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An embedding method for modeling micromechanical behavior and macroscopic properties of composite materials

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2005年第16-17期42卷 4588-4612页

作者： Wang, J Mogilevskaya, SG Crouch, SL Univ Florida Dept Civil & Coastal Engn Gainesville FL 32611 USA Univ Minnesota Dept Civil Engn Minneapolis MN 55455 USA

This paper presents a numerical method for modeling the micromechanical behavior and macroscopic properties of fiber-reinforced composites and perforated materials. The material is modeled by a finite rectangular domain containing multiple circular holes and elastic inclusions. The rectangular domain is assumed to be embedded within a larger circular domain with fictitious boundary loading represented by truncated Fourier series. The analytical solution for the complementary problem of a circular domain containing holes and inclusions is obtained by using a combination of the series expansion technique with a direct boundary integral method. The boundary conditions on the physical external boundary are satisfied by adopting an overspecification technique based on a least squares approximation. All of the integrals arising in the method can be evaluated analytically. As a result, the elastic fields and effective properties can be expressed explicitly in terms of the coefficients in the series expansions. Several numerical experiments are conducted to verify the accuracy and efficiency of the numerical method and to demonstrate its application in determination of the macroscopic properties of composite materials. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： embedding method fiber-reinforced composites perforated materials effective properties direct boundary integral method fourier series least squares

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DENA: display name embedding method for Chinese social network alignment

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NEURAL COMPUTING & APPLICATIONS 2023年第10期35卷 7443-7461页

作者： Li, Yao Liu, Huilin Northeastern Univ Coll Comp Sci & Engn Shenyang 110819 Peoples R China

Social network alignment, which aims at finding node correspondences between social networks, is the cornerstone of fusing big data from different social networks. Most of social network alignment solutions are based on English environment. Hence, the existing attribute-based solutions, which contain the unique features in English, are not suitable for Chinese social networks. Although structure-based methods are general, they suffer from the sparsity problem. To solve the Chinese social network alignment problem, in this paper, a novel display name embedding method is proposed, called DENA. It utilizes the morphological and phonetic information of Chinese characters to enhance the alignment accuracy. Specifically, in DENA, a hierarchical n-gram process framework is introduced to generate features from display names and their related morphological information (i.e., strokes) and phonetic information (i.e., pinyin). Then, an innovative graph called display name graph is proposed to transform them into an undirected and unweighted graph. By learning this graph, all features are embedded in to low-dimensional vectors. Therefore, the closeness between embedding vectors of display names represents the probability of the alignment between them. Experiments based on real-world datasets show that DENA outperforms traditional classification-based methods and the state-of-the-art word embedding methods in social network alignment.

关键词： Display names embedding method Network alignment Chinese social networks

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A Comparison of the embedding method With Multiparametric Programming, Mixed-Integer Programming, Gradient-Descent, and Hybrid Minimum Principle-Based methods

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2014年第5期22卷 1784-1800页

作者： Meyer, Richard T. Zefran, Milos DeCarlo, Raymond A. Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical nonlinear optimization, has not been extensively compared with alternative solution approaches. The goal of this paper is thus to compare the embedding approach with multiparametric programming, mixed-integer programming [mixed integer programming (MIP), commercial (CPLEX)], and gradient-descent-based methods in the context of five recently published examples: 1) a spring-mass system;2) moving-target tracking for a mobile robot;3) two-tank filling;dc-dc boost converter;and 5) skid-steered vehicle. A sixth example, an autonomous switched 11-region linear system, is used to compare a hybrid minimum principle method and traditional numerical programming. For a given performance index (PI) for each case, cost and solution times are presented. It is shown that there are numerical advantages of the embedding approach: lower PI cost (except in some instances when autonomous switches are present), generally faster solution time, and convergence to a solution when other methods may fail. In addition, the embedding method requires no ad hoc assumptions (e.g., predetermined mode sequences) or specialized control models. Theoretical advantages of the embedding approach over the other methods are also described;guaranteed existence of a solution under mild conditions, convexity of the embedded hybrid optimization problem (under the customary conditions on the PI), solvability with traditional techniques (e.g., sequential quadratic programming) avoiding the combinatorial complexity in the number of modes/discrete variables of MIP, applicability to affine nonlinear systems, and no need to explicitly assign discrete/mode variables to autonomous switches. Finally, common misconceptions regarding the embedding approach are addressed, including whe

