This study describes the settling velocity phenomenon and deals with the methods for its estimation. The accuracy of three previously proposed settling velocity equations is also checked in this study. After graphical and statistical analysis, the authors proposed generalized reduced gradient (GRG) and hybrid generalized reduced gradient–genetic algorithm (hybrid GRG-GA) approaches for the estimation of settling velocity. Hybrid GRG-GA-based settling velocity approach showed more precise results than GRG approach. In addition, hybrid GRG-GA and GRG approaches were compared with previously proposed equations using 226 data points. The graphical and statistical analysis shows that the hybrid GRG-GA and GRG approaches give better agreement with observed data points as compared to previously proposed equations. Application of hybrid GRG-GA reduces the sum of square of error in fall velocity by over 70% and 30% on an average as compared to previous equations during training and testing, respectively. This study highlights that the hybrid GRG-GA approach could be efficiently used for calculating the settling velocity.

本研究描述了沉降速度现象并讨论了其估计方法。本研究还检查了三个先前提出的沉降速度方程的准确性。经过图形和统计分析，作者提出了用于估计沉降速度的广义缩减梯度 (GRG) 和混合广义缩减梯度-遗传算法 (hybrid GRG-GA) 方法。基于混合 GRG-GA 的沉降速度方法显示出比 GRG 方法更精确的结果。此外，使用 226 个数据点将混合 GRG-GA 和 GRG 方法与先前提出的方程进行比较。图形和统计分析表明，与先前提出的方程相比，混合 GRG-GA 和 GRG 方法与观察到的数据点具有更好的一致性。与之前的训练和测试方程相比，混合 GRG-GA 的应用分别使下落速度的误差平方和平均降低了 70% 和 30% 以上。这项研究强调混合 GRG-GA 方法可以有效地用于计算沉降速度。