How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linea...How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).展开更多
Split ratio,i.e.the ratio of stator inner diameter to outer diameter,has a closed relationship with electromagnetic performance of permanent magnet(PM)motors.In this paper,the toroidal windings with short end-winding ...Split ratio,i.e.the ratio of stator inner diameter to outer diameter,has a closed relationship with electromagnetic performance of permanent magnet(PM)motors.In this paper,the toroidal windings with short end-winding axial length are employed in the 6-slot/2-pole(6s/2p)PM motor for high speed applications.The split ratio is optimized together with the ratio of inner slot to outer slot area,i.e.slot ratio,considering stator total loss(stator iron loss and copper loss).In addition,the influence of maximum stator iron flux density and tooth-tip on the optimal split ratio,slot ratio,and average torque is investigated.The analytical predictions show that when the slot ratio is 0.5,the maximum torque can be achieved,and the optimal split ratio increases with the decrease of slot ratio,as confirmed by the finite element(FE)analyses.Finally,some of predicted results are verified by the measured results of 6s/2p prototype motor with 0.5 slot ratio.展开更多
In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the opti...In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the optimal split point in the decision tree is conducted by inverting a t-test or a deviation measure test, both involving Chemoff type limiting distributions. In order to avoid estimating the nuisance parameters in the complicated limiting distribution, subsampling is proved to deliver the correct confidence interval/set.展开更多
基金support provided by the Ministry of Science and Technology,Taiwan,ROC under Contract No.MOST 110-2221-E-019-044.
文摘How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).
文摘Split ratio,i.e.the ratio of stator inner diameter to outer diameter,has a closed relationship with electromagnetic performance of permanent magnet(PM)motors.In this paper,the toroidal windings with short end-winding axial length are employed in the 6-slot/2-pole(6s/2p)PM motor for high speed applications.The split ratio is optimized together with the ratio of inner slot to outer slot area,i.e.slot ratio,considering stator total loss(stator iron loss and copper loss).In addition,the influence of maximum stator iron flux density and tooth-tip on the optimal split ratio,slot ratio,and average torque is investigated.The analytical predictions show that when the slot ratio is 0.5,the maximum torque can be achieved,and the optimal split ratio increases with the decrease of slot ratio,as confirmed by the finite element(FE)analyses.Finally,some of predicted results are verified by the measured results of 6s/2p prototype motor with 0.5 slot ratio.
文摘In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the optimal split point in the decision tree is conducted by inverting a t-test or a deviation measure test, both involving Chemoff type limiting distributions. In order to avoid estimating the nuisance parameters in the complicated limiting distribution, subsampling is proved to deliver the correct confidence interval/set.
