Improved Permutation Entropy Research Articles

Underwater Small Target Detection Method Based on the Short-Time Fourier Transform and the Improved Permutation Entropy

Underwater Small Target Detection Method Based on the Short-Time Fourier Transform and the Improved Permutation Entropy

Fetal QRS extraction from single-channel abdominal ECG using adaptive improved permutation entropy.

Fetal electrocardiogram (fECG) monitoring is crucial for assessing fetal condition during pregnancy. However, current fECG extraction algorithms are not suitable for wearable devices due to their high computational cost and multi-channel signal requirement. The paper introduces a novel and efficient algorithm called Adaptive Improved Permutation Entropy (AIPE), which can extract fetal QRS from a single-channel abdominal ECG (aECG). The proposed algorithm is robust and computationally efficient, making it a reliable and effective solution for wearable devices. To evaluate the performance of the proposed algorithm, we utilized our clinical data obtained from a pilot study with 10 subjects, each recording lasting 20min. Additionally, data from the PhysioNet 2013 Challenge bank with labeled QRS complex annotations were simulated. The proposed methodology demonstrates an average positive predictive value ([Formula: see text]) of 91.0227%, sensitivity (Se) of 90.4726%, and F1 score of 90.6525% from the PhysioNet 2013 Challenge bank, outperforming other methods. The results suggest that AIPE could enable continuous home-based monitoring of unborn babies, even when mothers are not engaging in any hard physical activities.

Research on the Threshold Determination Method of the Duffing Chaotic System Based on Improved Permutation Entropy and Poincaré Mapping.

The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Traditional methods such as Melnikov theory, the Poincaré section quantitative discrimination method, and experimental analyses based on phase diagram segmentation have limitations in accuracy and efficiency. In addition, they require large computational data and complex algorithms while having slow convergence. Improved permutation entropy incorporates signal amplitude information on the basis of permutation entropy and has better noise resistance. According to the characteristics of improved permutation entropy, a threshold determination method for the Duffing chaotic oscillator detection system based on improved permutation entropy (IPE) and Poincaré mapping (PM) is proposed. This new metric is called Poincaré mapping improved permutation entropy (PMIPE). The simulation results and the verification results of real underwater acoustic signals indicate that our proposed method outperforms traditional methods in terms of accuracy, simplicity, and stability.

Ensemble Improved Permutation Entropy: A New Approach for Time Series Analysis.

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper.

Novel QRS detection based on the Adaptive Improved Permutation Entropy

Detection of the QRS complex is the most important step in analyzing ECG signals for heart monitoring and diagnosis. There have been several QRS-peak detection methods reported in the literature. Most of these methods have low performance under noisy conditions. In this paper, we propose a novel QRS detection algorithm based on a new Permutation Entropy (PE) method that we developed and referred to as the Adaptive Improved Permutation Entropy (AIPE) method. The parameters of the AIPE method are determined based on the specific signal properties. Implementing the AIPE method leads to prominently preserving the QRS complex and eliminating noises of the ECG signal without smoothing the ECG signal. Our simulations show that the proposed QRS detection algorithm is effective and robust under noisy conditions. The algorithm is validated on the MIT-BIH Noise Stress Test Database for various SNR values. In addition, we examined the algorithm’s performance under motion noise conditions, mimicking a practical scenario. We used the metrics of sensitivity, positive predictive, and F1 score to evaluate the performance of our algorithm and compare it with several other algorithms explained in the literature. Our investigation shows that the proposed algorithm is efficient and effective. More importantly, it is robust under noisy conditions providing superior performance over other recent and popular QRS detection algorithms, including the popular Pan–Tompkins and the recent Advanced Adaptive Multilevel Thresholding (AAMT) algorithms.

Novel QRS Detection Based on the Adaptive Improved Permutation Entropy

Novel QRS Detection Based on the Adaptive Improved Permutation Entropy

Novel QRS Detection Based on the Adaptive Improved Permutation Entropy

Novel QRS Detection Based on the Adaptive Improved Permutation Entropy

Study on nonlinear analysis of MEG in patients with brain diseases

Magnetoencephalography (MEG) is a kind of brain function detection technology without trauma, which detects the electromagnetic physiological signal in the brain. It is widely used in depression research. We used permutation entropy, improved permutation entropy, conditional entropy to study the difference of MEG between depressed patients and healthy people, respectively. We implement three different entropy algorithms and compare the relative differences of entropy values in different brain regions of healthy people and depression patients under positive, neutral and negative emotional stimuli. The experimental results show that the relative difference of conditional entropy > the relative difference of improved permutation entropy > the relative difference of permutation entropy, and the difference of entropy value in the frontal region of human brain is the most obvious, which may provide the basis for the diagnosis of depression.

