Enabling reduced-order data-driven nonlinear identification and modeling through naïve elastic net regularization

This work discusses an improved method of reduced-order modeling for existing data-driven nonlinear identification techniques through the incorporation of naïve elastic net regularization. The data-driven methods considered for this study operate using basis functions to represent the observed nonlinearity. Elastic net regularization is used to minimize the number of non-zero coefficients, thus modifying the basis functions and providing a compact representation. The ability of the naïve elastic net to provide reduced-order nonlinear models that can both accurately fit various data sets and computationally simulate new responses is illustrated through studies considering both synthetic data and experimental data. In both cases, the results obtained with the naïve elastic net are shown to match or outperform those from other traditional methods.     

A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling

Although Reynolds-Averaged Navier–Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. However, the prediction performance of data-driven models inevitably depends on the choices of training flows. This work aims to identify a quantitative measure for a priori estimation of prediction confidence in data-driven turbulence modeling. This measure represents the distance in feature space between the training flows and the flow to be predicted. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. To examine the relationship between these two extrapolation metrics and the machine learning model prediction performance, the flow over periodic hills at Re = 10595 is used as test set and seven flows with different configurations are individually used as training sets. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of data source and to assess the prediction performance for data-driven turbulence modeling.     

并行计算结构力学的发展和展望

本文简要介绍了结构力学中并行分析方法的发展概况及笔者在这个领域所作的主要工作,并对该领域的未来发展趋势作了展望;指出并行机和并行算法在未来的科学研究和工程分析计算中,必定成为一种重要的工具和必不可少的方法．      

CLASSROOM DEMONSTRATION OF EXPERIMENT IN STRUCTURAL MECHANICS TEACHING1)

实验教学是很多理工科课程的重要教学环节,但是很多课程的实验教学模式还不够成熟,且开设困难。针对这一问题,本文以结构力学课程为例,分析当前高校结构力学实验开设难、开设少的原因,对比了几种典型实验方式的优劣。重点讨论了课堂演示实验的优势和实施办法,探索并列举了诸多简便易行的课堂演示实验案例。实践表明,课堂演示模型用日常简易材料制成,易于调动学生的参与积极性,同时增强学生的动手能力及理论联系实际的能力。最终提出了多种实验方式相结合的结构力学实验模式,可为当前高校结构力学和相关课程的课堂教学及实验环节提供借鉴。     

实验数据反演识别分析方法与力学表征

本文给出了两类基于实验(实测)数据的反演识别方法,简述了其在界面力学性能及工程实测数据分析中的应用.在粘接界面力学性能的反演识别实验研究中,基于不同加载速率的实验曲线,结合参数化界面力学模型,通过反演识别给出粘接界面力学性能参数,并对识别结果的适定性进行独立的实验验证;在基于工程实测数据的反演识别与力学建模方面,在分析盾构装备载荷特点的基础上,对海量的实测数据统计分类,提出了力学量纲分析的建模方法,并应用于盾构掘进载荷的反演识别研究.     

Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures

This paper reviews the basis and applications of the finite-difference time -domain (FD-TD) numerical modeling approach for Maxwell's equations. FD-TD is very simple in concept and execution. However, it is remarkably robust, providing highly accurate modeling predictions for a wide variety of electromagnetic wave interaction problems. The accuracy and breadth of FD-TD applications will be illustrated by a number of two- and three-dimensional examples. The objects modeled range in nature from simple geometric shapes to extremely complex aerospace and biological systems. In all cases where rigorous analytical, code-to-code, or experimental validations are possible, FD-TD predictive data for penetrating and scattered near fields as well as radar cross sections are in excellent agreement with the benchmarks. It will also be shown that opportunities are arising in applying FD-TD to model rapidly time-varying systems, microwave circuits, and inverse scattering. With continuing advances in FD-TD modeling theory as well as continuing advances in supercomputer technology, there is a strong possibility that FD-TD numerical modeling will occupy an important place in high-frequency engineering electromagnetics as we move into the 1990s.     

Fifty years of finite elements — a solid mechanics perspective

The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly from a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.     

