Computer Methods in Applied Mechanics and Engineering最新文献_第2页

Bayesian neural networks for predicting uncertainty in full-field material response 用于预测全场材料响应不确定性的贝叶斯神经网络

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-03 DOI: 10.1016/j.cma.2024.117486

Stress and material deformation field predictions are among the most important tasks in computational mechanics. These predictions are typically made by solving the governing equations of continuum mechanics using finite element analysis, which can become computationally prohibitive considering complex microstructures and material behaviors. Machine learning (ML) methods offer potentially cost effective surrogates for these applications. However, existing ML surrogates are either limited to low-dimensional problems and/or do not provide uncertainty estimates in the predictions. This work proposes an ML surrogate framework for stress field prediction and uncertainty quantification for diverse materials microstructures. A modified Bayesian U-net architecture is employed to provide a data-driven image-to-image mapping from initial microstructure to stress field with prediction (epistemic) uncertainty estimates. The Bayesian posterior distributions for the U-net parameters are estimated using three state-of-the-art inference algorithms: the posterior sampling-based Hamiltonian Monte Carlo method and two variational approaches, the Monte-Carlo Dropout method and the Bayes by Backprop algorithm. A systematic comparison of the predictive accuracy and uncertainty estimates for these methods is performed for a fiber reinforced composite material and polycrystalline microstructure application. It is shown that the proposed methods yield predictions of high accuracy compared to the FEA solution, while uncertainty estimates depend on the inference approach. Generally, the Hamiltonian Monte Carlo and Bayes by Backprop methods provide consistent uncertainty estimates. Uncertainty estimates from Monte Carlo Dropout, on the other hand, are more difficult to interpret and depend strongly on the method’s design.

应力和材料变形场预测是计算力学中最重要的任务之一。这些预测通常是通过使用有限元分析求解连续介质力学的控制方程来实现的，考虑到复杂的微结构和材料行为，这种方法在计算上会变得非常昂贵。机器学习（ML）方法为这些应用提供了具有潜在成本效益的替代方法。然而，现有的 ML 替代方法要么局限于低维问题，要么不能提供预测的不确定性估计。本研究提出了一种 ML 代理框架，用于应力场预测和各种材料微结构的不确定性量化。采用了一种改进的贝叶斯 U 型网络结构，提供从初始微观结构到应力场的数据驱动图像到图像映射，并提供预测（认识）不确定性估计。U 网参数的贝叶斯后验分布是利用三种最先进的推理算法估算的：基于后验采样的哈密尔顿蒙特卡洛方法和两种变异方法，即蒙特卡洛剔除法和贝叶斯后验算法。针对纤维增强复合材料和多晶微结构应用，对这些方法的预测精度和不确定性估计进行了系统比较。结果表明，与有限元分析解决方案相比，所提出的方法可获得较高的预测精度，而不确定性估计则取决于推理方法。一般来说，汉密尔顿蒙特卡洛法和贝叶斯反推法提供的不确定性估计值是一致的。而蒙特卡洛剔除法的不确定性估计值则更难解释，并且在很大程度上取决于方法的设计。

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引用次数: 0

A Review of Recent Advances in Surrogate Models for Uncertainty Quantification of High-Dimensional Engineering Applications 高维工程应用不确定性量化代用模型最新进展综述

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-02 DOI: 10.1016/j.cma.2024.117508

In fields where predictions may have vital consequences, uncertainty quantification (UQ) plays a crucial role, as it enables more accurate forecasts and mitigates the potential risks associated with decision-making. However, performing uncertainty quantification in real-world scenarios necessitates multiple evaluations of complex computational models, which can be both costly and time-consuming. To address these challenges, surrogate models (also known as meta-models)—which are low-cost approximations of computational models—can be an influential tool. Nonetheless, as the complexity of the problem increases and the number of input variables grows, the computational burden of constructing an efficient surrogate model also rises, leading to the so-called curse of dimensionality in uncertainty propagation from inputs to outputs. Additionally, dealing with constraints, ensuring the robustness and generalization of surrogate models across different inputs, and interpreting the output results can present significant difficulties. Therefore, techniques must be implemented to enhance the performance of these models. This paper reviews the developments of the past years in surrogate modeling for high-dimensional inputs, with the goal of quantifying output uncertainty. It proposes general approaches, including dimension reduction techniques, multi-fidelity surrogate models, and advanced sampling schemes, to overcome challenges in various practical problems. This comprehensive study provides an initial guide for effective surrogate modeling in engineering practices by outlining key components of solving algorithms and screening mathematical benchmark functions, all while ensuring sufficient accuracy for overall predictions. Additionally, this study identifies research gaps, suggests future directions, and describes the applications of the proposed solutions.

