The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems ...The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.展开更多
In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[...In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.展开更多
The nonlinear governing equations of the liquid sloshing modals in a cylindrical storage tank are established. Through analytical analysis, the analytical expressions of the solutions of this kind of system are obtain...The nonlinear governing equations of the liquid sloshing modals in a cylindrical storage tank are established. Through analytical analysis, the analytical expressions of the solutions of this kind of system are obtained. With different parameters, the dynamical behaviors of the solutions are different from the trivial ones. To prevent system instability, two selection principles that the stiffness equations are positive-definite and the nonlinear terms of the system are not regenerative elements are given. Meanwhile, numerical simulations are also given, which confirm the analytical results.展开更多
In the continuous development of the modern highway and bridge engineering industry,the reasonable selection of mega highway bridges and their design is crucial.Based on this,this paper takes the actual bridge project...In the continuous development of the modern highway and bridge engineering industry,the reasonable selection of mega highway bridges and their design is crucial.Based on this,this paper takes the actual bridge project as an example,and analyses the overall selection design of such highway bridges,including the basic overview of the project,the basic selection principle of mega highway bridge project structure and its design strategy,etc.,to provide scientific reference for its selection design.展开更多
We investigate a role of k-covers in selection principles theory. Some results about relationships between Ramsey theory and game theory and selection principles that involve k-covers are also given.
基金supported by the National Natural Science Foundation of China(61703228)
文摘The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.
基金University of Macao Multi-Year Research Grant Ref.No MYRG2016-00053-FST and MYRG2018-00168-FSTthe Science and Technology Development Fund,Macao SAR FDCT/0123/2018/A3.
文摘In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.
基金Project supported by the National Natural Science Foundation of China(Grant No.10632040)the Independent Innovation Foundation of Tianjin University
文摘The nonlinear governing equations of the liquid sloshing modals in a cylindrical storage tank are established. Through analytical analysis, the analytical expressions of the solutions of this kind of system are obtained. With different parameters, the dynamical behaviors of the solutions are different from the trivial ones. To prevent system instability, two selection principles that the stiffness equations are positive-definite and the nonlinear terms of the system are not regenerative elements are given. Meanwhile, numerical simulations are also given, which confirm the analytical results.
文摘In the continuous development of the modern highway and bridge engineering industry,the reasonable selection of mega highway bridges and their design is crucial.Based on this,this paper takes the actual bridge project as an example,and analyses the overall selection design of such highway bridges,including the basic overview of the project,the basic selection principle of mega highway bridge project structure and its design strategy,etc.,to provide scientific reference for its selection design.
文摘We investigate a role of k-covers in selection principles theory. Some results about relationships between Ramsey theory and game theory and selection principles that involve k-covers are also given.
