Due to the randomness of added noise, noise-assisted versions based on EMD (empirical mode decomposition) usually cause new “mode mixing” problem. In addition, these algorithms also have problems such as high time-consuming and large recovering error. For the reasons, a new method SN-EMD (Selective Noise-assisted EMD) is put forward in this paper. It determines whether to add noise as assistance by judging whether there is high frequency intermittent component contained in the signal or not. The new method was proved to have the optimal performance by comparing the performance parameters for evaluating the decomposition. In this paper, SN-EMD was used to decompose ship radiated noise. On account of the differences in the original information contained in each mode of radiated noise signals from different ship, we selected the first three modes for processing. Average instantaneous frequency, center frequency, energy density, and energy distribution ratio were extracted as mode feature of ship targets for classification and recognition. Spatial distribution of the feature quantities in three-dimensional space verified similarity of the same target and separability of different targets.
EMD [
The real signal is complex, and intermittency of frequency algorithm causes mode mixing in EMD. Namely, signal components on different time scales are decomposed into a mode, or signal components at the same time scale are decomposed into different modes. In order to solve the problem of mode mixing, based on the EMD algorithm, a series of noise-assisted algorithms named Ensemble Empirical Mode Decomposition (EEMD) [
The decomposition algorithms have applications in many fields, such as electrocardiograph (ECG) signal denoising and remote monitoring of the respiration and heartbeat of a patient [
This paper is organized as follows: Section
The EMD algorithm can be described as follows.
Set
Find all the maxima (minima) of
Compute the mean envelope
Compute the IMF candidate
Judge whether Yes. Set No. Treat
Continue until the final residue
The original signal
There is mode mixing problem in EMD decomposition, which makes it impossible for EMD to achieve separation of components of the signal at different frequency. The mode obtained by decomposition cannot reflect the instantaneous frequency characteristics of the signal and fundamentally loses the original intention of EMD algorithm. Meanwhile, the deficiency limits the engineering application of the algorithm.
In order to solve the problem of mode mixing, Wu, Z. [
EEMD algorithm also has some drawbacks: (I) Different realizations of finite variance white noise may produce different numbers of modes; (II) the average mode may not meet the requirements of effective IMF; (III) when IMFs are used to reconstruct the signal, the residual noise cannot be ignored; (IV) ensemble average in EEMD usually needs operation for several hundred times, which is very time-consuming.
Yeh, J.R. [
CEEMDAN proposed in [
In order to reduce the residual noise, Colominas, M.A. [
When there are high frequency intermittent components contained in the signal, the EMD will lead to the first type of mode mixing problem that signal components on different time scales in one mode. In order to solve the problem, a series of noise-assisted versions based on EMD have been proposed. However, due to the randomness of the added noise, the noise-assisted algorithms may cause the second type of mode mixing phenomenon that the signal components on the same time scale are decomposed into different modes. In addition, these algorithms also have problems such as high time-consuming and large residual error. For the reasons, a new method SN-EMD (Selective Noise-assisted EMD) is proposed in this paper. Therefore, in order to avoid the phenomenon of mode mixing, it is necessary to judge whether high frequency intermittent component is contained before decomposition and then decide whether to add noise for decomposition or not.
At the high frequency intermittent component of the signal, the interval time between the extrema of the signal envelope will decrease obviously. That is, at the beginning and the end of the intermittent component, the interval time between the extrema has a jump phenomenon. By detecting fluctuation of interval time between the extrema, whether there is high frequency intermittent component in the signal can be judged. In this paper, variance of interval time is used to judge whether there is intermittent component.
Let
We propose the SN-EMD algorithm as follows.
Set
Judge whether high frequency intermittent component is contained in Yes. Calculate the local means of No. Get the
Get the
Go to
Save all the modes from
Coefficient
SN-EMD algorithm flowchart.
In this section, two artificial signals are decomposed by several decomposition algorithms in Section
In order to accurately describe the performance of the mode decomposition algorithm, five quantitative evaluation indexes for mode separation are introduced: Consuming Time (
The larger the
As an example, we propose here a classical mode mixing example. The input signal is an intermittent high frequency sine component plus a sustained intermediate frequency component and a low frequency component for 1 second. The artificial input signal
Artificial signal.
In order to determine whether there is high frequency intermittent component in the input signal, the maximum and minimum values of the signal are marked first, and the time interval between the extrema is calculated. The maximum and minimum intervals are normalized to calculate the respective variances. The average value of the two variances is used as the final judgment parameter. Considering the divergent effect of the boundary in decomposition, the first two extrema and the last two extrema are discarded, so the number of extreme points is usually no less than 6. In this paper, the threshold is calculated from decomposition of white noise. Mean variances of normalized interval time between the extrema of white noise and each residue are calculated. The mean value of the several mean variances multiplied by 1.5 is set to be the final threshold, which is equal to 0.032. When the judgment parameter is greater than 0.032, the signal is considered to contain intermittent component.
Figure
Interval time between (a) maxima and (b) minima.
Decompose the artificial signal separately using the six algorithms in Section
Decomposition of artificial signal by (a) EMD, (b) EEMD, (c) CEEMD, (d) CEEMDAN, (e) improved CEEMDAN, and (f) SN-EMD.
From the comparison of Figures
Performance statistics of mode composition algorithms.
