## 1. Introduction

During the development of passive sonar, the ship-radiated noise signal has been widely used in the detection, tracking, and classification of ship targets. As it contains a lot of information about ship characteristics, ship-radiated noise has always been a research hotspot of underwater acoustic signal processing. Hence, extracting effective and reliable ship-radiated noise characteristic parameters is highly valuable [

1,

2]. Ship-radiated noise signals usually have time-variant and nonstationary characteristics. Especially in the early stage of signal processing, the ship feature is weak and is completely drowned out by the complexity of marine environments [

3,

4]. Therefore, in order to realize the effective ship signal, suppressing the background noise and effects of aliasing between the feature information from the original signal is becoming in urgent need of solving.

Due to the rapid development of ship-radiated noise signal processing technology, some researchers have proposed many nonlinear and nonstationary signal processing methods for the feature extraction of underwater acoustic target signals, such as empirical mode decomposition (EMD) [

5,

6], intrinsic time-scale decomposition (ITD) [

7,

8], local mean decomposition (LMD) [

9], and their improved algorithms [

10,

11,

12,

13,

14]. Hong [

15] proposed ensemble EMD (EEMD) and energy distribution to extract the energy difference, which is an efficient feature extraction technique for ship-radiated noise. Li [

16] proposed an improved energy feature extraction technique for ship-radiated noise, which combined CEEMDAN and EE to extract the hybrid energy feature. Frei [

17] proposed an adaptive time-frequency analysis method, which can decompose the nonstationary signal into a series of single component signals with the physical meanings of instantaneous frequencies. In recent decades, these studies have provided rich reference information, which is widely used in fault diagnosis [

18,

19], biomedicine [

20,

21], geophysics [

22], and hydroacoustics [

23,

24]. Compared with the EMD method, the ITD method has obvious advantages in terms of computational efficiency and processing edge effects. However, the definition of the baseline of the ITD method is based on the linear transformation of the signal itself, and may cause a glitch and distortion of the proper rotation components obtained by the decomposition. Based on this, we used akima interpolation [

25] to improve the ITD method; then, the IITD algorithm was proposed. Therefore, this is a feasible way to decompose the ship-radiated noise signal by IITD to extract effective ISCs.

Entropy theory can efficiently evaluate the complexity of the time series and reduce the dimension of the feature vector and fully represent the characteristics of the series. Hence, there are many methods for complexity measurement, including Shannon entropy [

26], sample entropy (SampEn) [

27,

28], permutation entropy (PE) [

29], and fuzzy entropy [

30], which have been successfully applied in the field of fault diagnosis and the medical field. However, SampEn is time consuming for large data calculations and is susceptible to mutated signals. While the PE is faster, it fails to consider the mean value of amplitudes and differences between the amplitudes value. In order to overcome the drawbacks of SampEn and PE, a new measure of the complexity method, named dispersion entropy (DE), was proposed by Mostafa Rostaghi and Hamed Azami in 2016 [

31]. The advantage of the DE algorithm is that the calculation speed is fast, the influence of the noisy signal is small, and it considers the influence of the magnitude relationship between amplitudes of the signal. Since all of the above methods are based on a single scale, they fail to account for the interrelationship of entropy and temporal scales. To remedy this, Costa etal. proposed the multiscale entropy (MSE) algorithm, in which scales are generated by the coarse-graining process [

32]. The coarse-graining process has better stability in feature extraction and can be combined with arbitrary entropy estimators for multiscale analysis. Regarding this advantage, a multiscale dispersion entropy (MDE) procedure was put forward to estimate the complexity of the original time series over a range of scales [

33]. Therefore, the MDE of the signal was adopted in this paper to identify the feature information of the ship-radiated noise signal.

In this paper, an effective feature extraction technique for ship-radiated noise via IITD and multiscale dispersion entropy (MDE) is introduced, named IITD-MDE. The proposed technique not only retains the advantages of existing techniques, but also overcomes the disadvantages of ITD and dispersion entropy (DE).

The rest of the paper is organized as follows:

Section 2 first describes the ITD and DE algorithms, and based on this, the IITD and MDE algorithms are proposed. The IITD-MDE method flow is described in

Section 3. The experiments are verified and analyzed by real ship-radiated noise datasets in

Section 4. The conclusions are given in

Section 5.

## 5. Conclusions

In this paper, we carried out an investigation aimed at gaining a better recognition accuracy of ship-radiated noise signals, a new feature extraction method based on IITD-MDE is present. We also introduced IITD and MDE to quantify the ship-radiated noise signal in this article.

The work done here has following implications. Firstly, we showed that IITD is appropriate approach, compared with ITD and EMD, when dealing with noise signal. We also found that MDE are suitable to quantify the extracted ship-radiated noise feature information, compared with MSE and MPE. Finally, the most consistent method to distinguish the different types of ship-radiated noise signals was IITD-MDE and recognition rate is 86%, compared with ITD-MDE, MDE, and MPE. Hence, the proposed method can extract ship feature and classify effectively.