4.2. Feature Extraction of Ship-Radiated Noise Based on HE
In this section, five types of ship-radiated noise were employed for the feature extraction (the ship-radiated noise of Ships D and E can be obtained from
https://www.nps.gov/glba/learn/nature/soundclips.htm). The sampling frequency of Ships A, B, and C was
kHz. As for Ships D and E, the sampling frequency was
kHz. Ship A was a cruise ship. The vessel was less than 50 m away from the hydrophone. The hydrophone depth was
m. Ship B was an ocean liner. The vessel was less than 50 m away from the hydrophone. The hydrophone depth was
m. Ship C was a motorboat. The distance between the vessel and the hydrophone changed from 50 m–100 m during the recording of the data approximately.
The hydrophone depth was
m. Further information for Ships A, B, and C can be found in [
30]. Ships D and E were downloaded from a public website [
31]. We chose a part of each signal and divided them into 100 segments separately. The length of each segment was 8192 sample points, namely
s of real-world data for Ships D and E and
s of real-world data for Ships A, B, and C. We can obtain 100 results for each type of ship-radiated noise by calculating the HE and MSE for every segment. The number of hierarchical decompositions was set as five. The waveform of five types of ship-radiated noise is demonstrated in
Figure 13.
Figure 14 gives the power spectrum density analysis results of the five types of signals.
Much useful information can be obtained from the power spectrum density analysis results of the five types of ship-radiated noise in
Figure 14. The narrow-band spectral lines existing in
Figure 14b,c make it easy to distinguish Ship B and Ship C. As for the rest of the types of ship, which are Ships A, D, and E in
Figure 14a,d,e, few spectral lines can be found for us to distinguish different types of ship. Especially for Ships D and E, the fact that there was no evident distinction existing in their broadband spectral envelops made it difficult for us to distinguish these two types of ships accurately. Therefore, classifying these five different ships using the spectrum as a feature is difficult.
The HE results of the five types of ship-radiated noise are illustrated in
Figure 15. In order to compare the performance when HE and MSE both calculate the same data length for their sub-signals,
Figure 16 shows the MSE result of the five types of ships from a scale of 1–16. Guarantee that when calculating the HE at a scale five, the length of the sub-signal was 512 points, the same as MSE at a scale of 16. Since it is difficult to see the differences between the five types of ship-radiated noise through
Figure 15, part of the HE results are also shown numerically through
Table 3. HE(n)represents the HE result at scale
n.
According to the MSE result demonstrated in
Figure 16, we can see that SE can only distinguish Ship C from other types of ship. Throughout the MSE result from a scale of 1–16, the entropy differences between Ships A and D and Ships B and E remained small.
To evaluate the performance of the above-mentioned feature extraction methods quantitatively, the results of two methods were separately classified and identified by a probabilistic neural network. Since the MSE’s results for the five types of ships were vectors of length 16, we fed the probabilistic neural network with these vectors to get the classification results. As for HE, we flattened the HE’s results from matrices into vectors of a length of 31, then fed the PNN with these vectors to get the classification results. The classification results are demonstrated in
Table 4,
Table 5 and
Table 6. The training set for each type of ship was 70, and the test set was 30.
Before assessing the performance of the PNN, the definitions of “sensitivity” and “specificity” are given as follows:
where TP, TN, FP, and FN are the abbreviations for “true positive”, “true negative ”, “false positive”, and “false negative”, respectively. It is important to note that “accuracy” calculates the overall classification accuracy of neural networks, which is also the average of “sensitivity”.
From
Table 4,
Table 5 and
Table 6, it is obvious that HE was able to classify five types of ships very well. Even for those types of ships that SE and MSE could not classify, their sensitivities in HE’s result were very high. The accuracy of HE increased
compared with MSE and
compared with SE. In order to eliminate the impact of sampling frequency, we reduced the sampling frequency of Ships A, B, and C from
kHz to
kHz, calculated the HE results for five types of ships, and passed the results through PNN. The classification result is demonstrated in
Table 7. Through the table, we can see that the classification accuracy was
, very close to the accuracy of not reducing the sampling frequency.
Moreover, we mixed five types of ship-radiated noise with Gaussian white noise. The SNR was set to be 5 dB, and the classification results are illustrated in
Table 8 and
Table 9.
According to the results shown in
Table 8 and
Table 9, as the noise mixed into the ship-radiated noise, both HE and MSE were affected. However, even though the accuracy of both methods decreased, HE’s accuracy remained higher compared with MSE. The accuracy of HE decreased by
with added noise, while the accuracy of MSE decreased by
under the same conditions. Furthermore, even when the ship-radiated noise was mixed with noise, HE could still distinguish Ship C very well.