Wavelet Scalogram Research Articles

Data enhanced deep transfer learning for health state evaluation of cutting tools

ABSTRACT Health state estimation of cutting tools is a key component for maintaining the reliability and stability of the manufacturing process. Although deep learning (DL) based tool wear indirect monitoring methods have been presented, most of them require a substantial amount of data to avoid high misclassification rates. To this end, this article proposes a novel estimation approach based on data-enhanced deep transfer learning (TL) methodology, which integrates multivariate data enhancements, deep convolution network, and generative adversarial learning for state assessment of the tool wear under small sample size. The proposed method includes three innovative points: 1) a multi-step data enhancement method is employed to augment the wavelet scalogram data as model input; 2) a novel training process is adopted to obtain optimal hyperparameters of TL-AlexNet and TL-VGGNet-16 model; 3) a deep transfer learning model for the enhanced data is presented to adaptively estimate the health state of the cutting tools. The proposed approach only requires a small quantity of data to achieve satisfactory estimation performance compared with other DL methods through experimental validation, and the average prediction accuracy for each stage is greater than 95%, which demonstrates the effectiveness and superiority of the presented model.

Wavelet Analysis and the Cone of Influence: Does the Cone of Influence Impact Wavelet Analysis Results?

Wavelet analysis (WA) decomposes laser Doppler (LD) microcirculatory signals into characteristic frequency intervals related to endothelial nitric oxide (NO)-independent, endothelial NO-dependent, neurogenic, myogenic, respiratory, and cardiac physiological influences. Since LD signals have a finite length, the WA results suffer from spectral leakage due to edge effects. The cone of influence (COI) delineates the regions of the wavelet scalogram where these effects become important. We aimed to determine whether accounting for the COI leads to significant differences in the WA results. Two typical patterns of LD signals were analysed: a baseline and a post-occlusive reactive hyperemia (PORH) signal. The WA spectra were constructed without and with excluding data affected by the COI. The relative power (RP = median power of each frequency interval/median power of the total spectrum) of the spectral components obtained without and with the COI was compared. Applying the COI correction did not significantly affect the baseline signals. On the contrary, in PORH, accounting for the COI resulted in significant differences in the RP of the endothelial NO-independent (p = 0.0005; Wilcoxon signed-rank test), endothelial NO-dependent (p = 0.0005), neurogenic (p = 0.0038), myogenic (p = 0.001), respiratory (p = 0.0002), and cardiac frequency bands (p = 0.0002). The results suggest that applying the COI correction to the WA results obtained from the LD signals is desirable, especially for transient signals.

Blood Pressure Estimation from Wavelet Scalogram of PPG signals using Convolutional Neural Networks

Introduction In this work, calibration-free blood pressure estimation using wavelet scalograms of PPG signals using Convolutional Neural Network (CNN) has been proposed. The PPG signal, easily obtained from a subject, serves as a reliable indicator for predicting blood pressure (BP). Methods The proposed methodology involves employing Continuous Wavelet Transform (CWT) scalograms of the PPG signal as inputs for the CNN. Two distinct architectures for BP estimation are explored: one employing regression with a fully connected neural network and another utilizing CNN with Support Vector Regression (SVR). Results The results demonstrate superior BP estimation with the CNN-SVR architecture. With the CNN-SVR model, the Systolic Blood Pressure (SBP) and Diastolic Blood Pressure (DBP) are estimated with a Root Mean Square Error (RMSE) of 6.7 mmHg and 8.9 mmHg, respectively. Conclusion The proposed CNN-SVR model gives 52% better estimation error performance in SBP estimation compared to a machine learning model reported in a previous work.

Enhanced EEG seizure recognition after hypoxia-ischemia in fetal sheep using transformer-based wavelet-scalogram deep learning

