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An improved hybrid-ORBIT algorithm based on point sorting and MLE technique

COMPUTATIONAL & APPLIED MATHEMATICS 2019年第4期38卷 1-20页

作者： Ahmadvand, Mohammad Esmaeilbeigi, Mohsen Kamandi, Ahmad Yaghoobi, Farajollah Mohammadi Islamic Azad Univ Hamedan Branch Dept Math Coll Basic Sci Hamadan Iran Malayer Univ Fac Math Sci Malayer Iran Univ Sci & Technol Mazandaran Fac Math Sci Behshahr Iran

Optimization using radial basis functions as an interpolation tool in trust region (ORBIT) is a derivative-free framework based on fully linear radial basis function (RBF) models. In this paper, an improved version of ORBIT algorithm based on two novel ideas is proposed. The accuracy and stability of RBFs depend on a so-called shape parameter, so it is more appropriate to determine the shape parameter according to the optimization problem. While ORBIT in all problems uses a fixed value as a shape parameter, our new version, Hybrid-ORBIT, uses a statistical technique to select an appropriate shape parameter. In addition, ORBIT uses some stored points to build a fully linear RBF model without considering their function values, while in the Hybrid-ORBIT algorithm the stored points are sorted based on their function values and the RBF model is built using the points with lower function values, and the best point in the sense of function value is defined as the trust-region center. Numerical results indicate the efficiency of the improved version compared with the original version.

关键词： Unconstrained optimization trust-region algorithm Radial basis function Maximum likelihood estimation Point sorting Center changing

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High Resolution ToA Estimation via Optimal Waveform Design

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IEEE TRANSACTIONS ON COMMUNICATIONS 2017年第3期65卷 1207-1218页

作者： Jamalabdollahi, Mohsen Zekavat, Seyed (Reza) Michigan Technol Univ Dept Elect & Comp Engn Houghton MI 49930 USA

This paper introduces a novel method to improve the Time of Arrival (ToA) estimation resolution for a fixed available bandwidth in the presence of unknown multipath frequency selective (MPFS) channels. Here, the maximum rising level detector technique is proposed which utilizes oversampling and multiple correlation paths to evaluate with high resolution the path corresponding to the maximum rising level of matched filters output. However, employing such technique demands for transmission of waveform that creates a very high rising level at autocorrelation center. This paper proposes an efficient technique to design proper waveforms (very high rising level at autocorrelation center) via minimization of weighted integrated sidelobe level, exploiting the trust-region algorithm. The performance of the proposed technique is evaluated via simulations of the ToA mean square error, and compared with the state-of-the-art approaches considering the same bandwidth, and Cramer-Rao lower bound as benchmark. Simulations confirm that the ToA resolution is improved as the number of correlation paths increases and verify the feasibility of the proposed technique compared with the available approaches for the MPFS channels.

关键词： Time-of-arrival matched-filter autocorrelation integrated sidelobe level trust-region algorithm waveform

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Structural damage identification using an optimization technique based on generalized flexibility matrix

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JOURNAL OF MECHANICS 2024年第40期40卷 10-17页

作者： Gao, Qianhui Li, Zhu Yu, Yongping Zheng, Shaopeng Jilin Univ Coll Construct Engn Changchun Peoples R China

A generalized flexibility matrix-based objective function utilized for structure damage identification is firstly constructed. After transforming the damage identification into a constrained nonlinear least squares optimization problem, the trust-region algorithm is applied to find the solution of the inverse problem in multiple damage cases. Thereinto, the sensitivity analysis of the objective function with respect to the design variables is derived using the Nelson's method. At last, two numerical examples with several damage cases are investigated, including a steel truss bridge model as well as a drilling rig derrick model. Based on the computational results, it is evident that the presented approach provides excellent validity and reliability for the large and complicated engineering structures.

