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International Conference on Advanced Engineering Materials and Technology (AEMT2011)International Conference on Civil Engineering and Building Materials (CEBM)

作者： Xue Qiwen Du Xiuyun Dalian Jiaotong Univ Adv Technol Lab Railway Vehicle Dalian 116028 Peoples R China Dalian Univ Technol Fac Infrastructure Engn Dalian 116023 Peoples R China Liaoning Normal Univ Dalian 116028 Peoples R China

ISBN: (纸本)9783037851920

In order to determine thermal parameters of mass concrete, this paper utilizes homotopy technique to solve an inverse transient heat conduction problem with multi-variables. A finite element model facilitating to sensitivity analysis for non-linear direct and inverse problems is derived, and a precise algorithm of time stepping is used in the transient analysis. Numerical validation has been given with an investigation of effects of noise data and initial guess on the results.

关键词： Inverse heat conduction problem homotopy algorithm Multi-variables Non-linear

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Measure prediction capability of data for collaborative filtering

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KNOWLEDGE AND INFORMATION SYSTEMS 2016年第3期49卷 975-1004页

作者： Liang, Xijun Xia, Zhonghang Pang, Liping Zhang, Liwei Zhang, Hongwei China Univ Petr Coll Sci Qingdao 266555 Peoples R China Western Kentucky Univ Dept Comp Sci Bowling Green KY 42101 USA Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China

Collaborative filtering (CF) approaches have been widely been employed in e-commerce to help users find items they like. Whereas most of existing work focuses on improving algorithmic performance, it is important to know whether the recommendation for users and items can be trustworthy. In this paper, we propose a metric, "relatedness," to measure the potential that a user's preference on an item can be accurately predicted. The relatedness of a user-item pair is determined by a community which consists of users and items most related to the pair. The relatedness is computed by solving a constrained -regularized least square problem with a generalized homotopy algorithm, and we design the homotopy-based community search algorithm to identify the community by alternately selecting the most related users and items. As an application of the relatedness metric, we develop the data-oriented combination (DOC) method for recommender systems by integrating a group of benchmark CF methods based on the relatedness of user-item pairs. In experimental studies, we examine the effectiveness of the relatedness metric and validate the performance of the DOC method by comparing it with benchmark methods.

关键词： Collaborative filtering Community Relatedness homotopy algorithm l(1)-Regularized least squares problem

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A bi-level approximation tool for the computation of FRFs in stochastic dynamic systems

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2016年 70-71卷 484-505页

作者： Chatterjee, Tanmoy Chakraborty, Souvik Chowdhury, Rajib Indian Inst Technol Roorkee Dept Civil Engn Roorkee 247667 Uttar Pradesh India

Frequency response functions (FRFs) are considered to be a significant aspect in the evaluation of structural response subjected to dynamic loading. A new approach, referred to as the hybrid polynomial correlated function expansion (H-PCFE) has been developed for predicting the natural frequencies and the FRF of stochastic dynamical systems. H-PCFE has been developed by incorporating the advantages of two available techniques namely, PCFE and Gaussian process (GP) modeling. These two methods are coupled in such a way that PCFE handles the global behavior of the model using a set of component functions and GP interpolates local variations as a function of the sample points, performing as a two level approximation. Implementation of the proposed approach for stochastic dynamic problems has been demonstrated with four problems. The main focus of this study lies in the prediction of FRFs. The efficiency and accuracy of H-PCFE to compute FRFs of stochastic dynamic systems is assessed by a comparison with direct Monte Carlo simulation (MCS). Excellent results in terms of accuracy and computational effort obtained makes the proposed methodology potential for application in large scale structural applications. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Hybrid PCFE Frequency response function Stochastic dynamics Gaussian process homotopy algorithm

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Assessment of polynomial correlated function expansion for high-fidelity structural reliability analysis

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STRUCTURAL SAFETY 2016年 59卷 9-19页

作者： Chakraborty, Souvik Chowdhury, Rajib Indian Inst Technol Roorkee Dept Civil Engneering Roorkee Uttar Pradesh India

Accurate prediction of failure probability of a given structural system subjected to parametric uncertainty often leads to a computationally challenging process requiring considerable amount of time. To overcome this issue, it is advantageous to develop non-intrusive model, that approximates the system response and perform all subsequent operations on the developed model. This paper presents a novel non-intrusive algorithm, referred to as polynomial correlated function expansion (PCFE), for high-fidelity reliability analysis. The proposed method expresses the output in a hierarchical order of component functions which facilitate (i) expressing the component functions in term of extended bases, (ii) determination of actual responses at quasi-random sample points, (iii) determination of the unknown coefficients associated with the bases by employing homotopy algorithm and (iv) Monte Carlo simulation. PCFE decouples the stochastic computations and finite element (FE) computations, and consecutively the FE code can be treated as a black box, as in the case of a commercial software. Six numerical problems, involving explicit performance functions and real-life problems described by implicit limit-state functions, have been solved to illustrate the performance of the proposed approach. It is observed that PCFE outperforms the existing approaches. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Polynomial correlated function expansion homotopy algorithm Failure probability High-fidelity Sobol's sequence Stochastic computation

