Optimal Wavelet Research Articles

Online diagnosis algorithm for random drift error in fiber optic current sensor

Focusing on the problem of random drift error in Fiber Optic Current Sensor (FOCS), a random drift error extraction algorithm of FOCS based on optimal wavelet packet and Long Short-Term Memory (LSTM) and Support Vector Machine (SVM) is proposed. Firstly, the characteristic of FOCS signal is analyzed, and the wavelet packet multi-resolution error signals are extracted. Secondly, since the time domain span of the random drift error is large and the short-term characteristics are not obvious, the output signal of the random drift error is extracted by the span interval. The low-frequency mean sequence is constructed by selecting mean parameters according to relevant evaluation indicators. Thirdly, segmentation sequence to construct signal database. The error signal prediction model based on LSTM is constructed by using historical data. Finally, current working state of the device is judged by the model prediction signal and SVM, then, random drift error prediction function is achieved. Experiment results show that the wavelet packet decomposition can extract equipment fault signal effectively. The prediction effect of LSTM model is better than BP neural network model. The LSTM-SVM model can be used to realize the state monitoring and fault warning for the random drift error of FOCS.

Expert system for detection of congestive heart failure using optimal wavelet and heart rate variability signals for wireless cloud‐based environment

AbstractCongestive heart failure (CHF) is a cardiac disorder caused due to inefficient pumping of the heart, which leads to insufficient blood flow to the various parts of the body. The electrocardiogram (ECG) is widely used for the detection of heart diseases. However, it is prone to noise resulting in the detection of P, Q, R, S, and T waves ambiguous and erroneous. The heart rate variability (HRV) is considered to be a good indicator of various cardiac abnormalities. Hence, HRV is preferred. HRV can depict the magnitude of pumping of the heart in the RR interval signals accurately. This work proposes a method to automatically identify CHF using two‐band stopband energy (SBE) optimized orthogonal wavelet filter bank with HRV signals. In the proposed method, we have segmented the HRV data into lengths of 500 and 2000 samples. The HRV signals are decomposed into six sub‐bands, and the wavelet coefficients obtained are used for the extraction of fuzzy entropy (FE) and log energy (LE) features. The extracted features are utilized to classify HRV signals into control and CHF‐affected patients using support vector machine (SVM), bagged tree, complex tree, k‐nearest neighbour (KNN), and linear discriminant classifiers. The SVM performed better than other classifiers yielding the classification accuracy and maximum classification accuracy of 99.30% with (2000 samples) using cubic SVM (CSVM). The 10‐fold cross‐validation method is employed during classification to reduce the over‐fitting phenomenon (Sharma, Dhiman, & Acharya, 2021). It appears that the proposed optimal wavelet‐based automated system can identify CHF accurately using HRV signals. Hence, the model may be applied in clinical usage during an emergency employing a cloud‐based wireless system after testing the developed model with more data.

A step toward cleaner energy production: A water saving-based optimization approach for economic dispatch in modern power systems

This paper proposes a novel approach to discover an optimal solution of multi-area dynamic economic dispatch integrated with wind power and pumped hydroelectric storage. Minimizing of water consumption associated with power production in thermal power plants is yet to be addressed in economic dispatch problem. Thus, it is crucial to modernize the conventional power industry to save the water utilization in the process of generating electric energy. As a result, making a feasible power generation schedule by finding a trade-off between total generation cost and water consumption is the main focus of this paper. Toward this end, this study introduces an effective optimization approach for decreasing the contaminants ‎produced by the combustion-based power plants via reflecting the impacts of wind power and storage systems in the proposed problem. An efficient optimization algorithm considering the merits of whale optimization algorithm and wavelet mutation is also proposed to handle the complications of the trade-off between generation cost and water consumption. The proposed approach is applied to 40-unit 4-area IEEE system by 1) scrutinizing the performance of the hybrid framework from different standpoints, 2) achieving an improvement about 5.4% in the operation cost, and 3) promoting the decarbonized economy by implementing ‎renewable energy.

