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Chaotic systems learning with hybrid echo state network/proper orthogonal decomposition based model 基于混合回波状态网络/适当正交分解模型的混沌系统学习
Q1 Mathematics Pub Date : 2021-10-13 DOI: 10.1017/dce.2021.17
Mathias Lesjak, N. Doan
Abstract We explore the possibility of combining a knowledge-based reduced order model (ROM) with a reservoir computing approach to learn and predict the dynamics of chaotic systems. The ROM is based on proper orthogonal decomposition (POD) with Galerkin projection to capture the essential dynamics of the chaotic system while the reservoir computing approach used is based on echo state networks (ESNs). Two different hybrid approaches are explored: one where the ESN corrects the modal coefficients of the ROM (hybrid-ESN-A) and one where the ESN uses and corrects the ROM prediction in full state space (hybrid-ESN-B). These approaches are applied on two chaotic systems: the Charney–DeVore system and the Kuramoto–Sivashinsky equation and are compared to the ROM obtained using POD/Galerkin projection and to the data-only approach based uniquely on the ESN. The hybrid-ESN-B approach is seen to provide the best prediction accuracy, outperforming the other hybrid approach, the POD/Galerkin projection ROM, and the data-only ESN, especially when using ESNs with a small number of neurons. In addition, the influence of the accuracy of the ROM on the overall prediction accuracy of the hybrid-ESN-B is assessed rigorously by considering ROMs composed of different numbers of POD modes. Further analysis on how hybrid-ESN-B blends the prediction from the ROM and the ESN to predict the evolution of the system is also provided.
摘要我们探索了将基于知识的降阶模型(ROM)与储层计算方法相结合来学习和预测混沌系统动力学的可能性。ROM基于具有Galerkin投影的适当正交分解(POD)来捕捉混沌系统的基本动力学,而所使用的储层计算方法基于回波状态网络(ESN)。探索了两种不同的混合方法:一种是ESN校正ROM的模态系数(hybrid-ESN-A),另一种是在全状态空间中使用并校正ROM预测(hybrid-ESN-B)。这些方法应用于两个混沌系统:Charney–DeVore系统和Kuramoto–Sivashinsky方程,并与使用POD/Galerkin投影获得的ROM和唯一基于ESN的纯数据方法进行了比较。混合-ESN-B方法被认为提供了最佳的预测精度,优于其他混合方法、POD/Galerkin投影ROM和仅数据ESN,尤其是当使用具有少量神经元的ESN时。此外,通过考虑由不同数量的POD模式组成的ROM,严格评估ROM的准确性对杂交-ESN-B的总体预测准确性的影响。还提供了关于hybrid-ESN-B如何混合来自ROM和ESN的预测以预测系统的进化的进一步分析。
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引用次数: 1
Multi-resolution dynamic mode decomposition for damage detection in wind turbine gearboxes 风电齿轮箱损伤检测的多分辨率动态模态分解
Q1 Mathematics Pub Date : 2021-10-08 DOI: 10.1017/dce.2022.34
Paolo Climaco, J. Garcke, Rodrigo Iza-Teran
Abstract We introduce an approach for damage detection in gearboxes based on the analysis of sensor data with the multi-resolution dynamic mode decomposition (mrDMD). The application focus is the condition monitoring of wind turbine gearboxes under varying load conditions, in particular irregular and stochastic wind fluctuations. We analyze data stemming from a simulated vibration response of a simple nonlinear gearbox model in a healthy and damaged scenario and under different wind conditions. With mrDMD applied on time-delay snapshots of the sensor data, we can extract components in these vibration signals that highlight features related to damage and enable its identification. A comparison with Fourier analysis, time synchronous averaging, and empirical mode decomposition shows the advantages of the proposed mrDMD-based data analysis approach for damage detection.
