Discrete Wavelet Packet Research Articles

Comparison of analysis methods for separating and recognizing multicomponent radar signals

This paper proposes a model for separating and recognizing a mixture of radar signals using combined multiresolution methods and convolution neural networks. The model involves three main steps: separating the signal into individual components using the Multiresolution analysis (MRA) methods: Empirical mode decomposition (EMD), Variational mode decomposition (VMD), and Maximal overlap discrete wavelet packet transform (MODWPT); transforming these components into the time-frequency domain using Wigner-Ville distribution (WVD) and storing them as images; and then feeding these images into the SqueezeNet for recognition. These multiresolution methods are then compared based on three criteria: The number of successful separations, the SNR ratio of the input signal, and the correlation between the separated signal components and the original signal components. Additionally, we evaluate the performance of the SqueezeNet with real-time signals.

Deciphering laser shock peening quality monitoring: Wavelet-driven network with interpretability

Quality monitoring of laser shock peening based on acoustic emission technology is a topical multidisciplinary issue that has received much attention in recent years. To acquire complex time-varying information in acoustic emission signals, convolutional neural networks with powerful learning capabilities have shown potential for a wide range of applications. However, the black-box property of the network imposes limitations on its further development and decision credibility. Therefore, this study proposes a wavelet-driven network with theoretical basis and physical significance. This network can cyclically utilize discrete wavelet packet transform to map input features to the wavelet domain during the learning process, thereby obtaining more robust and valuable information. This paper also constructs a novel wavelet attention mechanism that takes into account the difference between low-frequency and high-frequency information, and is able to allocate resources in both the decomposition component and the time-domain dimension. The proposed method can be seen as a multiresolution analysis technique that combines existing physical knowledge with nonlinear feature processing and feature selective enhancement. The results of the two laser shock peening cases show that the proposed method not only outperforms current state-of-the-art models in terms of monitoring performance, but also has better physical interpretability. Importantly, the proposed method has the potential to be further extended to other interpretable structural health monitoring.

Fault classification scheme for TCSC compensated transmission line using MODWPT-BTEC

This article proposes a fault classification algorithm for a Thyristor Controlled Series Compensated (TCSC) long transmission line. Such type of line imposes issues related to reactance modulation, voltage inversion, current inversion and TCSC control action. This scheme utilizes ½ cycle post-fault current signal, which is then processed by maximum overlap discrete wavelet packet transform (MODWPT), and energy feature is calculated. The proposed scheme has been validated on a modified Western System Coordinating Council (WSCC) 9 bus system with TCSC. Also, the scheme is certified for wind farm integration in grid connected mode. The bagged tree ensemble classifier outperformed various stable and ensemble combinations, including the decision tree, linear discriminative analysis, support vector machine, k-nearest neighbor, boosted/trees ensemble, and subspace/discriminant ensemble. The line with TCSC compensation is modeled using PSCAD/EMTDC software. The proposed scheme accurately classifies faults in all tested scenarios with 100% accuracy. The outcomes of the suggested algorithm along with a comparative study confirm the accuracy and fast protection measures for TCSC-compensated line.

Machine Learning Approach for LPRE Bearings Remaining Useful Life Estimation Based on Hidden Markov Models and Fatigue Modelling

Ball bearings are one of the most critical components of rotating machines. They ensure shaft support and friction reduction, thus their malfunctioning directly affects the machine’s performance. As a consequence, it is necessary to monitor the health conditions of such a component to avoid major degradations which could permanently damage the entire machine. In this context, HMS (Health Monitoring Systems) and PHM (Prognosis and Health Monitoring) methodologies propose a wide range of algorithms for bearing diagnosis and prognosis. The present article proposes an end-to-end PHM approach for ball bearing RUL (Remaining Useful Life) estimation. The proposed methodology is composed of three main steps: HI (Health Indicator) construction, bearing diagnosis and RUL estimation. The HI is obtained by processing non-stationary vibration data with the MODWPT (Maximum Overlap Discrete Wavelet Packet Transform). After that, a degradation profile is defined and coupled with crack initiation and crack propagation fatigue models. Lastly, a MB-HMM (Hidden Markov Model) is trained to capture the bearing degradation dynamics. This latter model is used to estimate the current degradation state as well as the RUL. The obtained results show good RUL prediction capabilities. In particular, the fatigue models allowed a reduction of the ML (Machine Learning) model size, improving the algorithms training phase.

