Discrete Wavelet Packet Transform Research Articles

Automated detection and localization system of myocardial infarction in single-beat ECG using Dual-Q TQWT and wavelet packet tensor decomposition

Background and objectiveIt is challenging to conduct real-time identification of myocardial infarction (MI) due to artifact corruption and high dimensionality of multi-lead electrocardiogram (ECG). In the present study, we proposed an automated single-beat MI detection and localization system using dual-Q tunable Q-factor wavelet transformation (Dual-Q TQWT) denoising algorithm. MethodsAfter denoising and segmentation of ECG, a fourth-order wavelet tensor (leads × subbands × samples × beats) was constructed based on the discrete wavelet packet transform (DWPT), to represent the features considering the information of inter-beat, intra-beat, inter-frequency, and inter-lead. To reduce the tensor dimension and preserve the intrinsic information, the multilinear principal component analysis (MPCA) was employed. Afterward, 84 discriminate features were fed into a classifier of bootstrap-aggregated decision trees (Treebagger). A total of 78 healthy and 328 MI (6 types) records including 57557 beats were chosen from PTB diagnostic ECG database for evaluation. ResultsThe validation results demonstrated that our proposed MI detection and localization system embedded with Dual-Q TQWT and wavelet packet tensor decomposition outperformed commonly used discrete wavelet transform (DWT), empirical mode decomposition (EMD) denoising methods and vector-based PCA method. With the Treebagger classifier, we obtained an accuracy of 99.98% in beat level and an accuracy of 97.46% in record level training/testing for MI detection. We also achieved an accuracy of 99.87% in beat level and an accuracy of 90.39% in record level for MI localization. ConclusionAltogether, the automated system brings potential improvement in automated detection and localization of MI in clinical practice.

Supervised Single Channel Speech Enhancement Based on Stationary Wavelet Transforms and Non-negative Matrix Factorization with Concatenated Framing Process and Subband Smooth Ratio Mask

In this paper, we propose a novel single channel speech enhancement approach that takes up the Stationary Wavelet Transform (SWT) and Nonnegative Matrix Factorization (NMF) with Concatenated Framing Process (CFP) and proposes Subband Smooth Ratio Mask (ssRM). Due to downsampling process after filtering, Discrete Wavelet Packet Transform (DWPT) suffers the absence of shift-invariance, and for this reason, some errors occur in the signal reconstruction and to mitigate the problem, firstly we use SWT and NMF with KL cost function. Secondly, we exploit the CFP to build each column of the matrix instead of using NMF directly to take advantage of smooth decomposition. Thirdly, we apply the Auto-Regressive Moving Average (ARMA) filtering process to the newly formed matrices for making the speech more stable and standardized. Finally, we propose an ssRM by combing the Standard Ratio Mask (sRM) and Square Root Ratio Mask (srRM) with Normalized Cross-Correlation Coefficients (NCCC) to take the advantages of them (sRM, srRM and NCCC). In short, the SWT divides the time-domain mixing speech signal into a set of subband signals and then framing and taking the absolute value of each subband signal, and we obtain nonnegative matrices. Then, we form the new matrices by applying the CFP where each column of the formed matrix contains five consequent frames of the nonnegative matrix and performs an ARMA filtering operation. After that, we apply NMF to each newly formed matrix and detect the speech components via proposed ssRM. Finally, the estimated signal can be achieved through them by applying inverse SWT. Our approach is evaluated using IEEE corpus and different types of noises. Objective speech quality and intelligibility improve significantly by applying this approach and outperforms related methods such as conventional STFT-NMF and DWPT-NMF.

Wavelet-packets Associated with Support Vector Machine Are Effective for Monophone Sorting in Music Signals

An abstract interpretation is usually required to analyze acoustic compositions. Nevertheless, there is much signal processing-related research focusing on music processing and similar topics. In that context, the semantic information contained in the melody involving major and minor chords, sharps and flats associated with semibreve, minim, crotchet, quaver, semiquaver and demisemiquaver notes can help in the study of musical sounds. Thus, multiresolution analysis based on discrete wavelet-packet transform (DWPT) associated with a support vector machine (SVM) is used in this paper to inspect and classify those signals, correlating them with a respective acoustic pattern. Results over hundreds of inputs provided almost full accuracy, reassuring the efficacy of the proposed approach for both off-line and real-time usage.

