Slope Entropy Research Articles

A novel scheme of condition monitoring and fault recognition based on time-shift multi-scale weighted slope entropy for rolling bearings under variable speed conditions

A novel scheme of condition monitoring and fault recognition based on time-shift multi-scale weighted slope entropy for rolling bearings under variable speed conditions

An adaptive slope entropy combined with hierarchical entropy applied to rolling bearing fault diagnosis

An adaptive slope entropy combined with hierarchical entropy applied to rolling bearing fault diagnosis

Refined time-shift multiscale slope entropy: a new nonlinear dynamic analysis tool for rotating machinery fault feature extraction

Refined time-shift multiscale slope entropy: a new nonlinear dynamic analysis tool for rotating machinery fault feature extraction

Radio Signal Modulation Recognition Method Based on Hybrid Feature and Ensemble Learning: For Radar and Jamming Signals.

The detection performance of radar is significantly impaired by active jamming and mutual interference from other radars. This paper proposes a radio signal modulation recognition method to accurately recognize these signals, which helps in the jamming cancellation decisions. Based on the ensemble learning stacking algorithm improved by meta-feature enhancement, the proposed method adopts random forests, K-nearest neighbors, and Gaussian naive Bayes as the base-learners, with logistic regression serving as the meta-learner. It takes the multi-domain features of signals as input, which include time-domain features including fuzzy entropy, slope entropy, and Hjorth parameters; frequency-domain features, including spectral entropy; and fractal-domain features, including fractal dimension. The simulation experiment, including seven common signal types of radar and active jamming, was performed for the effectiveness validation and performance evaluation. Results proved the proposed method's performance superiority to other classification methods, as well as its ability to meet the requirements of low signal-to-noise ratio and few-shot learning.

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.

Motor fault diagnosis based on composite multi-scale weighted reverse slope entropy and neighborhood preserving embedding

The motors are critical components of the electromechanical transmission in vehicles, and its operating status directly affects the maneuverability of vehicles. To quickly and accurately identify the operating status of motors, this paper proposes a new entropy - Composite Multi-scale Weighted Reverse Slope Entropy (CMWRSlE) for motor fault diagnosis, which is a more interpretable entropy due to its deep exploration of signals. Firstly, the composite multi-scale weighted reverse slope entropy values are extracted from the vibration signals of the motor in different states; Secondly, the extracted features are dimensionally reduced by the manifold learning algorithm – Neighbourhood Preserving Embedding (NPE) and classified by the hierarchical prototype-based approach (HPA) to achieve the fault diagnosis of the motor. Finally, the method proposed in this paper is validated through two sets of experimental data: motor rotor faults and motor bearing faults. The results show that the accuracy of the proposed method in motor fault diagnosis reaches 100 %, which indicates the effectiveness of the proposed method.

The double-feature extraction method based on slope entropy and symbolic dynamic entropy for the fault diagnosis of rolling bearing

The double-feature extraction method based on slope entropy and symbolic dynamic entropy for the fault diagnosis of rolling bearing

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.

Analyzing entropy features in time-series data for pattern recognition in neurological conditions

In the field of medical diagnosis and patient monitoring, effective pattern recognition in neurological time-series data is essential. Traditional methods predominantly based on statistical or probabilistic learning and inference often struggle with multivariate, multi-source, state-varying, and noisy data while also posing privacy risks due to excessive information collection and modeling. Furthermore, these methods often overlook critical statistical information, such as the distribution of data points and inherent uncertainties. To address these challenges, we introduce an information theory-based pipeline that leverages specialized features to identify patterns in neurological time-series data while minimizing privacy risks. We incorporate various entropy methods based on the characteristics of different scenarios and entropy. For stochastic state transition applications, we incorporate Shannon’s entropy, entropy rates, entropy production, and the von Neumann entropy of Markov chains. When state modeling is impractical, we select and employ approximate entropy, increment entropy, dispersion entropy, phase entropy, and slope entropy. The pipeline’s effectiveness and scalability are demonstrated through pattern analysis in a dementia care dataset and also an epileptic and a myocardial infarction dataset. The results indicate that our information theory-based pipeline can achieve average performance improvements across various models on the recall rate, F1 score, and accuracy by up to 13.08 percentage points, while enhancing inference efficiency by reducing the number of model parameters by an average of 3.10 times. Thus, our approach opens a promising avenue for improved, efficient, and critical statistical information-considered pattern recognition in medical time-series data.

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.

