Optimal Decomposition Level Research Articles

Applications of tunable-Q factor wavelet transform and AdaBoost classier for identification of high impedance faults: Towards the reliability of electrical distribution systems

This study presents a novel approach that employs a mixture of the tunable-Q wavelet transform (TQWT) and enhanced AdaBoost to address the issue of high impedance fault (HIF) recognition in power distribution networks. Traditional overcurrent protection relays frequently have lower fault current levels than normal current, making it exceedingly difficult to detect this HIF problem with the necessity to use a quick and effective approach to find HIF problems. Since the TQWT performs better with signals that exhibit oscillatory behavior, it has been utilized to extract special features for the training of the improved AdaBoost model. The procedure is accelerated by calculating the Kourtosis (K) value for each level and selecting the ideal level of decomposition to minimize computing work. Faulted zones are categorized using an enhanced AdaBoost approach. Under normal, noisy, and unbalanced conditions, the recommended approach is applied to an imbalanced 123-bus test system and an IEEE 33-bus test system. The efficiency of the recommended method is also being assessed for imbalanced distribution networks incorporating dispersed generation into real-time platforms. This procedure is quick compared to previous methods since it uses an upgraded AdaBoost classifier and optimal decomposition level.

Generalized Shannon entropy sparse wavelet packet transform for fault detection of traction motor bearings in high-speed trains

An effective structural health monitoring method of traction motor bearings is a powerful guarantee for the safety operation of high-speed trains. However, it is exceptionally difficult to detect bearing fault characteristics from the vibration signals of traction motor bearings operating at high rotational speeds. In this scenario, a generalized Shannon entropy sparse wavelet packet transform (GSWPT) for fault detection of motor bearings is proposed in this paper. Firstly, a generalized Shannon entropy sparse regularization method is proposed to obtain sparse wavelet reconstruction coefficients by extending the definition of the Shannon information entropy, and the non-convex sparse regularization function is minimized by synergistic swarm optimization algorithm. Then, the wavelet node coefficients are weighted according to the second-order cyclostationarity index of the wavelet packet node to further enhance the sparsity of the reconstructed signal. Moreover, the optimal decomposition level of GSWPT is adaptively selected by the maximum sparsity and cyclostationarity criterion. Particularly, in order to verify the bearing fault detection performance of GSWPT in practical engineering, a bearing fault dynamic model of traction motor in high-speed train was established based on Hertz contact theory and the fourth-order Runge-Kutta method to obtain simulated data under strong Gaussian white noise, and a corresponding test platform was constructed to collect experimental data under different operating conditions. Finally, the applications on the simulated and experimental signals of traction motor bearings in high-speed trains demonstrate that GSWPT significantly outperforms the conventional wavelet packet transform, dual-tree complex wavelet packet transform, blind deconvolution, modal decomposition, and Infogram methods to some extent for fault detection.

Research on Monitoring of Oil Metal Particle Pollution in Operation of Hydroelectric Generating Units Based on Internet of Things

Abstract Environmental protection has become very important in recent years. Traditional methods ignore the characteristics of metal particle pollution extraction in operating oil, which leads to low monitoring accuracy and low efficiency. Therefore, a monitoring method based on soft computing for oil pollution and metal pollution in the operation of a hydro-generator set is proposed in this article. The signal characteristics of oil and metal particles in the operation of a hydro-generator set are extracted by combining the maximum overlapping discrete wavelet transform method and the optimal decomposition level method to complete monitoring. The results show that the proposed method can accurately monitor the metal particle pollutants in the operating oil of hydroelectric generating units and has high execution efficiency. The proposed method will certainly assist in protecting the environment by monitoring carbon emissions and pollution through metal particles in the oil.

Wavelet denoising of fiber optic monitoring signals in permafrost regions.

To address the noise issue in fiber optic monitoring signals in frozen soil areas, this study employs wavelet denoising techniques to process the fiber optic signals. Since existing parameter choices for wavelets are typically based on conventional environments, selecting suitable parameters for frozen soil regions becomes crucial. In this work, an index library is constructed based on commonly used wavelet basis functions in civil engineering. An optimal wavelet basis function is objectively selected through specific criteria. Considering the characteristic of small root mean square error in fiber optic signals in frozen soil areas, a multi-index fusion approach is applied to determine the optimal decomposition level. Field observations validate that denoised signals, with parameters set appropriately, can more accurately identify locations where settlement occurs.