摘要介绍了一种基于多分辨率动态模式分解(mrDMD)对传感器数据进行分析的齿轮箱损伤检测方法。应用重点是在不同负载条件下,特别是不规则和随机的风波动下,对风力涡轮机齿轮箱进行状态监测。我们分析了一个简单非线性齿轮箱模型在健康和受损情况下以及在不同风况下的模拟振动响应数据。将mrDMD应用于传感器数据的延时快照,我们可以提取这些振动信号中突出与损伤相关特征的分量,并能够识别损伤。与傅立叶分析、时间同步平均和经验模式分解的比较表明了所提出的基于mrDMD的数据分析方法在损伤检测中的优势。
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引用次数: 2
Performance and accuracy assessments of an incompressible fluid solver coupled with a deep convolutional neural network 与深度卷积神经网络耦合的不可压缩流体求解器的性能和精度评估
Q1 Mathematics Pub Date : 2021-09-20 DOI: 10.1017/dce.2022.2
Ekhi Ajuria Illarramendi, M. Bauerheim, B. Cuenot
Abstract The resolution of the Poisson equation is usually one of the most computationally intensive steps for incompressible fluid solvers. Lately, DeepLearning, and especially convolutional neural networks (CNNs), has been introduced to solve this equation, leading to significant inference time reduction at the cost of a lack of guarantee on the accuracy of the solution.This drawback might lead to inaccuracies, potentially unstable simulations and prevent performing fair assessments of the CNN speedup for different network architectures. To circumvent this issue, a hybrid strategy is developed, which couples a CNN with a traditional iterative solver to ensure a user-defined accuracy level. The CNN hybrid method is tested on two flow cases: (a) the flow around a 2D cylinder and (b) the variable-density plumes with and without obstacles (both 2D and 3D), demonstrating remarkable generalization capabilities, ensuring both the accuracy and stability of the simulations. The error distribution of the predictions using several network architectures is further investigated in the plume test case. The introduced hybrid strategy allows a systematic evaluation of the CNN performance at the same accuracy level for various network architectures. In particular, the importance of incorporating multiple scales in the network architecture is demonstrated, since improving both the accuracy and the inference performance compared with feedforward CNN architectures. Thus, in addition to the pure networks’ performance evaluation, this study has also led to numerous guidelines and results on how to build neural networks and computational strategies to predict unsteady flows with both accuracy and stability requirements.
泊松方程的解算通常是不可压缩流体解算中计算量最大的步骤之一。最近,深度学习,特别是卷积神经网络(cnn)被引入来解决这个方程,导致推理时间显著减少,但代价是缺乏对解的准确性的保证。这个缺点可能会导致不准确,潜在的不稳定模拟,并阻止对不同网络架构的CNN加速进行公平评估。为了规避这一问题,开发了一种混合策略,将CNN与传统的迭代求解器耦合在一起,以确保用户自定义的精度水平。CNN混合方法在两种流动情况下进行了测试:(a)二维圆柱体周围的流动和(b)有障碍物和无障碍物的变密度羽流(2D和3D),证明了显著的泛化能力,保证了模拟的准确性和稳定性。在羽流测试用例中,进一步研究了使用几种网络架构的预测的误差分布。引入的混合策略允许对不同网络架构在相同精度水平下的CNN性能进行系统评估。特别是,在网络架构中加入多个尺度的重要性得到了证明,因为与前馈CNN架构相比,它提高了准确性和推理性能。因此,除了纯网络的性能评估之外,本研究还为如何构建神经网络和计算策略来预测非定常流动提供了许多指南和结果,同时满足精度和稳定性要求。
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引用次数: 9
Universal Digital Twin - A Dynamic Knowledge Graph 通用数字孪生——动态知识图谱
Q1 Mathematics Pub Date : 2021-09-06 DOI: 10.1017/dce.2021.10
J. Akroyd, S. Mosbach, A. Bhave, M. Kraft
Abstract This paper introduces a dynamic knowledge-graph approach for digital twins and illustrates how this approach is by design naturally suited to realizing the vision of a Universal Digital Twin. The dynamic knowledge graph is implemented using technologies from the Semantic Web. It is composed of concepts and instances that are defined using ontologies, and of computational agents that operate on both the concepts and instances to update the dynamic knowledge graph. By construction, it is distributed, supports cross-domain interoperability, and ensures that data are connected, portable, discoverable, and queryable via a uniform interface. The knowledge graph includes the notions of a “base world” that describes the real world and that is maintained by agents that incorporate real-time data, and of “parallel worlds” that support the intelligent exploration of alternative designs without affecting the base world. Use cases are presented that demonstrate the ability of the dynamic knowledge graph to host geospatial and chemical data, control chemistry experiments, perform cross-domain simulations, and perform scenario analysis. The questions of how to make intelligent suggestions for alternative scenarios and how to ensure alignment between the scenarios considered by the knowledge graph and the goals of society are considered. Work to extend the dynamic knowledge graph to develop a digital twin of the UK to support the decarbonization of the energy system is discussed. Important directions for future research are highlighted.