Optimized Fuzzy Slope Entropy: A Complexity Measure for Nonlinear Time Series

Optimized Fuzzy Slope Entropy: A Complexity Measure for Nonlinear Time Series

Optimized multivariate multiscale slope entropy for nonlinear dynamic analysis of mechanical signals

Slope entropy (SloEn) is an effective nonlinear dynamic method to represent the complexity of time series, which has been extensively applied to various mechanical signal processing. However, it is only applicable to the analysis of single-channel time series at a single scale. Additionally, thresholds γandδ of SloEn can affect the division of symbols. To address these limitations, this paper firstly develops multivariate SloEn (mvSloEn) and extends it to multiscale mvSloEn (mvMSloEn), which not only accounts for the correlation of time series complexity within and across channels, but also mirrors the complexity of multi-channel time series over multiple scales. Furthermore, the sea-horse optimization-mvMSloEn (SHO-mvMSloEn) is proposed through utilizing the sea-horse optimizer (SHO) to fine-tune the thresholds for improved performance. Finally, the proposed SHO-mvMSloEn is applied to three real-world datasets and the highest classification accuracies are all over 98 %, superior to the existing multivariate multiscale dispersion entropy (mvMDE), multivariate multiscale fuzzy entropy (mvMFE), and multivariate multiscale sample entropy (mvMSE), which demonstrates that the proposed SHO-mvMSloEn always exhibits the best feature extraction capability.

A new denoising method based on decomposition mixing of hydro-acoustic signal

Hydro-acoustic signal (HAS) contains abundant information. HAS denoising is of great significance for accurate identification of underwater targets, research of military detection equipment and monitoring of ocean ecological environment, and has good civil value and military application value. Because of complex characteristic of ocean circumstance and the temporal change characteristic of hydro-acoustic channel, HAS denoising faces great challenges. To denoise HAS effectively, a new denoising method based on improved variational mode decomposition by jumping spider optimization algorithm (JVMD), weighted fractional order slope entropy (WFrSlEn), dynamic adjacent threshold of correlation coefficient (DATC), improved one dimension (1-D) Gaussian-Laplacian smoothing (IGLS) and adaptive interval correlation wavelet transform (AICWT), named JVMD-WFrSlEn-DATC-IGLS-AICWT, is proposed. JVMD is proposed for the problem that the number of decomposition layer K and penalty factor α cannot be selected adaptively in variational mode decomposition (VMD). WFrSlEn is proposed for the problem that decomposition components are difficult to divide precisely. DATC is proposed for the problem that threshold of correlation coefficient (CC) is selected. IGLS is proposed to preserve more signal details. AICWT is proposed to solve the problem that wavelet transform cannot automatically select appropriate parameters. Firstly, the original signal is decomposed to many intrinsic mode functions (IMFs) with JVMD. Secondly, WFrSlEn and DATC distinguish pure IMFs, mixed IMFs and noisy IMFs. IGLS is performed on mixed IMFs and AICWT is performed on noisy IMFs. Finally, two processed IMFs are reconstructed with pure IMFs to obtain final denoised signal. The results show that the proposed denoising method can improve signal-to-noise ratio by 8∼10 dB for chaotic signal, make phase diagram clearer and smoother, and can effectively suppress noise for HAS.

System dynamics monitoring using PIC micro-controller-based PLSE

The permutation largest slope entropy (PLSE) algorithm has been shown to be effective to distinguish between regular and non-regular dynamics from time series analysis. However, as it is the case for many non-linear time series analysis algorithms, such a characterization is locally made and does not allow one to capture some micro-phenomena, such as intermittency, that may occur in the system behavior. This paper presents a PIC micro-controller based implementation of the PLSE for a real-time monitoring of system dynamics. The PLSE algorithm is optimized to fit the program and data memory of low-end processors using the XC8 compiler and the MPLAB X IDE. The resulting algorithm is implemented on the PIC16F18446 and deployed on the Explorer 8 development board. The effectiveness of the developed tool is validated by considering an electrical circuit of the Duffing oscillator that can generate both periodic and chaotic dynamics. By comparing the PLSE values with the phase portraits and previous results on the Duffing oscillator circuit, the developed tool efficiently allows one to monitor the behavior of dynamical systems.

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%.