关键词： generalized flexibility matrix damage identification constrained nonlinear least squares trust-region algorithm

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A numerical approach to solve an inverse problem in lubrication theory

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2014年第2期108卷 617-631页

作者： Lombera, Hassan Ignacio Tello, J. Univ Comp Sci Fac 5 Ctr Comp Sci Appl Ind Havana 19370 Cuba Univ Politecn Madrid EUI Informat Madrid 28031 Spain

In this paper we consider a numerical approach to reach the equilibrium position of a journal bearing with radial loading. The system consists of an external cylinder surrounding a rotating shaft. The problem is modelled by the hydrodynamic Reynolds equation with a cavitation model of Elrod-Adams. Both equations are coupled to Newton's second law which describes the position of the shaft. The problem is considered as an inverse problem where the coefficient of the equation is unknown. The numerical approach to solve the inverse problem is based on a trust-region algorithm along with the finite element method. The Heaviside function in the Elrod-Adams equation is approximated by a third order Hermite polynomial. The trust-region algorithm for solving the inverse problem showed another way of solution, different from the ones that exist at this moment.

关键词： Cavitation Elrod-Adams model Finite element method Inverse problem Journal bearing trust-region algorithm

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An efficient and accurate method for the relaxation of multiview registration error

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2008年第6期17卷 968-981页

作者： Shih, Sheng-Wen Chuang, Yao-Tung Yu, Tzu-Yi Natl Chi Nan Univ Dept Comp Sci & Informat Engn Puli 54561 Nantou Taiwan Natl Chi Nan Univ Dept Informat Management Puli 54561 Nantou Taiwan

This paper presents a new method for the relaxation of multiview registration error. The multiview registration problem is represented using a graph. Each node and each edge in the graph represents a 3-D data set and a pairwise registration, respectively. Assuming that all the pairwise registration processes have converged to fine results, this paper shows that the multiview registration problem can be converted into a quadratic programming problem of Lie algebra parameters. The constraints are obtained from every cycle of the graph to eliminate the accumulation errors of global registration. A linear solution is proposed to distribute the accumulation error to proper positions in the graph, as specified by the quadratic model. Since the proposed method does not involve the original 3-D data, it has low time and space complexity. Additionally, the proposed method can be embedded into a trust-region algorithm and, thus, can correctly handle the nonlinear effects of large accumulation errors, while preserving the global convergence property to the first-order critical point. Experimental results confirm both the efficiency and the accuracy of the proposed method.

关键词： equivalent circuit model Lie algebra Lie group multiview registration range image 3-D registration trust-region algorithm

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Packing Ellipsoids with Overlap

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SIAM REVIEW 2013年第4期55卷 671-706页

作者： Uhler, Caroline Wright, Stephen J. IST Austria A-3400 Klosterneuburg Austria Univ Wisconsin Dept Comp Sci Madison WI 53706 USA

The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. Convergence results are proved and computational experience is described and illustrated. The motivating application-chromosome organization in the human cell nucleus-is discussed briefly, and some illustrative results are presented.

关键词： ellipsoid packing trust-region algorithm semidefinite programming chromosome territories

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Magnetic resonance tissue quantification using optimal bSSFP pulse-sequence design

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OPTIMIZATION AND ENGINEERING 2007年第2期8卷 215-238页

作者： Anand, Christopher Kumar Sotirov, Renata Terlaky, Tamas Zheng, Zhuo McMaster Univ Dept Comp & Software Hamilton ON L8S 4K1 Canada

We propose a merit function for the expected contrast to noise ratio in tissue quantifications, and formulate a nonlinear, nonconvex semidefinite optimization problem to select locally-optimal balanced steady-state free precession (bSSFP) pulse-sequence design variables. The method could be applied to other pulse sequence types, arbitrary numbers of tissues, and numbers of images. To solve the problem we use a mixture of a grid search to get good starting points, and a sequential, semidefinite, trust-region method, where the subproblems contain only linear and semidefinite constraints. We give the results of numerical experiments for the case of three tissues and three, four or six images, in which we observe a better increase in contrast to noise than would be obtained by averaging the results of repeated experiments. As an illustration, we show how the pulse sequences designed numerically could be applied to the problem of quantifying intraluminal lipid deposits in the carotid artery.