在预测可能会产生重大影响的领域，不确定性量化（UQ）发挥着至关重要的作用，因为它可以做出更准确的预测，并降低与决策相关的潜在风险。然而，在现实世界中进行不确定性量化需要对复杂的计算模型进行多次评估，这可能既昂贵又耗时。为了应对这些挑战，代用模型（也称为元模型）--即计算模型的低成本近似值--可以成为一种有影响力的工具。然而，随着问题复杂度的提高和输入变量数量的增加，构建高效代用模型的计算负担也随之增加，从而导致从输入到输出的不确定性传播过程中出现所谓的 "维度诅咒"。此外，处理约束条件、确保代用模型在不同输入之间的稳健性和通用性以及解释输出结果都会带来巨大困难。因此，必须采用一些技术来提高这些模型的性能。本文回顾了过去几年在高维输入代用模型方面的发展，目的是量化输出的不确定性。它提出了包括降维技术、多保真度代用模型和高级采样方案在内的一般方法，以克服各种实际问题中的挑战。本综合研究通过概述求解算法的关键组成部分和筛选数学基准函数，为工程实践中的有效代用建模提供了初步指导，同时确保了整体预测的足够准确性。此外，本研究还指出了研究空白，提出了未来发展方向，并介绍了建议解决方案的应用。

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引用次数: 0

Finite element-integrated neural network framework for elastic and elastoplastic solids 弹性和弹塑性固体的有限元集成神经网络框架

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-01 DOI: 10.1016/j.cma.2024.117474

The Physics-informed neural network method (PINN) has shown promise in resolving unknown physical fields in solid mechanics, owing to its success in solving various partial differential equations. Nonetheless, effectively solving engineering-scale boundary value problems, particularly heterogeneity and path-dependent elastoplasticity, remains challenging for PINN. To address these issues, this study proposes a hybrid computational framework integrating finite element method (FEM) with PINN, known as FEINN. This framework employs finite elements for domain discretization instead of collocation points and utilizes the Gaussian integration scheme and strain-displacement matrix to establish the weak-form governing equation instead of the automatic differentiation operator. By harnessing the strengths of FEM and PINN, this framework exhibits inherent advantages in handling complex boundary conditions with heterogeneous materials. For addressing path-dependent elastoplasticity in material nonlinear boundary value problems, an incremental scheme is developed to accurately compute the stress. To validate the effectiveness of FEINN, five types of numerical experiments are conducted, involving homogenous and heterogeneous problems with various boundaries such as concentrated force, distributed force, and distributed displacement. Both linear elastic and elastoplastic (modified cam-clay) models are employed and evaluated. Using the solutions obtained from FEM as a reference, FEINN demonstrates exceptional accuracy and convergence rate in all experiments compared with previous PINNs. The mean absolute percentage errors between FEINN and FEM are consistently below 1%, and FEINN exhibits notably faster convergence rates than PINNs, highlighting its computational efficiency. Moreover, this study discusses the biases observed in regions of low stress and displacement, factors influencing FEINN's performance, and the potential applications of the FEINN framework.