摘要:本文介绍了一种数字孪生的动态知识图方法,并说明了这种方法如何在设计上自然地适合于实现通用数字孪生的愿景。动态知识图谱是利用语义网技术实现的。它由使用本体定义的概念和实例以及在概念和实例上操作以更新动态知识图的计算代理组成。通过构造,它是分布式的,支持跨域互操作性,并确保数据通过统一接口连接、可移植、可发现和可查询。知识图谱包括“基础世界”和“平行世界”的概念,前者描述了真实世界,并由整合实时数据的代理维护;后者支持在不影响基础世界的情况下对可选设计进行智能探索。用例展示了动态知识图承载地理空间和化学数据、控制化学实验、执行跨域模拟和执行场景分析的能力。如何为备选方案提出明智的建议,以及如何确保知识图所考虑的方案与社会目标之间的一致性。讨论了扩展动态知识图谱以开发英国数字孪生的工作,以支持能源系统的脱碳。指出了今后研究的重要方向。
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引用次数: 37
Emulating computer experiments of transport infrastructure slope stability using Gaussian processes and Bayesian inference 利用高斯过程和贝叶斯推理模拟交通基础设施边坡稳定性的计算机实验
Q1 Mathematics Pub Date : 2021-09-06 DOI: 10.1017/dce.2021.14
A. Svalova, P. Helm, D. Prangle, M. Rouainia, S. Glendinning, D. Wilkinson
Abstract We propose using fully Bayesian Gaussian process emulation (GPE) as a surrogate for expensive computer experiments of transport infrastructure cut slopes in high-plasticity clay soils that are associated with an increased risk of failure. Our deterioration experiments simulate the dissipation of excess pore water pressure and seasonal pore water pressure cycles to determine slope failure time. It is impractical to perform the number of computer simulations that would be sufficient to make slope stability predictions over a meaningful range of geometries and strength parameters. Therefore, a GPE is used as an interpolator over a set of optimally spaced simulator runs modeling the time to slope failure as a function of geometry, strength, and permeability. Bayesian inference and Markov chain Monte Carlo simulation are used to obtain posterior estimates of the GPE parameters. For the experiments that do not reach failure within model time of 184 years, the time to failure is stochastically imputed by the Bayesian model. The trained GPE has the potential to inform infrastructure slope design, management, and maintenance. The reduction in computational cost compared with the original simulator makes it a highly attractive tool which can be applied to the different spatio-temporal scales of transport networks.
