Normalized Permutation Entropy Research Articles

HEART SOUND NOISE SEPARATION FROM LUNG SOUND BASED ON ENHANCED VARIATIONAL MODE DECOMPOSITION FOR DIAGNOSING PULMONARY DISEASES

Lung sound (LS) signals are vital for diagnosing pulmonary disorders. However, heart sound (HS) interferes with the analysis of LS, leading to the misdiagnosis of lung disorders. To address this issue, we propose an Enhanced Variational Mode Decomposition (E-VMD) technique to remove HS interference from LSs effectively. The E-VMD method automatically determines the mode number for signal decomposition based on the characteristics of variational mode functions (VMFs) such as normalized permutation entropy, kurtosis index, extreme frequency domain, and energy loss coefficient. The performance of the proposed denoising technique was evaluated using six performance metrics: Signal-to-noise ratio (SNR), root mean square error (RMSE), normalized mean absolute error (nMAE), correlation coefficient factor (CCF), CPU[Formula: see text], and CPU[Formula: see text]. In comparison to other denoising methods such as empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), complementary ensemble empirical mode decomposition (CEEMD), singular spectrum analysis (SSA), and variational mode decomposition (VMD), the new E-VMD method demonstrates superior denoising outcome. The proposed method was evaluated using LS recorded from the outpatient department of Thoracic Medicine at Thanjavur Medical College and Hospital, Thanjavur. The obtained performance measures are as follows: RMSE: 0.02103 ± 0.00054, SNR: 28.52464 ± 0.00253, nMAE: 0.00009 ± 0.00056, CCF: 0.9962, CPU[Formula: see text]: 34.586, and CPU[Formula: see text]: 0.452 s. These results affirm the adaptability and robustness of the proposed method, even in the existence of HS noise. This method improves denoising accuracy and computational efficacy, making it a useful tool for improving the analysis of LS signals and assisting in medical diagnostics. This technique utilizes an electronic stethoscope, a common clinical device used by healthcare professionals for detecting lung disease.

Secure WDM communication based on second order differential feedback electro-optical chaotic mutual injection synchronization

An optical phase chaos and mutual injection chaos synchronization scheme based on second order differential feedback electro-optical loop is proposed for chaotic communication. The filtered chaotic waves for mutual injection synchronization and multi-channel signals are transmitted through wavelength division multiplexing (WDM) to realize large-capacity confidential communication. The results show that the bandwidth of the optical chaos is 41.38 GHz, the normalized permutation entropy is 0.999, and the chaos has the performance of time delay suppressing (TDS). This scheme achieves up to 7-channel 25 GBaud 16QAM with the multi-modulus algorithm (MMA) algorithm at OSNR of 25 dB after 100 km transmission. The bit-rate distance of 280,000 Gb/s km is successfully realized by 500 km transmission of 4-channel 35 GBaud 16QAM signals at 25 dB OSNR. The analysis proves that the performance of the second order digital differential electro-optical phase feedback (2nd order DEOP) chaos is better than that of the 1st order DEOP chaos and 3rd order DEOP chaos. The 2nd order DEOP chaos can be generated at a smaller feedback coefficient, the bandwidth of radio frequency chaos is wider, and the TDS suppression is better. This scheme realizes high-speed and large-capacity secure optical chaos communication, which can be widely used in WDM networks and has practical feasibility and application value.

Changes in the autonomic cardiorespiratory activity in parturient women with severe and moderate features of preeclampsia.

