摘要
蛋形断面临界水深计算需完成表达形式复杂且分3个区段给出的超越方程求解,针对解析法无法直接完成求解而采用常规的试算法计算工作量大、效率低、不便实际应用等问题,依据优化拟合理论,以标准剩余差最小为目标函数,在工程适用参数范围内,经拟合计算得到了一个表达形式简单直观、计算不分区段、便于实际应用的通用简化公式。精度分析及实例计算结果表明,该公式最大计算误差仅为0.649%,利用该公式完成蛋形断面临界水深计算可大大简化计算过程,提高工作效率。
A transcendental equation which has a complex expression form needs to be solved in three sub-sections in order to calculate the critical depth of an egg-shaped cross section. The equation can not be solved directly by an analytical method and the conventional trial method has the drawbacks of heavy computational effort, low efficiency and inconvenience for practical applications. Based on the optimal fitting theory, an objective function was chosen for the smallest standard residual difference. By fitting computation confined to suitable parameters in engineering, a general approximation formula was proposed. The formula has a simple expression, no sub-sections for calculation, easy for practical application. Precision analysis and computational results show that the maximum fitting error is only 0. 649% and the process for critical depth calculation of an egg-shaped cross section can be greatly simplified, and the working efficiency can be improved significantly.
出处
《水利水电科技进展》
CSCD
北大核心
2013年第6期37-39,47,共4页
Advances in Science and Technology of Water Resources
关键词
过水隧洞
蛋形断面
临界水深
优化拟合
近似计算
water tunnel
egg-shaped cross section
critical depth
optimal fitting
approximate calculation
