Reliability-based design and implementation of crow search algorithm for longitudinal dispersion coefficient estimation in rivers

The longitudinal dispersion coefficient (LDC) of river pollutants is considered as one of the prominent water quality parameters. In this regard, numerous research studies have been conducted in recent years, and various equations have been extracted based on hydrodynamic and geometric elements. LDC's estimated values obtained using different equations reveal a significant uncertainty due to this phenomenon's complexity. In the present study, the crow search algorithm (CSA) is applied to increase the equation's precision by employing evolutionary polynomial regression (EPR) to model an extensive amount of geometrical and hydraulic data. The results indicate that the CSA improves the performance of EPR in terms of R² (0.8), Willmott's index of agreement (0.93), Nash-Sutcliffe efficiency (0.77), and overall index (0.84). In addition, the reliability analysis of the proposed equation (i.e., CSA) reduced the failure probability (P_f) when the value of the failure state containing 50 to 600 m²/s is increasing for the P_f determination using the Monte Carlo simulation. The best-fitted function for correct failure probability prediction was the power with R² = 0.98 compared with linear and exponential functions.