In this work, the performance of reliability methods for the probabilistic analysis of local scour at a bridge pier is investigated. The reliability of bridge pier scour is one of the important issues for the risk assessment and safety evaluation of bridges. Typically, the depth prediction of bridge pier scour is estimated using deterministic equations, which do not consider the uncertainties related to scour parameters. To consider these uncertainties, a reliability analysis of bridge pier scour is required. In the recent years, a number of efficient reliability methods have been proposed for the reliability-based assessment of engineering problems based on simulation, such as Monte Carlo simulation (MCS), subset simulation (SS), importance sampling (IS), directional simulation (DS), and line sampling (LS). However, no general guideline recommending the most appropriate reliability method for the safety assessment of bridge pier scour has yet been proposed. For this purpose, we carried out a comparative study of the five efficient reliability methods so as to originate general guidelines for the probabilistic assessment of bridge pier scour. In addition, a sensitivity analysis was also carried out to find the effect of individual random variables on the reliability of bridge pier scour.

This study investigates the optimal and safe operation of pumping stations in water distribution systems (WDSs) with the aim of reducing the environmental footprint of water conveyance processes. We introduced the nonlinear chaotic honey badger algorithm (NCHBA), a novel and robust optimization method. The proposed method utilizes chaotic maps to enhance exploration and convergence speed, incorporating a nonlinear control parameter to effectively balance local and global search dynamics. Single-objective optimization results on a WDS show that NCHBA outperforms other algorithms in solution accuracy and convergence speed. The application of the proposed approach on a water network with two variable-speed pumps demonstrated a significant 27% reduction in energy consumption. Expanding our focus to the multi-objective optimization of pump scheduling programs in large-scale water distribution systems (WDSs), we employ the non-dominated sorting nonlinear chaotic honey badger algorithm (MONCHBA). The findings reveal that the use of variable-speed pumps not only enhances energy efficiency but also bolsters WDS reliability compared to the use of single-speed pumps. The results showcase the potential and robustness of the proposed multi-objective NCHBA in achieving an optimal Pareto front that effectively balances energy consumption, pressure levels, and water quality risk, facilitating carbon footprint reduction and sustainable management of WDSs.