摘要:我们建议使用完全贝叶斯高斯过程仿真(GPE)作为替代方法,对高塑性粘土中交通基础设施路堑边坡进行昂贵的计算机实验,这些边坡与破坏风险增加有关。我们的退化试验模拟了超孔隙水压力的耗散和季节性孔隙水压力循环,以确定边坡破坏时间。在一定的几何形状和强度参数范围内进行足够的边坡稳定性预测的计算机模拟是不切实际的。因此,GPE被用作一组最佳间隔模拟器运行的插值器,将斜坡破坏的时间建模为几何形状、强度和渗透率的函数。采用贝叶斯推理和马尔可夫链蒙特卡罗模拟得到GPE参数的后验估计。对于在184年模型时间内未达到失效的实验,采用贝叶斯模型随机推算失效时间。经过培训的GPE具有为基础设施边坡设计、管理和维护提供信息的潜力。与原始模拟器相比,计算成本的降低使其成为一种非常有吸引力的工具,可以应用于不同时空尺度的运输网络。
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引用次数: 7
On generative models as the basis for digital twins 论作为数字孪生基础的生成模型
Q1 Mathematics Pub Date : 2021-08-31 DOI: 10.1017/dce.2021.13
G. Tsialiamanis, D. Wagg, N. Dervilis, K. Worden
Abstract A framework is proposed for generative models as a basis for digital twins or mirrors of structures. The proposal is based on the premise that deterministic models cannot account for the uncertainty present in most structural modeling applications. Two different types of generative models are considered here. The first is a physics-based model based on the stochastic finite element (SFE) method, which is widely used when modeling structures that have material and loading uncertainties imposed. Such models can be calibrated according to data from the structure and would be expected to outperform any other model if the modeling accurately captures the true underlying physics of the structure. The potential use of SFE models as digital mirrors is illustrated via application to a linear structure with stochastic material properties. For situations where the physical formulation of such models does not suffice, a data-driven framework is proposed, using machine learning and conditional generative adversarial networks (cGANs). The latter algorithm is used to learn the distribution of the quantity of interest in a structure with material nonlinearities and uncertainties. For the examples considered in this work, the data-driven cGANs model outperforms the physics-based approach. Finally, an example is shown where the two methods are coupled such that a hybrid model approach is demonstrated.
摘要提出了一种生成模型框架,作为数字孪生或结构镜像的基础。该建议是基于确定性模型不能解释大多数结构建模应用中存在的不确定性的前提。这里考虑了两种不同类型的生成模型。第一种是基于随机有限元(SFE)方法的基于物理的模型,该模型广泛用于对具有材料和载荷不确定性的结构进行建模。这样的模型可以根据来自结构的数据进行校准,并且如果建模准确地捕获了结构的真实潜在物理特性,则有望优于任何其他模型。通过对具有随机材料特性的线性结构的应用,说明了SFE模型作为数字反射镜的潜在用途。对于这些模型的物理公式不能满足的情况,提出了一个数据驱动的框架,使用机器学习和条件生成对抗网络(cgan)。后一种算法用于学习具有材料非线性和不确定性的结构中感兴趣量的分布。对于本工作中考虑的示例,数据驱动的cgan模型优于基于物理的方法。最后,给出了一个示例,其中两种方法耦合在一起,从而演示了混合模型方法。
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引用次数: 8
A greedy data collection scheme for linear dynamical systems 线性动力系统的贪心数据采集方案
Q1 Mathematics Pub Date : 2021-07-28 DOI: 10.1017/dce.2022.16
Karim Cherifi, P. Goyal, P. Benner
Abstract Mathematical models are essential to analyze and understand the dynamics of complex systems. Recently, data-driven methodologies have gotten a lot of attention which is leveraged by advancements in sensor technology. However, the quality of obtained data plays a vital role in learning a good and reliable model. Therefore, in this paper, we propose an efficient heuristic methodology to collect data both in the frequency domain and the time domain, aiming at having more information gained from limited experimental data than equidistant points. In the frequency domain, the interpolation points are restricted to the imaginary axis as the transfer function can be estimated easily on the imaginary axis. The efficiency of the proposed methodology is illustrated by means of several examples, and its robustness in the presence of noisy data is shown.
