Refined Composite Multiscale Entropy Research Articles

A hybrid short-term load forecasting method using CEEMDAN-RCMSE and improved BiLSTM error correction

Accurate load forecasting is an important issue for safe and economic operation of power system. However, load data often has strong non-stationarity, nonlinearity and randomness, which increases the difficulty of load forecasting. To improve the prediction accuracy, a hybrid short-term load forecasting method using load feature extraction based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and refined composite multi-scale entropy (RCMSE) and improved bidirectional long short time memory (BiLSTM) error correction is proposed. Firstly, CEEMDAN is used to separate the detailed information and trend information of the original load series, RCMSE is used to reconstruct the feature information, and Spearman is used to screen the features. Secondly, an improved butterfly optimization algorithm (IBOA) is proposed to optimize BiLSTM, and the reconstructed components are predicted respectively. Finally, an error correction model is constructed to mine the hidden information contained in error sequence. The experimental results show that the MAE, MAPE and RMSE of the proposed method are 645 kW, 0.96% and 827.3 kW respectively, and MAPE is improved by about 10% compared with other hybrid models. Therefore, the proposed method can overcome the problem of inaccurate prediction caused by data and inherent defects of models and improve the prediction accuracy.

Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson's Disease.

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 healthy subjects (HS) were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE, RCMSE, and CIs showed to differentiate swPD from HS. MSE in the anteroposterior direction at τ4 and τ5, and MSE in the ML direction at τ4 showed to characterize the gait disorders of swPD with the best trade-off between positive and negative posttest probabilities and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can yield the best trade-off in terms of post-test probabilities when compared to other scale factors for detecting gait variability and complexity in swPD.

Multi-step-ahead significant wave height prediction using a hybrid model based on an innovative two-layer decomposition framework and LSTM

As waves are being developed as a renewable energy source, the development of new predictive algorithms to forecast wave height has garnered considerable interest. This study proposes an innovative hybrid model to predict the wave height, including a two-layer decomposition framework and long short-term memory (LSTM). First, the original wave height series is effectively and quickly decomposed into multiple sub-sequences using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). The refined composite multiscale entropy (RCMSE) is then applied to reconstruct these sub-sequences into high-frequency, medium-frequency, low-frequency, and trend components. The respective LSTM is adopted to predict the medium-frequency, low-frequency, and trend components and obtain the sub-results. Subsequently, a series of modes is obtained by the second decomposition of the high-frequency component with variational mode decomposition (VMD), and the sub-result is obtained by forecasting the modes with ensemble LSTM. Finally, we employ the ensemble LSTM to predict all sub-results and obtain the final wave height prediction result, rather than simply adding up all the sub-results linearly. The proposed hybrid model is tested geographically at two buoy stations in eastern New York and Gulf of Mexico. The results show that the proposed hybrid model is more accurate than other benchmark models.

Multiscale Analysis of Runoff Complexity in the Yanhe Watershed

Runoff complexity is an important indicator reflecting the sustainability of a watershed ecosystem. In order to explore the multiscale characteristics of runoff complexity and analyze its variation and influencing factors in the Yanhe watershed in China during the period 1991–2020, we established a new analysis method for watershed runoff complexity based on the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method for the decomposition of multiscale characteristics and the refined composite multiscale entropy (RCMSE) method for the quantification of the system complexity. The results show that runoff and its components all present multiscale complexity characteristics that are different from random signals, and the intermediate frequency modes contribute the most to runoff complexity. The runoff complexity of the Yanhe watershed has decreased gradually since 1991, and 2010 was a turning point of runoff complexity, when it changed from a decline to an increase, indicating that the ecological sustainability of this basin has improved since 2010, which was mainly related to the ecological restoration measures of the Grain for Green Project. This study expands the research perspective for analyzing the variation characteristics of runoff at the multiscale, and provides a reference for the study of watershed ecological sustainability and ecological management.

Longitudinal Changes and Recovery in Heart Rate Variability of Young Healthy Subjects When Exposure to a Hypobaric Hypoxic Environment.

