD based surrogate models of fields resulting from nonlinear FEM simulations 基于POD的非线性有限元模拟油田替代模型评价
Q3 MECHANICS Pub Date : 2021-11-03 DOI: 10.1186/s40323-021-00210-8
de Gooijer, Boukje M., Havinga, Jos, Geijselaers, Hubert J. M., van den Boogaard, Anton H.
Surrogate modelling is a powerful tool to replace computationally expensive nonlinear numerical simulations, with fast representations thereof, for inverse analysis, model-based control or optimization. For some problems, it is required that the surrogate model describes a complete output field. To construct such surrogate models, proper orthogonal decomposition (POD) can be used to reduce the dimensionality of the output data. The accuracy of the surrogate models strongly depends on the (pre)processing actions that are used to prepare the data for the dimensionality reduction. In this work, POD-based surrogate models with Radial Basis Function interpolation are used to model high-dimensional FE data fields. The effect of (pre)processing methods on the accuracy of the result field is systematically investigated. Different existing methods for surrogate model construction are compared with a novel method. Special attention is given to data fields consisting of several physical meanings, e.g. displacement, strain and stress. A distinction is made between the errors due to truncation and due to interpolation of the data. It is found that scaling the data per physical part substantially increases the accuracy of the surrogate model.
代理建模是一种强大的工具,可以取代计算昂贵的非线性数值模拟,具有快速表示,用于逆分析,基于模型的控制或优化。对于某些问题,需要代理模型描述完整的输出字段。为了构建这样的代理模型,可以使用适当的正交分解(POD)来降低输出数据的维数。代理模型的准确性很大程度上取决于用于准备数据以进行降维的(预)处理操作。在这项工作中,基于pod的代理模型与径向基函数插值被用于建模高维有限元数据场。系统地研究了各种预处理方法对结果场精度的影响。比较了现有的几种代理模型构建方法,提出了一种新的方法。特别注意由几个物理含义组成的数据字段,例如位移、应变和应力。对由于截断引起的误差和由于数据插值引起的误差进行了区分。研究发现,按物理部分对数据进行缩放可以大大提高代理模型的准确性。
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引用次数: 10
A comparison of mixed-variables Bayesian optimization approaches 混合变量贝叶斯优化方法的比较
Q3 MECHANICS Pub Date : 2021-10-30 DOI: 10.21203/rs.3.rs-1050987/v1
Jhouben Cuesta-Ramirez, R. Riche, O. Roustant, G. Perrin, Cédric Durantin, A. Glière
Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.
大多数实际的优化问题都是在混合搜索空间上定义的,其中变量既离散又连续。在工程应用中,目标函数通常使用数值昂贵的黑盒模拟进行计算。因此,一般的混合和昂贵的优化问题具有很大的实际意义,但它们的解决在很大程度上仍然是一个开放的科学问题。在本文中,通过高斯过程来处理代价高昂的混合问题,其中离散变量被松弛为连续的潜在变量。与混合空间相比,经典贝叶斯优化技术更容易获得连续空间。离散变量要么在连续优化之后恢复,要么与用增广拉格朗日算子处理的附加连续离散兼容性约束同时恢复。比较了这种贝叶斯混合优化器的几种可能的实现方式。特别是,具有连续潜变量的问题的重新表述与直接在混合空间中进行的搜索相竞争。在涉及潜在变量和增广拉格朗日量的算法中,特别关注拉格朗日乘子,研究了其局部和全局估计技术。比较是基于三个分析函数的重复优化和一个梁设计问题。
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引用次数: 7
Industrial Digital Twins based on the non-linear LATIN-PGD 基于非线性LATIN-PGD的工业数字孪生
Q3 MECHANICS Pub Date : 2021-10-04 DOI: 10.1186/s40323-021-00207-3
Barabinot, Philippe, Scanff, Ronan, Ladevèze, Pierre, Néron, David, Cauville, Bruno
Digital Twins, which tend to intervene over the entire life cycle of products from early design phase to predictive maintenance through optimization processes, are increasingly emerging as an essential component in the future of industries. To reduce the computational time reduced-order modeling (ROM) methods can be useful. However, the spread of ROM methods at an industrial level is currently hampered by the difficulty of introducing them into commercial finite element software, due to the strong intrusiveness of the associated algorithms, preventing from getting robust and reliable tools all integrated in a certified product. This work tries to circumvent this issue by introducing a weakly-invasive reformulation of the LATIN-PGD method which is intended to be directly embedded into Simcenter Samcef $$^{hbox {TM}}$$ finite element software. The originality of this approach lies in the remarkably general way of doing, allowing PGD method to deal with not only a particular application but with all facilities already included in such softwares—any non-linearities, any element types, any boundary conditions...—and thus providing a new high-performance all-inclusive non-linear solver.
