Multiscale Approximate Entropy Research Articles

Common bean under different water availability reveals classifiable stimuli-specific signatures in plant electrome

ABSTRACT Plant electrophysiology has unveiled the involvement of electrical signals in the physiology and behavior of plants. Spontaneously generated bioelectric activity can be altered in response to changes in environmental conditions, suggesting that a plant’s electrome may possess a distinct signature associated with various stimuli. Analyzing electrical signals, particularly the electrome, in conjunction with Machine Learning (ML) techniques has emerged as a promising approach to classify characteristic electrical signals corresponding to each stimulus. This study aimed to characterize the electrome of common bean (Phaseolus vulgaris L.) cv. BRS-Expedito, subjected to different water availabilities, seeking patterns linked to these stimuli. For this purpose, bean plants in the vegetative stage were subjected to the following treatments: (I) distilled water; (II) half-strength Hoagland’s nutrient solution; (III) −2 MPa PEG solution; and (IV) −2 MPa NaCl solution. Electrical signals were recorded within a Faraday’s cage using the MP36 electronic system for data acquisition. Concurrently, plant water status was assessed by monitoring leaf turgor variation. Leaf temperature was additionally measured. Various analyses were conducted on the electrical time series data, including arithmetic average of voltage variation, skewness, kurtosis, Probability Density Function (PDF), autocorrelation, Power Spectral Density (PSD), Approximate Entropy (ApEn), Fast Fourier Transform (FFT), and Multiscale Approximate Entropy (ApEn(s)). Statistical analyses were performed on leaf temperature, voltage variation, skewness, kurtosis, PDF µ exponent, autocorrelation, PSD β exponent, and approximate entropy data. Machine Learning analyses were applied to identify classifiable patterns in the electrical time series. Characterization of the electrome of BRS-Expedito beans revealed stimulus-dependent profiles, even when alterations in water availability stimuli were similar in terms of quality and intensity. Additionally, it was observed that the bean electrome exhibits high levels of complexity, which are altered by different stimuli, with more intense and aversive stimuli leading to drastic reductions in complexity levels. Notably, one of the significant findings was the 100% accuracy of Small Vector Machine in detecting salt stress using electrome data. Furthermore, the study highlighted alterations in the plant electrome under low water potential before observable leaf turgor changes. This work demonstrates the potential use of the electrome as a physiological indicator of the water status in bean plants.

A Novel Fault Diagnosis Method for a Power Transformer Based on Multi-Scale Approximate Entropy and Optimized Convolutional Networks.

Dissolved gas analysis (DGA) in transformer oil, which analyzes its gas content, is valuable for promptly detecting potential faults in oil-immersed transformers. Given the limitations of traditional transformer fault diagnostic methods, such as insufficient gas characteristic components and a high misjudgment rate for transformer faults, this study proposes a transformer fault diagnosis model based on multi-scale approximate entropy and optimized convolutional neural networks (CNNs). This study introduces an improved sparrow search algorithm (ISSA) for optimizing CNN parameters, establishing the ISSA-CNN transformer fault diagnosis model. The dissolved gas components in the transformer oil are analyzed, and the multi-scale approximate entropy of the gas content under different fault modes is calculated. The computed entropy values are then used as feature parameters for the ISSA-CNN model to derive diagnostic results. Experimental data analysis demonstrates that multi-scale approximate entropy effectively characterizes the dissolved gas components in the transformer oil, significantly improving the diagnostic efficiency. Comparative analysis with BPNN, ELM, and CNNs validates the effectiveness and superiority of the proposed ISSA-CNN diagnostic model across various evaluation metrics.

A Multi-Information Fusion Algorithm to Fault Diagnosis of Power Converter in Wind Power Generation Systems

Power electronics-based converters are the major and most vulnerable components in wind power generation systems. Converter faults will affect power quality,damage expensive equipment such asgenerators, or even pose a massive threat to the entire power grid. Fault diagnosis is considered as a powerful means to improve system reliability and reduce maintenance costs. Existing data-driven fault diagnosis methods related to improving feature extraction approaches to obtain high diagnostic accuracy are mostly based on single-scale feature of signals; this neglects the potentially valuable information of other scales. This paper proposes an algorithm of Dempster-Shafer and Deng entropy fusion multi-scale approximate entropy (DSDEMAE) for wind power converter fault diagnosis. Firstly, it calculates the multi-scale approximate entropy of fault signals, mining more potentially valuable information. Secondly, Dempster-Shafer is used to fuse features of various scales and effectively handles the conflicts and uncertainties between different features. Finally,Deng entropyis adopted to measure the uncertainty to adjust weight distribution, reducing the influence of highly conflicting features and mutually benefitting features of different scales. Extensive experimental results on simulated and experimental data demonstrate the effectiveness of the proposed algorithm. Compared with advanced methods, this method can diagnose the faults with higher accuracy and stronger robustness.