物理信息神经网络法（PINN）在求解各种偏微分方程方面取得了成功，因此在解决固体力学中的未知物理场问题方面大有可为。然而，有效解决工程规模的边界值问题，尤其是异质性和路径依赖性弹塑性问题，对 PINN 来说仍然具有挑战性。为解决这些问题，本研究提出了一种将有限元法（FEM）与 PINN 相结合的混合计算框架，即 FEINN。该框架采用有限元法进行域离散化，而不是采用定位点，并利用高斯积分方案和应变-位移矩阵来建立弱式控制方程，而不是自动微分算子。通过利用有限元和 PINN 的优势，该框架在处理异质材料的复杂边界条件时表现出固有优势。为解决材料非线性边界值问题中的路径依赖弹塑性问题，开发了一种增量方案来精确计算应力。为了验证 FEINN 的有效性，进行了五种类型的数值实验，涉及具有各种边界条件（如集中力、分布力和分布位移）的同质和异质问题。采用并评估了线性弹性和弹塑性（改良凸轮粘土）模型。与以前的 PINN 相比，FEINN 以有限元求解为参考，在所有实验中都表现出了极高的精度和收敛速度。FEINN 与 FEM 之间的平均绝对百分比误差始终低于 1%，而且 FEINN 的收敛速度明显快于 PINN，突出了其计算效率。此外，本研究还讨论了在低应力和低位移区域观察到的偏差、影响 FEINN 性能的因素以及 FEINN 框架的潜在应用。

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引用次数: 0

Homogenized models of mechanical metamaterials 机械超材料的同质化模型

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-01 DOI: 10.1016/j.cma.2024.117454

Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the computational modeling of metastructures at macroscopic scales. In the present work, we assess the continuum limit of mechanical metamaterials via homogenized models derived rigorously from variational methods. It is shown through multiple examples that micropolar-type effective energies, derived naturally from analysis, properly capture the kinematics of discrete lattices in two and three dimensions. Moreover, the convergence of the discrete energy to the continuum limit is shown numerically. We provide open-source computational implementations for all examples, including both discrete and homogenized models.

由于晶格与宏观结构尺寸之间的尺度分离，直接对机械超材料进行数值模拟的成本过高。因此，多尺度连续分析在宏观尺度的超材料计算建模中起着举足轻重的作用。在本研究中，我们通过变分法严格推导出的均质模型评估了机械超材料的连续极限。通过多个实例表明，从分析中自然推导出的微极型有效能量能够正确捕捉二维和三维离散晶格的运动学特性。此外，离散能量向连续极限的收敛性也得到了数值证明。我们为所有示例提供了开源计算实现，包括离散模型和均质模型。

引用次数: 0

An all Mach number semi-implicit hybrid Finite Volume/Virtual Element method for compressible viscous flows on Voronoi meshes 针对 Voronoi 网格上可压缩粘性流的全马赫数半隐式有限体积/虚拟元素混合方法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-01 DOI: 10.1016/j.cma.2024.117502

We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the operator splitting of the compressible Navier–Stokes equations into three sub-systems: a convective sub-system solved explicitly using a finite volume (FV) scheme, and the viscous and pressure sub-systems which are discretized implicitly with the aid of a virtual element method (VEM). Consequently, the time step restriction of the overall algorithm depends only on the mean flow velocity and not on the fast pressure waves nor on the viscous eigenvalues. As such, the proposed methodology is well suited for the solution of low Mach number flows at all Reynolds numbers. Moreover, the scheme is proven to be globally energy conserving so that shock capturing properties are retrieved in high Mach number flows while being only linearly implicit in time. To reach high order of accuracy in time and space, an IMEX Runge–Kutta time stepping strategy is employed together with high order spatial reconstructions in terms of CWENO polynomials and virtual element space basis functions. The chosen discretization techniques allow the use of general polygonal grids, a useful tool when dealing with complex domain configurations. The new scheme is carefully validated in both the incompressible limit and the high Mach number regime through a large set of classical benchmarks for fluid dynamics, assessing robustness and accuracy.

