A Complexity-Based Approach for the Detection of Weak Signals in Ocean Ambient Noise

Remote passive acoustic signal detection using multi-scale correlation networks and network spectrum distance in marine environment

Detecting acoustic signals in the ocean is crucial for port and coastal security, but existing methods often require informative priors. This paper introduces a new approach that transforms acoustic signal detection into network characterization using a MCN construction method. The method constructs a network representation of the acoustic signal by measuring pairwise correlations at different time scales. It proposes a network spectrum distance method that combines information geometry and graph signal processing theory to characterize these complex networks. By comparing the spectra of two networks, the method quantifies their similarity or dissimilarity, enabling comparisons of multi-scale correlation networks constructed from different time series data and tracking changes in nonlinear dynamics over time. The effectiveness of these methods is substantiated through comprehensive simulations and real-world data collected from the South China Sea. The results illustrate that the proposed approach attains a significant detection probability of over 90% when the signal-to-noise ratio exceeds -18 dB, whereas existing methods require a signal-to-noise ratio of at least -15 dB to achieve a comparable detection probability. This innovative approach holds promising applications in bolstering port security, facilitating coastal operations, and optimizing offshore activities by enabling more efficient detection of weak acoustic signals.

Hydrological changes caused by the construction of dams and reservoirs: The CECP analysis

We investigated the influence of the construction of cascade dams and reservoirs on the predictability and complexity of the streamflow of the São Francisco River, Brazil, by using complexity entropy causality plane (CECP) in its standard and weighted form. We analyzed daily streamflow time series recorded in three fluviometric stations: São Francisco (upstream of cascade dams), Juazeiro (downstream of Sobradinho dam), and Pão de Açúcar station (downstream of Sobradinho and Xingó dams). By comparing the values of CECP information quantifiers (permutation entropy and statistical complexity) for the periods before and after the construction of Sobradinho (1979) and Xingó (1994) dams, we found that the reservoirs' operations changed the temporal variability of streamflow series toward the less predictable regime as indicated by higher entropy (lower complexity) values. Weighted CECP provides some finer details in the predictability of streamflow due to the inclusion of amplitude information in the probability distribution of ordinal patterns. The time evolution of streamflow predictability was analyzed by applying CECP in 2 year sliding windows that revealed the influence of the Paulo Alfonso complex (located between Sobradinho and Xingó dams), construction of which started in the 1950s and was identified through the increased streamflow entropy in the downstream Pão de Açúcar station. The other streamflow alteration unrelated to the construction of the two largest dams was identified in the upstream unimpacted São Francisco station, as an increase in the entropy around 1960s, indicating that some natural factors could also play a role in the decreased predictability of streamflow dynamics.

Generalized weighted permutation entropy

A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods: Permutation entropy and Weighted permutation entropy. The method introduces a scaling parameter to discern the disorder and complexity of ordinal patterns with small and large fluctuations. Using this scaling parameter, the complexity-entropy causality plane is generalized to the complexity-entropy-scale causality box. Simulations conducted on synthetic series generated by stochastic, chaotic, and random processes, as well as real world data, are shown to produce unique signatures in this three dimensional representation.

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

In order to accurately identify various types of ships and develop coastal defenses, a single feature extraction method based on slope entropy (SlEn) and a double feature extraction method based on SlEn combined with permutation entropy (SlEn&PE) are proposed. Firstly, SlEn is used for the feature extraction of ship-radiated noise signal (SNS) compared with permutation entropy (PE), dispersion entropy (DE), fluctuation dispersion entropy (FDE), and reverse dispersion entropy (RDE), so that the effectiveness of SlEn is verified, and SlEn has the highest recognition rate calculated by the k-Nearest Neighbor (KNN) algorithm. Secondly, SlEn is combined with PE, DE, FDE, and RDE, respectively, to extract the feature of SNS for a higher recognition rate, and SlEn&PE has the highest recognition rate after the calculation of the KNN algorithm. Lastly, the recognition rates of SlEn and SlEn&PE are compared, and the recognition rates of SlEn&PE are higher than SlEn by 4.22%. Therefore, the double feature extraction method proposed in this paper is more effective in the application of ship type recognition.