Cardiorespiratory coupling (CRC) is a physiological phenomenon that reflects the mutual interaction between the cardiac and respiratory control systems. It is mainly associated with efferent vagal activity from the central autonomic network. Few studies have explored the autonomic changes of CRC in preeclampsia, a critical obstetric complication related to possible autonomic dysfunctions and inflammatory disturbances. This study examined the autonomic mechanisms of CRC in women with severe and moderate preeclampsia and healthy controls by applying nonlinear methods based on information theory, such as mutual information (MI) and Renyi's mutual information (RMI) and the linear and nonlinear analysis of the Pulse-Respiration Quotient (PRQ). We studied three groups of parturient women in the third trimester of pregnancy with a clinical diagnosis of preeclampsia without severe symptoms (P, 38.5 ± 1.4 weeks of pregnancy, n=19), preeclampsia with severe symptoms (SP, 37.5 ± 0.9 weeks of pregnancy, n=22), and normotensive control women (C, 39.1 ± 1.3 weeks of pregnancy, n=20). 10-minutes of abdominal electrocardiograms (ECG) and respiratory signals (RESP) were recorded in all the participants. Subsequently, we obtained the maternal beat-to-beat (RR) and breath-to-breath (BB) time series from ECG and RESP, respectively. The CRC between RR and BB was quantified by nonlinear methods based on information theory, such as MI and RMI, along with the analysis of the novel index of PRQ. Subsequently, we computed the mean PRQ (mPRQ) and the normalized permutation entropy (nPermEn_PRQ) from the PRQ time series generated from BB and RR. In addition, we examined the vagal activity in the three groups by the logarithm of the median of the distribution of the absolute values of successive RR differences (logRSA). The MI and RMI values were significantly lower (p<0.05) in the preeclamptic groups compared to the control group. However, no significant differences were found between the preeclamptic groups. The logRSA and nPermEn_PRQ indices were significantly lower (p<0.05) in SP compared to C and P. Our data suggest that parturient women with severe and mild preeclampsia may manifest an altered cardiorespiratory coupling compared with normotensive control women. Disrupted CRC in severe preeclampsia could be associated with vagal withdrawal and less complex cardiorespiratory dynamics. The difference in vagal activity between the preeclamptic groups may suggest a further reduction in vagal activity associated with the severity of the disease.

Detection of cardiac arrhythmia patterns in ECG through H × C plane.

The aim of this study is to formulate a new methodology based upon informational tools to detect patients with cardiac arrhythmias. As it is known, sudden death is the consequence of a final arrhythmia, and here lies the relevance of the efforts aimed at the early detection of arrhythmias. The information content in the time series from an electrocardiogram (ECG) signal is conveyed in the form of a probability distribution function, to compute the permutation entropy proposed by Bandt and Pompe. This selection was made seeking its remarkable conceptual simplicity, computational speed, and robustness to noise. In this work, two well-known databases were used, one containing normal sinus rhythms and another one containing arrhythmias, both from the MIT medical databank. For different values of embedding time delay τ, normalized permutation entropy and statistical complexity measure are computed to finally represent them on the horizontal and vertical axes, respectively, which define the causal plane H×C. To improve the results obtained in previous works, a feature set composed by these two magnitudes is built to train the following supervised machine learning algorithms: random forest (RF), support vector machine (SVM), and k nearest neighbors (kNN). To evaluate the performance of each classification technique, a 10-fold cross-validation scheme repeated 10 times was implemented. Finally, to select the best model, three quality parameters were computed, namely, accuracy, the area under the receiver operative characteristic (ROC) curve (AUC), and the F1-score. The results obtained show that the best classification model to detect the ECG coming from arrhythmic patients is RF. The values of the quality parameters were at the same levels reported in the available literature using a larger data set, thus supporting this proposal that uses a very small-sized feature space to train the model later used to classify. Summarizing, the attained results show the possibility to discriminate both groups of patients, with normal sinus rhythm or arrhythmic ECG, showing a promising efficiency in the definition of new markers for the detection of cardiovascular pathologies.

