Multiresolution Signal Analysis Research Articles

Impact force identification for composite structures using adaptive wavelet-regularised deconvolution

Impact force identification (IFI) through deconvolution methods from measured structural responses poses a challenge due to the ill-posed nature of the inversion problem. Regularisation techniques, such as Tikhonov, sparse, and wavelet regularisation, offer potential solutions to mitigate the ill-posedness. However, determining suitable regularisation parameters is time-consuming. This study presents an adaptive wavelet-regularised time-domain deconvolution method for efficient IFI, based on wavelet transform and multi-resolution analysis. By analysing impact sensor signals using wavelets, adaptive impact windows covering the entire impact duration are generated, reducing signal length for deconvolution. Multi-resolution analysis of sensor signals enables identification of wavelet bases for the multi-resolution representation of impact force history. Regularisation is achieved by filtering out insignificant wavelet bases based on their energy contributions. Validation is performed through experiments involving small-mass hammer and large-mass drop tower impacts, comparing against various deconvolution methods. Results demonstrate the superior computational efficiency and comparable accuracy of the proposed adaptive method in IFI across different time windows. Notably, accurate force deconvolution for large-mass impacts confirms the effectiveness of the deconvolution methods for IFI, particularly when the structure undergoes significant local deformation.

Multiresolution feature fusion for smart diagnosis of schizophrenia in adolescents using EEG signals.

Numerous studies on early detection of schizophrenia (SZ) have utilized all available channels or employed set of a few time domain or frequency domain features, while a limited number of features may not be sufficient enough to perform diagnosis efficiently. To encounter these problems, an automated diagnosis model is proposed for the efficient diagnosis of schizophrenia symptomatic adolescent subjects from electroencephalogram (EEG) signals via machine intelligence. A publicly accessible EEG dataset featuring 16-channels EEG obtained from 84 adolescents (45 SZ symptomatic and 39 healthy control) is used to demonstrate the work. Initially, the signals are decomposed into sub-bands using two multi-resolution signal analysis methods: Empirical Wavelet Transform and Empirical mode decomposition. 75 unique features from each sub-bands are extracted and the few selective prominent features are applied to machine learning classifiers for optimal sub-band selection. Subsequently, a hybrid model is proposed, combining convolutional neural network (CNN) and ensemble bagged tree, incorporating both deep learning and handcrafted features to perform SZ diagnosis. This innovative model achieved superior classification performance compared to existing methods, offering a promising approach for SZ diagnosis. Furthermore, the study explores the impact of different brain regions and combined regional data in SZ diagnosis comprehensively. Hence, this computer-assisted decision-making model minimizes the limitations of prior studies by providing a more robust and efficient diagnostic system for schizophrenia.

Tunable Q-factor wavelet transform based identification of diabetic patients using ECG signals

Diabetes is a chronic health condition that is characterized by increased levels of glucose (sugar) in the blood. It can have harmful effects on different parts of the body, such as the retina of the eyes, skin, nervous system, kidneys, and heart. Diabetes affects the structure of electrocardiogram (ECG) impulses by causing cardiovascular autonomic dysfunction. Multi-resolution analysis of the input ECG signal is utilized in this paper to develop a machine learning-based system for the automated detection of diabetic patients. In the first step, the input ECG signal is decomposed into sub-bands utilizing the tunable Q-factor wavelet transform (TQWT) technique. In the second step, four entropy-based characteristics are evaluated from each SB and elected using the K-W test method. To develop an automatic diabetes detection system, selected features are given as input with 10-fold validation to a SVM classifier using various kernel functions. The 3 rd sub-band of TQWT with the Coarse Gaussian kernel function kernel of the SVM classifier yields a classification accuracy of 91.5%. In the same dataset, the comparative analysis demonstrates that the proposed method outperforms other existing methods.

Automation of the Timed Up and Go Test Using a Doppler Radar System for Gait and Balance Analysis in Elderly People.