This study introduces transformer-based deep learning models as superior alternatives to convolutional neural network (CNN) architectures for seizure detection after hypoxia–ischemia (HI) in electroencephalography (EEG) recordings in the developing brain. We further demonstrate that these models excel in classifying of varied and subtle morphologies of electrographic seizures observed in the EEG of fetal sheep after HI. The study explores model training combinations from four cohorts of Romney/Suffolk fetal sheep (HI-normothermia-term (n = 7), HI-hypothermia-term (n = 14), sham-normothermia-term (n = 5), and HI-normothermia-preterm (n = 14)), totalling 31,015 EEG segments from 17,300 h of recordings. We evaluated multiple Transformer architectures using both 2D wavelet-scalograms (WS) and 1D raw EEG signals through leave-one-out and k-fold cross-validation, comparing models’ performance with or without sham-normothermia-term data and contrasting them with CNN-based results from our previous work. The Data-Efficient image Transformer (DeiT) emerged as the top-performing model, achieving 99.60 % accuracy (AUC = 0.992) when fed with WS, surpassing the 2D WS CNN result (98.94 % accuracy, AUC = 0.967) from our prior study. Notably, the Wav2Vec2 transformer model, fed with raw 1D EEG segments, demonstrated comparable performance with 99.60 % accuracy (AUC = 0.992), outperforming the 1D CNN result (98.43 % accuracy, AUC = 0.961) from the previous study. More importantly, the transformers can adeptly distinguish between seizures in both the preterm and term brain, and under the influence of treatment with 99.92 % accuracy (AUC = 0.997). Our findings highlight the superior ability of transformer models to capture long-range dependencies within EEG data, enhancing seizure detection without the added complexity of generating 2D WS images. Transformer models show promise for generalized automated seizure detection, irrespective of the perinatal brain maturation stage and the influence of hypothermia, offering potential improvements for seizure detection after HI in newborns.

Graph features based classification of bronchial and pleural rub sound signals: the potential of complex network unwrapped.

The study presents a novel technique for lung auscultation based on graph theory, emphasizing the potential of graph parameters in distinguishing lung sounds and supporting earlier detection of various respiratory pathologies. The frequency spread and the component magnitudes are revealed from the analysis of eighty-five bronchial (BS) and pleural rub (PS) lung sounds employing the power spectral density (PSD) plot and wavelet scalogram. The low-frequency spread, and persistence of the high-intensity frequency components are visible in BS sounds emanating from the uniform cross-sectional area of the trachea. The frictional rub between the pleurae causes a higher frequency spread of low-intensity intermittent frequency components in PS signals. From the complex networks of BS and PS, the extracted graph features are - graph density ([Formula: see text], transitivity ([Formula: see text], degree centrality ([Formula: see text]), betweenness centrality ([Formula: see text], eigenvector centrality ([Formula: see text]), and graph entropy (En). The high values of [Formula: see text] and [Formula: see text] show a strong correlation between distinct segments of the BS signal originating from a consistent cross-sectional tracheal diameter and, hence, the generation of high-intense low-spread frequency components. An intermittent low-intense and a relatively greater frequency spread in PS signal appear as high [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] values. With these complex network parameters as input attributes, the supervised machine learning techniques- discriminant analyses, support vector machines, k-nearest neighbors, and neural network pattern recognition (PRNN)- classify the signals with more than 90% accuracy, with PRNN having 25 neurons in the hidden layer achieving the highest (98.82%).

CNN-Based Pattern Classifiers for Precise Identification of Perinatal EEG Biomarkers of Brain Injury in Preterm Neonates

Electroencephalographic (EEG) monitoring is important for the diagnosis of hypoxic-ischemic (HI) brain injury in high-risk preterm infants. EEG monitoring is limited by the reliance on expert clinical observation. However, high-risk preterm infants often do not present observable symptoms due to their frailty. Thus, there is an urgent need to find better ways to automatically quantify changes in the EEG these high-risk babies. This article is a first step towards this goal. This innovative study demonstrates the effectiveness of deep Convolutional Neural Networks (CNN) pattern classifiers, trained on spectrally-detailed Wavelet Scalograms (WS) images derived from neonatal EEG sharp waves—a potential translational HI biomarker, at birth. The WS-CNN classifiers exhibit outstanding performance in identifying HI sharp waves within an exclusive clinical EEG recordings dataset of preterm infants immediately after birth. The work has impact as it demonstrates exceptional high accuracy of 99.34 ± 0.51% cross-validated across 13,624 EEG patterns over 48 h raw EEG at low 256 Hz clinical sampling rates. Furthermore, the WS-CNN pattern classifier is able to accurately identify the sharp-waves within the most critical first hours of birth (n = 8, 4:36 ± 1:09 h), regardless of potential morphological changes influenced by different treatments/drugs or the evolutionary ‘timing effects’ of the injury. This underscores its reliability as a tool for the identification and quantification of clinical EEG sharp-wave biomarkers at bedside.