Adaptive noise removal for biological Raman spectra with low SNR

Raman data with low signal-to-noise ratio (SNR) are often obtained in the process of rapid or low-power acquisition for biological samples. The noise removal out of a biological Raman spectrum is laborious owing to numerous and superimposed Raman peaks, and it often takes a lot of time to find the optimal preproceed parameters. In this study, an adaptive denoising method for biological Raman data has been proposed, using three comparisons and a quantitative prediction model to show its simplicity and effectiveness. In this work, we decomposed Raman spectra of human skin and rice leaf on Hilbert vibration decomposition (HVD) method, to obtain a series of initial values, for example as peak position, intensity and full width at half maximum (FWHM), then fitted Raman spectrum according the Vogit function until the indicator function F reached the minimum value. The SNR and the root mean square error（RMSE) of HVD denoised spectrum were 57.5864 dB and 0.0108, and were both better than those of preproceed data (35.1826 dB, 0.0337; 32.4120 dB, 0.0352; 38.0685 dB, 0.0226) by Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), and Local Complementary Ensemble Empirical Mode Decomposition (LCEMD), compared with adaptive denoising methods, EMD, EEMD and LCEEMD, the improved algorithm had the advantages of no modal aliasing, no noise residue and independence of normalized permutation entropy. Then HVD denoised data of rice leaf samples were compressed by principal component analysis (PCA) and used for chlorophyll content prediction model. The correlation coefficient and standard error for prediction set of HVD +PCA model were 0.856 and 5.38, and were also better than those of non-adaptive preproceed data models (Mobing Average Smoothing, Gaussian Filter Smoothing, Median Filter Smoothing, Savitzky-Golay Smoothing and Wavelet Transform Denoising). The final experimental comparison showed that the HVD denoising method can also be applied to the Raman spectrum noise removal of inorganic samples, but better performances had been shown in the noise removal of complex biological Raman spectra. Accurate denoising of biological Raman spectrum is of great significance for accurate quantitative prediction and qualitative analysis, and no prior setting of the preproceed parameters makes the HVD denoising method easy to operate.

Chaotic time-delay signature suppression using quantum noise.

The time-delay signature (TDS) suppression of semiconductor lasers with external optical feedback is necessary to ensure the security of chaos-based secure communications. Here we numerically and experimentally demonstrate a technique to effectively suppress the TDS of chaotic lasers using quantum noise. The TDS and dynamical complexity are quantified using the autocorrelation function and normalized permutation entropy at the feedback delay time, respectively. Quantum noise from quadrature fluctuations of the vacuum state is prepared through balanced homodyne measurement. The effects of strength and bandwidth of quantum noise on chaotic TDS suppression and complexity enhancement are investigated numerically and experimentally. Compared to the original dynamics, the TDS of this quantum noise improved chaos is suppressed up to 94%, and the bandwidth suppression ratio of quantum noise to chaotic laser is 1:25. The experiment agrees well with the theory. The improved chaotic laser is potentially beneficial to chaos-based random number generation and secure communication.

Complexity and entropy representation for machine component diagnostics.

The Complexity-entropy causality plane (CECP) is a parsimonious representation space for time series. It has only two dimensions: normalized permutation entropy () and Jensen-Shannon complexity () of a time series. This two-dimensional representation allows for detection of slow or rapid drifts in the condition of mechanical components monitored through sensor measurements. The CECP representation can be used for both predictive analytics and visual monitoring of changes in component condition. This method requires minimal pre-processing of raw signals. Furthermore, it is insensitive to noise, stationarity, and trends. These desirable properties make CECP a good candidate for machine condition monitoring and fault diagnostics. In this work we study the effectiveness of CECP on three rotary component condition assessment applications. We use CECP representation of vibration signals to differentiate various machine component health conditions for rotary machine components, namely roller bearing and gears. The results confirm that the CECP representation is able to detect, with high accuracy, changes in underlying dynamics of machine component degradation states. From class separability perspective, the CECP representation is able to generate linearly separable classes for the classification of different fault states. This classification performance improves with increasing signal length. For signal length of 16,384 data points, the fault classification accuracy varies from 90% to 100% for bearing applications, and from 85% to 100% for gear applications. We observed that the optimum parameter for CECP representatino depends on the application. For bearing applications we found that embedding dimension D = 4, 5, 6, and embedding delay τ = 1, 2, 3 are suitable for good fault classification. For gear applications we find that embedding dimension D = 4, 5, and embedding delay τ = 1, 5 are suitable for fault classification.

Strategy for Fault Diagnosis on Train Plug Doors Using Audio Sensors.