The timed up and go (TUG) test is a simple, valid, and reliable clinical tool that is widely used to assess mobility in elderly people. Several research studies have been conducted to automate the TUG test using wearable sensors or motion-tracking systems. Despite their promising results, the adopted technological systems present inconveniences in terms of acceptability and privacy protection. In this work, we propose to overcome these problems by using a Doppler radar system set into the backrest of a chair in order to automate the TUG test and extract additional information from its phases (i.e., transfer, walk, and turn). We intend to segment its phases and extract spatiotemporal gait parameters automatically. Our methodology is mainly based on a multiresolution analysis of radar signals. We proposed a segmentation technique based on the extraction of limbs oscillations signals through a semisupervised machine learning approach, on the one hand, and the application of the DARC algorithm on the other hand. Once the speed signals of torso and limbs oscillations were detected, we suggested estimating 14 gait parameters. All our approaches were validated by comparing outcomes to those obtained from a reference Vicon system. High correlation coefficients were obtained by comparing the speed signals of the torso (ρ=0.8), the speed signals of limbs oscillations (ρ=0.91), the initial and final indices of TUG phases (ρ=0.95), and the extracted parameters (percentage error < 4.8) obtained after radar signal processing to those obtained from the Vicon system.

Compressed Sensing Data with Performing Audio Signal Reconstruction for the Intelligent Classification of Chronic Respiratory Diseases.

Chronic obstructive pulmonary disease (COPD) concerns the serious decline of human lung functions. These have emerged as one of the most concerning health conditions over the last two decades, after cancer around the world. The early diagnosis of COPD, particularly of lung function degradation, together with monitoring the condition by physicians, and predicting the likelihood of exacerbation events in individual patients, remains an important challenge to overcome. The requirements for achieving scalable deployments of data-driven methods using artificial intelligence for meeting such a challenge in modern COPD healthcare have become of paramount and critical importance. In this study, we have established the experimental foundations for acquiring and indeed generating biomedical observation data, for good performance signal analysis and machine learning that will lead us to the intelligent diagnosis and monitoring of COPD conditions for individual patients. Further, we investigated on the multi-resolution analysis and compression of lung audio signals, while we performed their machine classification under two distinct experiments. These respectively refer to conditions involving (1) "Healthy" or "COPD" and (2) "Healthy", "COPD", or "Pneumonia" classes. Signal reconstruction with the extracted features for machine learning and testing was also performed for securing the integrity of the original audio recordings. These showed high levels of accuracy together with the performances of the selected machine learning-based classifiers using diverse metrics. Our study shows promising levels of accuracy in classifying Healthy and COPD and also Healthy, COPD, and Pneumonia conditions. Further work in this study will be imminently extended to new experiments using multi-modal sensing hardware and data fusion techniques for the development of the next generation diagnosis systems for COPD healthcare of the future.

A support system for automatic classification of hypertension using BCG signals

Hypertension (HPT) is a lethal medical disorder in which the blood vessels unusually have high pressure for an extended period. It may raise the risk of various health complications. Ballistocardiography (BCG) is an emerging tool to diagnose various heart-related diseases and is used to depict the repetitive vibrations in the human body induced by the sudden evacuation of blood into the major arteries with each heartbeat. This article presents the multi-resolution analysis of BCG signals for the screening of HPT patients using integrated tunable Q-factor wavelet transform (ITQWT). The TQWT decomposes an input BCG signal into various sub-bands (SBs). Specifying a predetermined accurate basis function for optimal decomposition utilizing TQWT is a difficult task. Therefore, in this study, for the first time, a multi-verse optimization (MVO) algorithm is integrated with TQWT for selecting optimum tuning parameters to decompose the input BCG signals into more representative SBs. To detect hypertensive BCG signals eleven statistical features are evaluated from each SB. Among them, a set of seven statistically-significant features are selected by applying the Kruskal–Wallis test and fed to a K-nearest neighbor (K-NN) classifier with six different kernels using a 10-fold validation scheme. The highest classification accuracy of 92.21%, sensitivity of 92.96%, and specificity of 91.60% are achieved using a weighted K-NN classifier. This paper presents, a non-parameterized approach for the optimal decomposition of BCG data to detect HPT more accurately. The primary benefit of the proposed support system is that it can detect HPT patients with high accuracy by reducing the clinician’s workload.

Theory and Design of Joint Time-Vertex Nonsubsampled Filter Banks

Graph signal processing (GSP) is a field that deals with data residing on irregular domains, i.e. graph signals. In this field, the graph filter bank is one of the most important developments, owing to its ability to provide multiresolution analysis of graph signals. However, most of the current research on graph filter bank focuses on static graph signals. The research does not exploit the temporal correlations of time-varying signals in real-world applications, such as in wireless sensor networks. In this paper, the theory and design of joint time-vertex nonsubsampled filter bank are developed, using a generalized product graph framework. Several methods are proposed to design the filter bank with perfect reconstruction, while still achieving filters with good spectral characteristics. A notable feature of the designed filter bank is that it can be completely realized in a distributed manner. The subband filters are either of polynomial type or defined implicitly via iterative equations. In either case, implementing the subband filters requires only the exchange of information between neighboring nodes. The filter banks are therefore of low implementation complexity and suitable for processing large time-varying datasets. Numerical examples will demonstrate the effectiveness of the proposed designed methods. Application in time-varying graph signal denoising will show the superiority of joint time-vertex filter bank over other methods.

