小麦发育后期茎秆抗倒性的数学模型探析  

Analysis of the Mathematical Model for Wheat Stem Lodging Resistance in Its Grown Period

作　　者：尹斌[1] 徐千州[1] 桑青华[1] 

机构地区：[1]东南大学自动化学院,江苏南京210096

出　　处：《数学的实践与认识》2012年第15期36-45,共10页Mathematics in Practice and Theory

摘　　要：围绕小麦发育后期茎秆抗倒性的数学模型建立的问题,首先,运用回归分析方法,得到了基于统计的倒伏指数的估计.然后,运用相关分析方法,并引入斐波那契数列及Euclidean距离,分析了小麦抗倒伏性与其茎秆形态参数之间的关系,得到了理想的小麦株型结构.最后,运用平衡理论、挠曲线近似方程、最小势能原理及弯矩平衡原理,考虑小麦自重和风载的共同作用,从平衡理论与弹性理论的角度建立了小麦茎秆抗倒伏性的精确模型.利用该模型结合估计的倒伏指数,对临界倒伏风速进行计算,结果验证了模型的有效性.The aim is to research the mathematical model for the wheat stem lodging resistance in its late development period. Firstly, the regression analysis was applied to build a statistical-based lodging resistance model. Then, introduced with the Fibonacci sequence and the Euclidean distance, the relationship between the stem traits and lodging resistance was proposed using correlation analysis method, and the ideal construction of wheat stem type was deduced. Finally, in the view of balance and elastic theory, an accurate model under both self-weight and wind load was obtained, which was based on the balance theory, the line of deflection equation, the principle of minimum potential energy and the moment equilibrium theory. The result of the critical lodging wind speed, which was calculated based on this model, showed the rationality of the proposed model.

关 键 词：抗倒伏模型 回归分析 相关分析 斐波那契数列 弯矩平衡 

分 类 号：O212.1[理学—概率论与数理统计] S512.1[理学—数学]