数字孪生(Digital Twins)往往会介入产品的整个生命周期,从早期设计阶段到预测性维护,再到优化过程,它正日益成为未来工业的重要组成部分。为了减少计算时间,降阶建模(ROM)方法是有用的。然而,由于相关算法具有很强的侵入性,因此很难将ROM方法引入商业有限元软件,这阻碍了ROM方法在工业层面的推广,从而阻止了在认证产品中集成强大可靠的工具。这项工作试图通过引入拉丁- pgd方法的弱侵入性重新制定来规避这个问题,该方法旨在直接嵌入Simcenter Samcef $$^{hbox {TM}}$$有限元软件中。这种方法的独创性在于其非常通用的处理方式,允许PGD方法不仅处理特定的应用程序,而且处理此类软件中已经包含的所有功能-任何非线性,任何元素类型,任何边界条件……从而提供了一种新的高性能全包非线性求解器。
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引用次数: 1
Enhanced parametric shape descriptions in PGD-based space separated representations 基于pgd的空间分隔表示中增强的参数形状描述
Q3 MECHANICS Pub Date : 2021-10-04 DOI: 10.1186/s40323-021-00208-2
Kazemzadeh-Parsi, Mohammad Javad, Ammar, Amine, Duval, Jean Louis, Chinesta, Francisco
Space separation within the Proper Generalized Decomposition—PGD—rationale allows solving high dimensional problems as a sequence of lower dimensional ones. In our former works, different geometrical transformations were proposed for addressing complex shapes and spatially non-separable domains. Efficient implementation of separated representations needs expressing the domain as a product of characteristic functions involving the different space coordinates. In the case of complex shapes, more sophisticated geometrical transformations are needed to map the complex physical domain into a regular one where computations are performed. This paper aims at proposing a very efficient route for accomplishing such space separation. A NURBS-based geometry representation, usual in computer aided design—CAD—, is retained and combined with a fully separated representation for allying efficiency (ensured by the fully separated representations) and generality (by addressing complex geometries). Some numerical examples are considered to prove the potential of the proposed methodology.
适当广义分解- pgd原理中的空间分离允许将高维问题作为一系列低维问题来解决。在我们以前的工作中,提出了不同的几何变换来处理复杂的形状和空间不可分离的域。分离表示的有效实现需要将域表示为涉及不同空间坐标的特征函数的乘积。在复杂形状的情况下,需要更复杂的几何变换来将复杂的物理域映射到执行计算的规则域。本文旨在提出一种非常有效的实现这种空间分离的途径。基于nurbs的几何表示(通常用于计算机辅助设计cad)被保留并与完全分离的表示相结合,以提高效率(通过完全分离的表示确保)和通用性(通过处理复杂的几何)。一些数值算例证明了所提方法的潜力。
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引用次数: 9
Coupling reduced-order blood flow and cardiac models through energy-consistent strategies: modeling and discretization 通过能量一致策略耦合低阶血流和心脏模型:建模和离散化
Q3 MECHANICS Pub Date : 2021-09-28 DOI: 10.1186/s40323-021-00206-4
Jessica Manganotti, F. Caforio, François Kimmig, P. Moireau, S. Imperiale
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引用次数: 2
A nonparametric probabilistic method to enhance PGD solutions with data-driven approach, application to the automated tape placement process 一种非参数概率方法,通过数据驱动方法增强PGD解决方案,应用于自动化胶带放置过程
Q3 MECHANICS Pub Date : 2021-09-21 DOI: 10.1186/s40323-021-00205-5
Ghnatios, Chady, Barasinski, Anais
A nonparametric method assessing the error and variability margins in solutions depicted in a separated form using experimental results is illustrated in this work. The method assess the total variability of the solution including the modeling error and the truncation error when experimental results are available. The illustrated method is based on the use of the PGD separated form solutions, enriched by transforming a part of the PGD basis vectors into probabilistic one. The constructed probabilistic vectors are restricted to the physical solution’s Stiefel manifold. The result is a real-time parametric PGD solution enhanced with the solution variability and the confidence intervals.
