# Improved FULMS Algorithm for Multi-Modal Active Control of Compressor Vibration and Noise Reduction
## 5 Conclusions  
Starting from the structure-sound radiation modal relationship, this paper studies the multi-modal active control of the compressor shell, designs a scheme, and tests the effect of the active control. The specific conclusions are as follows:  
(1) The relationship between the vibration mode and the sound radiation mode is determined by theoretical calculation, and it is confirmed that the sound radiation can be controlled by controlling the vibration mode.  
(2) Through the simulation analysis of the compressor excitation signal, the acceleration of the compressor shell is obtained. Compared with the experiment, it is determined that the main noise sources are electromagnetic force, pulsating pressure, and cylinder fluid pulsating pressure.  
(3) Based on the Nadam and step normalization method, the multi-mode active vibration control FULMS algorithm is improved to improve its convergence. According to the modal energy distribution of the compressor shell, it is determined that the modal orders to be controlled in multi-mode active control are the 7 th and 9 th orders.  
(4) The particle swarm optimization algorithm is used to determine the point combination with the strongest effect on vibration suppression and monitoring of the main  
Figure 10: Comparison of overall structural response.  
shell and establish a 6 \(\times\) 6 multi channel control model. Based on this, an active control simulation scheme is proposed, which is used to simulate the effect of active control and evaluate the performance of each algorithm. The improved FULMS algorithm converges faster and has better effect.  
Conceptualization and writing--original draft preparation and editing and methodology, X.W.; software and validation, C.L.; formal analysis and resources, M.Y.; writing--review and editing and data curation, Y.H.; supervision and resources, Q.H. All authors have read and agreed to the published version of the manuscript.  
Liazhou Science and Technology Project (No.: 2020 GAAA0403).  
Not applicable.  
The data used to support the findings of this study are included within the article.  
The authors declare no conflict of interest.  
The Filtered-U least mean square  
NADAM  
The Nesterov accelerated adaptive moment estimation  
LMS  
The Least Mean Squares  
NLMS  
The Normalized Least Mean Squares  
FKLMS  
The Filtered-X Least Mean Squares  
Adam  
adaptive moment estimation  
HMVSS  
Harmonic Mean dependent Variable Step-Size  
CM  
Classical Momentum  
NAG  
Nesterov's accelerated gradient  
FUNLMS  
The Filtered-U Normalized Least Mean Squares  
[\(m\)]  
the mass matrix  
[\(k\)]  
the stiffness matrix  
[\(Q(t)\)]  
the excitation matrix  
[\(x(t)\)]  
the displacement matrix  
[\(\omega\)]  
the excitation frequency  
[\(\omega_{r}\)]  
the r-th natural frequency  
[\(u^{r}\)]  
the r-th modal vector  
[\(N_{0r}\)]  
\(0r\)  
\(W\)  
acoustical power  
[\(Q\)]  
the characteristic matrix  
[\(\Lambda\)]  
the diagonal matrix  
[\(\
u\)]  
the normal velocity vector  
[\(\Lambda\)]  
the eigenvalue  
[\(S\)]  
area  
[\(\rho\)]  
density  
[\(c\)]  
velocity of sound  
[\(\sigma\)]  
the radiation ratio  
[\(R\)]  
the acoustic radiation resistance matrix  
[\(A\)]  
the velocity amplitude  
[\(\Phi\)]  
vibration mode  
[\(q\)]  
the acoustic radiation mode  
[\(Lp\)]  
sound pressure level  
[\(p\)]  
sound pressure  
[\(p_{e}\)]  
the effective sound pressure  
[\(\varepsilon\)]  
energy density of sound