Partial least squares (PLS) model maximizes the covariance between process variables and quality variables,making it widely used in quality-related fault detection.However,traditional PLS methods focus primarily on li...Partial least squares (PLS) model maximizes the covariance between process variables and quality variables,making it widely used in quality-related fault detection.However,traditional PLS methods focus primarily on linear processes,leading to poor performance in dynamic nonlinear processes.In this paper,a novel quality-related fault detection method,named DiCAE-PLS,is developed by combining dynamic-inner convolutional autoencoder with PLS.In the proposed DiCAE-PLS method,latent features are first extracted through dynamic-inner convolutional autoencoder (DiCAE) to capture process dynamics and nonlinearity from process variables.Then,a PLS model is established to build the relationship between the extracted latent features and the final product quality.To detect quality-related faults,Hotelling's T^(2) statistic is employed.The developed quality-related fault detection is applied to the widely used industrial benchmark of the Tennessee.展开更多
A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracki...A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.展开更多
An estimation approach using least squares method was presented for identificationof model parameters of pressure control in shield tunneling.The state equation ofthe pressure control system for shield tunneling was a...An estimation approach using least squares method was presented for identificationof model parameters of pressure control in shield tunneling.The state equation ofthe pressure control system for shield tunneling was analytically derived based on themass equilibrium principle that the entry mass of the pressure chamber from cutting headwas equal to excluding mass from the screw conveyor.The randomly observed noise wasnumerically simulated and mixed to simulated observation values of system responses.The numerical simulation shows that the state equation of the pressure control system forshield tunneling is reasonable and the proposed estimation approach is effective even ifthe random observation noise exists.The robustness of the controlling procedure is validatedby numerical simulation results.展开更多
For geophysical inversion problems,deterministic inversion methods can easily fall into local optimal solutions,while stochastic optimization methods can theoretically converge to global optimal solutions.These proble...For geophysical inversion problems,deterministic inversion methods can easily fall into local optimal solutions,while stochastic optimization methods can theoretically converge to global optimal solutions.These problems have always been a concern for researchers.Among many stochastic optimization methods,particle swarm optimization(PSO)has been applied to solve geophysical inversion problems due to its simple principle and the fact that only a few parameters require adjustment.To overcome the nonuniqueness of inversion,model constraints can be added to PSO optimization.However,using fixed regularization parameters in PSO iteration is equivalent to keeping the default model constraint at a certain level,yielding an inversion result that is considerably affected by the model constraint.This study proposes a hybrid method that combines the regularized least squares method(RLSM)with the PSO method.The RLSM is used to improve the global optimal particle and accelerate convergence,while the adaptive regularization strategy is used to update the regularization parameters to avoid the influence of model constraints on the inversion results.Further,the inversion results of the RLSM and hybrid algorithm are compared and analyzed by considering the audio magnetotelluric synthesis and field data as examples.Experiments show that the proposed hybrid method is superior to the RLSM.Furthermore,compared with the standard PSO algorithm,the hybrid algorithm needs a broader model space but a smaller particle swarm and fewer iteration steps,thus reducing the prior conditions and the computational cost used in the inversion.展开更多
A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems...A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.展开更多
In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering comp...In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.展开更多
The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of t...The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.展开更多
Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics.Inverse surface wave dispersion curves are a crucial step ...Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics.Inverse surface wave dispersion curves are a crucial step in most surface wave methods.Many inversion methods have been applied to surface wave dispersion curve inversion,including linearized inversion and nonlinearized inversion methods.In this study,a hybrid inversion method of Damped Least Squares(DLS) with Very Fast Simulated Annealing(VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion.Both synthetic and in situ fi eld data were used to verify the validity of the proposed method.The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum,especially when parameter searching space is adjacent to real values of the parameters.The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search.At high temperatures,the global search dominates the runs,while at a low temperatures,the local search dominates the runs.Thus,at low temperatures,the proposed method can almost directly approach the actual model.展开更多
The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features becau...The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.展开更多