一种非参数方法评估误差和可变性的边界在一个分离的形式描述的解决方案,使用实验结果说明了这一工作。当实验结果可用时,该方法评估了解决方案的总变异性,包括建模误差和截断误差。所示的方法是基于使用分离形式的PGD解,并通过将部分PGD基向量转换为概率基向量来丰富。所构造的概率向量被限制在物理解的Stiefel流形中。结果是一个实时的参数PGD解增强了解的可变性和置信区间。
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引用次数: 2
Greedy maximin distance sampling based model order reduction of prestressed and parametrized abdominal aortic aneurysms 基于贪心最大距离采样的预应力及参数化腹主动脉瘤模型阶数降阶方法
Q3 MECHANICS Pub Date : 2021-09-04 DOI: 10.1186/s40323-021-00203-7
Schein, Alexander, Gee, Michael W.
This work proposes a framework for projection-based model order reduction (MOR) of computational models aiming at a mechanical analysis of abdominal aortic aneurysms (AAAs). The underlying full-order model (FOM) is patient-specific, stationary and nonlinear. The quantities of interest are the von Mises stress and the von Mises strain field in the AAA wall, which result from loading the structure to the level of diastolic blood pressure at a fixed, imaged geometry (prestressing stage) and subsequent loading to the level of systolic blood pressure with associated deformation of the structure (deformation stage). Prestressing is performed with the modified updated Lagrangian formulation (MULF) approach. The proposed framework aims at a reduction of the computational cost in a many-query context resulting from model uncertainties in two material and one geometric parameter. We apply projection-based MOR to the MULF prestressing stage, which has not been presented to date. Additionally, we propose a reduced-order basis construction technique combining the concept of subspace angles and greedy maximin distance sampling. To further achieve computational speedup, the reduced-order model (ROM) is equipped with the energy-conserving mesh sampling and weighting hyper reduction method. Accuracy of the ROM is numerically tested in terms of the quantities of interest within given bounds of the parameter domain and performance of the proposed ROM in the many-query context is demonstrated by comparing ROM and FOM statistics built from Monte Carlo sampling for three different patient-specific AAAs.
本文提出了一种基于投影的模型降阶(MOR)的计算模型框架,旨在对腹主动脉瘤(AAAs)进行力学分析。其基础全阶模型(FOM)是特定于患者的、平稳的和非线性的。感兴趣的量是AAA壁的von Mises应力和von Mises应变场,这是由于在固定的成像几何形状下将结构加载到舒张压水平(预应力阶段),随后将结构加载到收缩压水平并伴有结构变形(变形阶段)。采用改进的拉格朗日公式(MULF)方法进行预应力。提出的框架旨在减少由于两种材料和一个几何参数的模型不确定性而导致的多查询上下文中的计算成本。我们将基于投影的MOR应用于MULF预应力阶段,这是迄今为止尚未提出的。此外,我们提出了一种结合子空间角度和贪心最大距离采样概念的降阶基构造技术。为了进一步提高计算速度,在降阶模型(ROM)中加入了节能的网格采样和加权超约简方法。根据给定参数域范围内感兴趣的数量,对ROM的准确性进行了数值测试,并通过比较从蒙特卡罗采样为三种不同的患者特定AAAs构建的ROM和FOM统计数据,证明了所提出的ROM在多查询上下文中的性能。
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引用次数: 0
Investigation of pollutants formation in a diesel engine using numerical simulation 柴油机污染物形成的数值模拟研究
Q3 MECHANICS Pub Date : 2021-09-04 DOI: 10.1186/s40323-021-00204-6
M. Zahid, Khalid S. Syed
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引用次数: 0
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Advanced Modeling and Simulation in Engineering Sciences
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