Using machine learning techniques in inverse problems of acoustical oceanography

AbstractThe goal of the work presented here is to study a novel approach for inverting acoustic signals recorded in the marine environment for the estimation of environmental parameters of the water column and/or the seabed. The proposed approach is based on signal feature extraction using a discrete wavelet packet transform, applied to the measured signal, and hidden Markov models that exploit the sequential patterns of the signals. The signal feature is thereafter used in the framework of a mixture density network, which, after training with sets of simulated signals calculated within a predefined search space, provides conditional posterior distributions of the recoverable parameters. The technique is tested with two test cases corresponding to different types of inverse problems. The first case corresponds to a simple problem of geoacoustic inversion, while the second is referred to a, rather unusual, still interesting problem of recovering the shape of a seamount using long‐range acoustic data. Both test cases are based on simulated experiments. The inversion results obtained using the proposed scheme are compared with inversion results using statistical features of the acoustic signal, which is another inversion approach well documented in the literature and is also based on the wavelet packet transform of the measured signal.

A maximal overlap discrete wavelet packet transform coupled with an LSTM deep learning model for improving multilevel groundwater level forecasts

Developing precise groundwater level (GWL) forecast models is essential for the optimal usage of limited groundwater resources and sustainable planning and management of water resources. In this study, an improved forecasting accuracy for up to 3 weeks ahead of GWLs in Bangladesh was achieved by employing a coupled Long Short Term Memory (LSTM) network-based deep learning algorithm and Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) data preprocessing. The coupled LSTM-MODWPT model’s performance was compared with that of the LSTM model. For both standalone LSTM and LSTM-MODWPT models, the Random Forest feature selection approach was employed to select the ideal inputs from the candidate GWL lags. In the LSTM-MODWPT model, input GWL time series were decomposed using MODWPT. The ‘Fejér-Korovkin’ mother wavelet with a filter length of 18 was used to obtain a collection of scaling coefficients and wavelets for every single input time series. Model performance was assessed using five performance indices: Root Mean Squared Error; Scatter Index; Maximum Absolute Error; Median Absolute Deviation; and an a-20 index. The LSTM-MODWPT model outperformed standalone LSTM models for all time horizons in GWL forecasting. The percentage improvements in the forecasting accuracies were 36.28%, 32.97%, and 30.77%, respectively, for 1-, 2-, and 3-weeks ahead forecasts at the observation well GT3330001. Accordingly, the coupled LSTM-MODWPT model could potentially be used to enhance multiscale GWL forecasts. This research demonstrates that the coupled LSTM-MODWPT model could generate more precise GWL forecasts at the Bangladesh study site, with potential applications in other geographic locations globally.

Accurate Criteria for Broken Bar Detection in Induction Motors Based on the Wavelet (Packet) Transform

Finding reliable and robust criteria for the detection of broken bars in induction motors is key for the maintenance of industrial engines, and some of the most efficient methods analyze the stator start-up current. Due to the transitory characteristics and short duration of the signal, suitable time-frequency mathematical tools are very useful for this purpose. We propose here algorithms based on the discrete wavelet and wavelet packet transform, combined with other tools in signal processing, to offer an accurate quantitative method for failure detection due to broken bars in induction motors. A good selection of the wavelet family is important for a good performance of the indicator, and the discrete approximation of the Meyer wavelet, ‘dmeyer’, consistently demonstrates the most favorable results. Our findings highlight the effectiveness of both the wavelet and wavelet packet transforms in accurately detecting broken bars in induction motors. This fact allows optimal monitoring strategies in industrial applications.

SEACKgram: a targeted method of optimal demodulation-band selection for compound faults diagnosis of rolling bearing

Rolling bearing plays an important role in carrying and transmitting power in rotating machinery, and the bearing fault is easy to lead to mechanical accidents, resulting in huge losses and casualties. Therefore, the condition monitoring and diagnosis of rolling bearings are very important to improve the safety of equipment. Compound fault is a common fault evolved from the initial defect, which is characterized by randomness, coupling, concealment, and secondary. The existence of these characteristics brings great challenges to the accurate diagnosis of compound faults. In the diagnosis of compound faults, the traditional methods that select the single optimal demodulation frequency band for analysis and identification sometimes cannot completely extract multiple fault components, which are prone to miss diagnosis and misdiagnosis. In order to solve this problem, the SEACKgram method is proposed by constructing a Square Envelope Unbiased Autocorrelation Correlation Kurtosis (SEACK) index. The frequency band of the original signal is divided by the Maximal Overlap Discrete Wavelet Packet Transform, and the SEACK index is used to quantitatively describe the fault signals of different frequency bands. According to the different fault periods, the resonant frequency bands of the maximum SEACK value are selected, then the resonance band signal is analyzed by square envelope spectrum, and the fault type is identified according to the fault characteristic frequency. The simulated and experimental vibration signals of rolling bearings with compound faults are used to verify the feasibility of the proposed method. The results show that the proposed SEACKgram can improve the accuracy of compound faults identification and would be applied in engineering practice to a certain extent.