When the total least squares(TLS)solution is used to solve the parameters in the errors-in-variables(EIV)model,the obtained parameter estimations will be unreliable in the observations containing systematic errors.To ...When the total least squares(TLS)solution is used to solve the parameters in the errors-in-variables(EIV)model,the obtained parameter estimations will be unreliable in the observations containing systematic errors.To solve this problem,we propose to add the nonparametric part(systematic errors)to the partial EIV model,and build the partial EIV model to weaken the influence of systematic errors.Then,having rewritten the model as a nonlinear model,we derive the formula of parameter estimations based on the penalized total least squares criterion.Furthermore,based on the second-order approximation method of precision estimation,we derive the second-order bias and covariance of parameter estimations and calculate the mean square error(MSE).Aiming at the selection of the smoothing factor,we propose to use the U curve method.The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information,which validates the feasibility and effectiveness of the proposed method.展开更多
Consider solving an overdetermined system of linear algebraic equations by both the least squares method (LS) and the total least squares method (TLS). Extensive published computational evidence shows that when the or...Consider solving an overdetermined system of linear algebraic equations by both the least squares method (LS) and the total least squares method (TLS). Extensive published computational evidence shows that when the original system is consistent. one often obtains more accurate solutions by using the TLS method rather than the LS method. These numerical observations contrast with existing analytic perturbation theories for the LS and TLS methods which show that the upper bounds for the LS solution are always smaller than the corresponding upper bounds for the TLS solutions. In this paper we derive a new upper bound for the TLS solution and indicate when the TLS method can be more accurate than the LS method.Many applied problems in signal processing lead to overdetermined systems of linear equations where the matrix and right hand side are determined by the experimental observations (usually in the form of a lime series). It often happens that as the number of columns of the matrix becomes larger, the展开更多
To adapt to the new requirement of the developing flatness control theory and technology,cubic patterns were introduced on the basis of the traditional linear,quadratic and quartic flatness basic patterns.Linear,quadr...To adapt to the new requirement of the developing flatness control theory and technology,cubic patterns were introduced on the basis of the traditional linear,quadratic and quartic flatness basic patterns.Linear,quadratic,cubic and quartic Legendre orthogonal polynomials were adopted to express the flatness basic patterns.In order to over-come the defects live in the existent recognition methods based on fuzzy,neural network and support vector regres-sion(SVR)theory,a novel flatness pattern recognition method based on least squares support vector regression(LS-SVR)was proposed.On this basis,for the purpose of determining the hyper-parameters of LS-SVR effectively and enhan-cing the recognition accuracy and generalization performance of the model,particle swarm optimization algorithm with leave-one-out(LOO)error as fitness function was adopted.To overcome the disadvantage of high computational complexity of naive cross-validation algorithm,a novel fast cross-validation algorithm was introduced to calculate the LOO error of LDSVR.Results of experiments on flatness data calculated by theory and a 900HC cold-rolling mill practically measured flatness signals demonstrate that the proposed approach can distinguish the types and define the magnitudes of the flatness defects effectively with high accuracy,high speed and strong generalization ability.展开更多
A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercriti...A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.展开更多
This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-eliminat...This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.展开更多
Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, co...Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting.展开更多
Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of s...Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.展开更多
A sparse approximation algorithm based on projection is presented in this paper in order to overcome the limitation of the non-sparsity of least squares support vector machines （LS-SVM）. The new inputs are projected...A sparse approximation algorithm based on projection is presented in this paper in order to overcome the limitation of the non-sparsity of least squares support vector machines （LS-SVM）. The new inputs are projected into the subspace spanned by previous basis vectors （BV） and those inputs whose squared distance from the subspace is higher than a threshold are added in the BV set, while others are rejected. This consequently results in the sparse approximation. In addition, a recursive approach to deleting an exiting vector in the BV set is proposed. Then the online LS-SVM, sparse approximation and BV removal are combined to produce the sparse online LS-SVM algorithm that can control the size of memory irrespective of the processed data size. The suggested algorithm is applied in the online modeling of a pH neutralizing process and the isomerization plant of a refinery, respectively. The detailed comparison of computing time and precision is also given between the suggested algorithm and the nonsparse one. The results show that the proposed algorithm greatly improves the sparsity just with little cost of precision.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning ...The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares. In this paper we reconsider the least squares method from the view point of Deep Learning and we carry out the computation thoroughly for the gradient descent sequence in a very simple setting. Depending on the values of the learning rate, an essential parameter of Deep Learning, the least squares methods of Statistics and Deep Learning reveal an interesting difference.展开更多
基金supported in part by the National Natural Science Foundation of China(62573387)the Natural Science Foundation of Zhejiang province,China(LY24F030004)the Fundamental Research Funds of Zhejiang Sci-Tech University(25222139-Y).