A recursive sparse representation strategy for bearing fault diagnosis

Partial faults of bearings trigger periodic vibration features, but the interference makes fault diagnosis more difficult. A recursive sparse representation (RSR) algorithm is proposed to solve the fault diagnosis of bearings from sparse representation in the time and frequency domains. The tunable Q-factor wavelet transform (TQWT) filtering strategy is used to adaptively obtain the best wavelet with the signal vibration features. The optimal wavelet data is used as a fragment of each basic atom to obtain an optimal atomic complete dictionary (OACD) by Toeplitz's complementary zero expansion. The sparse representation based on the OACD obtains sparse coefficients with time domain features. The sparse group lasso (SGL) based on Majorize-Minimization (MM) optimization solves the sparse coefficients and extracts the primary vibration information in the frequency domain. Simulation experiments, signal experiments, and a comparative analysis of spectral kurtosis (SK) prove that RSR can effectively extract the vibration characteristics of faulty bearings.

Arbitrarily Oriented Phase Randomization of Design Ground Motions by Continuous Wavelets

For dynamic analysis in seismic design, selection of input ground motions is of huge importance. In the presented scheme, complex Continuous Wavelet Transform (CWT) is utilized to simulate stochastic ground motions from historical records of earthquakes with phase disturbance arbitrarily localized in time-frequency domain. The complex arguments of wavelet coefficients are determined as phase spectrum and an innovative formulation is constructed to improve computational efficiency of inverse wavelet transform with a pair of random complex arguments introduced and make more candidate wavelets available in the article. The proposed methodology is evaluated by numerical simulations on a two-degree-of-freedom system including spectral analysis and dynamic analysis with Shannon wavelet basis and Gabor wavelet basis. The result shows that the presented scheme enables time-frequency range of disturbance in time-frequency domain arbitrarily oriented and complex Shannon wavelet basis is verified as the optimal candidate mother wavelet for the procedure in case of frequency information maintenance with phase perturbation.

Finding an optimal dictionary of different wavelet types using sparse modeling to denoise ECG signal

Abstract Sparse signal modeling often reconstructs a signal with few atoms from a pre-defined dictionary. Hence the choice of wavelet dictionary that represents the sparsity of the target signal is crucial in sparse modeling approach. The challenge of finding an optimal dictionary of different wavelet types using sparse denoising model (SDM) to denoise ECG signal is investigated in this work. A method of finding an optimal wavelet dictionary from a set of orthogonal wavelet sub-dictionaries by the means of the best correlation with ECG signal, is developed. The highly correlated sub-dictionaries from three wavelet dictionaries, namely daubechies, symlets, coiflets and discrete cosine transform are combined to construct an overcomplete dictionary. The weight of Akaike’s information criterion and the signal-to-noise ratio improvement are considered as a criterion to evaluate the performance of the proposed SDM. The results indicate that multi-wavelet dictionary of different types is highly sparse and efficient in denoising the target signal, e.g., ECG.

LVDC Microgrid를 위한 웨이브릿 변환 기반 지락고장 검출

LVDC Microgrid is a small-scale power grid that can increase the stability and efficiency of power supply in a small area, enabling independent operation and increasing the acceptability of DERs (Distributed Energy Resources). However, this is an ungrounded IT (Isolated Terre) grounding system, and even when a ground fault occurs, there is no fault current path and no significant difference compared to the steady state current, so fault detection is very difficult. WT (Wavelet Transform), an easy tool for transient analysis and signal identification, is to be applied to the detection of ground faults in LVDC Microgrid.<BR>In this paper, we propose a Wavelet transform-based ground fault detection method for an ungrounded LVDC Microgrid. By changing the level and order of various MW (Mother Wavelets) using the current collected in the existing pulse injection method, the optimal MW for ground fault detection method is derived. First, an ungrounded LVDC Microgrid is modeled using PSCAD s/w, and ground faults are simulated by varying the fault point and fault resistance. We implement the selected optimal Wavelet transform-based ground fault detection method using Matlab s/w. Finally, performance evaluation is performed through simulation using various collected signals.