A Novel and Optimized Sine–Cosine Transform Wavelet Threshold Denoising Method Based on the sym4 Basis Function and Adaptive Threshold Related to Noise Intensity

In digital shearography, the speckle noise of the phase fringe pattern has a negative effect on the accuracy and reliability of the phase unwrapping procedure. A novel and optimized sine–cosine transform wavelet threshold denoising method is proposed to suppress speckle noise. Fast phase denoising can be achieved by using the proposed method while preserving the phase reversal information. The details of the selected wavelet basis function, the optimal decomposition level, the threshold function, and the denoising threshold are also provided in this manuscript. In particular, the decomposition level is analyzed and optimized through simulation analysis according to the speckle suppression index and the adaptive denoising method. The experimental results show that the proposed method has more adaptive ability in practical application than the sine–cosine transform average denoising method with the selected mask and iterative procedure, which speeds the denoising process up and takes better-unwrapped phase patterns.

Gray wolf optimization and image enhancement with NLM Algorithm for multimodal medical fusion imaging system

Multimodal Medical fusion imaging is a significant aspect of image-guided medical diagnosis. A new improved non-sub sampled shearlet transform (NSST) based Multimodal Medical Fusion imaging System based on Gray Wolf Optimization (GWO) and Image Enhancement with NLM Algorithmic computer guided medical procedures. This paper proposes an efficient medical fusion imaging system that is evolved from the concept of Non-Sub sampled Shearlet Transform and the Gray Wolf Optimization algorithm. The initial procedure in this system includes histogram matching among one image and the other to facilitate common dynamic range for both images. Decomposition of multimodal medical images is done by NSST to be fused into their coefficients. Optimum decomposition level is scaled by EGOA with optimal gain parameters. Furthermore, denoising with enhancement procedure is performed to enhance its visual quality. If the images are corrupted by noise, the these traditional fusion methods performance is greatly hampered. Therefore, this is essential to create a fusion approach that can maintain accurate information even while distorting the images.

Analysis of pipeline leakage signal based on adaptive weighted frequency band entropy optimized VMD algorithm

The influence of pressure and environment on urban polyethylene (PE) gas pipeline makes structural deterioration and leaking to the pipeline and pipeline easy. This paper proposes an analysis method for optimizing Variational Mode Decomposition (VMD) algorithm. Firstly, the optimal bandwidth is obtained by using the adaptive weighted frequency band entropy (AFBE), and the optimal quadratic penalty factor is obtained by curve fitting. Then, the AFBE is used as the fitness function, and the optimal decomposition level is obtained by the optimized beetle whisker search algorithm. Experimental results show that the signal-to-noise ratio (SNR) is improved by 12.74% on average.

Discrete Wavelet Transform-based Approach of Real-time Wave Filtering for Dynamic Positioning of Marine Vessels

The ongoing development of deep-sea resources has contributed toward the widespread use of dynamic positioning (DP) systems that can operate in arbitrary sea areas without the limitation of operating water depth compared to mooring systems. The second-order slowly varying forces can be compensated by DP feedback control. Wave filtering techniques are crucial for designing the DP controller, which can improve the positioning performance and service of multiple actuators. The objective of wave filtering is to separate the motion induced by the first-order high-frequency oscillatory waves from the motion caused by the second-order low-frequency (LF) slowly varying disturbances. This paper proposes a novel real-time wave filtering approach for DP systems on the basis of the discrete wavelet transform without relying on the previous knowledge of dynamics of the vessel. Meanwhile, to suppress the end effects of wavelet filtering and achieve real-time application, symmetric boundary extension and the sliding window method are investigated in order to capture the slow time-varying LF motion of DP vessels. The proposed real-time wavelet filtering approach can significantly improve the quality of the separated components by selecting the optimal decomposition level, wavelet function parameters, and threshold denoising method. The real-time and filtering performance of the proposed approach is verified using a scaled model of an offshore supply vessel as well as full-scale experiments on the EXPLOERE I scientific investigation vessel under the action of winds, currents, and waves. The experimental results confirm that the proposed wave filtering algorithm is efficient and that the LF component waveform can be effectively recovered after wavelet filtering.