Crack detection in rotating shafts using combined wavelet analysis

There are many rotating mechanical systems on board ships that comprise the main shaft transmission element. Proper functioning of shafts depends on many factors: alignment system, connections with other elements - couplings, gearboxes, bearing elements with ball bearings or bushings, operated regime, and al. All these factors can lead to fatigue of the shaft over time and to appearance of internal/external cracks which can determine a total damage of the shaft at some point in time. To avoid these disasters the operation of these rotating systems is monitored based on vibration analysis of recorded signals (FFT and DFT analysis). Due to the transient modes and the presence of the noise, the processing of the recorded signals must be performed with methods that present a good resolution simultaneously in the time and frequency domain. In the paper, measurements are made on a stand with a rotating system and it is determined the influence of some factors (measuring points and directions, speed, operated mode, crack size, presence of misalignment, noise) on the quality of the Wavelet Transform results. In order to improve the clarity of amplitudes and frequencies changes at the initiation of shaft cracks, the authors are proposing the combined use of Continuous Wavelet Transform (CWT), Discrete Wavelet Transform (DWT) and Wavelet Packet Transform (WPT). The authors propose using power spectral density (PSD) as it is a method with good performance in detecting faults in rotating machines.

An evolution-dependent multi-objective ensemble model of vanishing moment with adversarial auto-encoder for short-term wind speed forecasting in Xinjiang wind farm, China

Wind speed forecasting can enhance the safety and economy of wind energy integration and conversion. The characteristic of the wind speed evolves over time. In this paper, a novel evolution-dependent multi-objective ensemble model of vanishing moment is proposed to solve the above problem. The proposed model can assign time-varying ensemble weights to base predictors with the different vanishing moments, so as to achieve better forecasting performance. In this model, the deep Adversarial Auto-Encoder (AAE) is firstly utilized to convert the wind speed into a two-dimension Gaussian distribution feature space. The Bat Algorithm (BA) is applied to partition the feature space into several sectors. Each sector represents a cluster of wind speed. Outlier Robust Extreme Learning Machines (ORELMs) improved by Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) with the different vanishing moments are applied as base predictors, and the Multi-Objective Feasible Enhanced Particle Swarm Optimization (MOFEPSO) is used to obtain the best ensemble weights for each cluster. At last, the suitable ensemble model is applied for forecasting at each time. Four actual wind speed series collected from Xinjiang wind farm are used to verify the effectiveness of the proposed model. The experimental results indicate the proposed model outperforms other benchmark models.

Supervised Single Channel Speech Enhancement Based on Dual-Tree Complex Wavelet Transforms and Nonnegative Matrix Factorization Using the Joint Learning Process and Subband Smooth Ratio Mask

In this paper, we propose a novel speech enhancement method based on dual-tree complex wavelet transforms (DTCWT) and nonnegative matrix factorization (NMF) that exploits the subband smooth ratio mask (ssRM) through a joint learning process. The discrete wavelet packet transform (DWPT) suffers the absence of shift invariance, due to downsampling after the filtering process, resulting in a reconstructed signal with significant noise. The redundant stationary wavelet transform (SWT) can solve this shift invariance problem. In this respect, we use efficient DTCWT with a shift invariance property and limited redundancy and calculate the ratio masks (RMs) between the clean training speech and noisy speech (i.e., training noise mixed with clean speech). We also compute RMs between the noise and noisy speech and then learn both RMs with their corresponding clean training clean speech and noise. The auto-regressive moving average (ARMA) filtering process is applied before NMF in previously generated matrices for smooth decomposition. An ssRM is proposed to exploit the advantage of the joint use of the standard ratio mask (sRM) and square root ratio mask (srRM). In short, the DTCWT produces a set of subband signals employing the time-domain signal. Subsequently, the framing scheme is applied to each subband signal to form matrices and calculates the RMs before concatenation with the previously generated matrices. The ARMA filter is implemented in the nonnegative matrix, which is formed by considering the absolute value. Through ssRM, speech components are detected using NMF in each newly formed matrix. Finally, the enhanced speech signal is obtained via the inverse DTCWT (IDTCWT). The performances are evaluated by considering an IEEE corpus, the GRID audio-visual corpus, and different types of noises. The proposed approach significantly improves objective speech quality and intelligibility and outperforms the conventional STFT-NMF, DWPT-NMF, and DNN-IRM methods.