Radio Frequency Fingerprint extraction based on Multiscale Approximate Entropy

Radio Frequency (RF) fingerprinting is the technology of recognizing the transmitter using the non-linear characteristics of an intercepted RF signal. The underlying inevitable impairments of the hardware chain in transmitters are used as unique RF signatures for the distinct identification of various radios. The technique can be applied to distinguish not only between the radio of different make but also between the radios of the same make and type. In this paper, we propose a novel RF fingerprinting method, based on Multi-Scale Approximate Entropy (MSAE) which utilizes the steady-state section of the RF signal, extracted through the Higuchi Fractal Dimension (HFD) method. The MSAE feature extraction method is validated using real-world data-set for Very High Frequency (VHF) radios. The proposed method uses MSAE features which are subsequently fed to Machine Learning (ML) algorithms for classification accuracy comparison. In terms of classification accuracy, the proposed MSAE features outperforms some of the existing steady-state methods, especially at low SNR.

Future Challenges of Particulate Matters (PMs) Monitoring by Computing Associations Among Extracted Multimodal Features Applying Bayesian Network Approach

ABSTRACT The particulate matter (PM) is emitted from diverse sources and affects the human health very badly. In the past, researchers applied different automated computational tools in the predication of PM. Accurate prediction of PM requires more relevant features and feature importance. In this research, we first extracted the multimodal features from time domain standard deviation average (SDAPM), standard deviation of standard deviation (SDSD), standard deviation of particulate matter (SDPM), root-mean square of standard deviation (RMSSD), and nonlinear dynamical measure wavelet entropy (WE) – Shannon, norm, threshold, multiscale entropy based on KD tree (MSEKD), and multiscale approximate entropy (MAEnt). We then applied the intelligent-based Bayesian inference approach to compute the strength of relationship among multimodal features. We also computed total incoming and outgoing forces between the features (nodes). The results reveal that there was a very highly significant correlation (p-value <0.05) between the selected nodes. The highest total force was yielded by WE-norm followed by SDAPM and SDPM. The association will further help to investigate that which extracted features are more positively or negatively correlated and associated with each other. The results revealed that the proposed methodology can further provide deeper insights into computing the association among the features.

An effective detection method for wheat mold based on ultra weak luminescence

It is widely known that mold is one of important indices in assessing the quality of stored wheat. First, mold will decrease the quality of wheat kernels; the wheat kernels infected by mold can produce secondary metabolites, such as aflatoxins, ochratoxin A, zearalenone, fumonisins and so on. Second, the mycotoxins metabolized by mycetes are extremely harmful to humans; once the food or feed is made of by those wheat kernels infected by mold, it will cause serious health problems on human beings as well as animals. Therefore, the effective and accurate detection of wheat mold is vitally important to evaluate the storage and subsequent processing quality of wheat kernels. However, traditional methods for detecting wheat mold mainly rely on biochemical methods, which always involve complex and long pretreatment processes, and waste part of wheat samples for each detection. In view of this, this paper proposes a type of eco-friendly and nondestructive wheat mold detection method based on ultra weak luminescence. The specific implementation process is as follows: firstly, ultra weak luminescence signals of the healthy and the moldy wheat subsamples are measured by a photon analyzer; secondly, the approximate entropy and multiscale approximate entropy are introduced as the main classification features separately; finally, the detection model has been established based on the support vector machine in order to classify two types of wheat subsamples. The receiver operating characteristic curve of the newly established detection model shows that the highest classification accuracy rate can reach 93.1%, which illustrates that our proposed detection model is feasible and promising for detecting wheat mold.

Rolling Bearing Fault Diagnosis Based on Refined Composite Multi-Scale Approximate Entropy and Optimized Probabilistic Neural Network.

A rolling bearing early fault diagnosis method is proposed in this paper, which is derived from a refined composite multi-scale approximate entropy (RCMAE) and improved coyote optimization algorithm based probabilistic neural network (ICOA-PNN) algorithm. Rolling bearing early fault diagnosis is a time-sensitive task, which is significant to ensure the reliability and safety of mechanical fault system. At the same time, the early fault features are masked by strong background noise, which also brings difficulties to fault diagnosis. So, we firstly utilize the composite ensemble intrinsic time-scale decomposition with adaptive noise method (CEITDAN) to decompose the signal at different scales, and then the refined composite multi-scale approximate entropy of the first signal component is calculated to analyze the complexity of describing the vibration signal. Afterwards, in order to obtain higher recognition accuracy, the improved coyote optimization algorithm based probabilistic neural network classifiers is employed for pattern recognition. Finally, the feasibility and effectiveness of this method are verified by rolling bearing early fault diagnosis experiment.