Evaluation of mother wavelets on steady-state visually-evoked potentials for triple-command brain-computer interfaces

Wavelet transform (WT) is an important tool to analyze the time-frequency structure of a signal. The WT relies on a prototype signal that is called the mother wavelet. However, there is no single universal wavelet that fits all signals. Thus, the selection of mother wavelet function might be challenging to represent the signal to achieve the optimum performance. There are some studies to determine the optimal mother wavelet for other biomedical signals; however, there exists no evaluation for steady-state visually-evoked potentials (SSVEP) signals that becomes very popular among signals manipulated for brain-computer interfaces (BCIs) recently. This study aims to explore, if any, the mother wavelet that suits best to represent SSVEP signals for classification purposes in BCIs. In this study, three common wavelet-based features (variance, energy, and entropy) extracted from SSVEP signals for five distinct EEG frequency bands (delta, theta, alpha, beta, and gamma) were classified to determine three different user commands using six fundamental classifier algorithms. The study was repeated for six different commonly-used mother wavelet functions (haar, daubechies, symlet, coiflet, biorthogonal, and reverse biorthogonal). The best discrimination was obtained with an accuracy of 100% and the average of 75.85%. Besides, ensemble learner gives the highest accuracies for half of the trials. Haar wavelet had the best performance in representing SSVEP signals among other all mother wavelets adopted in this study. Concomitantly, all three features of energy, variance, and entropy should be used together since none of these features had superior classifier performance alone.

Damage detection on rectangular laminated composite plates using wavelet based convolutional neural network technique

In this study, a novel method called the Wavelet Transform-based Convolutional Neural Network (WT-CNN) technique is proposed for damage detection of rectangular laminated composite plates (RLCPs). In the proposed method, the convolutional neural networks and two-dimensional wavelet transform are combined to detect the location of damages in RLCPs. The finite element model (FEM) of damaged RLCPs is developed to generate two-dimensional signals for feeding in the wavelet transform. In order to form a dataset, five hundred single-damage scenarios are applied on a typical RLCP and detected using optimal mother wavelet functions and vanishing moments. The correlation between the class of signals and their best (optimal) wavelet function is considered as the criterion for the best (optimal) wavelet selection. WT-CNN is trained to detect the location of damages in RLCPs. Results show that the proposed WT-CNN can predict and detect the location of damages in RLCPs with high accuracy and eliminate problems of trial and error simulations for future input signals of damaged RLCPs.

Quality evaluation of metal surfaces treatment by wavelet analysis

Purpose. Analyze the effectiveness of using wavelet analysis to assess the quality of metal surfaces. Investigate the possibility of using wavelet analysis in ultrasonic flaw detection. Determine the optimal wavelet families and their criteria for assessing the quality of metal surface processing.&#x0D; Research methods. Orthogonal wavelets are considered: Daubechies wavelet, Simlet wavelet and Coiflet wavelet, which provide the possibility of performing a discrete wavelet transform procedure. The criteria influencing the effectiveness of ultrasonic signal filtering by methods using wavelet analysis are considered. Ultrasonic signals were filtered using wavelet functions.&#x0D; Results. It has been determined that for successful signal filtering, the selected wavelet method must provide a discrete wavelet transformation and have a similarity in the wavelet function shape in the local features of the ultrasonic signals flaw detector. During the work, a rigid threshold for limiting the detail coefficients of wavelet analysis was chosen, as it is the best for filtering tasks. The filtering efficiency is confirmed by the relatively high signal to noise ratio, as well as by the fact that the shape of the pulse extracted from the defect remained almost unchanged.&#x0D; Scientific novelty. When using the Daubechies and Coiflet wavelets as basic functions, as a result of wavelet filtering, it was possible to increase the signal to noise ratio by 20 dB and confidently isolate the useful signal against the background noise, which indicates the prospects of using this kind of transformations in filtering problems.&#x0D; Practical value. The obtained solutions can be used for implementation in signal filtering algorithms in digital processing units of automated non-destructive ultrasonic control systems.