文摘Partial least squares (PLS) model maximizes the covariance between process variables and quality variables,making it widely used in quality-related fault detection.However,traditional PLS methods focus primarily on linear processes,leading to poor performance in dynamic nonlinear processes.In this paper,a novel quality-related fault detection method,named DiCAE-PLS,is developed by combining dynamic-inner convolutional autoencoder with PLS.In the proposed DiCAE-PLS method,latent features are first extracted through dynamic-inner convolutional autoencoder (DiCAE) to capture process dynamics and nonlinearity from process variables.Then,a PLS model is established to build the relationship between the extracted latent features and the final product quality.To detect quality-related faults,Hotelling's T^(2) statistic is employed.The developed quality-related fault detection is applied to the widely used industrial benchmark of the Tennessee.
文摘A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.
基金Supported by the National Basic Research Program of China(2007CB714006)the National Natural Science Foundation of China(90815023)
文摘An estimation approach using least squares method was presented for identificationof model parameters of pressure control in shield tunneling.The state equation ofthe pressure control system for shield tunneling was analytically derived based on themass equilibrium principle that the entry mass of the pressure chamber from cutting headwas equal to excluding mass from the screw conveyor.The randomly observed noise wasnumerically simulated and mixed to simulated observation values of system responses.The numerical simulation shows that the state equation of the pressure control system forshield tunneling is reasonable and the proposed estimation approach is effective even ifthe random observation noise exists.The robustness of the controlling procedure is validatedby numerical simulation results.
基金supported by the National Natural Science Foundation of China(NSFC)[grant number 41374133]
文摘For geophysical inversion problems,deterministic inversion methods can easily fall into local optimal solutions,while stochastic optimization methods can theoretically converge to global optimal solutions.These problems have always been a concern for researchers.Among many stochastic optimization methods,particle swarm optimization(PSO)has been applied to solve geophysical inversion problems due to its simple principle and the fact that only a few parameters require adjustment.To overcome the nonuniqueness of inversion,model constraints can be added to PSO optimization.However,using fixed regularization parameters in PSO iteration is equivalent to keeping the default model constraint at a certain level,yielding an inversion result that is considerably affected by the model constraint.This study proposes a hybrid method that combines the regularized least squares method(RLSM)with the PSO method.The RLSM is used to improve the global optimal particle and accelerate convergence,while the adaptive regularization strategy is used to update the regularization parameters to avoid the influence of model constraints on the inversion results.Further,the inversion results of the RLSM and hybrid algorithm are compared and analyzed by considering the audio magnetotelluric synthesis and field data as examples.Experiments show that the proposed hybrid method is superior to the RLSM.Furthermore,compared with the standard PSO algorithm,the hybrid algorithm needs a broader model space but a smaller particle swarm and fewer iteration steps,thus reducing the prior conditions and the computational cost used in the inversion.
基金supported by the National Natural Science Foundation of China (No. 11071033)the Fundamental Research Funds for the Central Universities (No. 090405013)
文摘A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.
文摘In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.
文摘The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.
基金International Science&Technology Cooperation Program of China under Grant No.2011DFA71100the National Key Technology R&D Program under Grant No.2014BAK03B01the National Basic Research Program of China(973 Program)under Grant No.2007CB714201
文摘Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics.Inverse surface wave dispersion curves are a crucial step in most surface wave methods.Many inversion methods have been applied to surface wave dispersion curve inversion,including linearized inversion and nonlinearized inversion methods.In this study,a hybrid inversion method of Damped Least Squares(DLS) with Very Fast Simulated Annealing(VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion.Both synthetic and in situ fi eld data were used to verify the validity of the proposed method.The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum,especially when parameter searching space is adjacent to real values of the parameters.The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search.At high temperatures,the global search dominates the runs,while at a low temperatures,the local search dominates the runs.Thus,at low temperatures,the proposed method can almost directly approach the actual model.
基金This project is supported by Research Foundation for Doctoral Program of Higher Education, China (No.98033532)
文摘The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.
