针对噪声环境下求解多个极值点的问题,本文提出了噪声环境下基于蒲丰距离的依概率多峰优化算法(Probabilistic multimodal optimization algorithm based on the Button distance,PMB).算法依据蒲丰投针原理提出噪声下的蒲丰距离和极值...针对噪声环境下求解多个极值点的问题,本文提出了噪声环境下基于蒲丰距离的依概率多峰优化算法(Probabilistic multimodal optimization algorithm based on the Button distance,PMB).算法依据蒲丰投针原理提出噪声下的蒲丰距离和极值分辨度概念,理论推导证明了二者与算法峰值检测率符合依概率关系.在全局范围内依据蒲丰距离划分搜索空间,可以使PMB算法保持较好的搜索多样性.在局部范围内利用改进的斐波那契法进行探索,减少了算法陷入噪声引起的局部最优的概率.基于34个测试函数,从依概率特性验证、寻优结果影响因素分析、多极值点寻优和多维函数寻优四个角度进行实验.证明了蒲丰距离与算法的峰值检测率符合所推导的依概率关系.对比噪声环境下的改进蝙蝠算法和粒子群算法,PMB算法在噪声环境中可以依定概率更精确地定位多峰函数的更多极值点,从而证明了PMB算法原理的正确性和噪声条件下全局寻优的依概率性能,具有理论意义和实用价值.展开更多
The nanoscale titania coated silica was prepared via a two-step precipitating approach, where the nanoscale silica nuclei were first prepared by passing an aqueous solution of sodium silicate through an ion-exchange r...The nanoscale titania coated silica was prepared via a two-step precipitating approach, where the nanoscale silica nuclei were first prepared by passing an aqueous solution of sodium silicate through an ion-exchange resin bed, then coated with the precipitation from hydrolyzed butyl titanate in an ethanol-hexane mixture at a low pH value in the presence of poly(ethylene oxide) polyamine salt(PPA) at a high temperature of 90 ℃. In the second-step precipitating process, the spontaneously precipitated titania shell on the silica nuclei was stabilized in the suspension solution with the help of the adsorption of PPA on the particles. A possible precipitating mechanism was suggested. Furthermore, the amorphous titania shell could undergo crystallization from the amorphous to the anatase structure at a high temperature of 650 ℃, and a further phase transition from the anatase to the rutile structure in the different sintering processes at a rising temperature of 750 ℃.展开更多
文摘针对噪声环境下求解多个极值点的问题,本文提出了噪声环境下基于蒲丰距离的依概率多峰优化算法(Probabilistic multimodal optimization algorithm based on the Button distance,PMB).算法依据蒲丰投针原理提出噪声下的蒲丰距离和极值分辨度概念,理论推导证明了二者与算法峰值检测率符合依概率关系.在全局范围内依据蒲丰距离划分搜索空间,可以使PMB算法保持较好的搜索多样性.在局部范围内利用改进的斐波那契法进行探索,减少了算法陷入噪声引起的局部最优的概率.基于34个测试函数,从依概率特性验证、寻优结果影响因素分析、多极值点寻优和多维函数寻优四个角度进行实验.证明了蒲丰距离与算法的峰值检测率符合所推导的依概率关系.对比噪声环境下的改进蝙蝠算法和粒子群算法,PMB算法在噪声环境中可以依定概率更精确地定位多峰函数的更多极值点,从而证明了PMB算法原理的正确性和噪声条件下全局寻优的依概率性能,具有理论意义和实用价值.
基金Supported by the State Key L aboratory of Shanghai Institute of Ceram ics and State Key L aboratory of Surface Physicsin China
文摘The nanoscale titania coated silica was prepared via a two-step precipitating approach, where the nanoscale silica nuclei were first prepared by passing an aqueous solution of sodium silicate through an ion-exchange resin bed, then coated with the precipitation from hydrolyzed butyl titanate in an ethanol-hexane mixture at a low pH value in the presence of poly(ethylene oxide) polyamine salt(PPA) at a high temperature of 90 ℃. In the second-step precipitating process, the spontaneously precipitated titania shell on the silica nuclei was stabilized in the suspension solution with the help of the adsorption of PPA on the particles. A possible precipitating mechanism was suggested. Furthermore, the amorphous titania shell could undergo crystallization from the amorphous to the anatase structure at a high temperature of 650 ℃, and a further phase transition from the anatase to the rutile structure in the different sintering processes at a rising temperature of 750 ℃.
