# Improved FULMS Algorithm for Multi-Modal Active Control of Compressor Vibration and Noise Reduction
###### Abstract  
Active control is currently a hot-button issue in the research of reducing vibration and noise created by rolling piston compressors. Active control can effectively suppress the modal vibration of the structure and reduce the modal resonance acoustic radiation. This paper, which focuses on the active control of the compressor shell's multiple modes with the control of acoustic radiation power being the research objective, studies the relationship between vibration modes and acoustic radiation modes of the compressor shell and the primary sources of noise. An improved Filtered-U least mean square (FULMS) algorithm for compressor vibration and noise control, which is based on the Nesterov accelerated adaptive moment estimation (NADAM) optimization algorithm, is proposed to determine the multi-order modes to be controlled from the perspective of sound energy, and a particle swarm algorithm is used to determine the location and number of secondary sources. The active control model of the compressor shell was established by using the joint simulation platform, and the performance of the improved algorithm was verified and analyzed by the simulation test process. The results show that compared with the traditional FULMS algorithm, the improved FULMS algorithm has better active vibration control effect, higher convergence speed and can effectively suppress structural mode vibration in a short period time. compressor vibration and noise reduction; structural acoustic mode; active control; improved FULMS algorithm  
23 February 202211 April 202211 April 202213 April 202  
signals with no feedback and the delay of secondary channels. [PERSON] [8] on the basis of LMS logarithm strengthened the evaluation of secondary channels to delay real-life signals and proposed the Filtered-X Least Mean Squares (FXLMS) algorithm. [PERSON] et al. [9] studied the effect of the approximation errors during the modeling of secondary channels on the performance of the FXLMS algorithm. [PERSON] [10] invented the multi-HYPER channel algorithm to eliminate the problem of multi-channel control is too complicated and difficult to realize. [PERSON] [11] improved the structure of active noise control with Fast Fourier Transformation and Hartley Transform to downsize the calculation. To tackle the problem that the feedback of output signals were not considered in the FXLMS algorithm, [PERSON] [12] proposed the Filtered-U Least Mean Squares (FULMS) algorithm. [PERSON] [13] became the first person to apply the FULMS algorithm in engineering problems. FULMS was employed to conduct active noise control of pipes and effectively reduced the noise in the pipes. However, due to the acoustic feedback problem in the structure, the active control effect is reduced and becomes unstable. [PERSON] [14] proposed and developed a Harmonic Mean Dependent Variable Step Size (HMVSS) method, which can effectively improve the convergence speed of active control in pipeline noise control and has a good noise reduction effect. Researchers have made numerous attempts to optimize stringency, stability, and applicability of active control algorithms, and the performance of those algorithms has been dramatically advanced and developed [15; 16; 17; 18]. In the meantime, those algorithms have been applied to real-life engineering fields with significant achievements. However, active vibration and noise control of objects with complex structures and irregular shapes still face essential challenges including optimized arrangement methods and controlling algorithms of sensors and actuators. Therefore, the novelty of this study is that the compressor structure is complex, and there are many excitation sources. Particularly noteworthy is that this paper, having rolling piston compressors as its research objective, studies the active control algorithm of the multiple modes of the compressor shell. The FULMS algorithm was optimized with the NADAM optimizer to enhance the efficiency and astringency of the algorithm. Finally, active control of the compressor shell was simulated.