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Simple heuristic for data-driven computational elasticity with material data involving noise and outliers: a local robust regression approach

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2018年第3期35卷 1085-1101页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

data-driven computing in applied mechanics utilizes the material data set directly, and hence is free from errors and uncertainties stemming from the conventional material modeling. For data-driven computing in elasticity, this paper presents a simple heuristic that is robust against noise and outliers in a data set. For each structural element, we extract the material property from some nearest data points. Using the nearest neighbors reduces the influence of noise, compared with the existing method that uses a single data point. Also, the robust regression is adopted to reduce the influence of outliers. Numerical experiments on the static equilibrium analysis of trusses are performed to illustrate that the proposed method is robust against the presence of noise and outliers.

关键词： data-driven computing Model-free computational mechanics Outlier Local regression Robust statistics

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data-driven micromorphic mechanics for materials with strain localization

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 429卷

作者： Ulloa, Jacinto Stainier, Laurent Ortiz, Michael Andrade, Jose E. CALTECH Div Engn & Appl Sci Pasadena CA 91125 USA Nantes Univ GeM CNRS Ecole Cent NantesUMR 6183 F-44000 Nantes France

This paper explores the role of generalized continuum mechanics, and the feasibility of model-free data-driven computing approaches thereof, in solids undergoing failure by strain localization. Specifically, we set forth a methodology for capturing material instabilities using data-driven mechanics without prior information regarding the failure mode. We show numerically that, in problems involving strain localization, the standard data-driven framework for Cauchy/Boltzmann continua fails to capture the length scale of the material, as expected. We address this shortcoming by formulating a generalized data-driven framework for micromorphic continua that effectively captures both stiffness and length-scale information, as encoded in the material data, in a model-free manner. These properties are exhibited systematically in a one-dimensional softening bar problem and further verified through selected plane-strain problems.

关键词： data-driven computing Micromorphic continuum Strain localization Softening materials

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A kernel method for learning constitutive relation in data-driven computational elasticity

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2021年第1期38卷 39-77页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

For numerical simulation of elastic structures, data-driven computational approaches attempt to use a data set of material responses, without resorting to conventional modeling of the material constitutive equation. In a material data set in the stress-strain space, the data points are considered to lie on or near a low-dimensional manifold, rather distribute ubiquitously in the space. This paper presents a kernel method for extracting this manifold. We formulate a regularized least-squares problem for learning a manifold, and show that its optimal solution corresponds to an eigenvector of a real symmetric matrix. Therefore, the method requires only simple computational task, and is easy to implement. We also give a description how to use the obtained solution in static equilibrium analysis of an elastic structure. Numerical experiments on two-dimensional continua are performed to demonstrate effectiveness and robustness of the proposed method.

关键词： Regularized least squares Kernel method Manifold learning data-driven computing Model-free computational mechanics

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Mixed-integer programming formulation of a data-driven solver in computational elasticity

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OPTIMIZATION LETTERS 2019年第7期13卷 1505-1514页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

This paper presents a mixed-integer quadratic programming formulation of an existing data-driven approach to computational elasticity. This formulation is suitable for application of a standard mixed-integer programming solver, which finds a global optimal solution. Therefore, the results obtained by the presented method can be used as benchmark instances for any other algorithm. Preliminary numerical experiments are performed to compare quality of solutions obtained by the proposed method and a heuristic conventionally used in the data-driven computational mechanics.

关键词： Global optimization Mixed-integer programming Exact solution method data-driven computing Model-free computational mechanics

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Model-free data-driven simulation of inelastic materials using structured data sets, tangent space information and transition rules

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COMPUTATIONAL MECHANICS 2022年第2期70卷 425-435页

作者： Ciftci, Kerem Hackl, Klaus Ruhr Univ Bochum Inst Mech Mat D-44801 Bochum Germany

Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the data set is minimized, subject to equilibrium and compatibility constraints. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one and the same point in stress-strain space might correspond to different material behaviour. In recent literature, this issue has been treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of specific internal variables. Thus, a mixed formulation of classical and data-driven modeling is obtained. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is divided into subsets corresponding to different material behaviour. Based on this classification, transition rules map the modeling points to the various subsets. The approach will be applied to non-linear elasticity and elasto-plasticity with isotropic hardening.

关键词： data-driven computing Tangent space information Transition rules Inelasticity data science

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A historical survey of algorithms and hardware architectures for neural-inspired and neuromorphic computing applications

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BIOLOGICALLY INSPIRED COGNITIVE ARCHITECTURES 2017年 19卷 49-64页

作者： James, Conrad D. Aimone, James B. Miner, Nadine E. Vineyard, Craig M. Rothganger, Fredrick H. Carlson, Kristofor D. Mulder, Samuel A. Draelos, Timothy J. Faust, Aleksandra Marinella, Matthew J. Naegle, John H. Plimpton, Steven J. Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA Google X Mountain View CA USA

Biological neural networks continue to inspire new developments in algorithms and microelectronic hardware to solve challenging data processing and classification problems. Here, we survey the history of neural-inspired and neuromorphic computing in order to examine the complex and intertwined trajectories of the mathematical theory and hardware developed in this field. Early research focused on adapting existing hardware to emulate the pattern recognition capabilities of living organisms. Contributions from psychologists, mathematicians, engineers, neuroscientists, and other professions were crucial to maturing the field from narrowly-tailored demonstrations to more generalizable systems capable of addressing difficult problem classes such as object detection and speech recognition. Algorithms that leverage fundamental principles found in neuroscience such as hierarchical structure, temporal integration, and robustness to error have been developed, and some of these approaches are achieving world-leading performance on particular data classification tasks. In addition, novel microelectronic hardware is being developed to perform logic and to serve as memory in neuromorphic computing systems with optimized system integration and improved energy efficiency. Key to such advancements was the incorporation of new discoveries in neuroscience research, the transition away from strict structural replication and towards the functional replication of neural systems, and the use of mathematical theory frameworks to guide algorithm and hardware developments. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Neuromorphic computing Algorithms Artificial neural networks data-driven computing Machine learning Pattern recognition