Multi-Scale Fractal Dimension to Quantify Heart Rate Variability and Systolic Blood Pressure Variability: A Postural Stress Analysis

This paper presents multi-scale fractal dimension (MFD) for the complexity assessment of heart rate variability (HRV) and systolic blood pressure variability (SBPV) under postural stress. A comparison of MFD with multi-scale approximate entropy (MAE) at multiple time scales ([Formula: see text]–10) is presented. The simulations were conducted on 50 random noise (RN), fractional Brownian motion (fBm), and MIX(p) [ 1 ] series along with standard EuroBaVar dataset. Also, 50 healthy volunteers, 20 post-acute myocardial infarction (AMI) patients participated in the study. It is observed that MFD and MAE decrease with [Formula: see text] for healthy volunteers and remained constant for post AMI and BRS failure patients. Average MFD of HRV in supine position is always significantly different than standing position scale except [Formula: see text], whereas the average MAE of HRV shows no significant difference ([Formula: see text]) between supine and standing postures at each [Formula: see text] except [Formula: see text] for healthy volunteers. Average MFD of HRV in supine position is significantly different than the standing position for [Formula: see text]–7, whereas the average MAE of HRV shows significant difference ([Formula: see text]) between supine and standing postures at [Formula: see text] for post AMI, and patients with impaired baroreflex sensitivity (BRS). Average MFD of SBPV in position is significantly different ([Formula: see text]) than standing position at each [Formula: see text], whereas the average MAE of SBPV shows no significant difference ([Formula: see text]) between supine and standing postures at each [Formula: see text] except [Formula: see text]. The complexity of HRV in standing position is less than that of supine position as shown by lower MFD and MAE values in standing than that of supine position, however, the complexity of SBPV decreases from standing to supine position indicating prevalence of sympathetic control.

Multiscale Approximate Entropy for Gait Analysis in Patients with Neurodegenerative Diseases

Neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS), Parkinson’s diseases (PD), and Huntington’s disease (HD) are not rare neurological diseases. They affect different neurological systems and present various characteristic gait abnormalities. We retrieved gait signals of the right and left feet from a public domain on the Physionet. There were 13 patients with ALS, 15 patients with PD, 20 patients with HD and 16 healthy controls (HC). We used multiscale approximate entropy (MAE) to analyze ground reaction force on both feet. Our study shows that MAE increases with scales in all tested subjects. The group HD has the highest MAE and group ALS has the lowest MAE. We can differentiate ALS from HC by MAE, while scale factors >10 in the left foot. There are few significant differences of MAE between the HC and HD. We found a good correlation of MAE between both feet in group ALS. In conclusion, our results indicate that MAE analysis of gait signals can be used for diagnosis and long-term assessment for ALS and probably HD. Similarity of MAE between both feet can also be a diagnostic marker for ALS.

Multiscale ApEn and SampEn in Quantifying Nonlinear Complexity of Depressed MEG

Depression is a neurophysiological disorder with recurrent dysregulations of self-mental states. Multiscale Approximate entropy (ApEn) and Sample entropy (SampEn) are employed to characterize nonlinear complexity of Magnetoencephalography (MEG) of depressive patients in our contribution. SampEn shares similarities with ApEn while has better distinctions between the MEGs of depression patients and normal people. Test results prove that nonlinear complexity of the depressive MEG is lower than that of the normal subjects, indicating weaker response of depression patients to emotional stimuli, and the optimum discriminations between the depressive and healthy people lie in frontal lobe of brain which is related to emotional regulation. Our .ndings provide valuable information about depression, highlight the loss of nonlinear complexity in MEG of depressive patient and can be used as clinical diagnostic aids.