Optimal selection of wavelet transform parameters for spatio-temporal analysis based on non-stationary NDVI MODIS time series in Mediterranean region

The multi-resolution analysis based on wavelet transform (WT) has widely proved its effectiveness for the analysis of non-stationary time series (TS) in the remote sensing field. However, there are three essential parameters affecting wavelet-aided data in vegetation dynamics detection. This study proposes a new methodology that serves for the proper selection of the most critical parameters to carry out an optimal analysis for vegetation seasonal and long-term dynamics, specifically adapted to NDVI TS. The specific objectives are: (1) to simulate a TS dataset to understand the best WT parameter performance for trend and seasonal changes detection, and (2) to assess the impact of those WT parameters using NDVI MODIS TS in the Mediterranean area along the period 2001–2019. Different types of trends and WT were considered (i.e., Discrete WT (DWT) and Maximal Overlap DWT (MODWT)) in the simulated dataset. The best WT parameters were calculated based on an iterative algorithm that computes the trend and seasonal components using the optimal level of decomposition for each TS and mother wavelet (MW). Then, the findings obtained from the simulated data were exploited using Earth observation data. In the step, the Theil–Sen’s slope (Q) derived for the best MWs was calculated to provide the trend magnitude and direction. The z-score and energy to Shannon entropy ratio (R(S)) were computed to select the most adequate MW based on pixel characterization. On one hand, the simulated results proved the Multi-resolution analysis DWT (MRA-DWT) as the most optimal wavelet type. Level 5 of decomposition was obtained in 99% and 72% of simulated TS according to the trend and seasonal analysis, respectively. Symlet family gave the optimal results in 92% (trend) and 64% (seasonal) of simulated TS. On the other hand, based on R(S), sym12 MW from Symlet family showed the most dominant wavelet for forest, savanna and mosaic land covers, followed by db14 MW from Daubechies family which was dominated in cropland. From more practical adaptation, sym12 was revealed as an effective solution for all the pixels in the Mediterranean area with a relative error lower than 15%. The vegetation change analysis in the Mediterranean area showed a relationship between QNDVI and precipitation in almost 37% of the area, being Turkey, Greece and North Africa the regions with a high correspondence with precipitation. Around 5% of the study area showed to be possibly affected by land degradation processes.

Application of Weld Scar Recognition in Small-Diameter Transportation Pipeline Positioning System

In order to improve the positioning accuracy of the pipeline inspection gauge (PIG), a pipeline positioning method, based on weld location, is proposed. The position of the welding scar is recognized by wavelet transform modulus maxima (WTMM). Equidistant welding scars provide positioning references to the strap-down inertial navigation system (SINS)/dead reckoning (DR) navigation system, which is the positioning algorithm in PIG. The following improvements have been made in relation to prior research. First, we suggest a selection strategy for the optimal mother wavelet and decomposition level; based on the strategy, WTMM can recognize the collision response between the PIG and submerged weld in the burst noise for the inertial measurement unit (IMU) output. Then, characteristic position (CP), which is the site of the weld scar, and non-holonomic constraints are utilized to decrease the position and the attitude error. By doing such, the SINS/DR/CP algorithm is proposed. The positioning error of the modified algorithm is 0.129% in the experiment, which performs better than other algorithms.

Information technology for quality assesment of the processing of metal surfaces by the method of wavelet analysis

Purpose. Analyze the effectiveness of using wavelet analysis to assess the quality of metal surfaces. Develop information technology information technology to automate the process of assessing the quality of metal surfaces by wavelet analysis.
 Methodology. The main parameters for assessing the processing of metal surfaces are considered. A multilevel decomposition of the profile using wavelets was performed.
 Findings. The developed software allows to calculate parameters of an assesment of processing of metal surfaces that will help to minimize number of routine operations and difficult mathematical calculations, and also gives illustrative graphs of waviness and roughness.
 The advantage of this software product is that it is focused and developed specifically for the analysis of signals-profilograms of metal surfaces and is free.
 In further development, this software product can be used in the mechanical engineering industry (milling) and will help reduce the cost of software.
 Originality. The method of optimal decomposition of a complex signal is considered, using the criterion of minimizing the total entropy of wavelet coefficients of both its components in determining the optimal level of decomposition, reconstruction of the signal by approximating wavelet coefficients of the optimal signal. Convenient software has been developed.
 Practical value. The developed information technology of the software product for estimating the parameters of non-stationary signals can be used in the analysis and diagnosis of objects of different nature, in the mechanical engineering (milling) industry, in particular obtaining of waviness and roughness profiles.