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A semi-analytical framework for structural reliability analysis

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2015年第Jun.1期289卷 475-497页

作者： Chakraborty, Souvik Chowdhury, Rajib Indian Inst Technol Roorkee Dept Civil Engn Roorkee Uttar Pradesh India

Estimation of the probability of failure of structural systems can often be computationally intensive and time consuming. Hence, alternative techniques for efficient computation of the probability of failure of complex structures while retaining the accuracy is of paramount importance to structural engineering community. This paper presents a semi-analytical approach for computing failure probability of structure. The proposed approach utilizes (i) polynomial correlated function expansion, a novel surrogate modelling technique, to determine the moments and (ii) maximum entropy method to determine an analytical expression for the response probability density function (PDF). Once the analytical expression for the PDF is obtained, failure probability is calculated by numerically integrating the PDF in the failure domain. As a special case, when only the first two moments of response are considered, an analytical formula for the probability of failure is also proposed. Four structural engineering problems are shown to illustrate the performance of the proposed approach. It is observed that the proposed approach outperforms other existing approaches. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Maximum entropy method Polynomial correlated function expansion Probability of failure homotopy algorithm Stochastic computation

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A Survey of Sparse Representation: algorithms and Applications

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IEEE ACCESS 2015年 3卷 490-530页

作者： Zhang, Zheng Xu, Yong Yang, Jian Li, Xuelong Zhang, David Harbin Inst Technol Shenzhen Grad Sch Biocomp Res Ctr Shenzhen 518055 Peoples R China Key Lab Network Oriented Intelligent Computat Shenzhen 518055 Peoples R China Nanjing Univ Sci & Technol Coll Comp Sci & Technol Nanjing 210094 Jiangsu Peoples R China Chinese Acad Sci Xian Inst Opt & Precis Mech Ctr Opt Imagery Anal & Learning State Key Lab Transient Opt & Photon Xian 710119 Shaanxi Peoples R China Hong Kong Polytech Univ Biometr Res Ctr Hong Kong Hong Kong Peoples R China

Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision, and pattern recognition. Sparse representation also has a good reputation in both theoretical research and practical applications. Many different algorithms have been proposed for sparse representation. The main purpose of this paper is to provide a comprehensive study and an updated review on sparse representation and to supply guidance for researchers. The taxonomy of sparse representation methods can be studied from various viewpoints. For example, in terms of different norm minimizations used in sparsity constraints, the methods can be roughly categorized into five groups: 1) sparse representation with L-0-norm minimization;2) sparse representation with L-p-norm (0 < p < 1) minimization;3) sparse representation with L-1-norm minimization;4) sparse representation with 12,1-norm minimization;and 5) sparse representation with 12-norm minimization. In this paper, a comprehensive overview of sparse representation is provided. The available sparse representation algorithms can also be empirically categorized into four groups: 1) greedy strategy approximation;2) constrained optimization;3) proximity algorithm-based optimization;and 4) homotopy algorithm-based sparse representation. The rationales of different algorithms in each category are analyzed and a wide range of sparse representation applications are summarized, which could sufficiently reveal the potential nature of the sparse representation theory. In particular, an experimentally comparative study of these sparse representation algorithms was presented.

关键词： Sparse representation compressive sensing greedy algorithm constrained optimization proximal algorithm homotopy algorithm dictionary learning

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Polynomial Correlated Function Expansion for Nonlinear Stochastic Dynamic Analysis

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JOURNAL OF ENGINEERING MECHANICS 2015年第3期141卷 04014132-04014132页

作者： Chakraborty, Souvik Chowdhury, Rajib Indian Inst Technol Dept Civil Engn Roorkee 247667 Uttar Pradesh India

A new computational tool, referred to as the polynomial correlated function expansion (PCFE), has been developed for predicting response statistics of nonlinear stochastic dynamic problems. This method facilitates a systematic mapping between the input and output by expressing the output as a ranked order of component functions, with higher-order component functions representing higher-order cooperative effects. The component functions are expressed in terms of extended bases, and the unknown coefficients associated with the basis are determined by using a homotopy algorithm. This algorithm considers the hierarchical orthogonality of the component functions as a constraint and determines the coefficients associated with the basis. Implementation of the proposed approach for nonlinear stochastic dynamic problems has been demonstrated with three numerical problems. Results obtained certify the accuracy of the proposed method. Furthermore, the proposed approach significantly reduces the number of calls to the partial differential equation solver, as observed in the numerical problems. (C) 2014 American Society of Civil Engineers.