关键词： Boost converter embedding method model predictive control multiparametric programming numerical optimization switched optimal control

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COUPLING VOF/PLIC AND embedding method FOR SIMULATING WAVE BREAKING ON A SLOPING BEACH

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JOURNAL OF MARINE SCIENCE AND TECHNOLOGY-TAIWAN 2015年第4期23卷 498-507页

作者： Hsu, Tai-Wen Hsieh, Chih-Min Tsai, Chin-Yen Ou, Shan-Hwei Natl Taiwan Ocean Univ Dept Habor & River Engn Keelung Taiwan Res Ctr Ocean Energy & Strategies Keelung Taiwan Natl Kaohsiung Marine Univ Dept Maritime Informat & Technol Kaohsiung Taiwan Natl Chen Kung Univ Dept Hydraul & Ocean Engn Tainan Taiwan

A 2-D numerical model was developed to simulate wave breaking on a sloping beach. The model solves the Reynolds Averaged Navier-Stokes (RANS) equations coupled with the k-s turbulence closure model. To track free surface configurations, the volume of fluid with piecewise linear interface calculation (VOF/PLIC) is employed. An embedding method (EB) is also used to treat complex bottom topography. Coupling these two methods for simulating wave breaking on a sloping beach, good agreement between numerical results and laboratory observations is found for spilling breaker. Wave breaking characteristics is in terms of free surface profiles, mean velocities and wave heights based on the numerical results. Turbulence transports under wave breaking were also investigated.

关键词： spilling breaker VOF/PLIC embedding method wave breaking

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The embedding method for Nonsmooth Equations

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Advances in Manufacturing 1997年第3期1卷 184-190页

作者：张建军王德人 College of Sciences Shanghai University Jiading Shanghai

In this paper. we present a class of' embedding methods for nonsmooth equations. Under suitable conditions, we Prove that there exists a homotopy solution curve, which is Unique and continuous. We also prove that the solution curve is singlcvalue-d with respect to the homotopy parameter. Then we construct all efficient algorithm for this class of equations and prove its convcrgcnce. Filially, we apply the algorithm to the nonlinear complementarity problem. The numerical results show that tile algorithm is satisfacotry.

关键词： nonsmooth equations embedding method nonlinear complementarity problem Newton method

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Stock Market embedding and Prediction: A Deep Learning method 15

Stock Market Embedding and Prediction: A Deep Learning Metho...

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15th International Conference on Service Systems and Service Management (ICSSSM)

作者： Chen, Yuzhou Wu, Junjie Bu, Hui Beihang Univ Sch Econ & Management Beijing Peoples R China Beijing Key Lab Emergency Support Simulat Technol Beijing Peoples R China Beihang Univ Beijing Adv Innovat Ctr Big Data & Brain Comp Beijing Peoples R China

ISBN: (纸本)9781538651780

It has always been a challenging issue for people to understand the stock market and make reasonable predictions. For a very long period, investors are trying to manually extract useful features from the financial market which generates an enormous volume of data every single day. People create a lot of technical indicators like MACD, TR, MFI to describe momentum, volume and volatility signals of the financial time series. However, the limitation is evident due to the efficiency of manually feature engineering. With the rapidly growing volume of data, deep neural network shows excellent performance in many research areas like natural language processing, voice recognition, image identification. It provides a new view to dig out potentially useful information automatically. In this paper, we present a novel end-to-end training using an embedding method to automatically extract features and get a summary representation of the daily market. Moreover, we apply the Long Short-Term Memory (LSTM) with attention mechanism to predict daily return ratio of HS300 index. The features extracted by the embedding layer show greater predictive power than manually defined technical signals by 92.42% lower MSE. Moreover, the use of attention mechanism also provides an average enhance of 55.68% in MSE. Our study shows that deep neuron network structure has a strong potential for better understanding market complex behaviors.

关键词： Market Vector embedding method Technical Indicator LSTM Market Prediction

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Monte Carlo method for the real and complex fuzzy system of linear algebraic equations

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SOFT COMPUTING 2020年第2期24卷 1255-1270页

作者： Fathi-Vajargah, Behrouz Hassanzadeh, Zeinab Univ Guilan Fac Math Sci Dept Stat POB 41335-19141 Rasht Iran Univ Guilan Fac Math Sci Dept Appl Math POB 41335-19141 Rasht Iran

In this paper, we apply the Monte Carlo method to solve the real and complex fuzzy system of linear algebraic equations via new techniques. At first, we determine the specified and simpler computing condition for convergence of the Monte Carlo method using Hadamard product related to select the transition probability matrix. Then, we employ the new strategy based on the exclusive characteristic of the Monte Carlo method to find the solution of the real and complex fuzzy system of linear algebraic equations. Finally, some numerical examples are proposed to demonstrate the validity and efficiency of the discussed theoretical concepts.

