This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity dis...This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.展开更多
This article presents an optimal hybrid fuzzy proportion integral derivative （HFPID） controller based on combination of proportion integral derivative （PID） and fuzzy controllers, by which the parameters could be ...This article presents an optimal hybrid fuzzy proportion integral derivative （HFPID） controller based on combination of proportion integral derivative （PID） and fuzzy controllers, by which the parameters could be evaluated by global optimization either in convergence velocity or in convergence reliability. Focusing on the nonlinear factors of hydraulic servo system, this article takes advantage of PID and fuzzy logic controller integrated with scaling factors to acquire precise tracking performances. To further improve the performances, it provides new developed optimization with rapid convergence to attain reliable approach probability. Focusing on the performance indictors of evolutionary algorithm, this article presents a new technique to predict reliability of the optimization algorithm. Statistics authenticates the effectiveness and robustness of the optimization. Further, many simulation and experimental results indicate that the optimal HFPID could acquire perfect immunity against parametric uncertainties with external disturbance.展开更多
Formulizations of mutation and crossover operators independent of representation of solutions are proposed. A kind of precisely quantitative Markov chain of populations of standard genetic algorithms is modeled. It is...Formulizations of mutation and crossover operators independent of representation of solutions are proposed. A kind of precisely quantitative Markov chain of populations of standard genetic algorithms is modeled. It is proved that inadequate parameters of mutation and crossover probabilities degenerate standard genetic algorithm to a class of random search algorithms without selection bias toward any solution based on fitness. After introducing elitist reservation, the stochastic matrix of Markov chain of the best-so-far individual with the highest fitness is derived.The average convergence velocity of genetic algorithms is defined as the mathematical expectation of the mean absorbing time steps that the best-so-far individual transfers from any initial solution to the global optimum. Using the stochastic matrix of the best-so-far individual, a theoretic method and the computing process of estimating the average convergence velocity are proposed.展开更多
文摘利用常规观测资料以及卫星、多普勒天气雷达、NCEP 1°×1°6 h再分析资料,对0906号"莫拉菲"造成广东、广西、云南台风暴雨进行诊断对比分析。结果表明:暴雨区与台风西北象限强风速辐合区位置相对应,强风速中心值与其前部风速辐合越大,地面降水越强;台风云系边界越清晰、结构越密实,相应地面降水量越大,且闭合200 K TBB强中心位置对应暴雨落区;随"莫拉菲"登陆后西北移,强上升及旋转运动中心随之向上移,垂直螺旋度经历由整层强正值中心柱状结构减弱为对流层中低层强正值区、高层负值区配置的变化,其强正中心量值剧增,对应地面雨强激增,正螺旋度强中心量值及增幅越大、中心所在位置越低,对应地面降水越强;台风暴雨水汽来源于孟加拉湾、南海和西太平洋,孟加拉湾、南海低空强西南急流水汽输送的贡献明显大于西太平洋,尤其是云南暴雨水汽主要源自孟加拉湾。
基金supported by the National Natural Science Foundation of China (Grant Nos. 91016027 and 91130018)
文摘This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.
基金Hi-tech Research and Development Program of China (2009AA04Z412)Chinese Education Ministry Program 985 Ⅱ+1 种基金Program 111(B07009)Program for New Century Excellent Talents in University and Beijing Teaching Innovation Program (NCET-04-0618)
文摘This article presents an optimal hybrid fuzzy proportion integral derivative （HFPID） controller based on combination of proportion integral derivative （PID） and fuzzy controllers, by which the parameters could be evaluated by global optimization either in convergence velocity or in convergence reliability. Focusing on the nonlinear factors of hydraulic servo system, this article takes advantage of PID and fuzzy logic controller integrated with scaling factors to acquire precise tracking performances. To further improve the performances, it provides new developed optimization with rapid convergence to attain reliable approach probability. Focusing on the performance indictors of evolutionary algorithm, this article presents a new technique to predict reliability of the optimization algorithm. Statistics authenticates the effectiveness and robustness of the optimization. Further, many simulation and experimental results indicate that the optimal HFPID could acquire perfect immunity against parametric uncertainties with external disturbance.
文摘Formulizations of mutation and crossover operators independent of representation of solutions are proposed. A kind of precisely quantitative Markov chain of populations of standard genetic algorithms is modeled. It is proved that inadequate parameters of mutation and crossover probabilities degenerate standard genetic algorithm to a class of random search algorithms without selection bias toward any solution based on fitness. After introducing elitist reservation, the stochastic matrix of Markov chain of the best-so-far individual with the highest fitness is derived.The average convergence velocity of genetic algorithms is defined as the mathematical expectation of the mean absorbing time steps that the best-so-far individual transfers from any initial solution to the global optimum. Using the stochastic matrix of the best-so-far individual, a theoretic method and the computing process of estimating the average convergence velocity are proposed.