Learning material law from displacement fields by artificial neural network

The recently developed data-driven approach can establish the material law for nonlinear elastic composite materials(especially newly developed materials) by the generated stress-strain data under different loading paths(Computational Mechanics, 2019). Generally, the displacement(or strain) fields can be obtained relatively easier using digital image correlation(DIC) technique experimentally, but the stress field is hard to be measured. This situation limits the applicability of the proposed data-driven approach. In this paper, a method based on artificial neural network(ANN) to identify stress fields and further obtain the material law of nonlinear elastic materials is presented, which can make the proposed data-driven approach more practical. A numerical example is given to prove the validity of the method. The limitations of the proposed approach are also discussed.     

再论约束最小二乘法

本文介绍的约束最小二乘法如同经典的最小二乘法一样,也普遍适用于各种科学领域。然而,这一方法仅在“模型修正”一类论文的附录中出现过。鉴于约束最小二乘法在计算力学和工程问题中愈来愈重要的作用,本文将作者十多年前提出的这一方法稍加扩展（如引入加权因子和讨论了自然权因子的应用等）后,再做一系统的介绍,并随意设计了一个简单考例,证实了约束最小二乘法的有效性。     

基于组合神经网络的雷诺平均湍流模型 多次修正方法

求解雷诺平均(Reynolds-averaged Navier-Stokes, RANS)方程依然是工程应用中有效且实用的方法, 但对雷诺应力建模的不确定性会导致该方法的预测精度具有很大差异. 随着人工智能的发展, 湍流闭合模型结合机器学习元素的数据驱动方法被认为是提高RANS模型预测性能的有效手段, 然而这种数据驱动方法的稳定性和预测精度仍有待进一步提高. 本文通过构建一个全连接神经网络对RANS方程中的涡黏系数进行预测以实现雷诺应力的隐式求解,该神经网络记作涡黏系数神经网络(eddy viscosity neural network, EVNN). 此外, 也使用张量基神经网络(tensor basis neural network, TBNN)预测未封闭量与解析量之间的高阶涡黏关系, 并利用基张量保证伽利略不变性. 最后, 采用多次修正的策略实现修正模型对流场预测的精度闭环. 上述方法使用大涡模拟(large eddy simulation, LES)方法产生的高保真数据, 以及RANS模拟获得的基线数据对由EVNN和TBNN组合的神经网络进行训练, 然后用训练好的模型预测新的RANS模拟的流场. 通过与高保真LES结果进行对比, 结果表明, 相比于原始RANS模型, 修正模型对后验速度场、下壁面平均压力系数和摩擦力系数的预测精度均有较大提升. 可以发现对雷诺应力线性部分的隐式处理可以增强数值求解的稳定性, 对雷诺应力非线性部分的修正可以提升模型对流场各向异性特征预测的性能, 并且多次修正后的模型表现出更高的预测精度. 因此, 该算法在数据驱动湍流建模和工程应用中具有很大的应用潜力.      

物理增强的流场深度学习建模与模拟方法

流体运动理论上可用Navier?Stokes方程描述, 但由于对流项带来的非线性, 仅在少数情况可求得方程解析解. 对于复杂工程流动问题, 数值模拟难以高效精准计算高雷诺数流场, 实验或现场测量难以获得流场丰富细节. 近年来, 人工智能技术快速发展, 深度学习等数据驱动技术可利用灵活网络结构, 借助高效优化算法, 获得对高维、非线性问题的强大逼近能力, 为研究流体力学计算方法带来新机遇. 有别于传统图像识别、自然语言处理等典型人工智能任务, 深度学习模型预测的流场需满足流体物理规律, 如Navier?Stokes方程、典型能谱等. 近期, 物理增强的流场深度学习建模与模拟方法快速发展, 正逐渐成为流体力学全新研究范式: 根据流体物理规律选取网络输入特征或设计网络架构的方法称为物理启发的深度学习方法, 直接将流体物理规律显式融入网络损失函数或网络架构的方法称为物理融合的深度学习方法. 研究内容涵盖流体力学降阶模型、流动控制方程求解领域.      