Despeckling of ultrasound images using directionally decimated wavelet packets with adaptive clustering

Two-dimensional transforms are extensively used for speckle noise reduction (despeckling) in ultrasound images. This work proposes a double filter bank structure consisting of a discrete wavelet packet transform (DWPT) and directional filter bank (DFB) along with a fuzzy-based clustering technique to despeckle ultrasound images. Wavelet packet transform can efficiently reject noises based on grey scale relational thresholding and DFB can efficiently preserve edge information. In this study, instead of conventional thresholding methods, fuzzy-based clustering techniques are applied for noise rejection. The algorithm provides a consistent improvement over the competing state-of-the-art speckle reduction algorithms due to the improved ability to preserve geometric features while rejecting speckle noise adaptively. The authors claim is validated by applying a number of clinical images with performance indices such as peak signal to noise ratio, mean structural similarity, signal to mean square error, speckle signal to noise ratio, speckle suppression index and edge preservation index.

Gear fault diagnosis using Autogram analysis

Rotary machines consist of various devices such as gears, bearings, and shafts that operate simultaneously. As a result, vibration signals have nonlinear and non-stationary behavior, and the fault signature is always buried in overwhelming and interfering contents, especially in the early stages. As one of the most powerful non-stationary signal processing techniques, Kurtogram has been widely used to detect gear failure. Usually, vibration signals contain a relatively strong non-Gaussian noise which makes the defective frequencies non-dominant in the spectrum compared to the discrete components, which reduce the performance of the above method. Autogram is a new sophisticated enhancement of the conventional Kurtogram. The modern approach decomposes the data signal by Maximal Overlap Discrete Wavelet Packet Transform into frequency bands and central frequencies called nodes. Subsequently, the unbiased autocorrelation of the squared envelope for each node is computed to select the node with the highest kurtosis value. Finally, Fourier transform is applied to that squared envelope to extract the fault signature. In this article, the proposed method is tested and compared to Fast Kurtogram for gearbox fault diagnosis using experimental vibration signals. The experimental results improve the detectability of the proposed method and affirm its effectiveness.

A Reliable Health Indicator for Fault Prognosis of Bearings.

Estimation of the remaining useful life (RUL) of bearings is important to avoid abrupt shutdowns in rotary machines. An important task in RUL estimation is the construction of a suitable health indicator (HI) to infer the bearing condition. Conventional health indicators rely on features of the vibration acceleration signal and are predominantly calculated without considering its non-stationary nature. This often results in an HI with a trend that is difficult to model, as well as random fluctuations and poor correlation with bearing degradation. Therefore, this paper presents a method for constructing a bearing’s HI by considering the non-stationarity of the vibration acceleration signals. The proposed method employs the discrete wavelet packet transform (DWPT) to decompose the raw signal into different sub-bands. The HI is extracted from each sub-band signal, smoothened using locally weighted regression, and evaluated using a gradient-based method. The HIs showing the best trends among all the sub-bands are iteratively accumulated to construct an HI with the best trend over the entire life of the bearing. The proposed method is tested on two benchmark bearing datasets. The results show that the proposed method yields an HI that correlates well with bearing degradation and is relatively easy to model.

NTL Detection in Electric Distribution Systems Using the Maximal Overlap Discrete Wavelet-Packet Transform and Random Undersampling Boosting

The illegal use of electricity, defective meters, and a malfunctioning infrastructure are major causes of Non-technical losses (NTLs) in electric distribution systems. Although the use of supervised machine learning techniques to detect NTLs has been widely studied, further research is needed in order to address some significant challenges. (i) Given that fraudulent consumers remarkably outnumber non-fraudulent ones, the imbalanced nature of the dataset can have a major negative impact on the performance of supervised machine learning methods. (ii) Given the large number of dimensions present in the time series data used for training and testing classifiers, advanced signal processing techniques are required in order to extract the most relevant information. (iii) The effectiveness of classifiers must be evaluated using meaningful performance measures for imbalanced data . This paper proposes a framework that addresses the three previous challenges. The core of the proposed framework is the application of the maximal overlap discrete wavelet-packet transform (MODWPT) for feature extraction from time series data and the random undersampling boosting (RUSBoost) algorithm for NTL detection. Moreover, our framework is evaluated using an extensive list of performance metrics. Experiments show that the MODWPT combined with the RUSBoost algorithm can significantly improve the quality of NTL predictions.

Harmonic Analysis of Electrospindle System with Wavelet Packet Transform

The electrospindle systems have been used in the maritime industry, they have recently become operative in automation systems. Along with the widespread use of harmonic generating machines and semi-conductor-based circuits in power and control systems, known reactive power compensation methods have been replaced by the use of filter-based compensation systems that consider harmonic distortion. This study used a voltage signal generated by an electrospindle generator with high harmonic distortion to obtain the amplitude time variation of the fundamental component by using Discrete Wavelet Packet Transform (DWPT). As a result of the analysis, it was observed that this method gives fast and accurate results that can be also used in real-time applications.