As the only entry/exit for passengers getting on and off a train, the train plug door is of great importance to keep train operation safe and reliable. As signal processing technologies develop rapidly, taking the easy acquisition advantages of sound signals, a novel fault diagnosis method for train plug doors using multi-scale normalized permutation entropy (MNPE) and an improved particle swarm optimization based multi-class support vector machine (IPSO-MSVM) is proposed. Firstly, sound samples are collected using high-precision audio sensor. In the features extraction process, a hybrid method blending empirical mode decomposition (EMD), multi-scale permutation entropy (MNPE) with Fisher discrimination criterion is utilized. First, EMD is used to decompose each sound signal into several intrinsic mode functions (IMFs) and a residue for stationary processing. Then, MNPE features are extracted from the IMFs. To obtain the most significant features, the Fisher discrimination criterion is further applied. To address the time-consuming defects of traditional grid based method for selecting the optimal parameters of multi-class SVM, an improved PSO (IPSO) is proposed. The superiority of the IPSO-MSVM model and the hybrid feature extraction method was tested on the collected sound samples by comparing to commonly applied methods. Results indicate the identification accuracy of the proposed method is highest, which reaches 90.54%, demonstrating its feasibility.

Specific Emitter Identification Based on Visibility Graph Entropy**Supported by the National Natural Science Foundation of China under Grant No U1530126, and the Fundamental Research Funds for the Central Universities under Grant No ZYGX2015J022.

The specific emitter identification (SEI) technique determines the unique emitter of a given signal by using some external feature measurements of the signal. It has recently attracted a great deal of attention because many applications can benefit from it. This work addresses the SEI problem using two methods, namely, the normalized visibility graph entropy (NVGE) and the normalized horizontal visibility graph entropy (NHVGE) based on treating emitters as nonlinear dynamical systems. Firstly, the visibility graph (VG) and the horizontal visibility graph (HVG) are used to convert the instantaneous amplitude, phase and frequency of received signals into graphs. Then, based on the information captured by the VG and the HVG, the normalized Shannon entropy (NSE) calculated from the corresponding degree distributions are utilized as the rf fingerprint. Finally, four emitters from the same manufacturer are utilized to evaluate the performance of the two methods. Experimental results demonstrate that both the NHVGE-based method and NVGE-based method are quite effective and they perform much better than the method based on the normalized permutation entropy (NPE) in the case of a small amount of data. The NVGE-based method performs better than the NHVGE-based method since the VG can extract more information than the HVG does. Moreover, our methods do not distinguish between the transient signal and the steady-state signal, making it practical.

Effect of Bias Current on Complexity and Time Delay Signature of Chaos in Semiconductor Laser With Time-Delayed Optical Feedback

The effect of bias current on the complexity and time-delay signature of chaotic signals in semiconductor lasers with polarization preserved optical feedback has been studied experimentally and theoretically. The peak value of the autocorrelation coefficient and the normalized permutation entropy at the feedback round trip time are used to quantify the time delay signature and complexity, respectively. The results show that the time-delay signature is approximately in an inverse relationship with the complexity of chaos when the semiconductor laser is subject to low or strong optical feedback. However, the inverse relationship disappears when the laser operates at higher bias currents with intermediate feedback strength. The simulation results are qualitatively agreed with the experimental results.

Effect of digital acquisition on the complexity of chaos.

The effect of data acquisition on the complexity of chaos using permutation entropy has been studied experimentally and numerically. The complexity of chaos is quantified using the normalized permutation entropy at the feedback round-trip time. Two "abnormal" variations of the complexity of chaos with bias current have been observed experimentally. The different vertical scales of the oscilloscope in data acquisition are attributed to this abnormal change. The method to remove the effect of data acquisition has also been proposed.

Current- and Feedback-Induced State Bistability in a 1550 nm-VCSEL With Negative Optoelectronic Feedback

We investigate experimentally the state bistability driven by current or feedback in a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL) with negative optoelectronic feedback (NOEF). The results show that through continuously varying the controlled parameters such as the bias current or the feedback strength along different routes, under a set of given system parameters, there may exist two kinds of output states, i.e., state bistability, which are critically dependent on the history of how the controlled parameters are varied to reach the given values. Within the varied range of bias current or feedback strength, the state bistability is shown via the time series, power spectrum, and phase portrait of the output signal, and the physical mechanisms for the state bistability appearing in the NOEF 1550 nm-VCSEL are analyzed. Furthermore, the complexities of the corresponding states are evaluated by calculating the characteristic value of the normalized permutation entropy of the output from the NOEF 1550 nm-VCSEL. Additionally, by revealing the evolution of the dynamical states under the increase and decrease in the controlled parameters, the ranges of the parameters required for generating current-induced or feedback-induced state bistability can be specified to certain degree.

