梯形明渠特征水深直接计算方法研究
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摘要
梯形明渠特征水深—正常水深、临界水深、共轭水深和收缩水深是水力学计算和水利工程设计中一个特别重要的参数。对这些特征水深的求解,实质是求解含多个未知参数的单变量超越方程或高次方程,但理论上多无解析解,常见的求解方法主要有试算法、迭代法、图表法和近似解法等。试算法计算繁杂,工作量大;迭代法的优劣与迭代格式及初值的选取密切相关,而且对初学者和无工程经验者往往因初值及迭代方程选取不合理而不收敛;图解法是利用已经制好的大量图表求解,精度欠佳,并且图解法必须要利用专门的图表,此类图表种类有多种,最常见的是水力学教材或水力计算手册中给出的用双对数表格绘制的求解图,或数值查算表,使用上都很麻烦,而且从理论上也不够完善;近似解法又存在计算复杂和计算结果不准确或适用范围太小等缺点。因此,这些方法还未达到简捷、准确、通用及理论化的统一。使水力学的基本水力计算方法没成一个完整的科学体系,求解方法的规律性及理论性较差,太盲目,太繁琐,同时也不能达到方便工程实际使用。所以本文在前人研究的基础上,通过系统地分析研究和比较,根据梯形明渠各种特征水深基本方程的特点和特殊函数求解方法及计算方法,利用迭代法、最小二乘拟合、二维优化拟合、回归分析、相似比例关系、卡尔丹一元三次方程、误差分析和数学软件等,提出了四套梯形明渠特征水深的直接计算公式,误差分析及实例计算表明,该直接计算公式形式简单,适用范围广,计算精度高。最后结合本研究的认识及体会,提出了一些展望,即在以上研究的基础上,把遗传算法、小波分析法、神经网络法和SPSS统计分析软件运用到梯形明渠特征水深—正常水深、临界水深、共轭水深和收缩水深的计算过程中,提出更简捷、准确、通用的直接计算公式。
Trapezoidal channel depth features - normal depth, critical depth, depth and contraction of conjugated water depth is calculated and mechanical design of a water conservancy project is particularly important parameters. These features depth of the solution, in essence, with a number of unknown parameters for single-variable equations or high beyond the equation, but, in theory, have no analytical solution, the solution of common major test algorithm, iterative method, charts law and the approximate solution, etc.. Test algorithm is complicated, heavy workload;The pros and cons of iterative methods and iterative format and is closely related to the selection of the initial value, but also for beginners and non-engineering experience are often iterative equation for initial selection and unreasonable without convergence; graphical method is to use has been a large number of good Solving charts, poor accuracy, and graphical method must use specialized charts, a number of these types of charts, the most common is teaching hydraulics manual or hydraulic calculation is the use of several forms of double-solving Figure Drawing or numerical investigation balance sheet, and the use of very troublesome, but in theory are not perfect and there are approximate solution of computational complexity and calculation results inaccurate or scope of such small shortcomings. Therefore, these methods are difficult to achieve simple, accurate, and General Theory of reunification. Hydraulics to the basic method of hydraulic calculation did not form a complete scientific system, the laws and methods to solve theoretical and poor, and too blind, too cumbersome, but also facilitate the project can not achieve practical use. Therefore, in this paper, on the basis of previous studies, through systematic study and analysis, the trapezoidal channel in accordance with the characteristics of the basic equation depth features and special functions solving method and calculation method, using iterative method, least squares fitting, 2 Victoria optimization, regression analysis, similar proportion, Cartan one yuan cubic equation, error analysis and mathematical software, to the depth of four trapezoidal channel features a direct calculation formula, error analysis and examples of shows that the formula for calculating the form of direct simple, apply a wide range of high precision. Finally this study and understanding of, a number of prospects, that is, on the basis of the above, the genetic algorithms, wavelet analysis, neural network and SPSS statistical analysis software to the use of trapezoidal channel depth features-normal depth, critical depth , conjugate depth and the depth of contraction process, to be more simple, accurate, and the direct universal formula.
Trapezoidal channel depth features - normal depth, critical depth, depth and contraction of conjugated water depth is calculated and mechanical design of a water conservancy project is particularly important parameters. These features depth of the solution, in essence, with a number of unknown parameters for single-variable equations or high beyond the equation, but, in theory, have no analytical solution, the solution of common major test algorithm, iterative method, charts law and the approximate solution, etc.. Test algorithm is complicated, heavy workload;The pros and cons of iterative methods and iterative format and is closely related to the selection of the initial value, but also for beginners and non-engineering experience are often iterative equation for initial selection and unreasonable without convergence; graphical method is to use has been a large number of good Solving charts, poor accuracy, and graphical method must use specialized charts, a number of these types of charts, the most common is teaching hydraulics manual or hydraulic calculation is the use of several forms of double-solving Figure Drawing or numerical investigation balance sheet, and the use of very troublesome, but in theory are not perfect and there are approximate solution of computational complexity and calculation results inaccurate or scope of such small shortcomings. Therefore, these methods are difficult to achieve simple, accurate, and General Theory of reunification. Hydraulics to the basic method of hydraulic calculation did not form a complete scientific system, the laws and methods to solve theoretical and poor, and too blind, too cumbersome, but also facilitate the project can not achieve practical use. Therefore, in this paper, on the basis of previous studies, through systematic study and analysis, the trapezoidal channel in accordance with the characteristics of the basic equation depth features and special functions solving method and calculation method, using iterative method, least squares fitting, 2 Victoria optimization, regression analysis, similar proportion, Cartan one yuan cubic equation, error analysis and mathematical software, to the depth of four trapezoidal channel features a direct calculation formula, error analysis and examples of shows that the formula for calculating the form of direct simple, apply a wide range of high precision. Finally this study and understanding of, a number of prospects, that is, on the basis of the above, the genetic algorithms, wavelet analysis, neural network and SPSS statistical analysis software to the use of trapezoidal channel depth features-normal depth, critical depth , conjugate depth and the depth of contraction process, to be more simple, accurate, and the direct universal formula.
引文
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