## 5 Experiment and Result Analysis of Shaft Frequency Extraction
### Experiment on Real Data  
In the simulation experiment, we trained the SSDAE-DRN model by using the simulated ship radiated noise envelope spectrum and a small amount of real ship radiated noise envelope spectrum. Next, we collected the real ship radiated noise data and extracted the ship shaft frequency using the pre-trained SSDAE-DRN model. The main process is shown in Figure 12.  
The measurement experiment of ship radiated noise was carried out in a certain area of Changjiang River, in January 2022, where the water depth was 14 m and a large number of cargo ships, tankers, large junks, and law enforcement vessels passed by. The hydrophone is fixed on a frame and placed at a depth of 12 m underwater, at a distance of 750 m from the center of the channel, and the radiated noise is automatically recorded when the ships pass  
Figure 11: Frequency distribution of error rate on shaft frequency extraction. Figure 12: Flow chart of ship shaft frequency extraction. on the river near the hydrophone. The hydrophone used in the experiment is icListen-900 m produced by Ocean Sonics, and the effective measurement frequency band is 0\(\sim\)10 kHz. The experiment equipment and time-frequency diagram of data are shown in Figure 13.  
The acquired data are influenced by the sea state and the target distance during the experiment and have the interference of environmental and other ship noise. The radiated noise data of 10 ships in 4 categories are obtained, and the sampling rate is 32 kHz. The ships sail at approximately uniform speed with a shaft frequency range of 2 Hz to 8 Hz. A total of 720 cargo ship samples, 480 tanker samples, 960 large junk samples, and 480 law enforcement vessel samples are obtained after pre-processing. The multi-subband weighted fusion DEMON spectrum estimation method [35] is used to obtain the modulation spectrum of real ship radiated noise, and the real shaft frequency calibration of the sample is then performed by manual interpretation combined with the speed record. The modulation spectrum of the real data is input into the SSDAE-DRN model to obtain the estimated value of ship shaft frequency. The results of shaft frequency extraction of ship radiated noise from four types of ships are shown in Figure 14. The real shaft frequencies of the cargo ship, tanker, law enforcement vessel, and large junk in the figure are 4.9 Hz, 3.1 Hz, 5.1 Hz, and 1.5 Hz, respectively. The red circles in the figures are the estimated values of the shaft frequency calculated by the SSDAE-DRN model. Figure 14: Shaft frequency extraction results of real ship radiation noise. **(a)** Modulation trace map of cargo ship; **(b)** modulation trace map of tanker; **(c)** modulation trace map of law enforcement vessel; **(d)** modulation trace map of large junk. Figure 13: Experiment equipment and time-frequency diagram of data. **(a)** Experiment equipment; **(b)** time-frequency diagram of the data. It can be seen from Figure 14 that the estimation shaft frequency in this method can be in good agreement with the shaft frequency line spectrum in the trace map. The shaft frequency and its harmonic line spectrum of cargo ships and large junks have a high signal-to-noise ratio and accurate extraction results. The shaft frequency and its harmonic line spectrum of tankers and law enforcement vessels have a low signal-to-noise ratio. Moreover, there is a significant line spectrum below the shaft frequency, which makes the estimated value have a large bias at some points. The MAE and MRE of this method are calculated using the estimated and calibrated values, and the comparison with the method of sequence matching is shown in Tables 4 and 5. The experimental results show that the SSDAE-DRN model proposed in this paper achieves better results on the real data with an average error rate of 9.7%, which is 16.7% lower than the method of sequence matching and has high accuracy and stability under the condition of line spectrum missing and noise interference.