数学模型对于分析和理解复杂系统的动力学是必不可少的。最近,由于传感器技术的进步,数据驱动的方法得到了很多关注。然而,获得的数据质量对于学习一个好的、可靠的模型起着至关重要的作用。因此,在本文中,我们提出了一种有效的启发式方法来收集频域和时域的数据,旨在从有限的实验数据中获得比等距点更多的信息。在频域内,由于传递函数在虚轴上易于估计,插值点被限制在虚轴上。通过几个算例说明了该方法的有效性,并证明了该方法在存在噪声数据时的鲁棒性。
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引用次数: 5
Bayesian model uncertainty quantification for hyperelastic soft tissue models 超弹性软组织模型贝叶斯模型不确定性量化
Q1 Mathematics Pub Date : 2021-07-13 DOI: 10.1017/dce.2021.9
Milad Zeraatpisheh, S. Bordas, L. Beex
Abstract Patient-specific surgical simulations require the patient-specific identification of the constitutive parameters. The sparsity of the experimental data and the substantial noise in the data (e.g., recovered during surgery) cause considerable uncertainty in the identification. In this exploratory work, parameter uncertainty for incompressible hyperelasticity, often used for soft tissues, is addressed by a probabilistic identification approach based on Bayesian inference. Our study particularly focuses on the uncertainty of the model: we investigate how the identified uncertainties of the constitutive parameters behave when different forms of model uncertainty are considered. The model uncertainty formulations range from uninformative ones to more accurate ones that incorporate more detailed extensions of incompressible hyperelasticity. The study shows that incorporating model uncertainty may improve the results, but this is not guaranteed.
摘要特定于患者的外科模拟需要特定于患者识别组成参数。实验数据的稀疏性和数据中的大量噪声(例如,在手术期间恢复的)在识别中造成了相当大的不确定性。在这项探索性工作中,通过基于贝叶斯推理的概率识别方法来解决通常用于软组织的不可压缩超弹性的参数不确定性。我们的研究特别关注模型的不确定性:我们研究了当考虑不同形式的模型不确定性时,本构参数的已识别不确定性如何表现。模型的不确定性公式从无信息的公式到包含不可压缩超弹性更详细扩展的更精确的公式。研究表明,加入模型的不确定性可能会改善结果,但这并不能保证。
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引用次数: 11
Data-based polyhedron model for optimization of engineering structures involving uncertainties 基于数据的多面体模型在不确定性工程结构优化中的应用
Q1 Mathematics Pub Date : 2021-06-29 DOI: 10.1017/dce.2021.8
Z. Qiu, Han Wu, I. Elishakoff, Dongliang Liu
Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.
摘要本文研究了基于数据的多面体模型及其在工程结构不确定线性优化中的应用,特别是在基于模糊集的方法中缺乏概率性质或隶属函数信息的情况下,用凸多面体来量化不确定性更为合适。首先,我们介绍了凸多面体方法的不确定性量化方法和切比雪夫不等式的模型修正方法。其次,研究了凸多面体线性规划最优解的性质。然后给出并证明了凸多面体线性规划的顶点解。其次,介绍了凸多面体线性规划在静力承载力问题中的应用。最后,通过一个平面特拉斯承载问题的实例验证了顶点解的有效性,并通过一个加筋复合板的承载问题验证了其有效性。
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引用次数: 2
Learning stable reduced-order models for hybrid twins 混合双胞胎的学习稳定降阶模型
Q1 Mathematics Pub Date : 2021-06-07 DOI: 10.1017/dce.2021.16
Abel Sancarlos, Morgan Cameron, Jean-Marc Le Peuvedic, J. Groulier, J. Duval, E. Cueto, F. Chinesta
Abstract The concept of “hybrid twin” (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model order reduction framework—to obtain real-time feedback rates—and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast, and accurate corrections in the HT framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several subvariants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.
由于强大的机器学习技术的可用性,“混合双胞胎”(HT)的概念最近受到了越来越多的关注。这个孪生概念结合了模型降阶框架内的基于物理的模型(以获得实时反馈率)和数据科学。因此,高温观测的主要思想是开发实时数据驱动的模型,以纠正测量结果与基于物理的模型预测之间可能存在的偏差。本文的重点是在HT框架下计算稳定、快速和准确的校正。此外,针对复杂而重要的稳定性问题,提出了一种新方法,该方法引入了几个子变量,保证了较低的计算成本和稳定的时间积分。
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引用次数: 10
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DataCentric Engineering
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