In this paper we study the higher accuracy methods - the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of Sobolev and viscoelasticity type equations. The global extr...In this paper we study the higher accuracy methods - the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of Sobolev and viscoelasticity type equations. The global extrapolation and the correction approximations of third order, rather than the pointwise extrapolation results are presented.展开更多
This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstr...This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.展开更多
In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeabili...In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.展开更多
文摘In this paper we study the higher accuracy methods - the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of Sobolev and viscoelasticity type equations. The global extrapolation and the correction approximations of third order, rather than the pointwise extrapolation results are presented.
基金supported by the National Natural Science Foundation of China(Grant Nos,60133010 and 60372045)the Graduate Innovation Fund of Xidian University(Grant No.05004),
文摘This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 50775147 and 50835004)the National Basic Research Program of China ("973" Project) (Grant No. 2005CB724103)the Science & Technology Commission of Shanghai Municipality (Grant No. 07JC14028)
文摘In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.
