Real-Time Active Control of Low-Frequency Pressure Pulsations in a Liquid-Filled Pipeline for Marine Applications: Online Secondary-Path Modeling and Experimental Validation

Low-frequency pressure pulsations generated by shipboard pumps can propagate through liquid-filled pipeline systems and exhibit distinct line-spectrum characteristics, potentially affecting ship acoustic stealth. Because the secondary path varies with operating conditions, fixed offline models are susceptible to modeling mismatch, making online secondary-path modeling essential for reliable active control performance. However, conventional auxiliary-noise-injection-based methods suffer from coupling between the modeling and control processes, while continuous auxiliary-noise injection may deteriorate steady-state noise reduction performance. To address these issues, this paper proposes a variable-step-size online secondary-path modeling method based on multi-power regulation. By jointly regulating the modeling process, control process, and auxiliary excitation power, the proposed method adaptively adjusts the modeling-filter step size, control-filter step size, and auxiliary excitation level, thereby reducing coupling-induced modeling bias and limiting the persistent influence of auxiliary excitation on the residual error signal. Simulation results demonstrate that, compared with typical online secondary-path modeling methods, the proposed method achieves lower steady-state modeling errors and improved noise reduction performance. Furthermore, experiments conducted on a liquid-filled pipeline test rig show that the proposed method achieves low-frequency pressure-pulsation line-spectrum attenuation levels ranging from 8.32 to 14.09 dB under different operating conditions, demonstrating its effectiveness for active pulsation control in liquid-filled pipeline systems.