Unsupervised classification of 12-lead ECG signals using wavelet tensor decomposition and two-dimensional Gaussian spectral clustering

Due to high dimensionality and multiple variables, unsupervised classification of 12-lead ECG signals involves challenges and difficulties. In order to automatically discover unknown physiological features from raw multivariate signals and detect abnormal cardiac activities of a subject, we proposed an unsupervised classification scheme of 12-lead ECG signals using wavelet tensor decomposition and two-dimensional Gaussian spectral clustering. After filtering and segmentation, each ECG sample is converted into a wavelet tensor by the Discrete Wavelet Packet Transform (DWPT). Main features of ECG samples can be clearly investigated in a multiple feature space constructed by the ECG lead, time and frequency sub-band. Then the Multilinear Principal Component Analysis (MPCA) is applied to reduce the dimensionality of ECG tensors as well as preserve the data interior structure. Taking account of both magnitude and orientation of feature vectors, a novel two-dimensional Gaussian spectral clustering (TGSC) is devised to cluster different 12-lead ECG samples. Furthermore, the dataset obtained from practical 12-lead ECG experiment and two datasets from PhysioBank are used to verify the efficiency of the proposed method. Clustering results show that more useful features of ECG signals can be extracted by the wavelet-tensor-based MPCA than by vector-based PCA. With the two-dimensional Gaussian proximity matrix, the clustering accuracy of TGSC is also higher than that of the traditional spectral clustering.

Forecasting electricity spot price for Nord Pool market with a hybridk‐factor GARMA–LLWNN model

AbstractThis paper proposes a new hybrid approach, based on the combination of parametric and nonparametric models by adopting wavelet estimation approach, to model and predict the price electricity for Nord Pool market. Our hybrid methodology consists into two steps. The first step aims at modeling the conditional mean of the time series, using a generalized fractional model withk‐factor of Gegenbauer termed thek‐factor GARMA model; the parameters of this model are estimated using the wavelet approach based on the discrete wavelet packet transform (DWPT). The second step aims at estimating the conditional variance, so we adopt the local linear wavelet neural network (LLWNN) model. The proposed hybrid model is tested using the hourly log‐returns of electricity spot price from the Nord Pool market. The empirical results were compared with the predictions of the ARFIMA–LLWNN, thek‐factor GARMA–FIGARCH and the individual LLWNN models. It is shown that the proposed hybridk‐factor GARMA–LLWNN model outperforms all other competing methods. Hence it is a robust tool in forecasting time series.

FPGA Implementation of Ultra-High Speed and Configurable Architecture of Direct/Inverse Discrete Wavelet Packet Transform Using Shared Parallel FIR Filters

FPGA Implementation of Ultra-High Speed and Configurable Architecture of Direct/Inverse Discrete Wavelet Packet Transform Using Shared Parallel FIR Filters

Advanced Multiresolution Wavelet Based Wideband Spectrum Sensing Technique for Cognitive Radio

An advance multiresolution wavelet based approach for wideband spectrum sensing for cognitive radio system is proposed in this paper. Prime focus is made on the coarse detection part for interweaved system, in which unoccupied spectrum can be used efficiently by the cognitive users. Quick and immediate shifting over the sensed vacant channel is extremely vital and is a challenging task. To overcome this issue, fast and efficient spectrum sensing technique is proposed for cognitive radios by improvising the Discrete Wavelet Packet Transform (DWPT) for multiresolution interweaved systems. This proposed scheme not only increases the system speed but also reduces complexity. Simulation results are used to analyse the system performance and numerical analysis for computing system complexity.

Optimal Sub-Band Analysis Based on the Envelope Power Spectrum for Effective Fault Detection in Bearing under Variable, Low Speeds.

Early identification of failures in rolling element bearings is an important research issue in mechanical systems. In this study, a reliable methodology for bearing fault detection is proposed, which is based on an optimal sub-band selection scheme using the discrete wavelet packet transform (DWPT) and envelope power analysis techniques. A DWPT-based decomposition is first performed to extract the characteristic defect features from the acquired acoustic emission (AE) signals. The envelope power spectrum (EPS) of each sub-band signal is then calculated to detect the characteristic defect frequencies to reveal abnormal symptoms in bearings. The selection of an appropriate sub-band is essential for effective fault diagnosis, as it can reveal intrinsically explicit information about different types of bearing faults. To address this issue, we propose a Gaussian distribution model-based health-related index (HI) that is a powerful quantitative parameter to accurately estimate the severity of bearing defects. The most optimal sub-band for fault detection is determined using two dimensional (2D) visualization analysis. The efficiency of the proposed approach is validated using several experiments in which different defect conditions are identified under variable, and low operational speeds.