Phase trajectory entropy: A promising tool for passive diver detection

Passive diver detection is really significant as it constitutes a potential real-time monitoring of serious underwater threats. Up to now, there is still a lack of an efficient approach to characterize the complexity and fickleness with non-parametric and non-information priors. To achieve an improvement, a phase trajectory entropy method is proposed that should be promising. A coarser-grained distribution is created during entropy counting. The value of phase trajectory entropy is demonstrated by simulation and applied to real recorded data. The results show that phase trajectory entropy method considerably outperforms narrowband energy detection and the bubble entropy method.

Permutation Entropy and Statistical Complexity Analysis of Brazilian Agricultural Commodities

Agricultural commodities are considered perhaps the most important commodities, as any abrupt increase in food prices has serious consequences on food security and welfare, especially in developing countries. In this work, we analyze predictability of Brazilian agricultural commodity prices during the period after 2007/2008 food crisis. We use information theory based method Complexity/Entropy causality plane (CECP) that was shown to be successful in the analysis of market efficiency and predictability. By estimating information quantifiers permutation entropy and statistical complexity, we associate to each commodity the position in CECP and compare their efficiency (lack of predictability) using the deviation from a random process. Coffee market shows highest efficiency (lowest predictability) while pork market shows lowest efficiency (highest predictability). By analyzing temporal evolution of commodities in the complexity–entropy causality plane, we observe that during the analyzed period (after 2007/2008 crisis) the efficiency of cotton, rice, and cattle markets increases, the soybeans market shows the decrease in efficiency until 2012, followed by the lower predictability and the increase of efficiency, while most commodities (8 out of total 12) exhibit relatively stable efficiency, indicating increased market integration in post-crisis period.

Feature Extraction of Ship-Radiated Noise Based on Intrinsic Time-Scale Decomposition and a Statistical Complexity Measure

Extracting effective features from ship-radiated noise is an important way to improve the detection and recognition performance of passive sonar. Complexity features of ship-radiated noise have attracted increasing amounts of attention. However, the traditional definition of complexity based on entropy (information stored in the system) is not accurate. To this end, a new statistical complexity measure is proposed in this paper based on spectrum entropy and disequilibrium. Since the spectrum features are unique to the class of the ship, our method can distinguish different ships according to their location in the two-dimensional plane composed of complexity and spectrum entropy (CSEP). To weaken the influence of ocean ambient noise, the intrinsic time-scale decomposition (ITD) is applied to preprocess the data in this study. The effectiveness of the proposed method is validated through a classification experiment of four types of marine vessels. The recognition rate of the ITD-CSEP methodology achieved 94%, which is much higher than that of traditional feature extraction methods. Moreover, the ITD-CSEP is fast and parameter free. Hence, the method can be applied in the real time processing practical applications.

A Complexity-Entropy Based Approach for the Detection of Fish Choruses

Automated acoustic indices to infer biological sounds from marine recordings have produced mixed levels of success. The use of such indices in complex marine environments, dominated by several anthropogenic and geophonic sources, have yet to be understood fully. In this study, we introduce a noise resilient method based on complexity-entropy (hereafter named C-H) for the detection of biophonic sounds originating from fish choruses. The C-H method was tested on data collected in Changhua and Miaoli (Taiwan) during the spring in both 2016 and 2017. Miaoli was exposed to continual shipping activity, which led to an increase of ~10 dB in low frequency ambient noise levels (5–500 Hz). The acoustic dataset was successively analyzed via the acoustic complexity index, the acoustic diversity index and the bioacoustic index. The C-H method was found to be strongly correlated with fish chorusing (Pearson correlation: r_H < −0.9; r_C > 0.89), and robust to noise originating from shipping activity or natural sources, such as wind and tides (r_H and r_C were between 0.22 and −0.19). Other indices produced lower or null correlations with fish chorusing due to missed identification of the choruses or sensitivity to other sound sources. In contrast to most acoustic indices, the C-H method does not require a prior setting of frequency and amplitude thresholds, and is therefore, more user friendly to untrained technicians. We conclude that the use of the C-H method has potential implications in the efficient detection of fish choruses for management or conservation purposes and could help with overcoming the limitations of acoustic indices in noisy marine environments.