Multi-scale orientation estimation using higher order Riesz transforms

In this paper, we unify the Riesz transform with the Teager–Kaiser energy operator (TKEO) and monogenic multi-resolution analysis in comparison to conventional gradient and Riesz transform-based approaches. We show that benefits of our approach maintain the following aspects of different known estimators: the stability of mixed (higher) order of derivatives, like given in TKEO, the all-pass filter characteristics featuring the Riesz transform and the scale-based analysis. Furthermore, we demonstrate the ability of the considered technique for extracting structural defects at different scales, estimating orientation or being used for 2D demodulation of amplitude- and phase modulated signals, like interferometric fringe patterns. Additionally, the abilities of orientation estimation of 3D data is demonstrated. From the viewpoint of mathematical analysis, we will emphasize the connection to monogenic higher dimensional signals, Clifford frames, and monogenic multi-resolution signal analysis. Furthermore, we will discuss higher order Riesz transform.

Recognition of Complex Power Quality Disturbances Using S-Transform Based Ruled Decision Tree

Deteriorated quality of power leads to problems, such as equipment failure, automatic device resets, data errors, failure of circuit boards, loss of memory, power supply issues, uninterrupted power supply (UPS) systems generate alarm, corruption of software, and heating of wires in distribution network. These problems become more severe when complex (multiple) power quality (PQ) disturbances appear. Hence, this manuscript introduces an algorithm for identification of the complex nature PQ events in which it is supported by Stockwell’s transform (ST) and decision tree (DT) using rules. PQ events with complex nature are generated in view of IEEE-1159 standard. Eighteen different types of complex PQ issues are considered and studied which include second, third, and fourth order disturbances. These are obtained by combining the single stage PQ events such as sag & swell in voltage, momentary interruption (MI), spike, flicker, harmonics, notch, impulsive transient (IT), and oscillatory transient (OT). The ST supported frequency contour and proposed plots such as amplitude, summing absolute values, phase and frequency-amplitude obtained by multi-resolution analysis (MRA) of signals are used to identify the complex PQ events. The statistical features such as sum factor, Skewness, amplitude factor, and Kurtosis extracted from these plots are utilized to classify the complex PQ events using rule-based DT. This is established that proposed approach effectively identifies a number of complex nature PQ events with accuracy above 98%. Performance of the proposed method is tested successfully even with noise level of 20 dB signal to noise ratio (SNR). Effectiveness of the proposed algorithm is established by comparing it with the methods reported in literature such as fuzzy c-means clustering (FCM) & adaptive particle swarm optimization (APSO), Wavelet transform (WT) & neural network (NN), spline WT & ST, ST & NN, and ST & fuzzy expert system (FES). Results of simulations are validated by comparing them with real time results computed by Real Time Digital Simulator (RTDS). Different stages for design of complex PQ monitoring device using the proposed approach are also described. It is verified that the proposed approach can effectively be employed for design of the online complex PQ monitoring devices.

DIAGNOSTIC OF THE COMBUSTION PROCESS USING THE ANALYSIS OF CHANGES IN FLAME LUMINOSITY

Monitoring of the combustion process is carried out in order to ensure its efficiency and stability. Selected aspects of the combustion process diagnostics using the analysis of changes in flame luminosity for two configurations: 100% pulverized coal fuel and a mixture of 80% coal and 20% biomass were presented in the article. The analysis of measurement data was conducted using selected statistical tools and a multiresolution analysis of signals.

A Novel Approach for Detection of Myocardial Infarction From ECG Signals of Multiple Electrodes