Background: The autonomic nervous system (ANS) is crucial for acclimatization. Investigating the responses of acute exposure to a hypoxic environment may provide some knowledge of the cardiopulmonary system’s adjustment mechanism.Objective: The present study investigates the longitudinal changes and recovery in heart rate variability (HRV) in a young healthy population when exposed to a simulated plateau environment.Methods: The study followed a strict experimental paradigm in which physiological signals were collected from 33 healthy college students (26 ± 2 years, 171 cm ± 7 cm, 64 ± 11 kg) using a medical-grade wearable device. The subjects were asked to sit in normoxic (approximately 101 kPa) and hypoxic (4,000 m above sea level, about 62 kPa) environments. The whole experimental process was divided into four stable resting measurement segments in chronological order to analyze the longitudinal changes of physical stress and recovery phases. Seventy-six time-domain, frequency-domain, and non-linear indicators characterizing rhythm variability were analyzed in the four groups.Results: Compared to normobaric normoxia, participants in hypobaric hypoxia had significantly lower HRV time-domain metrics, such as RMSSD, MeanNN, and MedianNN (p < 0.01), substantially higher frequency domain metrics such as LF/HF ratio (p < 0.05), significantly lower Poincaré plot parameters such as SD1/SD2 ratio and other Poincaré plot parameters are reduced considerably (p < 0.01), and Refined Composite Multi-Scale Entropy (RCMSE) curves are reduced significantly (p < 0.01).Conclusion: The present study shows that elevated heart rates, sympathetic activation, and reduced overall complexity were observed in healthy subjects exposed to a hypobaric and hypoxic environment. Moreover, the results indicated that Multiscale Entropy (MSE) analysis of RR interval series could characterize the degree of minor physiological changes. This novel index of HRV can better explain changes in the human ANS.

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants Compared to Full-Length Long Signals.

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions—as a function of time series length—present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

Entropy in Heart Rate Dynamics Reflects How HRV-Biofeedback Training Improves Neurovisceral Complexity during Stress-Cognition Interactions.

Despite considerable appeal, the growing appreciation of biosignals complexity reflects that system complexity needs additional support. A dynamically coordinated network of neurovisceral integration has been described that links prefrontal-subcortical inhibitory circuits to vagally-mediated heart rate variability. Chronic stress is known to alter network interactions by impairing amygdala functional connectivity. HRV-biofeedback training can counteract stress defects. We hypothesized the great value of an entropy-based approach of beat-to-beat biosignals to illustrate how HRVB training restores neurovisceral complexity, which should be reflected in signal complexity. In thirteen moderately-stressed participants, we obtained vagal tone markers and psychological indexes (state anxiety, cognitive workload, and Perceived Stress Scale) before and after five-weeks of daily HRVB training, at rest and during stressful cognitive tasking. Refined Composite Multiscale Entropy (RCMSE) was computed over short time scales as a marker of signal complexity. Heightened vagal tone at rest and during stressful tasking illustrates training benefits in the brain-to-heart circuitry. The entropy index reached the highest significance levels in both variance and ROC curves analyses. Restored vagal activity at rest correlated with gain in entropy. We conclude that HRVB training is efficient in restoring healthy neurovisceral complexity and stress defense, which is reflected in HRV signal complexity. The very mechanisms that are involved in system complexity remain to be elucidated, despite abundant literature existing on the role played by amygdala in brain interconnections.

A Short-Time Insomnia Detection System Based on Sleep EOG With RCMSE Analysis

Objective: Currently, the prevalence of insomnia in 30% of the population in the word. To diagnose sleep issues, all-night polysomnography is usually taken from the patients, and the recordings are scored by a clinical staff. Nevertheless, manual sleep scoring and diagnosis are time consuming and subjective. In this study, a short-time insomnia detection system based on single-channel sleep EOG with refined composite multiscale entropy (RCMSE) analysis was proposed, and the performance of the proposed system was assessed with the manual scoring based on polysomnography. Methods: The sleep data from 32 subjects were used to develop and evaluate the proposed system; one half was healthy individual and the other half was insomnia patient. The corresponding RCMSE was computed from the short time single-channel sleep EOG (<; 30 min). Then, the mean values of their RCMSEs were computed. Finally, the mean values were used as input to an SVM classifier for insomnia detection. Results: 16 subjects were used to train a classifier; one half was healthy individual and the other half was insomnia patient; and the others were used to test. The averaged accuracy, sensitivity, specificity, kappa coefficient, and F1 score of the proposed system were 89.31%, 96.63%, 82.00%, 0.79, and 90.04%, respectively. Conclusion: Our results showed that RCMSE is a useful and representative feature for short-time insomnia detection. In addition, the proposed method has high accuracy and is good homecare applicability because a single-channel sleep EOG is used. Significance: In the future, we can integrate the proposed system with an EOG eye mask and portable PSG system for sleep quality assessment or insomnia screening in the home environment.