A coloring and timing brain-computer interface for the nursing bed robot

The patient with a severely spinal injury needs an intention-controlled nursing bed (NB) robot to help the body actions. To recognize human intentions, the brain–computer interface (BCI) of the steady-state visual evoked potentials (SSVEPs) is usually used. For the BCI of the SSVEPs, the visual fatigue should be alleviated, and the intention recognition accuracy should be improved. Therefor this paper proposed a coloring and timing BCI (CT-BCI) to alleviate the visual fatigue, and find the optimal Wavelet vanishing moment parameter to improve the intention recognition accuracy. In addition, the intention coding and decoding are designed and implemented. Furthermore, the wireless communications are used among the CT-BCI and the robots in the internet of things. Experiments show that the proposed CT-BCI decreases the average evocation time for each intention by 0.8 s, and prolongs the eye non-fatigue duration by 5.45 s, and improves the intention recognition accuracy by 6.7% compared with the traditional BCI.

Research on Prediction Method of Distribution Network Activity in Green Electric Power through PSO-WNN

The convergence and prediction accuracy of the artificial neural network prediction model are affected by the initial parameter settings of the model, and the wavelet neural network (WNN) modeling algorithm can effectively overcome this defect and achieve better prediction results. In this paper, the particle swarm optimization (PSO) algorithm is used to optimize the initial weights, and the optimal value of the particle swarm algorithm is assigned to the WNN to replace the initial random assignment of the WNN. The WNN is trained according to the backpropagation (BP) algorithm until convergence. The particle swarm optimization wavelet neural network (PSO-WNN) model is used to predict the cost of a single grid activity based on the cost driver parameters of the power grid. The prediction error analysis shows that the model significantly improves the accuracy of the activity cost prediction, which is beneficial to the grid enterprise to effectively manage the cost drivers and track the specific effects of the grid activity cost which produced by the driver parameters.

Automated Characterization of Cyclic Alternating Pattern Using Wavelet-Based Features and Ensemble Learning Techniques with EEG Signals.

Sleep is highly essential for maintaining metabolism of the body and mental balance for increased productivity and concentration. Often, sleep is analyzed using macrostructure sleep stages which alone cannot provide information about the functional structure and stability of sleep. The cyclic alternating pattern (CAP) is a physiological recurring electroencephalogram (EEG) activity occurring in the brain during sleep and captures microstructure of the sleep and can be used to identify sleep instability. The CAP can also be associated with various sleep-related pathologies, and can be useful in identifying various sleep disorders. Conventionally, sleep is analyzed using polysomnogram (PSG) in various sleep laboratories by trained physicians and medical practitioners. However, PSG-based manual sleep analysis by trained medical practitioners is onerous, tedious and unfavourable for patients. Hence, a computerized, simple and patient convenient system is highly desirable for monitoring and analysis of sleep. In this study, we have proposed a system for automated identification of CAP phase-A and phase-B. To accomplish the task, we have utilized the openly accessible CAP sleep database. The study is performed using two single-channel EEG modalities and their combination. The model is developed using EEG signals of healthy subjects as well as patients suffering from six different sleep disorders namely nocturnal frontal lobe epilepsy (NFLE), sleep-disordered breathing (SDB), narcolepsy, periodic leg movement disorder (PLM), insomnia and rapid eye movement behavior disorder (RBD) subjects. An optimal orthogonal wavelet filter bank is used to perform the wavelet decomposition and subsequently, entropy and Hjorth parameters are extracted from the decomposed coefficients. The extracted features have been applied to different machine learning algorithms. The best performance is obtained using ensemble of bagged tress (EBagT) classifier. The proposed method has obtained the average classification accuracy of 84%, 83%, 81%, 78%, 77%, 76% and 72% for NFLE, healthy, SDB, narcolepsy, PLM, insomnia and RBD subjects, respectively in discriminating phases A and B using a balanced database. Our developed model yielded an average accuracy of 78% when all 77 subjects including healthy and sleep disordered patients are considered. Our proposed system can assist the sleep specialists in an automated and efficient analysis of sleep using sleep microstructure.