Transmission Line Fault Classification Based on the Combination of Scaled Wavelet Scalograms and CNNs Using a One-Side Sensor for Data Collection.

This research focuses on leveraging wavelet transform for fault classification within electrical power transmission networks. This study meticulously examines the influence of various parameters, such as fault resistance, fault inception angle, fault location, and other essential components, on the accuracy of fault classification. We endeavor to explore the interplay between classification accuracy and the input data while assessing the efficacy of combining wavelet analysis with deep learning methodologies. The data, sourced from network recorders, including phase currents and voltages, undergo a scaled continuous wavelet transform (S-CWT) to generate scalogram images. These images are subsequently utilized as inputs for pretrained deep learning models. The experiments encompass various fault scenarios, spanning distinct fault types, locations, times, and resistance values. A remarkable feature of the proposed work is the attainment of 100% classification accuracy, obviating the need for additional algorithmic enhancements. The foundation of this achievement is the deliberate selection of the right input. The decision to employ an identical number of samples as the number of scales for the CWT emerges as a pivotal factor. This approach underpins the high accuracy and renders supplementary algorithms superfluous. Furthermore, this research underscores the versatility of this approach, showcasing its effectiveness across diverse networks and scenarios. Wavelet transform, after rigorous experimentation, emerges as a reliable tool for capturing transient fault characteristics with an optimal balance between time and frequency resolutions.

Techniques for Accelerometer Reading Processing on Railway Transport Using Wavelet Transform

Introduction. Safety issues of railway transport are inevitably connected with the condition of railway tracks and railway wheels. Various defects, such as irregularities of the railway track, may lead to emergencies and incidents. Therefore, it is important to measure and calculate short and impulse irregularities. A joint analysis of vibration acceleration signals is needed in order to study the types and size of railway track irregularities.Aim. Development of an algorithm for irregularity search based on accelerometer readings with the vertical measurement axis.Materials and methods. The research encompassed wavelet transformation and wavelet-based signal processing including discrete-time signal processing and continuous wavelet processing. In addition, time-frequency analysis based on Fourier transform and continuous wavelet scalogram was used. These methods provide for time-frequency localization for irregularity detection and measurement.Results. Algorithms for vibrational signal processing using the continuous and discrete-time wavelet transform are proposed. The results show that the discrete wavelet transform is effective for multiresolution and multiband analysis, and continuous wavelet transform and wavelet scalogram allows extraction of irregularities and determination of their parameters. The relative error for irregularity depth was improved by 18 %, and the absolute error for irregularity length determinations was reduced by 7 times.Conclusion. Application of the discrete Fourier transform and Fourier spectrogram provides for fine resolution in the frequency domain. However, separation of signal components in the time-frequency domain is impeded. The continuous-time wavelet transform ensures sufficient resolution in the low-frequency domain for component localization and visualization of irregularities.

Inference of highly time-resolved melt pool visual characteristics and spatially-dependent lack-of-fusion defects in laser powder bed fusion using acoustic and thermal emission data

With a growing demand for high-quality fabrication, the interest in real-time process and defect monitoring of laser powder bed fusion (LPBF) has increased, leading manufacturers to incorporate a variety of online sensing methods including acoustic sensing, photodiode sensing, and high-speed imaging. However, real-time acquisition of high-resolution melt pool images in particular remains computationally demanding in practice due to the high variability of melt pool morphologies and the limitation of data caching and transfer, making it challenging to detect the local lack-of-fusion (LOF) defect occurrences. In this work, we propose a new acoustic and thermal information-based monitoring method that can robustly infer critical LPBF melt pool morphological features in image forms and detect spatially-dependent LOF defects within a short time period. We utilize wavelet scalogram matrices of acoustic and photodiode clip data to identify and predict highly time-resolved (within a 1.0 ms window) visual melt pool characteristics via a well-trained data-driven pipeline. With merely the acoustic and photodiode-collected thermal emission data as the input, the proposed pipeline enables data-driven inference and tracking of highly variable melt pool visual characteristics with R2≥0.8. We subsequently validate our proposed approach to infer local LOF defects between two adjacent scanlines, showing that our proposed approach can outperform our selected baseline theoretical model based on previous literature. Revealing the physical correlation between airborne acoustic emission, thermal emission, and melt pool morphology, our work demonstrates the feasibility of creating an efficient and cost-effective acoustic- and thermal-based approach to facilitate online visual melt pool characterization and LOF defect detection. We believe that our work can further contribute to the advances in quality control for LPBF.