A multi-view and multi-scale transfer learning based wind farm equivalent method

With the increasing capacity of wind farm (WF), detailed WF model is not appropriate for power system studies, and the equivalence of WF with the required accuracy level poses a complicated technical challenge. In this paper, a multi-view and multi-scale transfer learning based WF equivalent method is proposed. Three steps are taken in this method. (a) Extract feature from active and reactive power of wind turbine (WT) using refined composite multi-scale entropy (RCMSE), on this basis, construct clustering indicator considering view and scale two aspects. (b) Aiming at the feature of the clustering indicator, a multi-view and multi-scale fuzzy C-means (VS-FCM) clustering algorithm is proposed, and transfer learning is used in it for better WTs cluster performance. (c) transfer Q-learning is adopted to optimize the parameters of collector network for each equivalent WT, so as to improve parameter optimization efficiency. To verify the effectiveness of the proposed method, an actual system in East Inner Mongolia of China is utilized for case study. Simulation results shows that the dynamic characteristics and the robustness of the proposed model perform a good behavior in different wind scenarios and voltage sag levels, besides, the method has an advantage in the efficiency of simulation time and parameter optimization.

Entropy modeling on serrated flows in carburized steels

Samples comprised of carburized steel alloys, 4615, 4720, and 10B22, were tension tested at room temperature and at a strain rate of 2 × 10−4 s−1. The serrated-flow behavior was modeled and analyzed, using the refined composite multiscale entropy (RCMSE) method. High energy X-ray diffraction revealed the body-centered-cubic (BCC) structure of the three alloys in the as-received condition. Moreover, Vickers-hardness experiments were performed, which showed an increase in the hardness of the alloy that corresponded to increasing impurity concentrations. Here the diffusion coefficient of carbon in the three alloys were estimated, respectively, to be 2.5 × 10−11 m2/s, 5.1 × 10−11 m2/s, and 2.8 × 10−11 m2/s for alloys, 10B22, 4615, and 4720, respectively, which agree with the values found in the literature for α-iron. Moreover, the sample entropy, on average, increased with respect to the heating time, and, consequently, the amount of carbon that had diffused into the alloy. The above results show that the complexity of the serration behavior in the alloys studied increases with respect to the amount of carbon that has diffused into the material.

Temporal Analysis of Cardiovascular and Respiratory Complexity by Multiscale Entropy Based on Symbolic Dynamics.

The effect of an orthostatic stress on cardiovascular and respiratory complexity was investigated to detect impaired autonomic regulation in patients with vasovagal syncope (VVS). A total of 16 female patients and 12 age-matched healthy female subjects were enrolled in a passive 70° head-up tilt test. Also, 12 age-matched healthy male subjects were enrolled to study gender differences. Analysis was performed dynamically using various short-term (5 min) windows shifted by 1 min as well as by 20 min of orthostatic phase (OP) to evaluate local and global complexity. Complexity was determined over multiple time scales by the established method of refined composite multiscale entropy (RCMSE) and by a new proposed method of multiscale entropy based on symbolic dynamics (MSE-SD). Concerning heart rate variability (HRV) during OP, both methods revealed the highest complexity for female controls followed by lower complexity in male controls (p < 0.01) and by the lowest complexity in female patients (p < 0.01). For blood pressure variability (BPV), no gender differences in controls were shown by any method. However, MSE-SD demonstrated highly significantly increased BPV complexity in patients during OP (p < 0.01 on 4 time-scales after 7 min, p < 0.001 on 5 time-scales after 11 min) while RCMSE did not reveal considerable differences (p < 0.05 on 2 time scales after 7 min). Respiratory complexity was further increased in patients primary shown by MSE-SD. Findings indicated impaired autonomic regulation in VVS patients characterized by predominantly increased BPV complexity accompanied with decreased HRV complexity. In addition, results suggested extending the concept of complexity loss with disease.

Investigation of glucose fluctuations by approaches of multi-scale analysis.

