Research on Sea State Signal Recognition Based on Beluga Whale Optimization-Slope Entropy and One Dimensional-Convolutional Neural Network.

This study introduces a novel nonlinear dynamic analysis method, known as beluga whale optimization-slope entropy (BWO-SlEn), to address the challenge of recognizing sea state signals (SSSs) in complex marine environments. A method of underwater acoustic signal recognition based on BWO-SlEn and one-dimensional convolutional neural network (1D-CNN) is proposed. Firstly, particle swarm optimization-slope entropy (PSO-SlEn), BWO-SlEn, and Harris hawk optimization-slope entropy (HHO-SlEn) were used for feature extraction of noise signal and SSS. After 1D-CNN classification, BWO-SlEn were found to have the best recognition effect. Secondly, fuzzy entropy (FE), sample entropy (SE), permutation entropy (PE), and dispersion entropy (DE) were used to extract the signal features. After 1D-CNN classification, BWO-SlEn and 1D-CNN were found to have the highest recognition rate compared with them. Finally, compared with the other six recognition methods, the recognition rates of BWO-SlEn and 1D-CNN for the noise signal and SSS are at least 6% and 4.75% higher, respectively. Therefore, the BWO-SlEn and 1D-CNN recognition methods proposed in this paper are more effective in the application of SSS recognition.

Slope Entropy Characterisation: An Asymmetric Approach to Threshold Parameters Role Analysis.

Slope Entropy (SlpEn) is a novel method recently proposed in the field of time series entropy estimation. In addition to the well-known embedded dimension parameter, m, used in other methods, it applies two additional thresholds, denoted as δ and γ, to derive a symbolic representation of a data subsequence. The original paper introducing SlpEn provided some guidelines for recommended specific values of these two parameters, which have been successfully followed in subsequent studies. However, a deeper understanding of the role of these thresholds is necessary to explore the potential for further SlpEn optimisations. Some works have already addressed the role of δ, but in this paper, we extend this investigation to include the role of γ and explore the impact of using an asymmetric scheme to select threshold values. We conduct a comparative analysis between the standard SlpEn method as initially proposed and an optimised version obtained through a grid search to maximise signal classification performance based on SlpEn. The results confirm that the optimised version achieves higher time series classification accuracy, albeit at the cost of significantly increased computational complexity.

A Dual-Optimization Fault Diagnosis Method for Rolling Bearings Based on Hierarchical Slope Entropy and SVM Synergized with Shark Optimization Algorithm.

Slope entropy (SlopEn) has been widely applied in fault diagnosis and has exhibited excellent performance, while SlopEn suffers from the problem of threshold selection. Aiming to further enhance the identifying capability of SlopEn in fault diagnosis, on the basis of SlopEn, the concept of hierarchy is introduced, and a new complexity feature, namely hierarchical slope entropy (HSlopEn), is proposed. Meanwhile, to address the problems of the threshold selection of HSlopEn and a support vector machine (SVM), the white shark optimizer (WSO) is applied to optimize both HSlopEn and an SVM, and WSO-HSlopEn and WSO-SVM are proposed, respectively. Then, a dual-optimization fault diagnosis method for rolling bearings based on WSO-HSlopEn and WSO-SVM is put forward. We conducted measured experiments on single- and multi-feature scenarios, and the experimental results demonstrated that whether single-feature or multi-feature, the WSO-HSlopEn and WSO-SVM fault diagnosis method has the highest recognition rate compared to other hierarchical entropies; moreover, under multi-features, the recognition rates are all higher than 97.5%, and the more features we select, the better the recognition effect. When five nodes are selected, the highest recognition rate reaches 100%.

Optimized Ship-Radiated Noise Feature Extraction Approaches Based on CEEMDAN and Slope Entropy.

Slope entropy (Slopen) has been demonstrated to be an excellent approach to extracting ship-radiated noise signals (S-NSs) features by analyzing the complexity of the signals; however, its recognition ability is limited because it extracts the features of undecomposed S-NSs. To solve this problem, in this study, we combined complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to explore the differences of Slopen between the intrinsic mode components (IMFs) of the S-NSs and proposed a single-IMF optimized feature extraction approach. Aiming to further enhance its performance, the optimized combination of dual-IMFs was selected, and a dual-IMF optimized feature extraction approach was also proposed. We conducted three experiments to demonstrate the effectiveness of CEEMDAN, Slopen, and the proposed approaches. The experimental and comparative results revealed both of the proposed single- and dual-IMF optimized feature extraction approaches based on Slopen and CEEMDAN to be more effective than the original ship signal-based and IMF-based feature extraction approaches.

