Research on multi-objective optimization method of Z-shaped pipeline structure based on Kriging model

Slurry pipeline transportation is widely used in dredging and serves as an essential method for conveying solid materials. However, accurately describing the interaction between slurry and particles through numerical simulations, while optimizing the pipeline structure to improve the performance of slurry pipelines, poses a significant engineering challenge. In this study, a Z-shaped continuous pipeline, designed using B-spline curves, is implemented in the slurry circulation system. The validity of the CFD-DEM method is confirmed through slurry circulation experiments, and the effects of various structural parameters on transportation efficiency and flow characteristics are investigated. By integrating the Kriging surrogate model with the NSGA-II algorithm, a multi-objective optimization method is proposed to reduce computational complexity and improve the sediment-carrying capacity of the Z-shaped pipeline. Using a slurry shield tunneling machine with a diameter of 6.24 m as an example, this study optimizes a Z-shaped pipeline with an inner diameter of 0.3 m and an axial height of 1.5 m. The optimized structural parameters increase the average particle velocity by 8.9% and reduce particle accumulation by 21.3%. Additionally, the interaction between the pipeline's inclination angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}, the B-spline control parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{4}$$\end{document}, and the sediment-carrying capacity is analyzed.