Glucose variability provides detailed information on glucose control and fluctuation. The aim of this study is to investigate the glucose variability by multi-scale analysis approach on 72-h glucose series captured by continuous glucose monitoring system (CGMS), gaining insights into the variability and complexity of the glucose time series data. Ninety-eight type 2 DM patients participated in this study, and 72-h glucose series from each subject were recorded by CGMS. Subjects were divided into two subgroups according to the mean amplitude of glycemic excursions (MAGE) value threshold at 3.9 based on Chinese standard. In this study, we applied two types of multiple scales analysis methods on glucose time series: ensemble empirical mode decomposition (EEMD) and refined composite multi-scale entropy (RCMSE). With EEMD, glucose series was decomposed into several intrinsic mode function (IMF), and glucose variability was examined on multiple time scales with periods ranging from 0.5 to 12h. With RCMSE, complexity of the structure of glucose series was quantified at each time scale ranging from 5 to 30min. Subgroup with higher MAGE value (>3.9) presented higher glycemic baseline and variability. There were significant differences in glycemic variability on IMFs3-5 between subgroups with MAGE>3.9 and MAGE <=3.9 (p<0.001), but no significant differences in variability on IMFs1-2. The complexity of glucose series quantified by RCMSE showed statistically difference on each time scale from 5 to 30min between subgroups (p<0.05). Glucose series from subjects with higher MAGE value represented higher variability but lower complexity on multiple time scales. Compared with traditional matrices measuring the glucose variability, approaches of EEMD and RCMSE can quantify the dynamic glycemic fluctuation in multiple time scales and provide us more detailed information on glycemic variability and complexity.

Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals.

We propose a novel complexity measure to overcome the deficiencies of the widespread and powerful multiscale entropy (MSE), including, MSE values may be undefined for short signals, and MSE is slow for real-time applications. We introduce multiscale dispersion entropy (DisEn-MDE) as a very fast and powerful method to quantify the complexity of signals. MDE is based on our recently developed DisEn, which has a computation cost of O(N), compared with O(N2) for sample entropy used in MSE. We also propose the refined composite MDE (RCMDE) to improve the stability of MDE. We evaluate MDE, RCMDE, and refined composite MSE (RCMSE) on synthetic signals and three biomedical datasets. The MDE, RCMDE, and RCMSE methods show similar results, although the MDE and RCMDE are faster, lead to more stable results, and discriminate different types of physiological signals better than MSE and RCMSE. For noisy short and long time series, MDE and RCMDE are noticeably more stable than MSE and RCMSE, respectively. For short signals, MDE and RCMDE, unlike MSE and RCMSE, do not lead to undefined values. The proposed MDE and RCMDE are significantly faster than MSE and RCMSE, especially for long signals, and lead to larger differences between physiological conditions known to alter the complexity of the physiological recordings. MDE and RCMDE are expected to be useful for the analysis of physiological signals thanks to their ability to distinguish different types of dynamics. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/1982.

The complexity of daily life walking in older adult community-dwelling fallers and non-fallers

Complexity of human physiology and physical behavior has been suggested to decrease with aging and disease and make older adults more susceptible to falls. The present study investigates complexity in daily life walking in community-dwelling older adult fallers and non-fallers measured by a 3D inertial accelerometer sensor fixed to the lower back. Complexity was expressed using new metrics of entropy: refined composite multiscale entropy (RCME) and refined multiscale permutation entropy (RMPE). The study re-analyses data of 3 days daily-life activity originally described by Weiss et al. (2013). The data set contains inertial sensor data from 39 older persons reporting less than 2 falls and 32 older persons reporting two or more falls during the previous year. The RCME and the RMPE were derived for trunk acceleration and velocity signals from walking epochs of 50s using mean and variance coarse graining of the signals. Discriminant abilities of the entropy metrics were assessed using a partial least square discriminant analysis. Both RCME and RMPE successfully distinguished between the daily-life walking of the fallers and non-fallers (AUC>0.8) and performed better than the 35 conventional gait features investigated by Weiss et al. (2013). Higher complexity was found in the vertical and mediolateral directions in the non-fallers for both entropy metrics. These findings suggest that RCME and RMPE can be used to improve the assessment of fall risk in older people.

Multivariate refined composite multiscale entropy analysis

Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE.

EMD based refined composite multiscale entropy analysis of complex signals

Multiscale entropy (MSE) is an effective method to measure the complexity of signals from complex systems, which has been applied to various fields successfully. However, MSE may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse-graining procedure reduces the length of data considerably at large scales. Refined composite multiscale entropy (RCMSE) is then developed to solve this problem. However, trends superimposed in signals may significantly affect the complexity measurement. Thus we introduce an empirical mode decomposition based RCMSE, called EMD–RCMSE to first eliminate such effects of trends and then measure the complexity of signals. It is validated from simulated signals and has good estimation. In addition, this method is also applied to study the complexity of traffic signals and we obtain some interesting results: (1) Traffic signals are more complex than the results showing from RCMSE/MSE; (2) Weekday and weekend patterns (different combination of trends) greatly affect the results; (3) Complexity indices change with time at each day, due to the degree of human activities.

Analysis of complex time series using refined composite multiscale entropy

Abstract Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.