我们提出了一种新颖的高阶半隐式混合有限体积/虚元数值方案，用于求解沃罗诺网格上的可压缩流。该方法依靠算子将可压缩纳维-斯托克斯方程拆分为三个子系统：使用有限体积（FV）方案显式求解的对流子系统，以及借助虚拟元素方法（VEM）隐式离散的粘性和压力子系统。因此，整个算法的时间步长限制只取决于平均流速，而不取决于快速压力波或粘性特征值。因此，所提出的方法非常适合解决所有雷诺数下的低马赫数流动问题。此外，该方案被证明是全局能量守恒的，因此在高马赫数流动中可以检索到冲击捕捉特性，同时在时间上只是线性隐含的。为了在时间和空间上达到高阶精度，采用了 IMEX Runge-Kutta 时间步进策略，以及 CWENO 多项式和虚拟元素空间基函数的高阶空间重构。所选择的离散化技术允许使用通用多边形网格，这是在处理复杂领域配置时的有用工具。在不可压缩极限和高马赫数条件下，通过大量流体动力学经典基准，对新方案进行了仔细验证，以评估其稳健性和准确性。

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引用次数: 0

Uniform multiple laminates interpolation model and design method for double–double laminates based on multi-material topology optimization 基于多材料拓扑优化的均匀多层板插补模型和双层板设计方法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-01 DOI: 10.1016/j.cma.2024.117492

Double–Double (DD) laminates, incorporating a repetition of sub-plies featuring two groups of balanced angles, offer broad design flexibility together with the ease of design and manufacturing. In this work, a novel optimization design method is proposed for DD composite laminates based on multi-material topology optimization. First, the uniform multiple laminates interpolation (UMLI) model is proposed to describe the certainty of the stacking direction in multi-layer composite structures, inspired by the interpolation model in multi-material topology optimization. Specifically, the stiffness matrices of all alternative angle combinations of laminates are interpolated to form virtual laminates. The UMLI model eliminates the need for adding interlayer constraints during the optimization process. Then, the optimization problem is defined to minimize the compliance of the composite structures and is solved using the gradient-based optimization algorithm. Finally, the proposed method is applied to the design of the composite stiffened panel, the composite Unmanned Aerial Vehicle (UAV) wing, and the rear fuselage. The results demonstrate that the UMLI model and proposed optimization method have considerable potential in the angle optimization design of multi-layer structures.

双层（DD）复合材料层压板由具有两组平衡角的子层重复组成，具有设计灵活、易于设计和制造的特点。本研究提出了一种基于多材料拓扑优化的新型 DD 复合层压板优化设计方法。首先，受多材料拓扑优化中插值模型的启发，提出了均匀多层板插值（UMLI）模型来描述多层复合材料结构中堆叠方向的确定性。具体来说，对所有可选角度组合的层压板的刚度矩阵进行插值，形成虚拟层压板。UMLI 模型无需在优化过程中添加层间约束。然后，定义优化问题以最小化复合结构的顺应性，并使用基于梯度的优化算法进行求解。最后，将所提出的方法应用于复合材料加劲板、复合材料无人机（UAV）机翼和后机身的设计。结果表明，UMLI 模型和建议的优化方法在多层结构的角度优化设计中具有相当大的潜力。

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引用次数: 0

A geometrically exact thin-walled rod model with warping and stress-resultant-based plasticity obtained with a two-level computational approach 采用两级计算方法获得的具有翘曲和应力结果塑性的几何精确薄壁杆模型

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-30 DOI: 10.1016/j.cma.2024.117497

In this work, we propose an two-level computational approach to enrich a seven degree-of-freedom kinematically exact rod model for thin-walled members, allowing for a simple elastoplastic-hardening constitutive equation. The novelty lies in upper-level description, where the effects of coupled elastoplastic-local geometrical instabilities are characterized in terms of cross-sectional stress resultants and generalized rod strains in a fully 3D context. Torsion-warping degrees of freedom and arbitrary (plastic) failure mode capabilities are present, allowing for the modeling of complex structural behavior in thin-walled members. The lower level is based on a kinematically exact shell or 3D-solid model with usual von Mises plasticity and linear isotropic hardening. At such level, simulations are performed in a pre-process stage, with the resulting equivalent stress-resultant-based hardening plastic parameters directly transferred to the upper-level as input data. No iterative procedure further binding the upper/lower level representations is required. This rather phenomenological approach of incorporating local effects may satisfactorily replicate the overall behavior of thin-walled members consisted of ductile materials, such as, but not only, steel or aluminum beam/column profiles. Numerical solution of the upper-level is carried in the framework of operator split, whereby, the local variables are solved in an element-wise fashion through numerical condensation, thus not adding any extra DOFs to the upper-level. The model is implemented in an in-house finite element program for the analysis of flexible thin structures and is validated against reference solutions.

