Optimized Variational Mode Decomposition and Permutation Entropy with Their Application in Feature Extraction of Ship-Radiated Noise

Abstract

The complex and changeable marine environment surrounded by a variety of noise, including sounds of marine animals, industrial noise, traffic noise and the noise formed by molecular movement, not only interferes with the normal life of residents near the port, but also exerts a significant influence on feature extraction of ship-radiated noise (S-RN). In this paper, a novel feature extraction technique for S-RN signals based on optimized variational mode decomposition (OVMD), permutation entropy (PE), and normalized Spearman correlation coefficient (NSCC) is proposed. Firstly, with the mode number determined by reverse weighted permutation entropy (RWPE), OVMD decomposes the target signal into a set of intrinsic mode functions (IMFs). The PE of all the IMFs and SCC between each IMF with the raw signal are then calculated, respectively. Subsequently, feature parameters are extracted through the sum of PE weighted by NSCC for the IMFs. Lastly, the obtained feature vectors are input into the support vector machine multi-class classifier (SVM) to discriminate various types of ships. Experimental results indicate that five kinds of S-RN samples can be accurately identified with a recognition rate of 94% by the proposed scheme, which is higher than other previously published methods. Hence, the proposed method is more advantageous in practical applications.

Particle Swarm Optimization Fractional Slope Entropy: A New Time Series Complexity Indicator for Bearing Fault Diagnosis

“…It is concluded that WPE not only has the same advantages as PE, but also can detect the complexity of dynamic mutation by quantifying amplitude information. Concurrently, other application fields of PE and WPE have also received great attention [16][17][18][19].…”

On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy

“…The probability distribution of ordinal patterns (OP) implicitly captures information about the temporal structure of the time series and thus allows the extraction of several promising ordinal pattern-based indicators. These indicators are useful in a growing number of applications including biomedical signal and image processing [ 6 , 10 , 11 , 15 , 31 , 33 , 38 ], fault bearing diagnosis [ 30 , 39 , 40 , 41 , 42 , 43 , 44 ], financial time series analysis [ 7 ] and engineering physics [ 18 , 35 , 45 , 46 , 47 , 48 , 49 , 50 , 51 ].…”

“…As the PE has the ability to capture hidden dynamics of time series, various extensions of the PE, called multiscale PE (MPE), have been proposed to explore in depth the internal structure of signals at different time scales. Among the MPE techniques, we cite coarse-graining MPE [ 53 ], composite MPE [ 54 ], refined composite MPE [ 12 ], downspamling PE (DPE) [ 55 ], composite DPE [ 31 ], refined composite DPE [ 31 ], hierarchical PE [ 56 ], and data-driven decomposition-based MPE [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 57 , 58 , 59 ]. The main idea of these PE-based techniques is to combine PE with a preprocessing step of the signal of interest in order to reduce the number of patterns related to noise.…”

“…These MPE techniques can be roughly split into two categories regarding the preprocessing step. The first category applies a linear filtering [ 12 , 31 , 53 , 54 , 55 ], whereas the second category uses a nonlinear processing [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 57 , 58 , 59 ]. Despite the widely proven usefulness of these techniques, there is still a need to understand the impact of the preprocessing step on the MPE values and how this impact can significantly alter the interpretation of MPE results.…”

Double Feature Extraction Method of Ship-Radiated Noise Signal Based on Slope Entropy and Permutation Entropy

“…In 2002, PE was proposed for the first time; its advantages are simplicity, exceedingly fast calculation, robustness, etc. [ 25 , 26 , 27 ]. With the development of PE, it has gradually become more widely used in the field of SNS feature extraction, and the improved algorithms of PE were proposed and applied successively in the following years, such as reverse permutation entropy (RPE) [ 28 ], weighted-permutation entropy (W-PE) [ 29 , 30 ], and multi-scale permutation entropy (MPE) [ 31 , 32 ].…”