A Comparative Study of Multiscale Sample Entropy and Hierarchical Entropy and Its Application in Feature Extraction for Ship-Radiated Noise

The presence of marine ambient noise makes it difficult to extract effective features from ship-radiated noise. Traditional feature extraction methods based on the Fourier transform or wavelets are limited in such a complex ocean environment. Recently, entropy-based methods have been proven to have many advantages compared with traditional methods. In this paper, we propose a novel feature extraction method for ship-radiated noise based on hierarchical entropy (HE). Compared with the traditional entropy, namely multiscale sample entropy (MSE), which only considers information carried in the lower frequency components, HE takes into account both lower and higher frequency components of signals. We illustrate the different properties of HE and MSE by testing them on simulation signals. The results show that HE has better performance than MSE, especially when the difference in signals is mainly focused on higher frequency components. Furthermore, experiments on real-world data of five types of ship-radiated noise are conducted. A probabilistic neural network is employed to evaluate the performance of the obtained features. Results show that HE has a higher classification accuracy for the five types of ship-radiated noise compared with MSE. This indicates that the HE-based feature extraction method could be used to identify ships in the field of underwater acoustic signal processing.

A Denoising Method of Ship Radiated Noise Signal Based on Modified CEEMDAN, Dispersion Entropy, and Interval Thresholding

Due to the non-linear and non-stationary characteristics of ship radiated noise (SR-N) signal, the traditional linear and frequency-domain denoising methods cannot be used for such signals. In this paper, an SR-N signal denoising method based on modified complete ensemble empirical mode decomposition (EMD) with adaptive noise (CEEMDAN), dispersion entropy (DE), and interval thresholding is proposed. The proposed denoising method has the following advantages: (1) as an improved version of CEEMDAN, modified CEEMDAN (MCEEMDAN) combines the advantages of EMD and CEEMDAN, and it is more reliable than CEEMDAN and has less consuming time; (2) as a fast complexity measurement technology, DE can effectively identify the type of intrinsic mode function (IMF); and (3) interval thresholding is used for SR-N signal denoising, which avoids loss of amplitude information compared with traditional denoising methods. Firstly, the original signal is decomposed into a series of IMFs using MCEEMDAN. According to the DE value of IMF, the modes are divided into three types: noise IMF, noise-dominated IMF and pure IMF. After noise IMFs are removed, the noise-dominated IMFs are denoised using interval thresholding. Finally, the pure IMF and the processed noise-dominated IMFs are reconstructed to obtain the final denoised signal. The denoising experiments with the Chen’s chaotic system show that the proposed method has a higher signal-to-noise ratio (SNR) than the other three methods. Applying the proposed method to denoise the real SR-N signal, the topological structure of chaotic attractor can be recovered clearly. It is proved that the proposed method can effectively suppress the high-frequency noise of SR-N signal.

Auditory Inspired Convolutional Neural Networks for Ship Type Classification with Raw Hydrophone Data

Detecting and classifying ships based on radiated noise provide practical guidelines for the reduction of underwater noise footprint of shipping. In this paper, the detection and classification are implemented by auditory inspired convolutional neural networks trained from raw underwater acoustic signal. The proposed model includes three parts. The first part is performed by a multi-scale 1D time convolutional layer initialized by auditory filter banks. Signals are decomposed into frequency components by convolution operation. In the second part, the decomposed signals are converted into frequency domain by permute layer and energy pooling layer to form frequency distribution in auditory cortex. Then, 2D frequency convolutional layers are applied to discover spectro-temporal patterns, as well as preserve locality and reduce spectral variations in ship noise. In the third part, the whole model is optimized with an objective function of classification to obtain appropriate auditory filters and feature representations that are correlative with ship categories. The optimization reflects the plasticity of auditory system. Experiments on five ship types and background noise show that the proposed approach achieved an overall classification accuracy of 79.2%, which improved by 6% compared to conventional approaches. Auditory filter banks were adaptive in shape to improve accuracy of classification.