Optimum ECG Signal Filtering Based on Wavelet Transformation

The development of digital signal processing and microprocessor technology creates conditions for improving methods for diagnosing the functional state of organs. Wavelet analysis is a modern and promising method of information processing. In order to determine the effective optimal filtering of the electrocardiography signal based on the wavelet transform, wavelet filtering was performed using wavelets of different families, the efficiency of using different levels of decomposition, me¬thods for calculating the threshold and types of the threshold function was investigated. Aim. Determination of effective optimal filtering of electrocardiography signal based on wavelet transform. Materials and methods. Cardiograms were taken for analysis. Then they were digitized and entered into a computer for processing. A program was written in the Matlab environment that implements continuous and discrete wavelet transform. Results. As a result of the research, 56 combinations of noise reduction parameters were tested for three noise levels. It was found that the maximum degree of signal purification from noise was obtained using the Coiflets 5 wavelet using a rigid thresholding method, with a heuristic method for calculating the threshold value. Wavelet Simlet 8 has lower correlation coefficient values than Coiflets 5, at 35 dB the best result is 97%, the noise level is 40 dB the best result is 98.7%, the noise level is 45 dB the best result is 99.3%, which is generally negligible differs from the correlation coefficients of the wavelet Coiflets 5. Conclusion. As a result of the study, the first and the present work, the following conclusions were made: the optimal level of the wavelet decomposition of the ECG signal N = 2; the maximum degree of signal cleaning from noise was obtained using the Coiflets 5 wavelet using a rigid thresholding method, with a heuristic method for calculating the threshold value; Simlet 8 wavelet using a soft thresholding method with a minimax thresholding method also shows noteworthy results, slightly inferior to Coiflets 5 wavelet results.

A reliable optimization method of hybrid energy storage system based on standby storage element and secondary entropy strategy

In order to solve the problem of insufficient smoothing ability and excessive smoothing, this paper proposes a method combining exponential smoothing short-term wind power forecasting with wavelet packet decomposition. According to the optimal decomposition level, the output power in line with the grid connection standard can be obtained. To improve the service life and reliability of HESS, this paper further introduce the concept of standby storage. Then, this work propose a method combining CEEMDAN with NEE and NSE to achieve the optimal power allocation instructions of the HESS. According to the residual uniqueness and adaptive frequency division, the IMF and residual components of different orders can be achieved. Then, the cut-off point with the largest proportion of energy will be obtained by NEE and the cut-off point with the lowest self-similarity by NSE, which leads to the reasonable power allocation. In the simulation and experiment analysis, it further verifies that the introduction of standby storage element can effectively reduce the charge and discharge times of the HESS, decrease the fluctuation index of SOC, which improve the service life and identification accuracy of HESS. The result shows a certain feasibility and actual significance in the practical applications.

The Optimal Selection of Mother Wavelet Function and Decomposition Level for Denoising of DCG Signal.

The aim of this paper is to find the optimal mother wavelet function and wavelet decomposition level when denoising the Doppler cardiogram (DCG), the heart signal obtained by the Doppler radar sensor system. To select the best suited mother wavelet function and wavelet decomposition level, this paper presents the quantitative analysis results. Both the optimal mother wavelet and decomposition level are selected by evaluating signal-to-noise-ratio (SNR) efficiency of the denoised signals obtained by using the wavelet thresholding method. A total of 115 potential functions from six wavelet families were examined for the selection of the optimal mother wavelet function and 10 levels (1 to 10) were evaluated for the choice of the best decomposition level. According to the experimental results, the most efficient selections of the mother wavelet function are “db9” and “sym9” from Daubechies and Symlets families, and the most suitable decomposition level for the used signal is seven. As the evaluation criterion in this study rates the efficiency of the denoising process, it was found that a mother wavelet function longer than 22 is excessive. The experiment also revealed that the decomposition level can be predictable based on the frequency features of the DCG signal. The proposed selection of the mother wavelet function and the decomposition level could reduce noise effectively so as to improve the quality of the DCG signal in information field.