关键词： Polynomial correlated function expansion (PCFE) homotopy algorithm Sobol sequence Sampling Nonlinear dynamics Stochastic computation

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A Homotopic algorithm of NN and its Application for the End-Point Prediction Model of BOF Process

A Homotopic Algorithm of NN and its Application for the End-...

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International Conference on Advances in Materials Science and Information Technologies in Industry (AMSITI)

作者： Feng, Mingxia Chen, Ren Li, Qiang LiaoNing Inst Sci & Technol Met Engn Coll Benxi 117004 Peoples R China

ISBN: (纸本)9783038350125

A Homotopic BI neural network model is developed by combining the homotopy theory and the BI neural network model, to improve the defects of the steepest gradient descent algorithm itself, such as low speed converging and liable to be trapped in local minimum. The end-point carbon content and temperature of molten steel in BOF smelting process is predicted by the proposed model and the original. Result shows that the precision of new model is improved significantly. The hit rates are increased by about 5% and 10%, and the forecasting residuals have decreased 16.31% and 8.67% than the conventional ones, respectively. Also, the calculation time of the new model is 10% shorter than BI model.

关键词： homotopy algorithm Non-linear End-Point Prediction Model Neural Network

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Total Harmonic Reduction Using Switching Frequency in H-bridge Cascaded Multilevel Inverter

Total Harmonic Reduction Using Switching Frequency in H-brid...

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2nd International Conference on Mechanics and Control Engineering (ICMCE 2013)

作者： Dhal, P. K. Rajan, C. Christober Asir VelTech DR RR & DR SR Tech Univ Dept Elect & Elect Engn Madras 62 Tamil Nadu India Pondicherry Engn Coll Dept Elect & Elect Engn Pondicherry India

ISBN: (纸本)9783037859087

This paper presents total harmonics elimination in H-bridge Multi-Level Inverter. The basic concept of this reduction is to eliminate harmonics in different level with an appropriate choice of switching angles. This paper employs homotopy algorithm to solve the transcendental equations for finding the switching angles. This method solves the nonlinear transcendental equations. It is much simpler formulation without complex analytical calculations for any number of voltage levels. In this technique, it is not required transformer allows the use of a single dc power source (e.g., a battery or a fuel cell stack) with the remaining n 1 de sources being capacitors, which is referred to as hybrid cascaded H-bridge multilevel inverter (HCMLI). It has several informative Mat lab simulation results verify the validity and effectiveness of the proposed algorithm.

关键词： H-bridge multilevel inverter Harmonic elimination homotopy algorithm

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A GLOBALLY CONVERGENT PROBABILITY-ONE homotopy FOR LINEAR PROGRAMS WITH LINEAR COMPLEMENTARITY CONSTRAINTS

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SIAM JOURNAL ON OPTIMIZATION 2013年第2期23卷 1167-1188页

作者： Watson, Layne T. Billups, Stephen C. Mitchell, John E. Easterling, David R. Virginia Polytech Inst & State Univ Dept Comp Sci Blacksburg VA 24061 USA Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA Univ Colorado Dept Math Denver CO 80217 USA Rensselaer Polytech Inst Dept Math Sci Troy NY 12180 USA

A solution of the standard formulation of a linear program with linear complementarity constraints (LPCC) does not satisfy a constraint qualification. A family of relaxations of an LPCC, associated with a probability-one homotopy map, proposed here is shown to have several desirable properties. The homotopy map is nonlinear, replacing all the constraints with nonlinear relaxations of NCP functions. Under mild existence and rank assumptions, (1) the LPCC relaxations RLPCC(lambda) have a solution for 0 <= lambda <= 1;(2) RLPCC(1) is equivalent to LPCC;(3) the Kuhn-Tucker constraint qualification is satisfied at every local or global solution of RLPCC(lambda) for almost all 0 <= lambda < 1;(4) a point is a local solution of RLPCC(1) (and LPCC) if and only if it is a Kuhn-Tucker point for RLPCC(1);and (5) a homotopy algorithm can find a Kuhn-Tucker point for RLPCC(1). Since the homotopy map is a globally convergent probability-one homotopy, robust and efficient numerical algorithms exist to find solutions of RLPCC(1). Numerical results are included for some small problems.

关键词： complementarity constraint qualification globally convergent homotopy algorithm linear program probability-one homotopy

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