Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to...Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I （the set of polynomials satisfying all the homogeneous interpolation conditions are zero） and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O（τ^3） where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions （presented by lower sets） and then use fast GEPP to solve the linear system with O（（τ ＋ 3）τ^2） operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ/n], where n is the number of variables.展开更多
为贯彻落实新发展理念,助力实现双碳目标,文章对农村地区电动货车充电站选址进行了研究。运用以相似度矩阵为基础,依靠消息传递迭代更新的近邻传播(affinity propagation,AP)聚类算法,从现有乡镇货运站中筛选出电动货车充电站候选点。...为贯彻落实新发展理念,助力实现双碳目标,文章对农村地区电动货车充电站选址进行了研究。运用以相似度矩阵为基础,依靠消息传递迭代更新的近邻传播(affinity propagation,AP)聚类算法,从现有乡镇货运站中筛选出电动货车充电站候选点。在多个属性权重信息未知的情况下,采用基于离差最大化的区间直觉模糊优劣解距离法(technique for order preference by similarity to an ideal solution,TOPSIS)得到最佳选址点,使用遗传算法求解多个充电站多型号电动货车的车辆路径问题。应用实例表明,该方法可以有效地解决新能源货车充电站在农村地区的选址问题。展开更多
基金Supported by the National Natural Science Foundation of China(11271156 and 11171133)the Technology Development Plan of Jilin Province(20130522104JH)
文摘Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I （the set of polynomials satisfying all the homogeneous interpolation conditions are zero） and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O（τ^3） where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions （presented by lower sets） and then use fast GEPP to solve the linear system with O（（τ ＋ 3）τ^2） operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ/n], where n is the number of variables.
文摘为贯彻落实新发展理念,助力实现双碳目标,文章对农村地区电动货车充电站选址进行了研究。运用以相似度矩阵为基础,依靠消息传递迭代更新的近邻传播(affinity propagation,AP)聚类算法,从现有乡镇货运站中筛选出电动货车充电站候选点。在多个属性权重信息未知的情况下,采用基于离差最大化的区间直觉模糊优劣解距离法(technique for order preference by similarity to an ideal solution,TOPSIS)得到最佳选址点,使用遗传算法求解多个充电站多型号电动货车的车辆路径问题。应用实例表明,该方法可以有效地解决新能源货车充电站在农村地区的选址问题。
文摘为提高双点渐进成形(double-side incremental sheet forming,DSIF)制件的成形精度,以方锥盒制件作为试验制件,以刀具直径、层间距、成形角、板厚和成形深度等工艺参数为影响因素,以底部回弹值和侧壁鼓凸最小值作为优化目标设计正交试验,利用Abaqus数值仿真计算出试验结果数据,通过建立多输入和多输出的BP(back propagation)神经网络预测模型,结合带精英策略的非支配排序遗传算法(non-dominated sorting genetic algorithm,NAGA-Ⅱ)求解双点渐进成形工艺参数多目标优化问题,基于熵权逼近理想解排序法(technique for order preference by similarity to ideal solution,TOPSIS)从Pareto解集中决策出一组最优工艺参数组合以提高优化结果的精确度,通过优化和筛选得到的最佳工艺参数组合进行对应试验。结果表明,经实测得到制件的底部回弹值为0.693 mm,侧壁鼓凸值为0.934 mm,筛选出的目标值误差分别为6.31%和2.09%。由此可见,建立的多目标优化流程具有可行性,为双点渐进成形制件的回弹减少提供了有效的优化方案。
