With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival (TDOAs) and gain ratios of arrival (GROAs), an effi...With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival (TDOAs) and gain ratios of arrival (GROAs), an efficient algorithm for estimating the position is proposed, which exploits the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method to solve nonlinear equations at the source location under the additive measurement error. Although the accuracy of two-step weighted-least-square (WLS) method based on TDOAs and GROAs is very high, this method has a high computational complexity. While the proposed approach can achieve the same accuracy and bias with the lower computational complexity when the signal-to-noise ratio (SNR) is high, especially it can achieve better accuracy and smaller bias at a lower SNR. The proposed algorithm can be applied to the actual environment due to its real-time property and good robust performance. Simulation results show that with a good initial guess to begin with, the proposed estimator converges to the true solution and achieves the Cramer-Rao lower bound (CRLB) accuracy for both near-field and far-field sources.展开更多
The paper presents the Quasi Newton model of Artificial Neural Network for design of circular microstrip antenna (MSA). In this model, a closed form expression is used for accurate determination of the resonant freque...The paper presents the Quasi Newton model of Artificial Neural Network for design of circular microstrip antenna (MSA). In this model, a closed form expression is used for accurate determination of the resonant frequency of circular microstrip patch antenna. The calculated resonant frequency results are in good agreement with the experimental results reported elsewhere. The results show better agreement with the trained and tested data of ANN models. The results are verified by the experimental results to produce accurate ANN models. This presents ANN model practically as an alternative method to the detailed electromagnetic design of circular microstrip antenna.展开更多
In this paper, a switching method for unconstrained minimization is proposed. The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified upd...In this paper, a switching method for unconstrained minimization is proposed. The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified updates are evaluated and used in the switching rule. When the condition number of the modified SR1 update is superior to the modified BFGS update, the step in the proposed quasi-Newton method is the modified SR1 step. Otherwise the step is the modified BFGS step. The efficiency of the proposed method is tested by numerical experiments on small, medium and large scale optimization. The numerical results are reported and analyzed to show the superiority of the proposed method.展开更多
Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improv...Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment (DA) method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method (0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively). In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel's design contour is less than 1 mm. Finally, the iterations with different mesh sizes (40 mm, 35 mm, 30 mm, 25 mm, 20 mm) in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.展开更多
In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinea...In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems (with same stiffness matrix but different right-hand side) on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.展开更多
Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are comp...Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithmetic cores, field programmable gate array(FPGA) has become an attractive alternative to the acceleration of scientific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton(DFP-QN) method by proposing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.展开更多
We tested and modified the quasi-analytical algorithm (QAA) using 57 groups of field data collected in the spring of 2003 in the Yellow Sea and East China Sea. The QAA performs well in deriving total absorption coeffi...We tested and modified the quasi-analytical algorithm (QAA) using 57 groups of field data collected in the spring of 2003 in the Yellow Sea and East China Sea. The QAA performs well in deriving total absorption coefficients of typical coastal waters. The average percentage difference (APD) is in a range of 13.9%–38.5% for the total absorption coefficient (13.9% at 440 nm), and differences in particle backscattering coefficient bbp(λ) are less than 50% (in the case of the updated QAA). To obtain improved results, we modified the QAA by adjusting the empirical relationships. The modified algorithm is then applied to the field data to test its performance. The APDs were 44.7%–46.6% for bbp(λ) and 9.9%–32.8% (9.9% at 555 nm) for the total absorption coefficient. This indicates that the modified QAA derives better results. We also used the modified model to derive phytoplankton pigment absorption (aph) and detritus and CDOM absorption (adg) coefficients. The APDs for aph and adg at 440 nm are 37.1% and 19.8%. In this paper, we discuss error sources using the measured dataset. More independent field data can improve this algorithm and derive better results.展开更多
The purpose of this article is to propose a new hybrid projection method for a quasi-nonexpansive mapping. The strong convergence of the algorithm is proved in real Hilbert spaces. A numerical experiment is also inclu...The purpose of this article is to propose a new hybrid projection method for a quasi-nonexpansive mapping. The strong convergence of the algorithm is proved in real Hilbert spaces. A numerical experiment is also included to explain the effectiveness of the proposed methods. The results of this paper are interesting extensions of those known results.展开更多
In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the ...In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.展开更多
The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. ...The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn't hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle's invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.展开更多