Two broadband chaotic signals generated simultaneously by semiconductor ring laser with parallel chaotic injection

Recently semiconductor ring laser (SRL) as a novel device has received much attention, for its special cavity allows the output light to propagate in two opposite directions, namely the clockwise mode and counterclockwise mode. SRL does not require gratings or cleaved facets for optical feedback and can be a candidate for small sized photonic integrated circuits which have been developed for secure data transmission, with chaotic carriers and high rate random bit generated. In this paper, we propose a method to obtain two broadband chaotic signals with high unpredictability degree by utilizing injected slave SRL and further explore the physical mechanism and injection conditions. Based on a conventional master-slave configuration, the proposed method obtains two modes of chaotic signals by master SRL with external cross feedback, which are injected in parallel to a slave SRL correspondingly. According to the well-known Lang-Kobayashi rate equations, we establish rate equations and numerically investigate the influences of frequency detuning and injection strength on bandwidth and unpredictability degree. We adapt the given definition of bandwidth and the normalized permutation entropy to respectively evaluate bandwidth and unpredictability degree of chaotic signals. Furthermore, we reveal the underlying physical mechanism of bandwidth enhancement and asymmetric bandwidth-enhancing region by analyzing the radiofrequency and optical spectra of intensity time series. The results show that two chaotic signals have similar routes to enhancing the bandwidth in frequency domain. In the unlocking injection area, two broadband and unpredictability-enhancing chaotic signals generated by slave SRL are simultaneously achieved by choosing appropriate control parameters. Analyses of optical spectra reveal that high-frequency periodic oscillation generated between injection chaotic signals and slave light via beating is the physical mechanism of bandwidth enhncment. The bandwidthenhancing domains of two chaotic signals are asymmetrical due to redshift of master SRL frequency, with external chaotic signals injected. Bandwidth-enhanced chaotic signals are easier to obtain in the domain of negative frequency detuning. The asymmetrical injections contribute to reducing the locking region and extending the bandwidthenhancing region under high injection strength. This conventional master-slave configuration composed of two SRLs can be easily implemented on chip and save other optical devices. The slave SRL subjected to parallel injection signals from master SRL can be used as a wideband unpredictability-enhancing chaotic source, which is extremely useful for the high capacity security-enhancing multiple chaotic communications, as well as for the potential applications of high speed random number generators.

Permutation entropy analysis of complex magnetospheric dynamics

The present study is focused on the emergence of dynamical complexity in the Earth's magnetospheric dynamics during magnetic storms as monitored by SYM-H index. A long time series of SYM-H index covering the period from January 2000 to December 2004 is analyzed using a quite novel technique, the permutation entropy analysis. We show that the normalized permutation entropy values of the SYM-H time series decrease during geomagnetic disturbed periods revealing a gradual increase in the temporal correlation of the fluctuations which generates a gradual increase in the complexity degree of the magnetosphere response to the solar wind magnetic field and plasma parameter changes. These large changes in the normalized permutation entropy values and complexity degree observed during the disturbed periods can be interpreted as the signature of dynamical phase transitions happening in proximity to the occurrence of geomagnetic storms and substorms confirming results previously found using different methods. The dependence of the degree of complexity on both the magnitude of the geomagnetic disturbance and the IMF ByGSM and BzGSM components is investigated and discussed.

Influence of polarization mode competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback

The chaotic unpredictability of vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated optical feedback is evaluated quantitatively via the normalized permutation entropy H. The effect of polarization mode competition (PMC) is explored. For weak PMC, the H for X-polarization mode, Y-polarization mode, and total output are close to each other, while for strong PMC, the H for the total output is the highest one, which indicates that the permutation entropy is an effective tool for quantifying chaotic unpredictability of VCSELs and provides valuable information for choosing the proper chaotic carrier.

Forbidden patterns, permutation entropy and stock market inefficiency

In this paper we introduce two new quantifiers for the stock market inefficiency: the number of forbidden patterns and the normalized permutation entropy. They are model-independent measures, thus they have more general applicability. We find robust evidence that degree of market inefficiency is positively correlated with the number of forbidden patterns and negatively correlated with the permutation entropy. Our empirical results suggest that these two physical tools are useful to discriminate the stage of stock market development and can be easily implemented.