基金supported by the National Natural Science Foundation of China,Nos.41874001 and 41664001Support Program for Outstanding Youth Talents in Jiangxi Province,No.20162BCB23050National Key Research and Development Program,No.2016YFB0501405。
文摘When the total least squares(TLS)solution is used to solve the parameters in the errors-in-variables(EIV)model,the obtained parameter estimations will be unreliable in the observations containing systematic errors.To solve this problem,we propose to add the nonparametric part(systematic errors)to the partial EIV model,and build the partial EIV model to weaken the influence of systematic errors.Then,having rewritten the model as a nonlinear model,we derive the formula of parameter estimations based on the penalized total least squares criterion.Furthermore,based on the second-order approximation method of precision estimation,we derive the second-order bias and covariance of parameter estimations and calculate the mean square error(MSE).Aiming at the selection of the smoothing factor,we propose to use the U curve method.The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information,which validates the feasibility and effectiveness of the proposed method.
基金This author was supported by the National Natural Sciences Foundation,PRC. This author was supported by the Air Force Office of Scientific Research, USA, Grant No. AFOSR-91-0309
文摘Consider solving an overdetermined system of linear algebraic equations by both the least squares method (LS) and the total least squares method (TLS). Extensive published computational evidence shows that when the original system is consistent. one often obtains more accurate solutions by using the TLS method rather than the LS method. These numerical observations contrast with existing analytic perturbation theories for the LS and TLS methods which show that the upper bounds for the LS solution are always smaller than the corresponding upper bounds for the TLS solutions. In this paper we derive a new upper bound for the TLS solution and indicate when the TLS method can be more accurate than the LS method.Many applied problems in signal processing lead to overdetermined systems of linear equations where the matrix and right hand side are determined by the experimental observations (usually in the form of a lime series). It often happens that as the number of columns of the matrix becomes larger, the
基金Sponsored by National Natural Science Foundation of China(50675186)
文摘To adapt to the new requirement of the developing flatness control theory and technology,cubic patterns were introduced on the basis of the traditional linear,quadratic and quartic flatness basic patterns.Linear,quadratic,cubic and quartic Legendre orthogonal polynomials were adopted to express the flatness basic patterns.In order to over-come the defects live in the existent recognition methods based on fuzzy,neural network and support vector regres-sion(SVR)theory,a novel flatness pattern recognition method based on least squares support vector regression(LS-SVR)was proposed.On this basis,for the purpose of determining the hyper-parameters of LS-SVR effectively and enhan-cing the recognition accuracy and generalization performance of the model,particle swarm optimization algorithm with leave-one-out(LOO)error as fitness function was adopted.To overcome the disadvantage of high computational complexity of naive cross-validation algorithm,a novel fast cross-validation algorithm was introduced to calculate the LOO error of LDSVR.Results of experiments on flatness data calculated by theory and a 900HC cold-rolling mill practically measured flatness signals demonstrate that the proposed approach can distinguish the types and define the magnitudes of the flatness defects effectively with high accuracy,high speed and strong generalization ability.
基金the National Science Council ot Taiwan,China for funding this research(Project no.:NSC 94-2218-E-035-011)
文摘A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.
基金Supported by "863" Program of P. R. China(2002AA2Z4291)
文摘Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting.
基金the National Science Council of Taiwan for funding this research (NSC 96-2221-E-019-061).
文摘Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
基金supported by the National Creative Research Groups Science Foundation of China (NCRGSFC:60721062)National Basic Research Program of China (973 Program) (No.2007CB714000)
文摘A sparse approximation algorithm based on projection is presented in this paper in order to overcome the limitation of the non-sparsity of least squares support vector machines （LS-SVM）. The new inputs are projected into the subspace spanned by previous basis vectors （BV） and those inputs whose squared distance from the subspace is higher than a threshold are added in the BV set, while others are rejected. This consequently results in the sparse approximation. In addition, a recursive approach to deleting an exiting vector in the BV set is proposed. Then the online LS-SVM, sparse approximation and BV removal are combined to produce the sparse online LS-SVM algorithm that can control the size of memory irrespective of the processed data size. The suggested algorithm is applied in the online modeling of a pH neutralizing process and the isomerization plant of a refinery, respectively. The detailed comparison of computing time and precision is also given between the suggested algorithm and the nonsparse one. The results show that the proposed algorithm greatly improves the sparsity just with little cost of precision.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
文摘The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares. In this paper we reconsider the least squares method from the view point of Deep Learning and we carry out the computation thoroughly for the gradient descent sequence in a very simple setting. Depending on the values of the learning rate, an essential parameter of Deep Learning, the least squares methods of Statistics and Deep Learning reveal an interesting difference.
