## 4 Results and Discussion
### Simulation Validation of Proposed Method  
In order to further verify the effectiveness of the proposed method for ANC, the noise attenuation effect of machine gun noise is analyzed with the proposed method by formulating four simulation schemes shown in Figure 6 and using the sound pressure level (SPL) as the evaluation index. The noise attenuation effects of ANC in an obstacle-free rectangular enclosed space are shown in Figure 13a,b. It reveals that the SPL in the enclosed space is between 29.75 and 56.31 dB without ANC as shown in Figure 13a. However, with ANC based on proposed method, the SPL in the space is approximately \(-\)23.27 dB, as shown in Figure 13b. Figure 12: The learning curves of proposed method and several other methods. Figure 13: The ANC simulation results of rectangular enclosed space, **(a)** SPL without ANC for Obstacle-free Rectangular Enclosed Space, **(b)** SPL with ANC for Obstacle-free Rectangular Enclosed Space, **(c)** SPL without ANC for Rectangular Enclosed Space with Obstacle, **(d)** SPL with ANC for Rectangular Enclosed Space with Obstacle. For the simulation condition of rectangular enclosed space with obstacle, the SPL without ANC in the enclosed space is between \(2.76\) and \(39.3\) dB, as shown in Figure 13c. With ANC based on proposed method, the SPL at the noise control point is basically around \(-21.6\) dB as shown Figure 13d. It demonstrates that the method proposed in this paper can well achieve the noise attenuation for rectangular enclosed space. The simulation results of trapezoidal enclosed space are shown in Figure 14. The noise attenuation effects of ANC in an obstacle-free trapezoidal enclosed space are shown in Figure 14a,b. It reveals that the SPL in the enclosed space is basically between \(-7.49\) and \(27.28\) dB without ANC as shown in Figure 14a. However, after the ANC using the proposed method, the SPL in the space is approximately \(-19.08\) dB, as shown in Figure 14b. For the simulation condition of trapezoidal enclosed space with obstacle, the SPL in the enclosed space is between \(-4.71\) and \(27.6\) dB without ANC as shown in Figure 14c. With ANC based on proposed method, the SPL at the noise control point is approximately \(-15.48\) dB, as shown Figure 14d. It also demonstrates that the method proposed in this paper can achieve the noise attenuation for trapezoidal enclosed space. In another example, LMS, RLS, RF, SVM and ANN algorithms were used for ANC of machine gun noise using the four simulation schemes as above. Their noise attenuation effects are shown in Figure 15. The noise attenuation effect of the LMS algorithm for four simulation schemes are \(-13.47\) dB, \(-10.9\) dB, \(-7.78\) dB and \(-2.75\) dB respectively. The noise attenuation effect of the RLS algorithm for the four simulation schemes are \(-14.93\) dB, \(-12.72\) dB, \(-9.46\) dB and \(-4.53\) dB respectively. The noise attenuation effect of the RF algorithm for four simulation schemes are \(-16.96\) dB, \(-14.5\) dB, \(-11.06\) dB and \(-6.59\) dB respectively. The noise attenuation effect of the SVM algorithm for four simulation schemes are \(-17.86\) dB, \(-14.77\) dB, \(-11.72\) dB and \(-7.54\) dB respectively. The noise attenuation effect of ANN algorithm for four simulation schemes are \(-19.03\) dB, \(-16.54\) dB, \(-13.18\) dB and \(-8.26\) dB respectively. Therefore, it can be found that the noise attenuation effect of the proposed method is much better than that of algorithms of LMS, RLS, RF, SVM and ANN. From the simulation results of the above four cases, it can be seen that with increasing spatial irregularity, it would be more difficult to achieve ANC, but the algorithm proposed in this paper can meet the actual needs of practical engineering applications on the whole.