An investigation of oil–water two-phase flow instability using multivariate multi-scale weighted permutation entropy

The present study is devoted to the investigation of oil–water two-phase flow instability using multivariate multi-scale weighted permutation entropy (MWMPE). Four typical multivariate multi-scale entropies, namely MWMPE, multivariate multi-scale permutation entropy (MMPE), multivariate multi-scale sample entropy (MMSE) and multivariate multi-scale approximate entropy (MMAE) are applied in Lorenz system with the addition of different kinds of noises. The comparison results indicate that MWMPE presents the superiorities of being sensitive to the variation in scale, showing a monotonous increasing trend as well as the best anti-noise ability. Accordingly, with the fluctuating signals from an eight-electrode rotating electrical field conductance sensor used for the measurement of oil–water flows, we extract MWMPE for the whole experimental flow conditions, in terms of which the effects of mixture velocity and water-cut on oil–water two-phase flow instability are illuminated. Our research provides an effective method for uncovering the underlying evolution instability of the flow structures in oil–water flows.

Characterising Dynamic Instability in High Water-Cut Oil-Water Flows Using High-Resolution Microwave Sensor Signals

Abstract In the present study, multi-scale entropy algorithm was used to characterise the complex flow phenomena of turbulent droplets in high water-cut oil-water two-phase flow. First, we compared multi-scale weighted permutation entropy (MWPE), multi-scale approximate entropy (MAE), multi-scale sample entropy (MSE) and multi-scale complexity measure (MCM) for typical nonlinear systems. The results show that MWPE presents satisfied variability with scale and anti-noise ability. Accordingly, we conducted an experiment of vertical upward oil-water two-phase flow with high water-cut and collected the signals of a high-resolution microwave resonant sensor, based on which two indexes, the entropy rate and mean value of MWPE, were extracted. Besides, the effects of total flow rate and water-cut on these two indexes were analysed. Our researches show that MWPE is an effective method to uncover the dynamic instability of oil-water two-phase flow with high water-cut.

An adaptive technique for multiscale approximate entropy (MAEbin) threshold (r) selection: application to heart rate variability (HRV) and systolic blood pressure variability (SBPV) under postural stress.

Multiscale approximate entropy (MAE) is used to quantify the complexity of a time series as a function of time scale τ. Approximate entropy (ApEn) tolerance threshold selection 'r' is based on either: (1) arbitrary selection in the recommended range (0.1-0.25) times standard deviation of time series (2) or finding maximum ApEn (ApEnmax) i.e., the point where self-matches start to prevail over other matches and choosing the corresponding 'r' (rmax) as threshold (3) or computing rchon by empirically finding the relation between rmax, SD1/SD2 ratio and N using curve fitting, where, SD1 and SD2 are short-term and long-term variability of a time series respectively. None of these methods is gold standard for selection of 'r'. In our previous study [1], an adaptive procedure for selection of 'r' is proposed for approximate entropy (ApEn). In this paper, this is extended to multiple time scales using MAEbin and multiscale cross-MAEbin (XMAEbin). We applied this to simulations i.e. 50 realizations (n=50) of random number series, fractional Brownian motion (fBm) and MIX (P) [1] series of data length of N=300 and short term recordings of HRV and SBPV performed under postural stress from supine to standing. MAEbin and XMAEbin analysis was performed on laboratory recorded data of 50 healthy young subjects experiencing postural stress from supine to upright. The study showed that (i) ApEnbin of HRV is more than SBPV in supine position but is lower than SBPV in upright position (ii) ApEnbin of HRV decreases from supine i.e. 1.7324±0.112 (mean±SD) to upright 1.4916±0.108 due to vagal inhibition (iii) ApEnbin of SBPV increases from supine i.e. 1.5535±0.098 to upright i.e. 1.6241±0.101 due sympathetic activation (iv) individual and cross complexities of RRi and systolic blood pressure (SBP) series depend on time scale under consideration (v) XMAEbin calculated using ApEnmax is correlated with cross-MAE calculated using ApEn (0.1-0.26) in steps of 0.02 at each time scale in supine and upright position and is concluded that ApEn0.26 has highest correlation at most scales (vi) choice of 'r' is critical in interpreting interactions between RRi and SBP and in ascertaining true complexity of the individual RRi and SBP series.

Multi-Scale Approximate Entropy Analysis of Foreign Exchange Markets Efficiency

Market efficiency analysis is an important aspect in financial engineering.Based on weak-form efficient markets hypothesis (EMH), we characterize the market efficiency in foreign exchange (FX) markets by using the multi-scale approximate entropy (MApEn) to assess the randomness in FX markets. We split 17 daily FX rates from 1984 to 2011 into there periods by two global events, Southeast Asia currency crisis and American sub-prime crisis. The empirical results indicate that the developed FX markets is more efficient than emerging FX markets, and that the financial crisis promotes the market efficiency in FX markets significantly, especially in emerging markets, like China, Hong Kong, Korea and African market.