## 3 Simulation Results and Discussion
### ANC Simulation Results and Discussion
Figure 5c shows the power spectral density for 0.5-0.6 s, the period in which all ANC algorithms converge. In the case of FxLMS, the low frequency error signal was greatly reduced, but it did not show great performance in the high frequency band. On the other hand, in the case of LSTM, convergence also occurred very quickly and exhibited excellent noise removal performance in all frequency bands. One of the characteristics of LSTM is to predict one output datum that will appear next through several time series input data. Thus, when trained on sounds of the same frequency, the LSTM network can reduce noise in all bands, whether low or high frequencies. As shown in Figure 6, the simulation used a superposed harmonic noise signal with main frequencies of 33, 35, 50, and 60 Hz measured from a diesel engine. The noise sounds in this simulation were generated by the superposition of each harmonic response. As shown in Figure 6a, the noise control via the FxLMS algorithm achieves a noise level of less than 10% approximately 0.2 s after starting. Compared with the previous active control for the single-fundamental-frequency noise, the convergence of the FxLMS algorithm is delayed owing to the complexity of the reference sounds. The proposed method accomplishes ANC completely, despite the increase in the number of fundamental frequencies of the reference sounds. As shown in Figure 6b, with various fundamental frequencies applied, the noise level in the low-frequency band increases. As a result of the ANC using the FxLMS algorithm, the noise in the low-frequency bands is removed, but the noise components in the high-frequency bands remain. In the case of the LSTM controller, the residual noise increases slightly as the low-frequency noise level increases. All other components in the high-frequency bands are removed. The equivalent continuous sound levels for the original noise, FxLMS, and LSTM are 78.3, 54.9, and 50.9 dB, respectively, confirming that broadband noise is remarkably eliminated by the proposed method, even though the LSTM neural networks were trained only on harmonic signals comprising a single fundamental frequency. As can be seen in Figure 6c, since the superposed harmonic noise signal consists of a high level of low-frequency noise, the low-frequency noise cancellation performance in the period where both FXLMS and LSTM converge is almost similar. Nevertheless, the LSTM performed excellent cancellation in the high frequency band, and the sound equivalent level was further reduced by about 1.1 dB compared to the FxLMS algorithm in the period 0.5-0.6 s.  
The ANC simulation results for impulsive noises measured during the start-up of the diesel engine are shown in Figure 7. The reference sounds consisted of white noise at 0-1.5 s, and the impulsive sounds owing to the engine started at 1.5-3 s. Steady-state harmonic sounds also contributed to the noise. As shown in Figure 7a, the FxLMS algorithm updates the adaptive filter to converge its weights during 0-1.5 s. When impulsive sounds are generated after 1.5 s, the noise residue of the FxLMS algorithm instantaneously increases again. The adaptation process of the FxLMS is repeated to adjust the weights. At 3 s, the  
Figure 5: ANC simulation result using FxLMS and LSTM for diesel engine sounds with a main frequency of 60 Hz. (**a**) Time data of the diesel engine noise and ANC results; (**b**) short-time Fourier transform analysis of original noise and noise residue; (**c**) power spectral density of the diesel engine noise and ANC result in the period when the error signal is minimized. noise residue of the FxLMS algorithm decreases when the impulsive signal disappears and the harmonic noise is sustained. Through this simulation, it can be confirmed that the FxLMS algorithm shows limited performance for the control of transient sounds. Among the noises occurring in actual situations, impact sounds are the most prominent, as they are difficult to remove through masking or sound absorbers.