Focusing on the meso-scales of multi-scale phenomena—In search for a new paradigm in chemical engineering

To celebrate the 90th birthday of Professor Mooson Kwauk, who supervised the multi-scale research at this Institute in the last three decades, we dedicate this paper outlining our thoughts on this subject accumulated from our previous studies. In the process of developing, improving and extending the energy- minimization multi-scale （EMMS） method, we have gradually recognized that meso-scales are critical to the understanding of the different kinds of multi-scale structures and systems. It is a common challenge not only for chemical engineering but also for almost all disciplines of science and engineering, due to its importance in bridging micro- and macro-behaviors and in displaying complexity and diversity. It is believed that there may exist a common law behind meso-scales of different problems, possibly even in different fields. Therefore, a breakthrough in the understanding of meso-scales will help materialize a revolutionary progress, with respect to modeling, computation and application.     

Simulation of Entry-Region Flow in Open-Cell Metal Foam and Experimental Validation

Open-cell metal foam is distinguished from traditional porous media by its very high porosities (often greater than 90 %), and its web-like open structure and good permeability. As such, the foam is a very attractive core for many engineered systems, e.g., heat exchangers, filtration devices, catalysts, and reactors. The flow field inside the foam is rather complex due to flow reversal and vigorous mixing. This complexity is increased by the possible presence of an entry region. The entrance region in metal foam is usually underestimated and ignored, just like its counterpart in traditional porous media. In this paper, the actual entry length is determined by simulation and direct experiment on commercial open-cell aluminum foam. It is shown to be dependent on flow velocity and to reach a constant value for higher velocities. The complex and intrinsically random architecture of the foam is idealized using a unit geometrical model, in order to numerically investigate the flow field and pressure drop inside the foam. The Navier–Stokes equations are solved directly, and velocity and pressure fields are obtained for various approach velocities using a commercial numerical package. The entry length is ascertained from the behavior of the velocity field close to the entrance. Comparisons to experimental data were also carried out. The commercial foam that was used in the experiment had 10 ppi and porosity of 91.2 %. Air was forced to flow inside the foam using an open-loop wind tunnel. Good qualitative agreement between the modeling and experimental results are obtained. The agreement lends confidence to the modeling approach and the determined entry length.     

数智流体力学的发展及油气渗流领域应用

大数据及人工智能技术的崛起推动了数智流体力学的快速发展.数智流体力学是将流体力学、大数据和人工智能相结合,以流体力学场景需求为导向,形成以“数”为基础,以“智”为核心,以算力为支撑的新研究范式.核心内涵是要以数据驱动为主,融合物理信息、专家经验等先验知识,利用智能化手段构建“数据+物理”双驱动的数智模型,解决场景需求问题.数智流体力学在建模灵活性、运算效率、计算精度方面具有十分明显的优势,其应用潜力已经在多尺度流动、多场耦合以及流场建模等方面得到验证.数智流体力学研究范式包括数据治理和智能算法构建,其中数据治理工作尤为重要,治理后的数据质量是智能算法能否发挥其价值的关键.智能算法中“数据+物理”协同驱动主要存在四种引入机制,分别是基于输入数据的嵌入机制、基于模型架构的嵌入机制、基于损失函数的嵌入机制和基于模型优化的嵌入机制.以油气领域应用为例,介绍了数智流体力学在储层物性参数预测、压裂效果评价以及注采参数优化等方面的一系列研究进展.数智流体力学是流体力学未来的重要发展方向之一,以场景需求为导向、深度融合物理信息等先验知识的新一代智能理论与方法是数智流体力学发展的必然趋势,能够从崭新的角...     