SO-slope entropy coupled with SVMD: A novel adaptive feature extraction method for ship-radiated noise

Slope entropy (SloEn) has been applied as a powerful nonlinear dynamic tool for signal complexity measurement and is widely used for ship-radiated noise signal (S-RNS) feature extraction. However, the thresholds of SloEn affect the entropy value, which influences the effect of feature extraction. Aimed at addressing the problem, this paper uses the snake optimizer (SO) to optimize SloEn and proposes a new entropy indicator, named SO SloEn (SO-SloEn), and then a novel adaptive S-RNS feature extraction method is put forward in combination with the successive variational mode decomposition (SVMD) and SO-SloEn, which solves the parameter selection problem of variational mode decomposition (VMD). First, SVMD is employed to decompose the S-RNS into several intrinsic mode functions (IMFs); after that, the SO-SloEn of IMFs is calculated to obtain the feature matrix dataset; finally, optimal IMF combinations are obtained through feature selection. The effectiveness of the proposed method is verified by two S-RNS cases, and the results indicate that the recognition rate of the proposed method is always the highest compared with other decomposition algorithms and other entropy indicators under the condition of extracting different numbers of IMFs; moreover, the highest recognition rate can reach more than 92% in both cases.

A novel hybrid feature extraction approach of marine vessel signal via improved empirical mode decomposition and measuring complexity

The feature extraction of marine vessel-radiated noise (MVRN) under the complex ocean background is explored. To this end, a hybrid approach is presented based on the analysis of MVRN in subspaces of intrinsic mode functions (IMF) extracted using the improved empirical mode decomposition (IEMD) and measuring complexity. The restriction of the end-effect is an important problem when employing the EMD algorithm. In this study, first, to reduce the end-effects, an IEMD algorithm based on the correlation expansion model is proposed. Then, a comparative study of IEMD, classic EMD (CEMD), and EMD by other expansion methods are conducted on several signals. Next, IEMD, CEMD, and variational mode decomposition (VMD) algorithms are utilized to extract a group of IMFs for three types of MVRN. Later, one obtained IMF from each method that contains the most dominant information is selected. Lastly, two statistical complexity measures (i.e., permutation entropy (PE) and slope entropy (SlopEn)) are used as the features of the chosen IMF to improve the underwater signal separability and stability. Experimental results indicate that the suggested approach (IEMD-PE/SlopEn) can effectively extract the feature information of underwater signals. Additionally, it has a better ability to discriminate between various kinds of MVRN.

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.

Rolling bearing state assessment based on the composite multiscale weight slope entropy and hierarchical prototype-based approach

To evaluate the state of rolling bearing more accurately, a new feature called composite multiscale weight slope entropy was proposed for the complexity measurement of vibration signals. On the basis of analyzing the fault signal structure, the new feature could consider the influence of the nonlinearity, the multiscale characteristics, the fluctuation of the amplitude, and the amplitude itself on the fault signals. In the following, different fault types and the corresponding damage degree of rolling bearings were identified with the hierarchical prototype-based approach. Compared with the results of different modified slope entropy, it is shown that composite multiscale weight slope entropy could significantly improve the identification accuracy. In the two designed testing schemes, ten and sixty state types of rolling bearings are respectively calculated, and the identification accuracy could reach up to 100% and 96.5% respectively, which illustrate the effectiveness and the validity of the proposed approach.

Feature extraction method of ship radiated noise based on BOA-VMD and slope entropy

Although the technical requirements for the feature extraction of ship radiated noise (SRN) in the fields of national defense and economy increase with each passing day, the complexity of the marine environment makes the feature extraction of SRN difficult. The traditional feature extraction method based on variational mode decomposition (VMD) is widely used in the feature extraction of SRN. Nevertheless, the use of VMD is greatly affected by parameters. In this paper, the butterfly optimization algorithm (BOA) is introduced to optimize VMD, which is called BOA-VMD algorithm, and realizes the optimal selection of VMD parameters K and α. To further improve the efficiency of feature extraction method, combined with slope entropy (SE), a feature extraction method of SRN based on BOA-VMD and SE is proposed. The experimental results of the simulated signal show that the BOA-VMD algorithm has a smaller envelope entropy value and better decomposition effect than the genetic algorithm (GA) and particle swarm optimization (PSO). The experimental results of feature extraction of SRN show that the highest recognition rate of the four entropy values improve with the increase of the number of extracted features, compared with the three entropy values of dispersion entropy (DE), fluctuation dispersion entropy (FDE) and permutation entropy (PE), the SRN feature extraction method based on BOA-VMD and SE has the highest recognition rate under different quantity features, and the recognition rate has reached 100% under three features.