Research on De-noising of Downhole Engineering Parameters by Wavelet based on Improved Threshold Function

The measurement of downhole engineering parameters is greatly disturbed by the working environment. Effective de-noising methods are required for processing logging-while-drilling (LWD) acquisition signals, in order to obtain downhole engineering parameters accurately and effectively. In this paper, a new de-noising method for measuring downhole engineering parameters was presented, based on a feedback method and a wavelet transform threshold function. Firstly, in view of the mutability and density of downhole engineering data, an improved wavelet threshold function was proposed to de-noise the signal, so as to overcome the shortcomings of data oscillation and deviation caused by the traditional threshold function. Secondly, due to the unknown true value, traditional single denoising effect evaluation cannot meet the requirements of quality evaluation very well. So the root mean square error (RMSE), signal-to-noise ratio (SNR), smoothness (R) and fusion indexs (F) are used as the evaluation parameters of the de-noising effect, which can determine the optimal wavelet decomposition scale and the best wavelet basis. Finally, the proposed method was verified based on the measured downhole data. The experimental results showed that the improved wavelet de-noising method could reduce all kinds of interferences in the LWD signal, providing reliable measurement for analyzing the working status of the drilling bit.

Shock Signal Trend Term Error Correction Method Based on Discrete Wavelet Transform and Low-Frequency Oscillator Combination

Shock response spectrum (SRS), calculated according to shock loading signal, is the primary metric for assessing the shock resistance ability of shipborne equipment. Nevertheless, the measured shock acceleration signal contains a trend term error that severely distorts the low frequency of the SRS. The accuracy of present correction methods cannot be assured due to a lack of reference. A discrete wavelet transform (DWT) and low-frequency oscillator combination method is proposed for correcting shock signals in this paper. The optimal wavelet parameters can be selected according to a low-frequency spectrum baseline fitted by the measured relative displacement to reject low-frequency trend term errors. Shock machine test results show that the average difference between the low-frequency spectrum baseline and uncorrected SRS is reduced from 89.8% to 3.2%, while the SRS slope rolled off to 5.8 dB/oct after imposing the proposed correction. The corrected SRS can faithfully show the actual shock loading characteristics of shipborne equipment in shock tests.

Continuous Leak Location in Gas-Filled Steel Pipe Based on Optimum Wavelet Analysis of Leak AE Signal

Abstract This study is investigates how to reconstruct the continuous leak acoustic emission (AE) signal to precisely locate the leak source on a gas-filled steel pipe based on cross-correlation location theory. Thus, in this article, the determination method for the optimum mother wavelet was proposed. The frequency distribution of the continuous leak AE event was firstly extracted through wavelet transform (WT) with optimum mother wavelet. In the considered frequency range, the WT coefficients were further used to reconstruct the raw continuous leak AE signal. The correlation-based location experiments were finally carried out to evaluate the performance of the proposed method. The results show that the location errors of the leak source were decreased by some 10 % compared with those achieved by only using the raw AE signals. Thus, improvement verifies the validity of choice of the optimum mother wavelet. Meanwhile, it is also founded that, whether the reconstructed signals or raw signals were used, the localization accuracy of the leak source using the speed of the T wave is greater than that using the speed of the L wave and theoretical acoustic speed under the same symmetry of the AE sensors with reference to the leak source. Therefore, defining the acoustic speed with the speed of the T wave was recommended to use on-site for detection of the continuous leak source on a gas-filled steel pipe.

A New Spike Sorting Algorithm Based on Continuous Wavelet Transform and Investigating Its Effect on Improving Neural Decoding Accuracy

Spike sorting is an essential step in extracting neuronal discharge patterns which help to decode different activities in the neural system. Therefore, improving the spike sorting accuracy can improve neural decoding performance subsequently. Although many methods are suggested for spike sorting, few studies have evaluated their effect on neural decoding performance. In this paper, a method of spike sorting based on an optimized selection of the parameters in the continuous wavelet transform (CWT) is proposed. The proposed algorithm was tested on a simulated dataset and two publicly available benchmark datasets to evaluate its performance in spike sorting. To evaluate the effect of utilizing different spike sorting algorithms on neural decoding performance, real data was used in which the aim was to decode the force applied by the rat's hand to a pedal continuously from the intra-cortical data of the primary motor area of the cortex. The extracted neuronal firing rates by the spike sorting algorithms were applied to a partial least squares regression to decode the force signal. In the simulation study, the proposed spike sorting algorithm based on optimized wavelet parameter selection outperformed both the WaveClus spike sorting and traditional PCA-based spike sorting algorithms. The results showed the superiority of the spike sorting algorithm based on optimal wavelet parameters compared to classical discrete wavelet transform (DWT) or PCA-based spike sorting methods in decoding real intracortical data. Overall, the results indicate that it is possible to improve neural decoding performance by improving the spike sorting accuracy.