Reliability enhancement of hybrid microgrid protection against communication data loss and converter faults using cubic-spline interpolation, Savitzky Golay filtering and GRU network

A primary challenge towards adoption of hybrid AC-DC microgrid pertains to the complexity of the protection scheme. Among other challenges, the high resemblance of voltage and current dynamics for converter faults and line faults, hinders use of threshold-based protection schemes. Further the high dependence of the protection mechanism on the communication network results in reduced reliability during data packet loss in the communication channel. In this regard, a protection scheme is proposed based on the combination of cubic spline interpolation, Savitzky-Golay (SG) filtering, maximum overlap discrete wavelet packet transform (MODWPT) and gated recurrent unit (GRU)-neural network. The impact of data packet loss (modelled using Markov chain model) in the communication channel has been minimized by reconstructing the original signal from lossy data using spline interpolation and SG filter. With the reconstructed signal, significant attributes are extracted using MODWPT, which are further utilized to perform fault detection, fault classification and faulty section identification using a set of GRU classifiers. Unlike the reported techniques whose fault detection and classification accuracy are severely compromised during packet loss, the signal reconstruction module in the proposed framework makes it immune to packet loss. The inclusion of a module for distinguishing between converter faults and line faults allows for avoiding relay maloperation during switching failures. The proposed scheme has been extensively validated for a wide range of operating and fault scenarios under converter faults, PV array faults, varying degrees of packet loss, burst length and dynamic loading conditions. For packet loss rate ranging from 5 % to 30 % and burst length from 0.0167 s to 0.1 s, the proposed scheme achieves dependability and security in excess of 99.85 % and 99.46 % respectively.

A novel design employing arbitrary tree structure for adaptive thrsholding discrete wavelet packet transformation

A novel design employing arbitrary tree structure for adaptive thrsholding discrete wavelet packet transformation

Precise disturbance localization of long distance fiber interferometer vibration senor based on an improved time–frequency variation feature extraction scheme

Locating intrusions with high accuracy is crucial for prompting long distance distributed optical fiber vibration sensing systems to practical applications in engineering filed. To achieve the high measurement accuracy and real-time performance simultaneously, in this paper, an intensity-modulated ultra-long distance distributed optical fiber vibration sensing system using an asymmetric dual Mach-Zehnder interferometer is experimentally established. More importantly, a positioning approach based on an ameliorated time–frequency feature extraction scheme is proposed with both theoretically analysis and experimental demonstration. In particular, an endpoint detection algorithm based on differential operation is firstly utilized to rapidly and accurately locate the endpoints of the received vibration signals. Thus the large-band width signals can be successfully acquired by setting an approximate window. Then, the ameliorated time–frequency feature extraction scheme based on a maximal overlap discrete wavelet packet transform is applied to eliminate the asymmetry of the large-band width signals, as it could lead to an erroneous positioning result when directly using a cross-correlation time delay estimation algorithm. Finally, the vibration positions along the sensing fiber link of the established sensing system can be successfully demodulated with the help of the extracted time–frequency features. To validate the effectiveness of the proposed scheme, vibration positioning tests were conducted in a real perimeter security scenario. And the results show that a mean positioning error of 11.12 m and a mean processing time of 0.276 s have been realized in a sensing length of 101 km. Thus, it is believed that through continuous technological advancements and refine algorithm optimization, the long distance distributed optical fiber vibration sensor founded on the proposed positioning strategy is poised to play an important role in the practical engineering applications.