Myocardial infarction (MI) is also called the heart attack, and it results in the death of heart muscle cells due to the lacking in the supply of oxygen and other nutrients. The early and accurate detection of MI using the 12-lead electrocardiogram (ECG) is helpful in the clinical standard for saving the lives of the patients suffering from this pathology. This paper proposes a novel approach for the detection of MI pathology using the multiresolution analysis of 12-lead ECG signals. The approach is based on the use of Fourier-Bessel series expansion-based empirical wavelet transform (FBSE-EWT) for the time-scale decomposition of 12-lead ECG signals. For each lead ECG signal, nine subband signals are evaluated using FBSE-EWT. The statistical features such as the kurtosis, the skewness, and the entropy are evaluated from the subband signals of each ECG lead. The deep neural network such as the deep layer least-square support-vector machine (DL-LSSVM) which is formulated using the hidden layers of sparse auto-encoders and the LSSVM is used for the detection of MI from the feature vector of 12-lead ECG. The experimental results demonstrate that the combination of FBSE-EWT-based entropy features and DL-LSSVM has the mean accuracy, the mean sensitivity, and the mean specificity values of 99.74%, 99.87%, and 99.60%, respectively, for the detection of MI. The accuracy value of the proposed method is improved by more than 3% as compared to the wavelet-based features for the detection of MI.

Recognition of voltage sag causes using fractionally delayed biorthogonal wavelet

In this work, a new fractionally delayed biorthogonal wavelet is designed for recognition of voltage sag causes. This work addresses the classification of voltage sag causes into three categories, i.e., fault events (namely line-to-ground fault, line-to-line fault, double-line-to-ground fault and symmetrical fault), induction motor starting and transformer energization. Fractionally delayed biorthogonal Coiflet wavelet of order 2 (named as Coiflet fraclet) is designed using Lagrange interpolation and employed for the multiresolution analysis of voltage sag signals. To achieve higher classification accuracy, event information is derived from both time-frequency domain and frequency domain. Frequency information is obtained by applying multiple signal classification (MUSIC) algorithm on voltage sag signals. Both the time-frequency domain and frequency domain features are concatenated to implement the feature level fusion for strengthening the feature set. The feature set obtained after feature level fusion is used for training the recursive reduced kernel based extreme learning machine which addresses the problem of highly complex structure due to huge dataset of large dimensions. The classifier has shown robustness to the presence of noise also and classified the voltage sag causes with high accuracy.

REMOVAL OF ELECTROENCEPHALOGRAPHY EEG EYE-BLINK ARTIFACT USING WAVELET FUNCTION

This paper presents a study related to awareness about concepts of Electroencephalography (EEG) and it's one type of artifact i.e. Eye-Blink Artifact. This is one form of Ocular Artifact. To study brain functioning and problems if any, Neurologists uses Electroencephalography technique. But while recording brain signals, noise (Artifact) gets induced and became part of EEG recording. This creates problems for Nero Experts to analyse and interpret it and hence it is necessary to remove such artifact from recordings. Ocular artifact related to Eye movement is in existence which may also resemble to disordered pattern. One can detect and remove this using Wavelet Function available.Sub sampling and multi resolution analysis of signal is the key idea for identifying typical trendy pattern of required frequency band and nullifying their impact. Discrete Wavelet Transform provides sufficient information both for analysis and synthesis of the original signal.MODWT, IMODWT and MODWTMRA are the wavelet functions used to localise required pattern and remove from the signal.

Multiresolution Analysis of ECG Signals in Heart Rhythm Monitoring

The paper is devoted to multiresolution analysis of ECG signals in heart rhythm monitoring. The proposed method for R-wave detection in ECG signals is based on extracting detail coefficients from the wavelet decomposition of the ECG signal. It uses nonlinear transforms and the adaptive threshold algorithm. The suggested approach is compared to existing methods for R-wave detection in ECG signals used for processing clinical ECG records from the MIT Physionet database.

Shift-invariant and sampling spaces associated with the special affine Fourier transform

The Special Affine Fourier Transformation or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Shift-invariant spaces also play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. Shannon's sampling theorem, which is at the heart of modern digital communications, is a special case of sampling in shift-invariant spaces. Furthermore, it is well known that the Poisson summation formula is equivalent to the sampling theorem and that the Zak transform is closely connected to the sampling theorem and the Poisson summation formula. These results have been known to hold in the Fourier transform domain for decades and were recently shown to hold in the Fractional Fourier transform domain by A. Bhandari and A. Zayed. The main goal of this article is to show that these results also hold true in the SAFT domain. We provide a short, self-contained proof of Shannon's theorem for functions bandlimited in the SAFT domain and then show that sampling in the SAFT domain is equivalent to orthogonal projection of functions onto a subspace of bandlimited basis associated with the SAFT domain. This interpretation of sampling leads to least-squares optimal sampling theorem. Furthermore, we show that this approximation procedure is linked with convolution and semi-discrete convolution operators that are associated with the SAFT domain. We conclude the article with an application of fractional delay filtering of SAFT bandlimited functions.