关键词： System of linear algebraic equations Complex fuzzy number Transition probability matrix Hadamard product Markov chain Monte Carlo embedding method

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PDEs on moving surfaces via the closest point method and a modified grid based particle method

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JOURNAL OF COMPUTATIONAL PHYSICS 2016年 312卷 139-156页

作者： Petras, A. Ruuth, S. J. Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada

Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman (2008) [20]) is a recent embedding method that has been used to solve a variety of PDEs on smooth surfaces using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. The original closest point method (CPM) was designed for problems posed on static surfaces, however the solution of PDEs on moving surfaces is of considerable interest as well. Here we propose solving PDEs on moving surfaces using a combination of the CPM and a modification of the grid based particle method (Leung and Zhao (2009) [12]). The grid based particle method (GBPM) represents and tracks surfaces using meshless particles and an Eulerian reference grid. Our modification of the GBPM introduces a reconstruction step into the original method to ensure that all the grid points within a computational tube surrounding the surface are active. We present a number of examples to illustrate the numerical convergence properties of our combined method. Experiments for advection-diffusion equations that are strongly coupled to the velocity of the surface are also presented. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Partial differential equations on moving surfaces Closest point method Grid based particle method Closest point representation embedding method Lagrangian particles

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An RBF-FD closest point method for solving PDEs on surfaces

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JOURNAL OF COMPUTATIONAL PHYSICS 2018年 370卷 43-57页

作者： Petras, A. Ling, L. Ruuth, S. J. Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada BCAM Bilbao 48009 Basque Country Spain Hong Kong Baptist Univ Dept Math Kowloon Tong Hong Kong Peoples R China

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman (2008) [17]) is an embedding method for solving PDEs on surfaces using standard finite difference schemes. In this paper, we formulate an explicit closest point method using finite difference schemes derived from radial basis functions (RBF-FD). Unlike the orthogonal gradients method (Piret (2012) [22]), our proposed method uses RBF centers on regular grid nodes. This formulation not only reduces the computational cost but also avoids the ill-conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm (Leung and Zhao (2009) [26]). When compared to the standard finite difference discretization of the closest point method, the proposed method requires a smaller computational domain surrounding the surface, resulting in a decrease in the number of sampling points on the surface. In addition, higher-order schemes can easily be constructed by increasing the number of points in the RBF-FD stencil. Applications to a variety of examples are provided to illustrate the numerical convergence of the method. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Closest point method embedding method Radial basis functions Finite differences

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Small sample scene cancer classification method based on combined feature dimensionality reduction 16

Small sample scene cancer classification method based on com...

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16th International Conference on Computer and Automation Engineering (ICCAE)

作者： Zhang, Shilong Qin, Feng Xu, Jingli Zhang, Jinbo Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu Peoples R China Yangtze Univ Sch Foreign Studies Jingzhou Peoples R China Chengdu Jwell Grp Co Ltd Chengdu Peoples R China

ISBN: (纸本)9798350370058;9798350370164

Accurately predicting cancer is a crucial task, especially in scenarios with small sample sizes. Machine learning-based cancer classification methods are widely employed due to their high accuracy. However, in small sample scenarios, the limited availability of training samples poses significant challenges. Therefore, this paper proposes a small-sample cancer classification method based on mixed feature dimensionality reduction. Firstly, it utilizes embedding-based feature selection technology to identify the most representative features. Secondly, the calculation of dynamic correlation weights is introduced to preserve the correlation between features. Finally, PCA technology is employed for feature extraction, and the optimal feature subset is extracted from small sample scenarios for model training. The model is then evaluated using common machine learning prediction models through in-depth comparative analysis. Numerous experiments demonstrate that the proposed model performs well in small sample scenarios. It effectively reduces the dimensionality of cancer data, accurately classifies different types of cancer, and achieves favorable prediction results.

关键词： Small sample scenario embedding method feature selection PCA feature extraction dimensionality reduction cancer classification

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