Maximum overlap discrete wavelet packet transform-based feature extraction for recognition of freezing of gait in parkinson's disease using gait signals

Maximum overlap discrete wavelet packet transform-based feature extraction for recognition of freezing of gait in parkinson's disease using gait signals

A new epileptic seizure prediction model based on maximal overlap discrete wavelet packet transform, homogeneity index, and machine learning using ECG signals

Epilepsy, a complex pathology with various etiological origins, is characterized by producing hyperexcitability in the brain, which can have multiple disruptive symptoms. It impacts about 40 million people worldwide, of which 20 to 30% have chronic and intractable seizures. Each seizure can create hazardous situations for patients resulting from fractures, burns, submersion accidents, and soft-tissue injuries. Therefore, a method capable of predicting a seizure with sufficient window time before its onset is highly desirable because it will allow the patient to locate a safe place or take appropriate precautionary actions. In this article, a novel method is presented through adroit integration of maximal overlap wavelet packet transform, homogeneity index, and a K-Nearest Neighbors classifier to predict an epileptic event twenty minutes before its onset using electrocardiogram (ECG) signals. The method's effectiveness for predicting an epileptic seizure is verified by employing a database provided by the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH), which includes seven patients with ten epileptic seizures. The results show that the proposed method effectively predicts an epileptic seizure 20 min prior to its onset with an accuracy of 93.25%.

De-noising of microwave reflectometry signal using maximal overlap discrete wavelet packet transform for plasma density measurement

For microwave reflectometry-based fusion plasma diagnostics, the acquired data is contaminated by the surrounding noise environment, making it difficult to measure the beat frequency accurately. Discrete wavelet and wavelet packet transforms are unsuitable as the former cannot decompose detailed coefficients, and the latter is a time-variant transform. This paper presents a correlation-based Maximal Overlap Discrete Wavelet Packet Transform (MODWPT), which decomposes the signal using different mother wavelet families. The suitable mother wavelet is chosen based on the metrics like signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), mean squared error (MSE), and mean absolute error (MAE). The data used for analysis is the stationary tokamak wall, for which the beat frequency and distance are measured. After rigorous analysis, it is found that sym12 outperforms with the following values 0.0493 (MSE), 0.1736 (MAE), 4.3334(SNR(dB)), 13.0634(PSNR(dB)) respectively. This technique can be extended to plasma scenarios for accurately measuring beat frequency and density profile.

Comparative analysis of ANN performance of four feature extraction methods used in the detection of epileptic seizures

Epilepsy, a prevalent neurological disorder characterized by disrupted brain activity, affects over 70 million individuals worldwide, as reported by the World Health Organization (WHO). The development of computer-aided diagnosis systems has become vital in assessing epilepsy severity promptly and initiating timely treatment. These systems enable the detection of epileptic seizures by analyzing the electrical activity in the EEG recordings of the patients. In addition, it helps doctors to choose suitable treatment by quickly determining the type, duration, and characteristics of seizures and increases the patient's quality of life. The proposed computer-aided diagnosis system in this study comprises three modules: preprocessing, feature extraction, and classification. The initial module employs a low-pass Chebyshev II filter to eliminate noise artifacts from signal recordings. The second module involves deriving feature vectors using Bispectrum Analysis, Empirical Mode Decomposition, Discrete Wavelet Transform, and Wavelet Packet Analysis. The third module employs the Artificial Neural Networks method for epileptic seizure detection. This study not only enables the comparison of feature extraction efficacy among Bispectrum Analysis, Empirical Mode Decomposition, Discrete Wavelet Transform, and Wavelet Packet Analysis techniques, but it also reveals that Bispectrum Analysis and Empirical Mode Decomposition yield the highest accuracy rate. The method achieves 100% accuracy in detecting epileptic seizures. Additionally, sensitivity analysis has been conducted to enhance the success of Discrete Wavelet Transform and Wavelet Packet Analysis methods and to identify significant features.

Method for Denoising the Vibration Signal of Rotating Machinery through VMD and MODWPT.

The vibration signals from rotating machinery are constantly mixed with other noises during the acquisition process, which has a negative impact on the accuracy of signal feature extraction. For vibration signals from rotating machinery, the conventional linear filtering-based denoising method is ineffective. To address this issue, this paper suggests an enhanced signal denoising method based on maximum overlap discrete wavelet packet transform (MODWPT) and variational mode decomposition (VMD). VMD decomposes the vibration signal of rotating machinery to produce a set of intrinsic mode functions (IMFs). By computing the composite weighted entropy (CWE), the phantom IMF component is then removed. In the end, the sensitive component is obtained by computing the value of the degree of difference (DID) after the high-frequency noise component has been decomposed through MODWPT. The denoised signal reconstructs the signal's intrinsic characteristics as well as the denoised high-frequency IMF component. This technique was used to analyze the simulated and real-world signals of gear faults and it was compared to wavelet threshold denoising (WTD), empirical mode decomposition reconstruction denoising (EMD-RD), and ensemble empirical mode decomposition wavelet threshold denoising (EEMD-WTD). The outcomes demonstrate that this method can accurately extract the signal feature information while filtering out the noise components in the signal.