Multiscale Entropy Feature Extraction Method of Running Power Equipment Sound.

The equipment condition monitoring based on computer hearing is a new pattern recognition approach, and the system formed by it has the advantages of noncontact and strong early warning abilities. Extracting effective features from the sound data of the running power equipment help to improve the equipment monitoring accuracy. However, the sound of running equipment often has the characteristics of serious noise, non-linearity and instationary, which makes it difficult to extract features. To solve this problem, a feature extraction method based on the improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and multiscale improved permutation entropy (MIPE) is proposed. Firstly, the ICEEMDAN is utilized to obtain a group of intrinsic mode functions (IMFs) from the sound of running power equipment. The noise IMFs are then identified and eliminated through mutual information (MI) and mean mutual information (meanMI) of IMFs. Next, the normalized mutual information (norMI) and MIPE are calculated respectively, and norMI is utilized to weigh the corresponding MIPE result. Finally, based on the separability criterion, the weighted MIPE results are feature-dimensionally reduced to obtain the multiscale entropy feature of the sound. The experimental results show that the classification accuracies of the method under the conditions of no noise and 5 dB reach 96.7% and 89.9%, respectively. In practice, the proposed method has higher reliability and stability for the sound feature extraction of the running power equipment.

Rope Tension Fault Diagnosis in Hoisting Systems Based on Vibration Signals Using EEMD, Improved Permutation Entropy, and PSO-SVM.

Fault diagnosis of rope tension is significantly important for hoisting safety, especially in mine hoists. Conventional diagnosis methods based on force sensors face some challenges regarding sensor installation, data transmission, safety, and reliability in harsh mine environments. In this paper, a novel fault diagnosis method for rope tension based on the vibration signals of head sheaves is proposed. First, the vibration signal is decomposed into some intrinsic mode functions (IMFs) by the ensemble empirical mode decomposition (EEMD) method. Second, a sensitivity index is proposed to extract the main IMFs, then the de-noised signal is obtained by the sum of the main IMFs. Third, the energy and the proposed improved permutation entropy (IPE) values of the main IMFs and the de-noised signal are calculated to create the feature vectors. The IPE is proposed to improve the PE by adding the amplitude information, and it proved to be more sensitive in simulations of impulse detecting and signal segmentation. Fourth, vibration samples in different tension states are used to train a particle swarm optimization–support vector machine (PSO-SVM) model. Lastly, the trained model is implemented to detect tension faults in practice. Two experimental results validated the effectiveness of the proposed method to detect tension faults, such as overload, underload, and imbalance, in both single-rope and multi-rope hoists. This study provides a new perspective for detecting tension faults in hoisting systems.

Coded Permutation Entropy: A Measure for Dynamical Changes Based on the Secondary Partitioning of Amplitude Information.

An improved permutation entropy (PE) algorithm named coded permutation entropy (CPE) is proposed in this paper to optimize the problems existing in PE based on the secondary partitioning. The principle of CPE algorithm is given, and the performance of it for dynamical change detection is analyzed using synthetic signal, logistic map and Lorenz map. The detection ability of CPE algorithm in different signal-to-noise ratios (SNR) is studied and the algorithm complexity is discussed. The results show that CPE can accurately capture minor feature information and amplify the detection results of dynamical changes compared with PE, weighted permutation entropy (WPE) and amplitude-aware permutation entropy (AAPE), but it has less robustness to noise and requires a higher computation cost than the others. Finally, we use the new algorithm to analyze the rolling bearing fault signals. The application of actual signals illustrates that CPE performs better in detecting abnormal pulse of the rolling bearing when the embedded dimension is small. From all the analyses in this paper, we find that CPE has a better performance for dynamical change detection compared with the other three algorithms when there is a larger repetition rate of permutation pattern in the position sequences.

A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy.