EMD | EEMD | CEEMD | CEEMDAN | Improved CEEMDAN | SN-EMD | |
---|---|---|---|---|---|---|
| 0.23 | 13.49 | 12.97 | 36.04 | 29.42 | 1.91 |
| 0.19 | 0.11 | 0.10 | 0.41 | 0.31 | 0.056 |
| 0.26 | 0.32 | 0.32 | 0.28 | 0.34 | 0.37 |
Comparing the evaluation indexes in Table
When using the noise-assisted method, due to added random noise, there is residual noise in each mode, which generally decreases with the increase of the average number of times. The ensemble average number of times
Residual error when recovering (a)
As can be seen from Figures
To research the decomposition with noise, another example is proposed. The input signal is composed of two sine components and noise. The artificial input signal
Artificial signal with noise.
Decompose the artificial signal separately using the six algorithms and the modes are shown in Figures
Decomposition of artificial signal with noise by (a) EMD, (b) EEMD, (c) CEEMD, (d) CEEMDAN, (e) improved CEEMDAN, and (f) SN-EMD.
Obviously, the noise
Interval time between (a) maxima and (b) minima.
Comparing the evaluation indexes shown in Table
Performance statistics of mode composition algorithms.
EMD | EEMD | CEEMD | CEEMDAN | Improved CEEMDAN | SN-EMD | |
---|---|---|---|---|---|---|
| 0.29 | 15.47 | 15.14 | 38. 40 | 33.67 | 1.88 |
| 0.38 | 0.31 | 0.27 | 0.64 | 0.44 | 0.011 |
| 0.24 | 0.28 | 0.29 | 0.22 | 0.32 | 0.35 |
The ensemble average number of times
Residual error when recovering (a)
The mode decomposition of the ship radiated noise is to adaptively divide the original signal according to different time scales. The original information contained in the signal is also assigned to each mode when decomposing the signal. For different types of ships, the distribution of the original information contained in each mode is different. Based on these differences, time-frequency features can be extracted for each mode as a standard for classification and recognition. The flowchart of mode feature extraction from ship radiated noise based on SN-EMD is shown in Figure
Flowchart of mode feature extraction.
The average instantaneous frequency can exhibit the frequency distribution of a mode. The instantaneous frequency
The center frequency is the average instantaneous frequency weighted by the instantaneous amplitude per unit time. The instantaneous amplitude
The energy density reflects the average energy of the mode per unit time. The energy density is defined as
The energy distribution ratio
Two sets of ship radiated noise data are collected from a large ship named “Target A,” and other two sets are collected from a boat and a yacht, which are named “Target B” and “Target C,” respectively. Figure
Decomposition of ship radiated noise signal (a) Target A1; (b) Target A2; (c) Target B; (d) Target C.
The mean variances of normalized interval time between the maxima and minima of Target A1’s signal and first 7 residues are 0.019, 0.022, 0.066, 0.019, 0.018, 0.018, 0.024, and 0.027. So only the second-order residue contains intermittent component. The mean variances of other targets will not be listed here.
It can be seen that the amplitude of each mode is greatly reduced after the fourth-order mode in Figure
Instantaneous phase of first 8 modes of Target A1’s radiated noise.
Instantaneous frequency and instantaneous amplitude are obtained for the first 4 modes. 30 average instantaneous frequencies and 30 central frequencies calculated by grouping and weighting average are shown in Figures
Statistics for average instantaneous frequency of first 4 modes.
Statistics for center frequency of first 4 modes.
From Figures
The energy density and energy distribution ratio of the first four modes of the four sets of data are counted as shown in Figures
Statistics for energy density of first 4 modes.
Statistics for energy distribution ratio of first 4 modes.
Classifying and recognizing ship targets require that the mode feature of different targets should be distinguishable, while the mode feature of the same target is similar. In order to verify the separability of average instantaneous frequency, center frequency, energy density, and energy distribution ratio feature, feature quantities of the first 3 modes extracted from the four sets of data are displayed in the three-dimensional space. As shown in Figure
Feature quantities of first 3 modes distributed in three-dimensional space: (a) average instantaneous frequency; (b) center frequency; (c) energy density; (d) energy distribution ratio.
The feature quantities extracted from the two sets of data of Target A present mixed distribution in the same three-dimensional space range, while the feature quantities of the three targets mostly have different spatial distributions. This shows that the average instantaneous frequency, center frequency, energy density, and energy distribution ratio are easy to separate, and these feature quantities provide a basis for ship target classification and identification.
Based on the adaptive mode decomposition, the mode decomposition of ship radiated noise and mode feature extraction have been studied in this paper. Firstly, several existing mode decomposition algorithms were introduced, and the advantage and disadvantage were studied. Secondly, the SN-EMD algorithm was proposed to overcome the problems of the existing mode decomposition algorithms. Furthermore, the method of judging whether the signal contains intermittent component was given. By contrasting the performance parameters of these algorithms, the results showed that the new algorithm has better performance on resisting mode mixing and time-consuming than other noise-assisted algorithms, and residual error when recovering signal components and reconstruction error are also relatively minimal. Finally, based on the differences in the original information contained in each mode of different ships’ radiated noise, the first 3 modes were selected to extract the average instantaneous frequency, center frequency, energy density, and energy distribution ratio. In the three-dimensional space, distribution of feature quantities verifies that features of the same target are similar and the features of different targets are separable. As a result, the feature quantities can be seen as the basis for ship classification and identification.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was partially supported by the National Natural Science Foundation of China (Grant No. 61371171, 11374072, 61501061), Open Foundation of National Key Laboratory of Science and Technology on Underwater Acoustic Antagonizing (SSDKKFJJ-2017-02-01), and Acoustic Science and Technology Laboratory Stable Support Project (SSJSWDZC2018002).