Speech Enhancement Based on Discrete Wavelet Packet Transform and Itakura-Saito Nonnegative Matrix Factorisation

Nonnegative matrix factorization (NMF) is one of the most popular machine learning tools for speech enhancement (SE). However, there are two problems reducing the performance of the traditional NMFbased SE algorithms. One is related to the overlap-and-add operation used in the short time Fourier transform (STFT) based signal reconstruction, and the other is the Euclidean distance used commonly as an objective function; these methods can cause distortion in the SE process. In order to get over these shortcomings, we propose a novel SE joint framework which combines the discrete wavelet packet transform (DWPT) and the Itakura-Saito nonnegative matrix factorisation (ISNMF). In this approach, the speech signal was first split into a series of subband signals using the DWPT. Then, the ISNMF was used to enhance the speech for each subband signal. Finally, the inverse DWPT (IDWT) was utilised to reconstruct these enhanced speech subband signals. The experimental results show that the proposed joint framework effectively enhances the performance of speech enhancement and performs better in the unseen noise case compared to the traditional NMF methods.

A novel rolling bearing fault diagnosis method based on Adaptive Denoising Convolutional Neural Network under noise background

In recent years, significant progress has been made in intelligent fault diagnosis algorithms for rolling bearings. However, their real industrial application performance is hindered by challenges related to noise and variable load conditions. To solve this problem, we proposed an adaptive denoising convolutional neural network (ADCNN) which integrates adaptive denoising units to remove noise while preserving sensitive fault features, eliminating the need for manual denoising function settings. In addition, we use Maximum Overlap Discrete Wavelet Packet Transform to separate out the interfering components of noisy signal. To further improve ADCNN's noise immunity, we adopt a strategy of gradually decreasing the number of channels and using large convolutional kernels. ADCNN was evaluated alongside the latest methods on two different datasets, and the results demonstrate that ADCNN outperforms other methods both accuracy and robustness. Therefore, our approach presents a promising solution for diagnosing mechanical systems in noisy environments.

Intelligent fault classification of air compressors using Harris hawks optimization and machine learning algorithms

Due to their complexity and often harsh working environment, air compressors are inevitably exposed to a variety of faults and defects during their operation. Thus, condition monitoring is critically required for early fault recognition and detection to avoid any type industrial failures. In this paper, an intelligent algorithm for reciprocating air compressor fault diagnosis is developed using real-time acoustic signals acquired from an air compressor with one healthy and seven different faulty states such as leakage inlet valve (LIV), leakage outlet valve (LOV), non-return valve (NRV), piston ring, flywheel, rider-belt and bearing defects. The proposed algorithm mainly consists of three steps: feature extraction, selection, and classification. For feature extraction, experimental acoustic signals are decomposed using maximal overlap discrete wavelet packet transform (MODWPT) by six levels into 64 wavelet coefficients (nodes). Thereafter, time domain features are calculated for each node to build each air compressor’s health state feature matrix. Each feature matrix dimension is reduced by selecting the most useful features using Harris hawks optimization (HHO) in the feature selection step. Finally, for feature classification, selected features are used as inputs for random forest (RF), ensemble tree (ET) and K-nearest neighbors (KNN) to detect, identify, and classify the compressor health states with high classification accuracy. Comparative studies with several feature extraction and selection methods prove the proposed approach’s efficiency in detecting, identifying, and classifying all air compressor faults.

Wavelet-Based Harmonic Magnitude Measurement in the Presence of Interharmonics

The increasing proliferation of power electronic converters, nonlinear loads, and distributed generation are leading to increased levels of harmonic and interharmonics in power networks. As a consequence, power quality (PQ) has become a critical performance indicator for power utilities and end-users. This study proposes a novel harmonic estimation method based on the real-time stationary discrete wavelet packet transform (RT-SDWPT). The proposed technique decomposes an input signal into frequency bands with harmonic information at cutoff frequencies and uses a compensation strategy to estimate root mean square (RMS) values of harmonics at every sampling period. The performance and effectiveness of the proposed method are assessed using real measurement data from field cases and experimental setup. The real measurements include challenging scenarios with harmonics, subharmonics, interharmonics, frequency deviation, and non-stationary PQ events. The proposed method outperforms the harmonic estimation provided by the discrete Fourier transform (DFT)-based approach and existing wavelet packet-based methods in terms of accuracy and speed.