Active control of longitudinal vibration in ship propulsion shaft systems based on an improved feedback variable-leakage FxLMS algorithm

The feedback filter-x least mean squares (FxLMS) algorithm effectively addresses challenges posed by difficult-to-obtain reference signals and secondary path variations through online modeling of the secondary path. However, control stability may be compromised in the presence of broadband noise. This paper proposes an improved feedback variable leakage factor FxLMS algorithm targeting the variable stiffness longitudinal vibration model of a ship propulsion shaft system. First, models of the disturbance channel and the control channel are established based on elastic wave theory and the transfer matrix method. Then, the proposed algorithm integrates an enhanced feedback FxLMS approach with a leakage factor dynamically adjusted based on error signals. Simulation comparisons with alternative algorithms demonstrate superior control performance, identification accuracy, and energy utilization efficiency in the time domain. The study further investigates the established dynamic leakage factor adjustment method on suppressing longitudinal vibrations in the propulsion shaft system. Finally, using experimental data from the stern bearing position as the excitation signal, the proposed algorithm enables rapid convergence and stabilization of the time-domain acceleration response, effectively suppressing vibrations.