在这项工作中，我们提出了一种两级计算方法，以丰富薄壁构件的七自由度运动学精确杆模型，并允许使用简单的弹塑性硬化构成方程。新颖之处在于上层描述，即在全三维背景下，通过横截面应力结果和广义杆应变来描述弹塑性耦合局部几何不稳定性的影响。此外，还具有扭转自由度和任意（塑性）失效模式功能，可对薄壁构件的复杂结构行为进行建模。较低层次基于运动学上精确的壳体或三维实体模型，具有通常的 von Mises 塑性和线性各向同性硬化。在这一层次中，模拟在预处理阶段进行，由此产生的基于等效应力结果的硬化塑性参数作为输入数据直接传输到上一层次。无需迭代程序进一步绑定上层/下层表示。这种包含局部效应的现象学方法可以令人满意地复制由韧性材料组成的薄壁构件的整体行为，例如但不仅限于钢或铝梁/柱型材。上层的数值求解是在算子拆分的框架下进行的，即通过数值凝聚以元素为单位的方式求解局部变量，从而不会给上层增加任何额外的 DOF。该模型在内部有限元程序中实施，用于分析柔性薄结构，并根据参考解法进行了验证。

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引用次数: 0

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements NeuroSEM：通过耦合 PINNs 和频谱元素模拟多物理场问题的混合框架

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-30 DOI: 10.1016/j.cma.2024.117498

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. This study introduces NeuroSEM, a hybrid framework integrating PINNs with the high-fidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh–Bénard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU–CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

多物理场问题的特点是流体动力学、热传递、结构力学和电磁学之间复杂的相互作用，由于其耦合性质，这些问题本身就具有挑战性。虽然可以获得某些状态变量的实验数据，但将这些数据与数值求解器进行整合仍是一项重大挑战。物理信息神经网络（PINNs）在各种工程学科中都取得了可喜的成果，特别是在处理噪声数据和解决偏微分方程（PDEs）中的逆问题方面。然而，它们在预测多物理场中的非线性现象，尤其是涉及湍流的非线性现象方面的有效性尚未完全确立。本研究介绍了 NeuroSEM，这是一个将 PINNs 与高保真谱元法 (SEM) 求解器 Nektar++ 相结合的混合框架。NeuroSEM 充分利用了 PINNs 和 SEM 的优势，为多物理场问题提供了稳健的解决方案。PINNs 经过训练，可以在特定子域中吸收数据并模拟物理现象，然后将其集成到 Nektar++ 求解器中。我们展示了 NeuroSEM 在空腔流热对流和流过圆柱体方面的效率和准确性。该框架通过处理数据可用的子域和状态变量，有效地处理了数据同化问题。我们将 NeuroSEM 应用于 Rayleigh-Bénard 对流系统，包括热边界条件缺失和数据集嘈杂的情况。最后，我们将提出的 NeuroSEM 框架应用于实际粒子图像测速仪（PIV）数据，以捕捉以马蹄形涡旋结构为特征的流动模式。结果表明，NeuroSEM 能准确模拟物理现象，并在指定的子域内同化数据。该框架的即插即用特性便于将其扩展到其他多物理场或多尺度问题。此外，NeuroSEM 经过优化，可在新兴的 GPU-CPU 集成架构上高效执行。这种混合方法提高了模拟的精度和效率，使其成为应对各种科学领域复杂工程挑战的强大工具。

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引用次数: 0

Surrogate construction via weight parameterization of residual neural networks 通过残差神经网络的权重参数化构建代用系统

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-30 DOI: 10.1016/j.cma.2024.117468

Surrogate model development is a critical step for uncertainty quantification or other sample-intensive tasks for complex computational models. In this work we develop a multi-output surrogate form using a class of neural networks (NNs) that employ shortcut connections, namely Residual NNs (ResNets). ResNets are known to regularize the surrogate learning problem and improve the efficiency and accuracy of the resulting surrogate. Inspired by the continuous, Neural ODE analogy, we augment ResNets with weight parameterization strategy with respect to ResNet depth. Weight-parameterized ResNets regularize the NN surrogate learning problem and allow better generalization with a drastically reduced number of learnable parameters. We demonstrate that weight-parameterized ResNets are more accurate and efficient than conventional feed-forward multi-layer perceptron networks. We also compare various options for parameterization of the weights as functions of ResNet depth. We demonstrate the results on both synthetic examples and a large scale earth system model of interest.