Algorithm for spectrum hole identification in cognitive radio network based on discrete wavelet packet transform enhanced with Hilbert transform

As wireless devices and applications increase, it is envisioned that spectrum utilization by licensed users will go from low to medium occupancy state. The CRs will need to sense wider bands to obtain free channels. Therefore development of enhanced wideband sensing algorithms is needed. Enhancing old tools for new applications could be quite useful. The discrete wavelet packet transform (DWPT) is a good mathematical tool that can be enhanced for better application in wireless communications. This paper presents an algorithm to identify spectrum holes in a cognitive radio system. The algorithm is based on the application of discrete wavelet packet transform enhanced with Hilbert transform in spectrum sensing. The enhancement with Hilbert transform has the effect of sharpening the PSD edges for better detection. Using histogram analysis for a discrete wavelet packet decomposed signal, the algorithm which we call DWPT-HiSHIA (Discrete Wavelet Packet Transform – Histogram Spectrum Hole Identification Algorithm) determines if a sub-band channel has a spectrum hole or not. Simulation results show the effectiveness of the algorithm in the identification of spectrum holes in sub-band channels for a discrete wavelet packet decomposed signal.

A wavelet tensor fuzzy clustering scheme for multi-sensor human activity recognition

With the increasing number of wearable sensors and mobile devices, human activity recognition (HAR) based on multiple sensors has attracted more and more attention in recent years. On account of the diversity of human actions, the analysis of multivariate signals of activities is still a challenging task. Clustering is an unsupervised classification technique which can directly work on unlabeled data and automatically identify unknown activities. Therefore, a new wavelet tensor fuzzy clustering scheme (WTFCS) for multi-sensor activity recognition is proposed in this paper. Firstly, feature tensors of multiple activity signals are constructed using the discrete wavelet packet transform (DWPT). Then Multilinear Principal Component Analysis (MPCA) is utilized to reduce the dimensionality of feature tensors so as to keep the inherent data structure. On the basis of the principal feature initialization and the tensor fuzzy membership, a new fuzzy clustering (PTFC) is developed to identify different activity feature tensor groups. Finally, the open HAR dataset (DSAD) is used to verify the efficiency of the WTFCS. Clustering results of seventeen activities of eight subjects show that potential useful features of human activities can be captured through combining DWPT-based feature extraction with MPCA-based dimensionality reduction. The PTFC is capable of discriminating various human activities effectively. Its correctness rate of activity recognition is higher than those of fuzzy c-means clustering and the fuzzy clustering based on the tensor distance.

Rolling Bearing Fault Diagnosis Using Modified Neighborhood Preserving Embedding and Maximal Overlap Discrete Wavelet Packet Transform with Sensitive Features Selection

In order to enhance the performance of bearing fault diagnosis and classification, features extraction and features dimensionality reduction have become more important. The original statistical feature set was calculated from single branch reconstruction vibration signals obtained by using maximal overlap discrete wavelet packet transform (MODWPT). In order to reduce redundancy information of original statistical feature set, features selection by adjusted rand index and sum of within-class mean deviations (FSASD) was proposed to select fault sensitive features. Furthermore, a modified features dimensionality reduction method, supervised neighborhood preserving embedding with label information (SNPEL), was proposed to realize low-dimensional representations for high-dimensional feature space. Finally, vibration signals collected from two experimental test rigs were employed to evaluate the performance of the proposed procedure. The results show that the effectiveness, adaptability, and superiority of the proposed procedure can serve as an intelligent bearing fault diagnosis system.

Design and application of discrete wavelet packet transform based multiresolution controller for liquid level system

A new controller based on discrete wavelet packet transform (DWPT) for liquid level system (LLS) has been presented here. This controller generates control signal using node coefficients of the error signal which interprets many implicit phenomena such as process dynamics, measurement noise and effect of external disturbances. Through simulation results on LLS problem, this controller is shown to perform faster than both the discrete wavelet transform based controller and conventional proportional integral controller. Also, it is more efficient in terms of its ability to provide better noise rejection. To overcome the wind up phenomenon by considering the saturation due to presence of actuator, anti-wind up technique is applied to the conventional PI controller and compared to the wavelet packet transform based controller. In this case also, packet controller is found better than the other ones. This similar work has been extended for analogous first order RC plant as well as second order plant also.