Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ...In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.展开更多
In this paper, we investigate the effect of weight function in the nonlinear part on global solvability of the Cauchy problem for a class of semi-linear hyperbolic equations with damping.
The shape and size optimization of brackets in hull structures was conducted to achieve the simultaneous reduction of mass and high stress,where the parametric finite element model was built based on Patran Command La...The shape and size optimization of brackets in hull structures was conducted to achieve the simultaneous reduction of mass and high stress,where the parametric finite element model was built based on Patran Command Language codes.The optimization procedure was executed on Isight platform,on which the linear dimensionless method was introduced to establish the weighted multi-objective function.The extreme processing method was applied and proved effective to normalize the objectives.The bracket was optimized under the typical single loads and design waves,accompanied by the different proportions of weights in the objective function,in which the safety factor function was further established,including yielding,buckling,and fatigue strength,and the weight minimization and safety maximization of the bracket were obtained.The findings of this study illustrate that the dimensionless objectives share equal contributions to the multi-objective function,which enhances the role of weights in the optimization.展开更多
This paper deals with the stability of Takagi-Sugeno fuzzy models with time delay. Using fuzzy weighting- dependent Lyapunov-Krasovskii functionals, new sufficient stability criteria are established in terms of Linear...This paper deals with the stability of Takagi-Sugeno fuzzy models with time delay. Using fuzzy weighting- dependent Lyapunov-Krasovskii functionals, new sufficient stability criteria are established in terms of Linear Matrix Inequality;hence the stability bound of upper bound delay time can be easily estimated. Finally, numeric simulations are given to validate the developed approach.展开更多
The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective t...The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective two person zero-sum matrix games with I-fuzzy goals.In this article,a class of piecewise linear membership and non-membership functions for I-fuzzy goals is constructed.These functions are more effective in real games because marginal rate of increase(decrease)of such membership functions(non-membership functions)is different in different intervals of tolerance errors.Finally,one numerical example is given to examine the effectiveness and advantages of the proposed results.展开更多
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
基金Supported by University Science Research Project of Anhui Province(2023AH052921)Outstanding Youth Talent Project of Anhui Province(gxyq2021254)。
文摘In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.
文摘In this paper, we investigate the effect of weight function in the nonlinear part on global solvability of the Cauchy problem for a class of semi-linear hyperbolic equations with damping.
基金This work was financially supported by the Key Research and Development Project of Shandong Province(Grant No.2020CXGC010702).
文摘The shape and size optimization of brackets in hull structures was conducted to achieve the simultaneous reduction of mass and high stress,where the parametric finite element model was built based on Patran Command Language codes.The optimization procedure was executed on Isight platform,on which the linear dimensionless method was introduced to establish the weighted multi-objective function.The extreme processing method was applied and proved effective to normalize the objectives.The bracket was optimized under the typical single loads and design waves,accompanied by the different proportions of weights in the objective function,in which the safety factor function was further established,including yielding,buckling,and fatigue strength,and the weight minimization and safety maximization of the bracket were obtained.The findings of this study illustrate that the dimensionless objectives share equal contributions to the multi-objective function,which enhances the role of weights in the optimization.
文摘This paper deals with the stability of Takagi-Sugeno fuzzy models with time delay. Using fuzzy weighting- dependent Lyapunov-Krasovskii functionals, new sufficient stability criteria are established in terms of Linear Matrix Inequality;hence the stability bound of upper bound delay time can be easily estimated. Finally, numeric simulations are given to validate the developed approach.
文摘The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective two person zero-sum matrix games with I-fuzzy goals.In this article,a class of piecewise linear membership and non-membership functions for I-fuzzy goals is constructed.These functions are more effective in real games because marginal rate of increase(decrease)of such membership functions(non-membership functions)is different in different intervals of tolerance errors.Finally,one numerical example is given to examine the effectiveness and advantages of the proposed results.