Extracting useful features from ship-radiated noise can improve the performance of passive sonar. The entropy feature is an important supplement to existing technologies for ship classification. However, the existing entropy feature extraction methods for ship-radiated noise are less reliable under noisy conditions because they lack noise reduction procedures or are single-scale based. In order to simultaneously solve these problems, a new feature extraction method is proposed based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), normalized mutual information (norMI), and multiscale improved permutation entropy (MIPE). Firstly, the ICEEMDAN is utilized to obtain a group of intrinsic mode functions (IMFs) from ship-radiated noise. The noise reduction process is then conducted by identifying and eliminating the noise IMFs. Next, the norMI and MIPE of the signal-dominant IMFs are calculated, respectively; and the norMI is used to weigh the corresponding MIPE result. The multi-scale entropy feature is finally defined as the sum of the weighted MIPE results. Experimental results show that the recognition rate of the proposed method achieves 90.67% and 83%, respectively, under noise free and 5 dB conditions, which is much higher than existing entropy feature extraction algorithms. Hence, the proposed method is more reliable and suitable for feature extraction of ship-radiated noise in practice.

Improved Permutation Entropy for Measuring Complexity of Time Series under Noisy Condition

Measuring complexity of observed time series plays an important role for understanding the characteristics of the system under study. Permutation entropy (PE) is a powerful tool for complexity analysis, but it has some limitations. For example, the amplitude information is discarded; the equalities (i.e., equal values in the analysed signal) are not properly dealt with; and the performance under noisy condition remains to be improved. In this paper, the improved permutation entropy (IPE) is proposed. The presented method combines some advantages of previous modifications of PE. Its effectiveness is validated through both synthetic and experimental analyses. Compared with PE, IPE is capable of detecting spiky features and correctly differentiating heart rate variability (HRV) signals. Moreover, it performs better under noisy condition. Ship classification experiment results demonstrate that IPE achieves 28.66% higher recognition rate than PE at 0dB. Hence, IPE could be used as an alternative of PE for analysing time series under noisy condition.

Feature Extraction Strategy with Improved Permutation Entropy and Its Application in Fault Diagnosis of Bearings

Feature extraction is one of the most difficult aspects of mechanical fault diagnosis, and it is directly related to the accuracy of bearing fault diagnosis. In this study, improved permutation entropy (IPE) is defined as the feature for bearing fault diagnosis. In this method, ensemble empirical mode decomposition (EEMD), a self‐adaptive time‐frequency analysis method, is used to process the vibration signals, and a set of intrinsic mode functions (IMFs) can thus be obtained. A feature extraction strategy based on statistical analysis is then presented for IPE, where the so‐called optimal number of permutation entropy (PE) values used for an IPE is adaptively selected. The obtained IPE‐based samples are then input to a support vector machine (SVM) model. Subsequently, a trained SVM can be constructed as the classifier for bearing fault diagnosis. Finally, experimental vibration signals are applied to validate the effectiveness of the proposed method, and the results show that the proposed method can effectively and accurately diagnose bearing faults, such as inner race faults, outer race faults, and ball faults.

Quantitative selection of sensor data based on improved permutation entropy for system remaining useful life prediction

Condition monitoring is an effective tool for diagnosing and predicting the system fault or failure. One class of method in system condition monitoring is based on the condition data (i.e., data-driven methodology). However, not all the collected condition data can be utilized for the data-driven methodology. Hence, the selection of reasonable condition data is crucial for the application of the data-driven methodology. This is especially useful for the system which has the characteristics of degradation. In such system, the condition data that have the increasing or decreasing trend are desirable. This article proposes the quantitative selection of sensor data for system remaining useful life prediction. The main advantage of the proposed metric to select sensors is that the information theory is adopted. Hence, the selection of sensors can be determined by the proposed quantitative metric. Two case studies which include one simulation data set and one practical data set are carried out to evaluate the effectiveness of the proposed metric. The detailed experiments prove the advantage of the proposed approach.

Multi-Scale Permutation Entropy: A Complexity Measure for Discriminating Two-Phase Flow Dynamics

We propose an improved permutation entropy method, i.e., multi-scale permutation entropy (MSPE), for discriminating two-phase flow dynamics. We first take the signals from different typical dynamical systems as examples to demonstrate the effectiveness of the methods. In particular, we compute the MSPE values of sinusoidal signal, logistic, Lorenz and Chen chaotic signals and their signals with white Gaussian noise added. We find that the MSPE method can be an effective tool for analyzing the time series with distinct dynamics. We finally calculate the multi-scale permutation entropy and rate of MSPE from 66 groups of conductance fluctuating signals and find that these two measures can be used to identify different flow patterns and further explore dynamical characteristics of gas-liquid flow patterns. These results suggest that the MSPE can potentially be a useful tool for revealing the dynamical complexity of two-phase flow on different scales.