Recognition of power quality disturbances using S-transform based ruled decision tree and fuzzy C-means clustering classifiers

A method based on Stockwell's transform and Fuzzy C-means (FCM) clustering initialized by decision tree has been proposed in this paper for detection and classification of power quality (PQ) disturbances. Performance of this method is compared with S-transform based ruled decision tree. PQ disturbances are simulated in conformity with standard IEEE-1159 using MATLAB software. Different statistical features of PQ disturbance signals are obtained using Stockwell's transform based multi-resolution analysis of signals. These features are given as input to the proposed techniques such as rule-based decision tree and FCM clustering initialized by ruled decision tree for classification of various PQ disturbances. The PQ disturbances investigated in this study include voltage swell, voltage sag, interruption, notch, harmonics, spike, flicker, impulsive transient and oscillatory transient. It has been observed that the efficiency of classification based on ruled decision tree deteriorates in the presence of noise. However, the classification based on Fuzzy C-means clustering initialized by decision tree gives results with high accuracy even in the noisy environment. Validity of simulation results has been verified through comparisons with results in real time obtained using the Real Time Digital Simulator (RTDS) in hardware synchronization mode. The proposed algorithm is established effectively by results of high accuracy to detect and classify various electrical power quality disturbances.

Multiresolution Analysis of EEG Signals

Abstract This paper reports on a multiresolution analysis of EEG signals. The dominant frequency components of signals with and without observed epileptic discharges were compared. The study showed that there were significant differences in dominant frequency between the signals with epileptic discharges and the signals without discharges. This gives the ability to identify epilepsy during EEG examination. The frequency of the signals coming from the frontal, central, parietal and occipital channels are similar. Multiresolution analysis can be used to describe the activity of brain waves and to try to predict epileptic seizures, thereby contributing to precise medical diagnoses.

Fusion Framework for Emotional Electrocardiogram and Galvanic Skin Response Recognition: Applying Wavelet Transform

Introduction To extract and combine information from different modalities, fusion techniques are commonly applied to promote system performance. In this study, we aimed to examine the effectiveness of fusion techniques in emotion recognition. Materials and Methods Electrocardiogram (ECG) and galvanic skin responses (GSR) of 11 healthy female students (mean age: 22.73±1.68 years) were collected while the subjects were listening to emotional music clips. For multi-resolution analysis of signals, wavelet transform (Coiflets 5 at level 14) was used. Moreover, a novel feature-level fusion method was employed, in which low-frequency sub-band coefficients of GSR signals and high-frequency sub-band coefficients of ECG signals were fused to reconstruct a new feature. To reduce the dimensionality of the feature vector, the absolute value of some statistical indices was calculated and considered as input of PNN classifier. To describe emotions, two-dimensional models (four quadrants of valence and arousal dimensions), valence-based emotional states, and emotional arousal were applied. Results The highest recognition rates were obtained from sigma=0.01. Mean classification rate of 100% was achieved through applying the proposed fusion methodology. However, the accuracy rates of 97.90% and 97.20% were attained for GSR and ECG signals, respectively. Conclusion Compared to the previously published articles in the field of emotion recognition using musical stimuli, promising results were obtained through application of the proposed methodology.

Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach

In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficient orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test different choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.

Rectangular prism pressure coherence by modified Morlet continuous wavelet transform

This study investigates the use of time-frequency coherence analysis for detecting and evaluating coherent "structures" of surface pressures and wind turbulence components, simultaneously on the time-frequency plane. The continuous wavelet transform-based coherence is employed in this time-frequency examination since it enables multi-resolution analysis of non-stationary signals. The wavelet coherence quantity is used to identify highly coherent "events" and the "coherent structure" of both wind turbulence components and surface pressures on rectangular prisms, which are measured experimentally. The study also examines, by proposing a "modified" complex Morlet wavelet function, the influence of the time-frequency resolution and wavelet parameters (i.e., central frequency and bandwidth) on the wavelet coherence of the surface pressures. It is found that the time-frequency resolution may significantly affect the accuracy of the time-frequency coherence; the selection of the central frequency in the modified complex Morlet wavelet is the key parameter for the time-frequency resolution analysis. Furthermore, the concepts of time-averaged wavelet coherence and wavelet coherence ridge are used to better investigate the time-frequency coherence, the coherently dominant events and the time-varying coherence distribution. Experimental data derived from physical measurements of turbulent flow and surface pressures on rectangular prisms with slenderness ratios B/D=1:1 and B/D=5:1, are analyzed.