TESTING OF D16T DURALUMIN SAMPLES UNDER STATIC LOADING USING THE ACOUSTIC EMISSION METHOD

Tests of samples made of D16T duralumin were carried out under static loading until failure under normal conditions, at positive and negative temperatures. Information was recorded using the acoustic emission method. In this case, a stable location of signals from defects corresponding to the beginning of sample destruction was observed. It was shown that at a low temperature of –50 oС the number of recorded signals increased, but the energy of the high-frequency component of the AE signals decreased, and the maximum energy was in the frequency band 550…600 kHz. At a temperature of +80 oC, the number of recorded signals decreased. Wavelet scalograms were constructed at various temperatures and loads. The sensitivity of the main informative parameters of acoustic emission signals, which made it possible to determine the onset of destruction of the sample material, was analyzed.

An Online Monitoring Approach of Carbon Steel Corrosion via the Use of Electrochemical Noise and Wavelet Analysis

In this study, carbon steel was examined under different corrosive conditions using electrochemical noise (EN) as the primary method of investigation. The corroded carbon steel surfaces were examined using 3D profilometry to gather information about localized defects (pits). A post-EN analysis approach was used using the discrete wavelet transform (DWT) method, which emphasizes the necessity of employing wavelet analysis as a quantitative analysis approach for electrochemical noise. A well-established approach to extract features from wavelet scalogram images, based on the concept of local binary patterns (LBPs), was used to extract features from these wavelet images. The results demonstrated that electrochemical noise associated with wavelet transform analysis, particularly wavelet scalograms, is an effective tool for monitoring the localized corrosion of carbon steel.

Effectiveness of Wavelet Scalogram on Partial Discharge Pattern Classification of XLPE Cable Insulation

Effectiveness of Wavelet Scalogram on Partial Discharge Pattern Classification of XLPE Cable Insulation

A new similarity measurement method for time series based on image fusion of recurrence plots and wavelet scalogram

The core of data series classification and clustering is how to evaluate the similarity between time series. However, for one-dimensional time series, the vast majority of similarity measurement methods currently relied on one-dimensional information. Although some classifications of time series were achieved by the images transformed from time series, they mostly relied on a single imaging mechanism (time domain or frequency domain). In order to give a new idea for time series similarity measurement, this paper proposed a similarity measurement method of time series based on the fused images. According to recurrence plots (RP) and wavelet scalogram (WS), the original time series was first transformed into images. Then, RP and WS were fused into an image. Next, the feature in the image was extracted by ResNet-18. Finally, the similarity of the time series can be obtained by the Euclidean distance between the features extracted by ResNet-18. The proposed method was verified by the time series from UCR Time Series Classification/Clustering Homepage. The results showed that the similarity measurement of time series can be effectively improved by fusing the images obtained by different imaging mechanisms in the time domain and frequency domain.

Fault Detection on Power Transmission Line Based on Wavelet Transform and Scalogram Image Analysis

Given the massive increase in demand for electrical energy, particularly owing to global climate change and population expansion, as well as the development of complicated electrical systems due to the urgent need for a sophisticated component to enhance power delivery, it becomes important to adopt a smart and contemporary approach that is also appropriate for the aim of protecting transmission lines (TLs) and ensuring the continuous delivery of electric power to customers. Consequently, a unique and highly reliable approach for identifying faults in TLs is presented in this work, which employs Wavelet Transform and is evaluated using Matlab simulation. Wavelets of various kinds were utilized to demonstrate their dependability. Furthermore, utilizing this approach has shown itself to be highly successful and has yielded spectacular results even when it is used on a complicated electrical network. Moreover, many types of faults were presented and afterward evaluated and verified for the network in various settings, which also demonstrated their potential to recognize faults within a relatively short space of time. This innovation will alter the idea of fault detection by providing a complete and integrated model for detecting faults in a TL, and it may be regarded as a revolution in the renewal of core principles in TL protection.

