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探究与“圆”有关的交汇问题
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作者 黄汉桥 《河北理科教学研究》 2023年第1期23-25,28,共4页
圆在解析几何、立体几何、向量、解三角形等方面应用广泛.有时候,在解决数学问题时,题目看似跟圆没什么关系,但是根据题设所给的条件,能发现圆的踪迹,这就是隐形圆问题.解决这类问题,可以从圆的定义、方程特点等角度挖掘和转化,数形结合... 圆在解析几何、立体几何、向量、解三角形等方面应用广泛.有时候,在解决数学问题时,题目看似跟圆没什么关系,但是根据题设所给的条件,能发现圆的踪迹,这就是隐形圆问题.解决这类问题,可以从圆的定义、方程特点等角度挖掘和转化,数形结合,迎刃而解. 展开更多
关键词 隐形圆 换元法 轨迹 数形结合
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Artificial bee colony algorithm with comprehensive search mechanism for numerical optimization 被引量:5
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作者 Mudong Li Hui Zhao +1 位作者 Xingwei Weng hanqiao huang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第3期603-617,共15页
The artificial bee colony (ABC) algorithm is a sim- ple and effective global optimization algorithm which has been successfully applied in practical optimization problems of various fields. However, the algorithm is... The artificial bee colony (ABC) algorithm is a sim- ple and effective global optimization algorithm which has been successfully applied in practical optimization problems of various fields. However, the algorithm is still insufficient in balancing ex- ploration and exploitation. To solve this problem, we put forward an improved algorithm with a comprehensive search mechanism. The search mechanism contains three main strategies. Firstly, the heuristic Gaussian search strategy composed of three different search equations is proposed for the employed bees, which fully utilizes and balances the exploration and exploitation of the three different search equations by introducing the selectivity probability P,. Secondly, in order to improve the search accuracy, we propose the Gbest-guided neighborhood search strategy for onlooker bees to improve the exploitation performance of ABC. Thirdly, the self- adaptive population perturbation strategy for the current colony is used by random perturbation or Gaussian perturbation to en- hance the diversity of the population. In addition, to improve the quality of the initial population, we introduce the chaotic opposition- based learning method for initialization. The experimental results and Wilcoxon signed ranks test based on 27 benchmark func- tions show that the proposed algorithm, especially for solving high dimensional and complex function optimization problems, has a higher convergence speed and search precision than ABC and three other current ABC-based algorithms. 展开更多
关键词 artificial bee colony (ABC) function optimization search strategy population initialization Wilcoxon signed ranks test.
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Integrated guidance and control design of the suicide UCAV for terminal attack 被引量:2
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作者 Huan Zhou Hui Zhao +1 位作者 hanqiao huang Xin Zhao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第3期546-555,共10页
A novel integrated guidance and control (IGC) design method is proposed to solve problems of low control accuracy for a suicide unmanned combat aerial vehicle (UCAV) in the terminal attack stage. First of all, the IGC... A novel integrated guidance and control (IGC) design method is proposed to solve problems of low control accuracy for a suicide unmanned combat aerial vehicle (UCAV) in the terminal attack stage. First of all, the IGC system model of the UCAV is built based on the three-channel independent design idea, which reduces the difficulties of designing the controller. Then, IGC control laws are designed using the trajectory linearization control (TLC). A nonlinear disturbance observer (NDO) is introduced to the IGC controller to reject various uncertainties, such as the aerodynamic parameter perturbation and the measurement error interference. The stability of the closed-loop system is proven by using the Lyapunov theorem. The performance of the proposed IGC design method is verified in a terminal attack mission of the suicide UCAV. Finally, simulation results demonstrate the superiority and effectiveness in the aspects of guidance accuracy and system robustness. 展开更多
关键词 integrated guidance and control (IGC) unmanned combat aerial vehicle (UCAV) trajectory linearization control (TLC) terminal attack nonlinear disturbance observer (NDO)
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Trajectory online optimization for unmanned combat aerial vehicle using combined strategy 被引量:1
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作者 Kangsheng Dong hanqiao huang +1 位作者 Changqiang huang Zhuoran Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第5期963-970,共8页
This paper presents a combined strategy to solve the trajectory online optimization problem for unmanned combat aerial vehicle (UCAV). Firstly, as trajectory directly optimizing is quite time costing, an online trajec... This paper presents a combined strategy to solve the trajectory online optimization problem for unmanned combat aerial vehicle (UCAV). Firstly, as trajectory directly optimizing is quite time costing, an online trajectory functional representation method is proposed. Considering the practical requirement of online trajectory, the 4-order polynomial function is used to represent the trajectory, and which can be determined by two independent parameters with the trajectory terminal conditions; thus, the trajectory online optimization problem is converted into the optimization of the two parameters, which largely lowers the complexity of the optimization problem. Furthermore, the scopes of the two parameters have been assessed into small ranges using the golden section ratio method. Secondly, a multi-population rotation strategy differential evolution approach (MPRDE) is designed to optimize the two parameters; in which, 'current-to-best/1/bin', 'current-to-rand/1/bin' and 'rand/2/bin' strategies with fixed parameter settings are designed, these strategies are rotationally used by three subpopulations. Thirdly, the rolling optimization method is applied to model the online trajectory optimization process. Finally, simulation results demonstrate the efficiency and real-time calculation capability of the designed combined strategy for UCAV trajectory online optimizing under dynamic and complicated environments. 展开更多
关键词 unmanned combat aerial vehicle (UCAV) trajectory online optimization functional representation parameter optimization rolling optimization differential evolution
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高三数学微专题复习有效性的思考 被引量:1
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作者 黄汉桥 江君香 《河北理科教学研究》 2022年第4期40-44,共5页
微专题的质量直接影响着学生的复习效果,因此对微专题的选择要慎重,要结合学生的实际情况逐步提升.以复合函数零点问题为课例,认为微专题的选取要立足于学情、考情,适合学生的最近区,激发学习的热情和兴趣,课堂教学要善于变化,吸引学生... 微专题的质量直接影响着学生的复习效果,因此对微专题的选择要慎重,要结合学生的实际情况逐步提升.以复合函数零点问题为课例,认为微专题的选取要立足于学情、考情,适合学生的最近区,激发学习的热情和兴趣,课堂教学要善于变化,吸引学生主动参与,最终提高复习效率. 展开更多
关键词 微专题复习 有效性 思考
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