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THE RANDOM FEATURE MODEL FOR INPUT-OUTPUT MAPS BETWEEN BANACH SPACES

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SIAM JOURNAL ON SCIENTIFIC computing 2021年第5期43卷 A3212-A3243页

作者： Nelsen, Nicholas H. Stuart, Andrew M. CALTECH Div Engn & Appl Sci Pasadena CA 91125 USA

Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to the real line. In this paper, we instead propose a methodology for use of the random feature model as a data-driven surrogate for operators that map an input Banach space to an output Banach space. Although the methodology is quite general, we consider operators defined by partial differential equations (PDEs);here, the inputs and outputs are themselves functions, with the input parameters being functions required to specify the problem, such as initial data or coefficients, and the outputs being solutions of the problem. Upon discretization, the model inherits several desirable attributes from this infinite-dimensional viewpoint, including mesh-invariant approximation error with respect to the true PDE solution map and the capability to be trained at one mesh resolution and then deployed at different mesh resolutions. We view the random feature model as a nonintrusive data-driven emulator, provide a mathematical framework for its interpretation, and demonstrate its ability to efficiently and accurately approximate the nonlinear parameter-to-solution maps of two prototypical PDEs arising in physical science and engineering applications: the viscous Burgers' equation and a variable coefficient elliptic equation.

关键词： random feature surrogate model emulator solution map high-dimensional approximation model reduction parametric PDE supervised learning data-driven computing

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data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2024年第3期41卷 1501-1534页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

关键词： data-driven computing Mixed-integer programming Global optimization Order statistics Reliability with unknown distribution

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data-driven multiscale method for composite plates

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COMPUTATIONAL MECHANICS 2022年第5期70卷 1025-1040页

作者： Yan, Wei Huang, Wei Huang, Qun Yang, Jie Giunta, Gaetano Belouettar, Salim Hu, Heng Wuhan Univ Sch Civil Engn 8 South Rd East Lake Wuhan 430072 Peoples R China Luxembourg Inst Sci & Technol 5 Ave Hauts Fourneaux L-4362 Esch Sur Alzette Luxembourg

Composite plates are widely used in many engineering fields such as aerospace and automotive. An accurate and efficient multiscale modeling and simulation strategy is of paramount importance to improve design and manufacture. To this end, we propose an efficient data-driven computing scheme based on the classical plate theory for the multiscale analysis of composite plates. In order to accurately describe the relationship between the macroscopic mechanical properties and the microscopic architecture, the multiscale finite element method (FE2) is adopted to compute the generalized strain and stress fields. These data are then used to construct a database for data-driven computing. Since the database is offline populated, the data-driven computing scheme allows for a reduced computational cost when compared to the traditional multiscale method, where the concurrent coupling of different scales is still a burden. And data are obtained from a reduced structural model for computational efficiency. The proposed scheme is therefore addressed as Structural-Genome-driven (SGD) modeling of plates. Compared to the general data-driven computational mechanics modeling of plates, SGD is found to be more efficient since the number of integration points is significantly reduced. This scheme provides a robust alternative computational tool for composite plate structures analysis.

关键词： data-driven computing Structural-Genome-driven Multiscale finite element method Composite plates

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Quality Evaluation of Rock Mass Using RMR14 Based on Multi-Source data Fusion

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SENSORS 2021年第21期21卷 7108-7108页

作者： Zhang, Qi Jiang, Qing Li, Yuanhai Wang, Ning He, Lei Southeast Univ Sch Civil Engn Nanjing 211189 Peoples R China China Univ Min Technol State Key Lab GeoMech & Deep Underground Engn Xuzhou 221116 Jiangsu Peoples R China Southeast Univ Inst Future Underground Space Nanjing 211189 Peoples R China

The uncertainties in quality evaluations of rock mass are embedded in the underlying multi-source data composed by a variety of testing methods and some specialized sensors. To mitigate this issue, a proper method of data-driven computing for quality evaluation of rock mass based on the theory of multi-source data fusion is required. As the theory of multi-source data fusion, Dempster-Shafer (D-S) evidence theory is applied to the quality evaluation of rock mass. As the correlation between different rock mass indices is too large to be ignored, belief reinforcement and Murphy's average belief theory are introduced to process the multi-source data of rock mass. The proposed method is designed based on RMR14, one of the most widely used quality-evaluating methods for rock mass in the world. To validate the proposed method, the data of rock mass is generated randomly to realize the data fusion based on the proposed method and the conventional D-S theory. The fusion results based on these two methods are compared. The result of the comparison shows the proposed method amplifies the distance between the possibilities at different ratings from 0.0666 to 0.5882, which makes the exact decision more accurate than the other. A case study is carried out in Daxiagu tunnel in China to prove the practical value of the proposed method. The result shows the rock mass rating of the studied section of the tunnel is in level III with the maximum possibility of 0.9838, which agrees with the geological survey report.

关键词： rock mass quality evaluation data-driven computing multi-source data fusion D-S evidence theory belief reinforcement

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