Identification of corona discharges based on wavelet scalogram images with deep convolutional neural networks

This paper presents a new wavelet-based approach to automate the identification of positive and negative DC corona discharge current pulses. Two electrode systems with variable gap spacings formed corona discharges, and two commercial sensors (a high-frequency current transformer (HFCT) and a shunt resistor) captured transient corona discharge currents. The proposed method employs a continuous wavelet transform to generate time-frequency representations of corona discharge pulse currents, called scalogram images. The effects of sampling interval, data acquisition time, data shifting, and external noise components in the signals on the scalogram images were examined. The well-known pre-trained convolutional neural network models, AlexNet, MobileNet, and ShuffleNet, were tailored, and their ensemble structure was generated to discriminate scalogram images of discharge pulses. A framework was constructed to increase the generalization ability of the study. The results demonstrate that the scalogram images are robust candidates for corona discharge identification.

Optimal Combination of Mother Wavelet and AI Model for Precise Classification of Pediatric Electroretinogram Signals.

The continuous advancements in healthcare technology have empowered the discovery, diagnosis, and prediction of diseases, revolutionizing the field. Artificial intelligence (AI) is expected to play a pivotal role in achieving the goals of precision medicine, particularly in disease prevention, detection, and personalized treatment. This study aims to determine the optimal combination of the mother wavelet and AI model for the analysis of pediatric electroretinogram (ERG) signals. The dataset, consisting of signals and corresponding diagnoses, undergoes Continuous Wavelet Transform (CWT) using commonly used wavelets to obtain a time-frequency representation. Wavelet images were used for the training of five widely used deep learning models: VGG-11, ResNet-50, DensNet-121, ResNext-50, and Vision Transformer, to evaluate their accuracy in classifying healthy and unhealthy patients. The findings demonstrate that the combination of Ricker Wavelet and Vision Transformer consistently yields the highest median accuracy values for ERG analysis, as evidenced by the upper and lower quartile values. The median balanced accuracy of the obtained combination of the three considered types of ERG signals in the article are 0.83, 0.85, and 0.88. However, other wavelet types also achieved high accuracy levels, indicating the importance of carefully selecting the mother wavelet for accurate classification. The study provides valuable insights into the effectiveness of different combinations of wavelets and models in classifying ERG wavelet scalograms.

OculusGraphy: Signal Analysis of the Electroretinogram in a Rabbit Model of Endophthalmitis Using Discrete and Continuous Wavelet Transforms.

The electroretinogram is a clinical test used to assess the function of the photoreceptors and retinal circuits of various cells in the eye, with the recorded waveform being the result of the summated response of neural generators across the retina. The present investigation involved an analysis of the electroretinogram waveform in both the time and time-frequency domains through the utilization of the discrete wavelet transform and continuous wavelet transform techniques. The primary aim of this study was to monitor and evaluate the effects of treatment in a New Zealand rabbit model of endophthalmitis via electroretinogram waveform analysis and to compare these with normal human electroretinograms. The wavelet scalograms were analyzed using various mother wavelets, including the Daubechies, Ricker, Wavelet Biorthogonal 3.1 (bior3.1), Morlet, Haar, and Gaussian wavelets. Distinctive variances were identified in the wavelet scalograms between rabbit and human electroretinograms. The wavelet scalograms in the rabbit model of endophthalmitis showed recovery with treatment in parallel with the time-domain features. The study compared adult, child, and rabbit electroretinogram responses using DWT and CWT, finding that adult signals had higher power than child signals, and that rabbit signals showed differences in the a-wave and b-wave depending on the type of response tested, while the Haar wavelet was found to be superior in visualizing frequency components in electrophysiological signals for following the treatment of endophthalmitis and may give additional outcome measures for the management of retinal disease.

Machine-learning Assisted Differentiation Between Physiological Oscillation Epochs and Muscle or Epileptiform activity in EEGs (S30.005)