对于复杂计算模型的不确定性量化或其他样本密集型任务来说，代用模型的开发是一个关键步骤。在这项工作中，我们利用一类采用捷径连接的神经网络（NN），即残差神经网络（ResNets），开发了一种多输出代用形式。众所周知，残差神经网络可以规范代用学习问题，并提高代用结果的效率和准确性。受连续神经 ODE 类比的启发，我们采用与 ResNet 深度相关的权重参数化策略来增强 ResNets。权重参数化 ResNets 可规范化 NN 代理学习问题，并在大幅减少可学习参数数量的情况下实现更好的泛化。我们证明，权重参数化 ResNets 比传统的前馈多层感知器网络更准确、更高效。我们还比较了权重参数化作为 ResNet 深度函数的各种选项。我们在合成示例和感兴趣的大型地球系统模型上演示了结果。

引用次数: 0

A dual experimental/computational data-driven approach for random field modeling based strength estimation analysis of composite structures 基于随机场建模的复合材料结构强度估算分析的实验/计算数据双驱动方法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-30 DOI: 10.1016/j.cma.2024.117476

This paper proposes a dual experimental/computational data-driven analysis framework for apparent strength estimation of composite structures consisting of randomly arranged unidirectional fiber-reinforced plastics. In the proposed framework, multiscale stochastic analysis is performed with random field modeling of local apparent quantities such as apparent elastic modulus or strength. Significant improvements are needed in terms of computational accuracy, uncertainty quantification, random field modeling, and computational efficiency for the quantitative strength estimation by numerical analysis. For this problem, a novel computational framework assisted by the dual data-driven approach is established in this research. In the proposed approach, the accuracy of the strength estimation analysis for deterministic conditions is improved by an experimental data-driven approach based on the in-situ microscopic full-field displacement measurement. A computational data-driven approach based on random field modeling assisted by machine learning is employed for non-deterministic conditions. In this paper, the outline of the proposed dual data-driven multiscale stochastic analysis framework is introduced first. Subsequently, the details of the proposed experimental data-driven approach for determining the microscopic fracture criteria are presented, and the computational data-driven approach for improving the effectiveness and efficiency of the random field modeling-based probabilistic analysis is described. The presented approach is applied to the strength estimation of a randomly arranged unidirectional fiber-reinforced composite plate under transverse tensile loading, and its validity and effectiveness are discussed with comparisons between the experimental and numerical results obtained assuming several computational conditions.

本文针对由随机排列的单向纤维增强塑料组成的复合材料结构的表观强度估算，提出了一种实验/计算数据驱动的双重分析框架。在该框架中，通过对局部表观量（如表观弹性模量或强度）进行随机场建模来进行多尺度随机分析。通过数值分析进行定量强度估算需要在计算精度、不确定性量化、随机场建模和计算效率方面进行重大改进。针对这一问题，本研究建立了由双重数据驱动方法辅助的新型计算框架。在所提出的方法中，基于原位微观全场位移测量的实验数据驱动方法提高了确定性条件下强度估算分析的准确性。对于非确定性条件，则采用基于机器学习辅助随机场建模的计算数据驱动方法。本文首先介绍了所提出的双数据驱动多尺度随机分析框架的概要。随后，详细介绍了用于确定微观断裂标准的实验数据驱动方法，并介绍了用于提高基于随机场建模的概率分析的有效性和效率的计算数据驱动方法。所提出的方法被应用于横向拉伸载荷下随机排列的单向纤维增强复合材料板的强度估算，并通过对假设多种计算条件下获得的实验结果和数值结果进行比较，讨论了该方法的有效性和有效性。

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引用次数: 0