Slope Entropy Characterisation: The Role of the δ Parameter.

Many time series entropy calculation methods have been proposed in the last few years. They are mainly used as numerical features for signal classification in any scientific field where data series are involved. We recently proposed a new method, Slope Entropy (SlpEn), based on the relative frequency of differences between consecutive samples of a time series, thresholded using two input parameters, γ and δ. In principle, δ was proposed to account for differences in the vicinity of the 0 region (namely, ties) and, therefore, was usually set at small values such as 0.001. However, there is no study that really quantifies the role of this parameter using this default or other configurations, despite the good SlpEn results so far. The present paper addresses this issue, removing δ from the SlpEn calculation to assess its real influence on classification performance, or optimising its value by means of a grid search in order to find out if other values beyond the 0.001 value provide significant time series classification accuracy gains. Although the inclusion of this parameter does improve classification accuracy according to experimental results, gains of 5% at most probably do not support the additional effort required. Therefore, SlpEn simplification could be seen as a real alternative.

Slope Entropy Normalisation by Means of Analytical and Heuristic Reference Values.

Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical [0,1] interval. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. It is based on a max-min normalisation scheme, described in two steps. First, an analytic normalisation is proposed using known but very conservative bounds. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. The results confirm the suitability of the approach proposed, using a mixture of the two methods.

Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis.

Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.

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.

Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study.

Bipolar Disorder (BD) is an illness with high prevalence and a huge social and economic impact. It is recurrent, with a long-term evolution in most cases. Early treatment and continuous monitoring have proven to be very effective in mitigating the causes and consequences of BD. However, no tools are currently available for a massive and semi-automatic BD patient monitoring and control. Taking advantage of recent technological developments in the field of wearables, this paper studies the feasibility of a BD episodes classification analysis while using entropy measures, an approach successfully applied in a myriad of other physiological frameworks. This is a very difficult task, since actigraphy records are highly non-stationary and corrupted with artifacts (no activity). The method devised uses a preprocessing stage to extract epochs of activity, and then applies a quantification measure, Slope Entropy, recently proposed, which outperforms the most common entropy measures used in biomedical time series. The results confirm the feasibility of the approach proposed, since the three states that are involved in BD, depression, mania, and remission, can be significantly distinguished.

Fever Time Series Analysis Using Slope Entropy. Application to Early Unobtrusive Differential Diagnosis.

Fever is a readily measurable physiological response that has been used in medicine for centuries. However, the information provided has been greatly limited by a plain thresholding approach, overlooking the additional information provided by temporal variations and temperature values below such threshold that are also representative of the subject status. In this paper, we propose to utilize continuous body temperature time series of patients that developed a fever, in order to apply a method capable of diagnosing the specific underlying fever cause only by means of a pattern relative frequency analysis. This analysis was based on a recently proposed measure, Slope Entropy, applied to a variety of records coming from dengue and malaria patients, among other fever diseases. After an input parameter customization, a classification analysis of malaria and dengue records took place, quantified by the Matthews Correlation Coefficient. This classification yielded a high accuracy, with more than 90% of the records correctly labelled in some cases, demonstrating the feasibility of the approach proposed. This approach, after further studies, or combined with more measures such as Sample Entropy, is certainly very promising in becoming an early diagnosis tool based solely on body temperature temporal patterns, which is of great interest in the current Covid-19 pandemic scenario.

Refined composite multiscale slope entropy and its application in rolling bearing fault diagnosis.

Rolling bearing is the key component of rotating machinery, and its vibration signal usually exhibits nonlinear and nonstationary characteristics when failure occurs. Multiscale permutation entropy (MPE) is an effective nonlinear dynamics analysis tool, which has been successfully applied to rolling bearing fault diagnosis in recent years. However, MPE ignores the deep amplitude information when measuring the complexity of the time series and the original multiscale coarse-graining is insufficient, which requires further research and improvement. In order to protect the integrity of information structure, a novel nonlinear dynamic analysis method termed refined composite multiscale slope entropy (RCMSlE) is proposed in this paper, which introduced the concept of refined composite to further boost the performance of MPE in nonlinear dynamical complexity analysis. Furthermore, RCMSlE utilizes a novel symbolic representation that takes full account of mode and amplitude information, which overcomes the weaknesses in describing the complexity and regularity of bearing signals. Based on this, a GWO-SVM multi-classifier is introduced to fulfill mode recognition, and then a new intelligent fault diagnosis method for rolling bearing based on RCMSlE and GWO-SVM is proposed. The experimental results show that the proposed method can not only accurately identify different fault types and degrees of rolling bearing, but also has a short computation time and better performance than other comparative methods.