An optimization method based on the Legendre wavelets for 3D rotating, squeezing and stretching magnetohydrodymanic flow in a channel with porous wall

In this paper, the 3D flow in a rotating channel with the lower permeable stretching wall is investigated. The unsteady squeezing flow in the presence of transverse magnetic flux is mathematically modeled by utilizing Navier-Stokes equations. A new optimal wavelet method based on coupling the Legendre wavelets and the hat functions with some auxiliary convergence-control parameters is proposed to solve the obtained fourth-order system of nonlinear differential equations. In the proposed method, the residual function and its error of norm two are employed for converting the main problem into an optimization one to optimally choose the auxiliary convergence-control parameters. The main idea behind this approach is to reduce solving such problems to those of solving optimization ones which greatly simplifies the problem and also leads to obtaining a good approximate solution for the problem under consideration.

Optimum wavelet selection for nonparametric analysis toward structural health monitoring for processing big data from sensor network: A comparative study

A critical problem encountered in structural health monitoring of civil engineering structures, and other structures such as mechanical or aircraft structures, is how to convincingly analyze the nonstationary data that is coming online, how to reduce the high-dimensional features, and how to extract informative features associated with damage to infer structural conditions. Wavelet transform among other techniques has proven to be an effective technique for processing and analyzing nonstationary data due to its unique characteristics. However, the biggest challenge frequently encountered in assuring the effectiveness of wavelet transform in analyzing massive nonstationary data from civil engineering structures, and in structural health diagnosis, is how to select the right wavelet. The question of which wavelet function is appropriate for processing and analyzing the nonstationary data in civil engineering structures has not been clearly addressed, and no clear guidelines or rules have been reported in the literature to show how the right wavelet is chosen. Therefore, this study aims to address an important question in this regard by proposing a new framework for choosing a proper wavelet that can be customized for massive nonstationary data analysis, disturbances separation, and extraction of informative features associated with damage. The proposed method takes into account data type, data and wavelet characteristics, similarity, sharing information, and data recovery accuracy. The novelty of this study lies in integrating multi-criteria which are associated directly with features that correlated well with change in structures due to damage, including common criteria such as energy, entropy, linear correlation index, and variance. Also, it introduces and considers new proposed measures, such as wavelet-based nonlinear correlation such as cosh spectral distance and mutual information, wavelet-based energy fluctuation, measures-based recovery accuracy, such as sensitive feature extraction, noise reduction, and others to evaluate various base wavelets’ function capabilities for appropriate decomposition and reconstruction of structural dynamic responses. The proposed method is verified by experimental and simulated data. The results revealed that the proposed method has a satisfactory performance for base wavelet selection and the small order of Daubechies and Symlet provide the best results, especially order 3. The idea behind our proposed framework can be applied to other structural applications.

EFFECT OF WAVELET DE-NOISING ON THE CLASSIFICATION OF PIG BEHAVIOUR

To efficiently eliminate the noise generated by the triaxial accelerometer when collecting pigs’ behavioural data, this paper adopted SNR and MSE as the indexes to evaluate the de-noising effect of pigs’ acceleration signal under various combinations of wavelet basis, decomposition layer, threshold rule and threshold function. Based on the optimal wavelet parameter combinations, the de-noised data were divided into a training dataset and test dataset to conduct a 3-fold cross validation. The results showed that Db4 wavelet can achieve a satisfactory de-noising effect when used as a wavelet basis for 8 layers wavelet decomposition based on Rigrsure threshold rules and the new improved threshold function. As a result, compared with traditional wavelet hard threshold de-noising, soft threshold de-noising and EMD de-noising method, the improved threshold function improved the stability of signal filtering, which was shown to be more practical, effective and feasible. As such, wavelet de-noising was found to significantly improve the classification accuracy of all four behaviour classes (lying, standing, walking and exploring) considered for this study, and the overall major mean accuracy was improved from 0.680 to 0.826.