A quasi physical algorithm was proposed for solving the linear separation problem of point set in n dimensional space.The original idea of the quasi physical algorithm is to find an equivalent physical world for the p...A quasi physical algorithm was proposed for solving the linear separation problem of point set in n dimensional space.The original idea of the quasi physical algorithm is to find an equivalent physical world for the primitive mathematical problem and to observe the vivid images of the motion of matter in it so as to be inspired to obtain an algorithm for solving the mathematical problem. In this work, the electrostatics with two kinds of matter is found to be the equivalent physical world. As a result,the proposed algorithm is evidently more efficient and robust than the famous LMS algorithm and ETL algorithm. The efficiency of the quasi physical algorithm is about 10-50 times of the LMS algorithm’s for representative instances. A typical Boolean valued instance shows that it is hard for ETL algorithm but very easy for the quasi physical algorithm.In this instance, point set A and B is {000, 010, 011, 111} and {001,100}, respectively.展开更多
An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are mad...An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.展开更多
Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability...Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability. In this paper, we propose to inject distributed power generation into a distribution system while minimizing active energy losses. This injection should be done at a grid node (which is a point where energy can be injected into or recovered from the grid) that will be considered the optimal node when total active losses in the radial distribution system are minimal. The focus is on meeting energy demand using renewable energy sources. The main criterion is the minimization of active energy losses during injection. The method used is the algorithm of bee colony (ABC) associated with Newtonian energy flow transfer equations. The method has been implemented in MATLAB for optimal node search in IEEE 14, 33 and 57 nodes networks. The active energy loss results of this hybrid algorithm were compared with the results of previous searches. This comparison shows that the proposed algorithm allows to have reduced losses with the power injected that we have found.展开更多
A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly ...A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly in the heavy part in- dustry,where the resulting casting size and shape may deviate from expectations,the balancing process discovers whether or not the design model is totally enclosed in the actual part to be machined.The alignment is an iterative process involving nonlinear con- strained optimization,which forces data points to lie outside the nominal model under a specific order of priority.Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing.In this paper, Newton methods are applied to the balancing of blank part.The aforesaid algorithm is demonstrated in term of a marine propeller blade,and result shows that The Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods widely used today.展开更多
基金supported by the Major National Science&Technology Projects(2010ZX03006-002-04)the National Natural Science Foundation of China(61072070)+4 种基金the Doctorial Programs Foundation of the Ministry of Education(20110203110011)the"111 Project"(B08038)the Fundamental Research Funds of the Ministry of Education(72124338)the Key Programs for Natural Science Foundation of Shanxi Province(2012JZ8002)the Foundation of State Key Laboratory of Integrated Services Networks(ISN1101002)
文摘With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival (TDOAs) and gain ratios of arrival (GROAs), an efficient algorithm for estimating the position is proposed, which exploits the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method to solve nonlinear equations at the source location under the additive measurement error. Although the accuracy of two-step weighted-least-square (WLS) method based on TDOAs and GROAs is very high, this method has a high computational complexity. While the proposed approach can achieve the same accuracy and bias with the lower computational complexity when the signal-to-noise ratio (SNR) is high, especially it can achieve better accuracy and smaller bias at a lower SNR. The proposed algorithm can be applied to the actual environment due to its real-time property and good robust performance. Simulation results show that with a good initial guess to begin with, the proposed estimator converges to the true solution and achieves the Cramer-Rao lower bound (CRLB) accuracy for both near-field and far-field sources.
文摘The paper presents the Quasi Newton model of Artificial Neural Network for design of circular microstrip antenna (MSA). In this model, a closed form expression is used for accurate determination of the resonant frequency of circular microstrip patch antenna. The calculated resonant frequency results are in good agreement with the experimental results reported elsewhere. The results show better agreement with the trained and tested data of ANN models. The results are verified by the experimental results to produce accurate ANN models. This presents ANN model practically as an alternative method to the detailed electromagnetic design of circular microstrip antenna.
基金This work is supported by National Natural Key product Foundations of China 10231060.
文摘In this paper, a switching method for unconstrained minimization is proposed. The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified updates are evaluated and used in the switching rule. When the condition number of the modified SR1 update is superior to the modified BFGS update, the step in the proposed quasi-Newton method is the modified SR1 step. Otherwise the step is the modified BFGS step. The efficiency of the proposed method is tested by numerical experiments on small, medium and large scale optimization. The numerical results are reported and analyzed to show the superiority of the proposed method.
文摘Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment (DA) method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method (0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively). In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel's design contour is less than 1 mm. Finally, the iterations with different mesh sizes (40 mm, 35 mm, 30 mm, 25 mm, 20 mm) in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.
基金supported by National Foundation of Natural Science under the Grant 11071216
文摘In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems (with same stiffness matrix but different right-hand side) on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.