关键词： magnetic resonance imaging balanced steady-state free precession Dixon method semidefinite programming trust-region algorithm

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Multi-start approach for an integer determinant maximization problem

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OPTIMIZATION 2013年第1期62卷 101-114页

作者： Sotirov, R. Terlaky, T. Tilburg Univ Dept Econometr & Operat Res Tilburg Netherlands Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA

In this article, we present a multi-start approach to solve a determinant maximization problem of an integer matrix variable that has a constant trace. In order to enforce that elements of the matrix variable are integer, we add a nonlinear repeller term to the objective function. To solve this nonlinear optimization problem we implement our sequential conic trust-region-based algorithm within a multi-start framework. To demonstrate the potential of our approach, we use a determinant maximization model from crystallography.

关键词： determinant maximization trust-region algorithm conic optimization multi-start framework 90C22 90C90

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Parameters Estimation of Photovoltaic Module Using Nonlinear Least Square algorithm: A Comparative Study

Parameters Estimation of Photovoltaic Module Using Nonlinear...

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10th Annual Conference of the IEEE-India-Council (INDICON)

作者： Nayak, B. K. Mohapatra, A. Mohanty, K. B. KIIT Univ Sch Elect Engn Bhubaneswar Orissa India NIT Univ Dept Elect Engn Rourkela India

ISBN: (纸本)9781479922741;9781479922758

This paper compares different methods for extraction of photovoltaic (PV) module parameters. Nonlinear least-square method based on trust-region algorithm is proposed here to extract five unknown parameters such as series resistance (R-s), shunt resistance (R-p), diode ideality factor (a), dark saturation current (I-0) and photo-generated current (I-pv) under standard test conditions (STC) of PV module. Comparative analysis has been drawn between the proposed method and two other popular methods such as Villalva's iterative method and modified Newton-Raphson method. The principle of trust-region algorithm is briefly reviewed. Two parameters Rs and Rp are only extracted by Villalva's iterative method whereas all five unknown parameters can be extracted by the proposed method and by modified Newton-Raphson method. The accuracy of estimated parameters depends on tolerance band and initial conditions. The time of computation for parameter extraction of different methods has been compared.

关键词： Single diode PV module Parameter extraction trust-region algorithm nonlinear least square method

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Mathematical Modeling of Human Emotions Using Sub-band Coefficients of Wavelet Analysis 2

Mathematical Modeling of Human Emotions Using Sub-band Coeff...

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2nd International Conference on Electrical Engineering and Information and Communication Technology (ICEEICT)

作者： Islam, Monira Ahmad, Mohiuddin Yusuf, Md Salah Uddin Ahmed, Tazrin KUET Dept Elect & Elect Engn Khulna 9203 Bangladesh

ISBN: (纸本)9781467366762

Human emotion reflects on human behavior which plays a vital role in physiological research and real-time application. Mathematical modeling of emotional states plays a significant role in this scope which can correlate between human cognition, emotion and mental behavior. In this paper, we propose a new approach to model the emotional states with mathematical expressions based on wavelet analysis and trust region algorithm. The brain signals are collected using BIOPAC automated MP36 system and transformed on time-frequency domain using Daubechies4 wavelet function on different emotional states such as relax, memory, pleasant, fear, motor action, and enjoying music to extract the wavelet coefficients of these different states. The emotional states are modeled with different mathematical expressions which can be verified with these wavelet coefficients from the adjusted R-square percentage and the sum of square errors. The adjusted R-square percentage of the mathematical modeled states with the actual emotional states are 78.4% for relax, 77.18% for motor action and for memory, pleasant, enjoying music and fear they are 93%, 95.6%, 97.7% and 91.5% respectively. The main focus of this paper is to propose the mathematical modeling of these states which can be further applied for practical hardware implementation of human emotion based systems.

关键词： discrete wavelet transform EEG emotional state mathematical modeling trust-region algorithm

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