Noise Reduction Method of Underwater Acoustic Signals Based on Uniform Phase Empirical Mode Decomposition, Amplitude-Aware Permutation Entropy, and Pearson Correlation Coefficient

Noise reduction of underwater acoustic signals is of great significance in the fields of military and ocean exploration. Based on the adaptive decomposition characteristic of uniform phase empirical mode decomposition (UPEMD), a noise reduction method for underwater acoustic signals is proposed, which combines amplitude-aware permutation entropy (AAPE) and Pearson correlation coefficient (PCC). UPEMD is a recently proposed improved empirical mode decomposition (EMD) algorithm that alleviates the mode splitting and residual noise effects of EMD. AAPE is a tool to quantify the information content of nonlinear time series. Unlike permutation entropy (PE), AAPE can reflect the amplitude information on time series. Firstly, the original signal is decomposed into a series of intrinsic mode functions (IMFs) by UPEMD. The AAPE of each IMF is calculated. The modes are separated into high-frequency IMFs and low-frequency IMFs, and all low-frequency IMFs are determined as useful IMFs (UIMFs). Then, the PCC between the high-frequency IMF with the smallest AAPE and the original signal is calculated. If PCC is greater than the threshold, the IMF is also determined as a UIMF. Finally, all UIMFs are reconstructed and the denoised signal is obtained. Chaotic signals with different signal-to-noise ratios (SNRs) are used for denoising experiments. Compared with EMD and extreme-point symmetric mode decomposition (ESMD), the proposed method has higher SNR and smaller root mean square error (RMSE). The proposed method is applied to noise reduction of real underwater acoustic signals. The results show that the method can further eliminate noise and the chaotic attractors are smoother and clearer.

Characterizing time series by extended complexity-entropy curves based on Tsallis, Rényi, and power spectral entropy

In this paper, we create three different entropy curves, Tsallis q-complexity-entropy curve, Rényi r-complexity-entropy curve, and Tsallis-Rényi entropy curve via extending the traditional complexity-entropy causality plane and replacing the permutation entropy into power spectral entropy. This kind of method is free of any parameters and some features that are obscure in the time domain can be extracted in the frequency domain. Results from numerical simulations verify that these three entropy curves can characterize time series efficiently. Chaotic and stochastic time series can be distinguished based on whether the q-complexity-entropy curves are opened or closed. The unrelated stochastic process has a negative curvature associated with the Rényi r-complexity-entropy curve, whereas there are positive curvatures for related cases. In addition, the Tsallis-Rényi entropy curve can display the relationship between two entropies. Finally, we apply this method to sleep electrocardiogram and electroencephalography signals. It is proved that these signals possess similar features with long-range correlated 1/f noise. It is robust enough to exhibit different characteristics for each sleep stage. By using surrogate data sets, the nonlinearity of simulated chaotic time series and sleep data can be identified.

Hierarchical Cosine Similarity Entropy for Feature Extraction of Ship-Radiated Noise

The classification performance of passive sonar can be improved by extracting the features of ship-radiated noise. Traditional feature extraction methods neglect the nonlinear features in ship-radiated noise, such as entropy. The multiscale sample entropy (MSE) algorithm has been widely used for quantifying the entropy of a signal, but there are still some limitations. To remedy this, the hierarchical cosine similarity entropy (HCSE) is proposed in this paper. Firstly, the hierarchical decomposition is utilized to decompose a time series into some subsequences. Then, the sample entropy (SE) is modified by utilizing Shannon entropy rather than conditional entropy and employing angular distance instead of Chebyshev distance. Finally, the complexity of each subsequence is quantified by the modified SE. Simulation results show that the HCSE method overcomes some limitations in MSE. For example, undefined entropy is not likely to occur in HCSE, and it is more suitable for short time series. Compared with MSE, the experimental results illustrate that the classification accuracy of real ship-radiated noise is significantly improved from 75% to 95.63% by using HCSE. Consequently, the proposed HCSE can be applied in practical applications.

Compression of a Deep Competitive Network Based on Mutual Information for Underwater Acoustic Targets Recognition

The accuracy of underwater acoustic targets recognition via limited ship radiated noise can be improved by a deep neural network trained with a large number of unlabeled samples. However, redundant features learned by deep neural network have negative effects on recognition accuracy and efficiency. A compressed deep competitive network is proposed to learn and extract features from ship radiated noise. The core idea of the algorithm includes: (1) Competitive learning: By integrating competitive learning into the restricted Boltzmann machine learning algorithm, the hidden units could share the weights in each predefined group; (2) Network pruning: The pruning based on mutual information is deployed to remove the redundant parameters and further compress the network. Experiments based on real ship radiated noise show that the network can increase recognition accuracy with fewer informative features. The compressed deep competitive network can achieve a classification accuracy of 89.1%, which is 5.3% higher than deep competitive network and 13.1% higher than the state-of-the-art signal processing feature extraction methods.