<h3>Objective:</h3> Machine-learning assisted separation of spontaneous cognition-relevant EEG oscillations from EEG perturbation induced by epileptiform events and muscle artifacts. <h3>Background:</h3> Transient band-limited alpha and gamma frequency oscillations in EEGs of awake subjects reflect cognitive processes and integrity of excitation-inhibition balance. These oscillations are diminished in disorders such as mitochondrial encephalopathies as we have previously shown. Automated capture of such oscillation epochs in prolonged EEGs can prove valuable for numerous clinical and research studies. However, EEG recordings can be degraded by superimposed high frequency activity inherent in movement and epileptiform discharges. <h3>Design/Methods:</h3> Forty band-limited alpha and gamma spontaneous oscillation epochs were recorded from electrode C3 in a standard 20-lead EEG configuration. The gaussian distribution of non-event wavelet scalogram allowed automated identification of outlier putative events, which were then confirmed or rejected by a human observer. An instantaneous wavelet scalogram “cross-section” of the event was used to generate a representative frequency waveform for that event and analyzed using action potential waveform sorting Wave clus (<i>Neural Computation</i> 16, 1661–1687; 2004). This protocol was applied to EEGs containing muscle (27 events) and to EEGs with epileptiform activity (36 events) due to mitochondrial pyruvate dehydrogenase deficiency. <h3>Results:</h3> Oscillation epoch waveforms exhibited distinct band-limited peaks which were absent for muscle or epileptiform activity. Muscle events uniformly displayed broad-band high-frequencies, whereas epileptiform events were more variable. Oscillation epoch wavelet coefficients were reliably differentiated from other events (MANOVA p&lt;10⁻⁴). A support vector machine-learning protocol examining the difference between epochs and muscle and epileptiform events demonstrated a misclassification rate of zero and 1.3%, respectively, and an area under the curve for a receiver operating characteristic curve of 1 for both. <h3>Conclusions:</h3> Instantaneous wavelet scalogram profiles provide high precision in differentiating oscillation epochs from muscle or epileptiform activity, allowing for automated oscillation epoch detection in subjects with epilepsy. <b>Disclosure:</b> Dr. Jakkamsetti has nothing to disclose. Miss Kathote has nothing to disclose. Mr. Avila has nothing to disclose. Sharon Primeaux has nothing to disclose. Mr. Dobariya has nothing to disclose. Dr. Malaga Dieguez has nothing to disclose. Dr. Pascual has received personal compensation in the range of $500-$4,999 for serving as an Editor, Associate Editor, or Editorial Advisory Board Member for Elsevir. The institution of Dr. Pascual has received research support from NIH.

Automated cataloguing of American silver perch (Bairdiella chrysoura) calls using machine learning

ABSTRACT The American silver perch (Bairdiella chrysoura) is a numerically dominant and ecologically important species found throughout coastal habitats along the eastern United States and Gulf of Mexico. During spawning in the spring and summer, male silver perch produce distinctive knocking sounds to attract females. These sounds are readily identifiable through aural and visual analysis of underwater acoustic recordings, providing a means to track the distribution and spawning activity of these fish. However, as the volume of passive acoustic datasets grows, there is an essential need to automate the process of cataloguing silver perch vocalisations. The approach presented here utilises a (1) detection stage, where candidate calls are identified based on the properties of signal kurtosis and signal-to-noise ratio, (2) a feature extraction stage where layer activations are returned from the pre-trained ResNet-50 convolutional neural network operating on a wavelet scalogram of these signals, and (3) a one-vs-all support-vector-machine classifier. The labelled data used to build the classifier consists of 6000 perch calls and 6000 other signals that sample diverse acoustic conditions within the Pamlico Sound estuary, USA. The model accuracy is 98.9%, and the accompanying software provides an efficient tool to investigate silver perch calling patterns within passive acoustic data.

Sectoral integration on an emerging stock market: a multi-scale approach

The purpose of this study is to examine the connectedness of industry sectors on the Johannesburg Stock Exchange in a time–frequency domain. We use econophysics-based methods like the wavelet multiple correlation and wavelet scalogram difference to identify the evolution of the connectedness of the sectors over time and at different frequencies. The findings show that the sectors on the Johannesburg Stock Exchange are especially integrated at lower frequencies. Wavelet multiple correlation peaks in response to local and global shocks like the black-swan COVID-19 pandemic in 2020 and the downgrading of South African debt by Fitch in 2013. Though there are opportunities for sectoral diversification on the JSE, this fails when it is most needed, during crisis periods. Investors should therefore consider other asset classes that could serve as a haven in times of crisis. Though extant literature has examined sectoral dependencies on the stock markets of developed and developing countries, to the best of our knowledge, this is the first study to examine this connectedness in a South African context using multiple nonparametric methods that are robust to non-normality, presence of outliers as well as non-stationary data.