Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured...Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.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
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
An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors...An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.展开更多
We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.
The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI). Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI, based on t...The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI). Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI, based on the assumption that a well-defined physiological signal which also has a smooth form "hides" inside the noisy EEG signal, a Quasi-Newton-SVM recognition method based on Quasi-Newton method and SVM algorithm was presented. Firstly, the EEG signals were preprocessed by Quasi-Newton method and got the signals which were fit for SVM. Secondly, the preprocessed signals were classified by SVM method. The present simulation results indicated the Quasi-Newton-SVM approach improved the recognition rate compared with using SVM method; we also discussed the relationship between the artificial smooth signals and the classification errors.展开更多
ΔF-N curves are usually used to predict the fatigue life of spot welding in engineering,but they are time-consuming and laborious and not universal.For the purpose of predicting the fatigue life of spot welding accur...ΔF-N curves are usually used to predict the fatigue life of spot welding in engineering,but they are time-consuming and laborious and not universal.For the purpose of predicting the fatigue life of spot welding accurately and efficiently,tensile-shear fatigue tests were conducted to obtain the fatigue life of spot-welded specimens with different sheet thicknesses combinations.These specimens were simulated by using the finite element method,and the structural stress was theoretically calculated.In the double logarithmic coordinate system,the structural stress-fatigue life(S-N)curve of spot welding was fitted by the least-squares method,based on the quasi-Newton method.The square of the correlation coefficient of the S-N curve was taken as the optimization objective,with the correction coefficients of force,bending moment,spot welding diameter,and sheet thickness as the variables.During the optimization process,three different ways were utilized to get three optimized spot welding S-N curves,which are suitable for different situations.The results show that the fitting effect of the S-N curve is improved,the data points are more compact,and the optimization effect is significant.These S-N curves can be used to predict the fatigue life,which provide the basis for practical engineering application.展开更多
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
To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method a...To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.展开更多
Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and i...Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.展开更多
In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, ...In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.展开更多
基金financially supported by the National Natural Science Foundation of China(No.41774125)Key Program of National Natural Science Foundation of China(No.41530320)+1 种基金the Key National Research Project of China(Nos.2016YFC0303100 and 2017YFC0601900)the Strategic Priority Research Program of Chinese Academy of Sciences Pilot Special(No.XDA 14020102)
文摘Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.
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.
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.
基金Project supported by the National Natural Science Foundation of China (No. 10372014).
文摘An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.
文摘We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.
基金The paper was supported by Jiangsu Education Nature Foundation(06KJD310050,06KJB520022)
文摘The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI). Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI, based on the assumption that a well-defined physiological signal which also has a smooth form "hides" inside the noisy EEG signal, a Quasi-Newton-SVM recognition method based on Quasi-Newton method and SVM algorithm was presented. Firstly, the EEG signals were preprocessed by Quasi-Newton method and got the signals which were fit for SVM. Secondly, the preprocessed signals were classified by SVM method. The present simulation results indicated the Quasi-Newton-SVM approach improved the recognition rate compared with using SVM method; we also discussed the relationship between the artificial smooth signals and the classification errors.
基金Supported by National Natural Science Foundation of China(Grant Nos.U1534209,51675446)Independent Subject of State Key Laboratory of Traction Power(Grant No.2019TPL-T13).
文摘ΔF-N curves are usually used to predict the fatigue life of spot welding in engineering,but they are time-consuming and laborious and not universal.For the purpose of predicting the fatigue life of spot welding accurately and efficiently,tensile-shear fatigue tests were conducted to obtain the fatigue life of spot-welded specimens with different sheet thicknesses combinations.These specimens were simulated by using the finite element method,and the structural stress was theoretically calculated.In the double logarithmic coordinate system,the structural stress-fatigue life(S-N)curve of spot welding was fitted by the least-squares method,based on the quasi-Newton method.The square of the correlation coefficient of the S-N curve was taken as the optimization objective,with the correction coefficients of force,bending moment,spot welding diameter,and sheet thickness as the variables.During the optimization process,three different ways were utilized to get three optimized spot welding S-N curves,which are suitable for different situations.The results show that the fitting effect of the S-N curve is improved,the data points are more compact,and the optimization effect is significant.These S-N curves can be used to predict the fatigue life,which provide the basis for practical engineering application.
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.
基金Supported by the National High Technology Research and Development Programme of China ( No. 2007AA041901 )the National Natural Science Foundation of China ( No. 50775117 )+1 种基金the National S&T Major Project ( No. 2009XZ04001-025 )the Technology Innovation Fund of AVIC ( No.2009E 13224 )
文摘To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.
基金supported by the National Natural Science Foundation of China(Grant No.NSFC-11971118).
文摘Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.
基金Foundation item： the National Natural Science Foundation of China （No. 60472071） the Science Foundation of Beijing Municipal Commission of Education （No. KM200710028001）.
文摘In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.
