## 3 Simulation Results and Discussion
### ANC Simulation Results and Discussion  
The measured diesel engine sounds at various rotation frequencies were used to train multiple LSTM layers. The noises for the ANC tests comprised completely different fundamental frequencies and situations according to the training set for the diesel engine noises. Each training set consisted of 10 different rotational frequencies of diesel engine noises with a sample size of 200. The multiple LSTM layers were trained for 30 epochs per training set. Parametric studies were conducted to determine the adaptation step size parameter and filter size of the FxLMS algorithm that minimized the noise residue. The filter size was 20 and the adaptation step size was 0.01. The primary and secondary paths were selected as arbitrary filters with lengths of 7. The trained LSTM algorithm was used to actively control the diesel engine noise. The results were compared with those from active control using the conventional FxLMS algorithm. A short-time Fourier transform (STFT) analysis was performed on the noise residue to investigate the characteristics and performance of the algorithm. The first simulation was used to verify the performance of the harmonics of 60 Hz noise cancellation using the conventional FxLMS algorithm and proposed method with the LSTM neural networks. As shown in Figure 5a, the noise sounds are shown in grey, and the noise residues from the ANC using FxLMS and LSTM are shown in red and blue, respectively. Considering the results of both ANC algorithms for single harmonic sounds,  
Figure 4: Experimental setup for the reference noise acquisition: (**a**) schematic diagram of the engine and control room and (**b**) 1600-cc single-cylinder diesel engine and measurement location of microphone. The diesel engine operated at various rotational frequencies as the noise signal was measured. The impulsive signal generated when the diesel engine was started was also measured. the conventional FxLMS approach and proposed LSTM controller both eliminate diesel engine noise well during the first 0.6 s. The FxLMS algorithm reaches a noise control level of less than 10% approximately 0.1 s after noise control begins, owing to the convergence. Meanwhile, the LSTM algorithm performs ANC immediately without any convergence time, as the weights of the LSTM units are already determined from the training data. LSTM network predicts the next output data as soon as a fixed number of input data is received in many-to-one mode, so its latency is very short compared to FxLMS. The sampling frequency of the sound samples used in the test is 22,050 Hz, and the output data are predicted with 10 input data, so the latency is 1/4410 s. Because of the characteristics, the LSTM algorithm can directly perform ANC without convergence time. Figure 5b shows the results from the STFT analysis of the noisy data and ANC results. The diesel engine operates at a fundamental frequency of 60 Hz but simultaneously generates various high-frequency components. While performing active control with the FxLMS algorithm, the noise at the fundamental frequency is significantly reduced, but high-frequency noise components remain. When using the LSTM algorithm for ANC, the noise is canceled over the entire frequency range (extremely small intensity of low-frequency components). To compare the noise levels during ANC, the equivalent continuous sound level for each noise was calculated. The equivalent continuous sound level is defined as a sound pressure level that has a total energy equal to the actual fluctuating noise over a given period of time. Thus, the equivalent continuous sound level is in fact the RMS sound level with the measurement duration used as the averaging time. The equivalent continuous sound levels of the original noise, FxLMS, and LSTM approaches are 80.6, 55.1, and 47.7 dB, respectively, thus confirming that the noise reduction of the proposed LSTM algorithm is better than that of the FxLMS algorithm owing to the convergence rate.