基金Supported by the National Natural Science Foundation of China(No.61574099)
文摘Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithmetic cores, field programmable gate array(FPGA) has become an attractive alternative to the acceleration of scientific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton(DFP-QN) method by proposing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.
基金Supported by the National Natural Science Foundation of China (Nos.40706060,60802089)the National High Technology Research and Development Program of China (863 Program) (No.2007AA092102)the Dragon Project (No.5292)
文摘We tested and modified the quasi-analytical algorithm (QAA) using 57 groups of field data collected in the spring of 2003 in the Yellow Sea and East China Sea. The QAA performs well in deriving total absorption coefficients of typical coastal waters. The average percentage difference (APD) is in a range of 13.9%–38.5% for the total absorption coefficient (13.9% at 440 nm), and differences in particle backscattering coefficient bbp(λ) are less than 50% (in the case of the updated QAA). To obtain improved results, we modified the QAA by adjusting the empirical relationships. The modified algorithm is then applied to the field data to test its performance. The APDs were 44.7%–46.6% for bbp(λ) and 9.9%–32.8% (9.9% at 555 nm) for the total absorption coefficient. This indicates that the modified QAA derives better results. We also used the modified model to derive phytoplankton pigment absorption (aph) and detritus and CDOM absorption (adg) coefficients. The APDs for aph and adg at 440 nm are 37.1% and 19.8%. In this paper, we discuss error sources using the measured dataset. More independent field data can improve this algorithm and derive better results.
基金The NSF(11071053)of ChinaNatural Science Basic Research Plan(2014JM2-1003)in Shaanxi Province of ChinaScientific Research Project(YD2016-12)of Yan’an University
文摘The purpose of this article is to propose a new hybrid projection method for a quasi-nonexpansive mapping. The strong convergence of the algorithm is proved in real Hilbert spaces. A numerical experiment is also included to explain the effectiveness of the proposed methods. The results of this paper are interesting extensions of those known results.
文摘In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.
基金supported in part by the National Outstanding Youth Foundation of P.R.China (60525303)the National Natural Science Foundation of P.R.China(60404022,60604004)+2 种基金the Natural Science Foundation of Hebei Province (102160)the special projects in mathematics funded by the Natural Science Foundation of Hebei Province(07M005)the NS of Education Office in Hebei Province (2004123).
文摘The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn't hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle's invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.
基金TheNationalKeyBasicResearchProgram (973) (No .G 19980 30 6 0 0 )
文摘A quasi physical algorithm was proposed for solving the linear separation problem of point set in n dimensional space.The original idea of the quasi physical algorithm is to find an equivalent physical world for the primitive mathematical problem and to observe the vivid images of the motion of matter in it so as to be inspired to obtain an algorithm for solving the mathematical problem. In this work, the electrostatics with two kinds of matter is found to be the equivalent physical world. As a result,the proposed algorithm is evidently more efficient and robust than the famous LMS algorithm and ETL algorithm. The efficiency of the quasi physical algorithm is about 10-50 times of the LMS algorithm’s for representative instances. A typical Boolean valued instance shows that it is hard for ETL algorithm but very easy for the quasi physical algorithm.In this instance, point set A and B is {000, 010, 011, 111} and {001,100}, respectively.
基金Project (2002CB312200) supported by the National Key Basic Research and Development Program of China Project(03JJY3109) supported by the Natural Science Foundation of Hunan Province
文摘An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.
文摘Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability. In this paper, we propose to inject distributed power generation into a distribution system while minimizing active energy losses. This injection should be done at a grid node (which is a point where energy can be injected into or recovered from the grid) that will be considered the optimal node when total active losses in the radial distribution system are minimal. The focus is on meeting energy demand using renewable energy sources. The main criterion is the minimization of active energy losses during injection. The method used is the algorithm of bee colony (ABC) associated with Newtonian energy flow transfer equations. The method has been implemented in MATLAB for optimal node search in IEEE 14, 33 and 57 nodes networks. The active energy loss results of this hybrid algorithm were compared with the results of previous searches. This comparison shows that the proposed algorithm allows to have reduced losses with the power injected that we have found.
文摘A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly in the heavy part in- dustry,where the resulting casting size and shape may deviate from expectations,the balancing process discovers whether or not the design model is totally enclosed in the actual part to be machined.The alignment is an iterative process involving nonlinear con- strained optimization,which forces data points to lie outside the nominal model under a specific order of priority.Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing.In this paper, Newton methods are applied to the balancing of blank part.The aforesaid algorithm is demonstrated in term of a marine propeller blade,and result shows that The Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods widely used today.