基于弹性力学第一性原理的数据驱动力学建模

提出了一种基于弹性力学第一性原理的数据驱动力学建模方法,其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF,从梁的载荷和位移数据中自动识别出了Timoshenko梁形式的弯曲控制微分方程,得到了三种不同加载条件下剪切影响系数关于结构尺寸和力学参数的函数表达式。揭示了经典模型适用的加载条件,同时还给出了一种未发现的新模型。通过将基于弹性力学的第一性原理计算与数据驱动范式相结合,克服了传统建模方法的局限性和对人类经验的强依赖性,为建立简洁的力学模型提供了一种新途径。     

An efficient Tabu-search optimized regression for data-driven modeling

In the past decade, data science became trendy and in-demand due to the necessity to capture, process, maintain, analyze and communicate data. Multiple regressions and artificial neural networks are both used for the analysis and handling of data. This work explores the use of meta-heuristic optimization to find optimal regression kernel for data fitting. It is shown that optimizing the regression kernel improve both the fitting and predictive ability of the regression. For instance, Tabu-search optimization is used to find the best least-squares regression kernel for different applications of buckling of straight columns and artificially generated data. Four independent parameters were used as input and a large pool of monomial search domain is initially considered. Different input parameters are also tested and the benefits of using of independent input parameters is shown.     

人工智能在复合材料研究中的应用

复合材料以其轻质高强高模、可设计性强等优点成为结构轻量化的重要用材. 然而, 随着复合材料组分、结构以及性能需求的日益复杂化, 以实验观测、理论建模和数值模拟为主体的传统研究范式, 在复合材料力学性能分析、设计和制造等方面遇到了新的科学问题与技术瓶颈. 其中, 实验观测不足、理论模型缺乏、数值分析受限、结果验证困难等问题在一定程度上制约了先进复合材料在面向未来工程领域中应用的发展. 人工智能方法以数据驱动的模型替代传统研究中的数学力学模型, 直接由高维高通量数据建立变量间的复杂关系, 捕捉传统力学研究方法难以发现的规律, 在复杂系统的分析、预测、优化方面拥有与生俱来的优势. 而通过人工智能赋能来寻求复合材料中传统研究方法所面临难题的新的解决方案, 目前已成为复合材料研究领域的发展趋势. 本文综述并评价了人工智能方法在复合材料性能预测、优化设计、制造检测及健康监测等方面的研究进展, 并对未来发展方向进行了探讨和展望.      

多尺度方法在复合材料力学分析中的研究进展

简要介绍了多尺度方法的分类及各自的适用范围,重点阐述了主要的多尺度分析方法------均匀化理论,详细论述了多尺度分析方法在纤维增强复合材料弹性、黏弹性、塑性、失效退化、热力学等力学性能中的研究进展,最后对多尺度分析方法的前景进行了展望.      

复杂时间序列的多尺度分析

为纪念郑哲敏先生仙逝一周年, 作者回忆在读研期间先生对自己的教诲, 介绍先生和自己在非线性科学领域的一些工作, 及后来这些工作如何被拓展并演变成一些非线性问题通用的分析方法. 具体的方法包括混沌时间序列分析的相空间最优重构, 混沌的直接动力学判据, 基于依赖于尺度的李雅普诺夫指数(SDLE)的多尺度分析及自适应分形分析. 特别, SDLE可以非常好地刻画已知的所有类的时间序列模型, 因此, 可以统一已知的各种复杂性的度量. 自适应分形分析基于自适应滤波, 能非常好地决定趋势, 包括各种震荡模式和回归分析的非线性回归曲线, 也能非常好地去噪, 并把时间序列分解成各种内在固有模式. 这些方法已被广泛用于自然科学、工程技术和社会科学的诸多领域. 它们特别适用于各领域(包括运维)的故障诊断, 生物医学数据的分析及不确定性的度量. 郑先生从不囿于他自己熟悉的领域, 而是随着时代发展不断拓展新的领域. 身处百年未遇之大变局时期, 我们必须发扬光大先生的这种求真务实和开拓进取的精神.      

Fast data-driven model reduction for nonlinear dynamical systems

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling method SSMLearn uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to a normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, we provide a novel method for timelag selection when delay-embedding signals from multimodal systems. We show that our alternative approach to data-driven SSM construction yields accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics on both numerical and experimental datasets. Aside from a major reduction in complexity, our new method allows an increase in the training data dimensionality by several orders of magnitude. This promises to extend data-driven, SSM-based modeling to problems with hundreds of thousands of degrees of freedom.