Multi-Objective Optimization Method for Marine Propulsion Shaft Alignment Under Multiple Operating Conditions

Marine propulsion shaft alignment is affected by bearing offsets, hull deformation, thermal growth, and condition-dependent propeller and gear loads. An alignment scheme optimized for a single condition may therefore lead to unbalanced bearing reactions or excessive shaft-line deformation in service. To improve multi-condition alignment performance while reducing the reliance on repeated direct finite element evaluations during optimization, this study proposes a hybrid surrogate-assisted multi-objective optimization framework for a container-ship propulsion shafting system. A beam finite element model based on Euler–Bernoulli theory is established and numerically checked using jack-up calculations. Cold static, hot operating, and zero-pitch conditions are considered. Bearing-load uniformity, maximum coupling vertical offset, and maximum shaft slope are selected as objectives. According to response characteristics, an extremely randomized trees model is used for the nonlinear load-uniformity response, whereas response surface models are used for the smoother coupling-offset and shaft-slope responses. The Pareto front is obtained using multi-objective particle swarm optimization, and a compromise scheme is selected using entropy-weighted TOPSIS. For the investigated case, the preferred scheme reduces the three objectives by 44.36%, 38.62%, and 8.65%, respectively, relative to the pre-optimization scheme, and finite element recalculation gives prediction deviations below 5%. The proposed framework provides a practical reference for propulsion shaft alignment optimization under operating conditions.