Ultra-High Frequency Partial Discharge Signal Recognition in GIS based on Fisher Linear Discriminant Theory

In this paper, dual tree complex wavelet transform (DT-CWT) is used to decompose UHF partial discharge (PD) signal in multi-scale. The optimal decomposition level of complex wavelet is solved. The wavelet energy features of real part and imaginary part of UHF-PD signal under the optimal decomposition scale are extracted. Fisher linear discriminant method is used to select the features of energy features and to identify the PD types. The results show that the optimized real part and imaginary part high frequency wavelet energy features can effectively identify four kinds of typical insulation defects, and the recognition rate can reach to 92.5%. Meanwhile, the optimal complex wavelet energy (OCWEF) feature has better sensitivity and recognition effect in PD type identification.

Complex scale feature extraction for gearbox via adaptive multi-mode manifold learning

The transient impacts with sideband modulation caused by some fault of gearbox are the technical basis for fault diagnosis, which will be inevitably interfered by heavy background noise distributed in complex modulation frequency bands. Generally, only the principle components under the selected scale is remained and analyzed as the evidence of fault diagnosis, while some crucial features spread in other scales are ignored. Specially, the selected signal still has lots of in-band noise interference. Motivated by these issues, a new adaptive multi-mode manifold learning (AM2ML) method is proposed to enhance the useful gearbox features distributed complex scales with the in-band noise suppressed. Firstly, a series of mode components are obtained by adaptive variational mode decomposition, where the optimal decomposition level is automatically achieved by the k-value. Time-frequency manifold learning is then respectively employed to mine their corresponding potential structural characteristics. And a reconstructed signal contained multi-scale features are represented via the proportion weights of the correlation coefficients. Therefore, the denoised signal of each manifold mode will be rebuilt by phase preserving and a series of inverse transform while the in-band noise is suppressed. With the weight coefficients of each mode, the final multi-scale features are synthesized. As the result shows, the sub-band energy ratio is introduced to evaluate the effectiveness of the method. The sub-band energy ratio of AM2ML method is about 3 times of VMD method, and about 2 times of fast-kurtogram method. It can be seen that the multiple modes can be adaptively decomposed with the complex scale structural characteristics enhanced by manifold learning, and the expected characteristics distributed in all scales can be well rebuilt via a dynamic weight reconstruction in a self-learning way. The effectiveness of the proposed AM2ML method is verified by the self-made gearbox.

A Study of Chosen an Optimum Type of Wavelet Filter for De-Noising an ECG signal

Among various biological signals for the diagnosing of cardiac arrhythmia, Electrocardiographic (ECG) signal is the most significant one. The interesting challenge is an accurate analysis of the noisy ECG signal. Prior to accurate analysis, these signals need for de-noising to remove these unwanted noises in the signal to get an accurate diagnosis. In order to get the best de-noising results, it should have an accurate decision about the filters that we deal with for de-noising the signals. So, in this paper we present a study for choosing the optimum wavelet filter for de-noising the electrocardiograph (ECG) signal. Signals were stored as a one-dimensional matrix and series of procedure were performed to reduce the noise. The wavelets filters were chosen that very close to the original signal after applied a random-noises to the ECG signals to get familiar with the possible noise that can the signal affected with it. Also, estimation the most standard wavelet families namely Symlets, Coiflet, and Daubechies with different methods of threshold and decomposition levels were done. The purposes of this study to conclude the convenient wavelet functions in decomposition, the de-noising and the reconstruction, the method of the threshold, and the optimal decomposition level of the wavelet.

Optimal level of wavelet decomposition for daily inflow forecasting

A methodology to select the maximum level of wavelet decomposition to forecast seven days of daily inflows by a hybrid model wavelet-based artificial neural network (WANN) is proposed. The wavelet decomposition was employed to decompose an input time series into approximation and detail components, and the approximations were used as inputs to artificial neural networks (ANN) for WANN hybrid models. In this study, it was used daily inflows from January 1931 to December 2010 to three Brazilian reservoirs with different discharge patterns, and evaluated the accuracy of the WANN models when using seven different mother-wavelets, including Haar, Daubechies, Biorthogonal, Biorthogonal Reverse, Symlet, Coiflet and Discrete Meyer. It was found that the model performance is dependent on the input sets and the selected mother-wavelets. Based on the obtained results, it was observed that the maximum level of decomposition was five, because upper than this level, independently on the inflow magnitude, there is no guarantee that the WANN hybrid models would perform better than the ANN model.

A comparative study of wavelet families for electromyography signal classification based on discrete wavelet transform

Automatic detection of neuromuscular disorders performed using electromyography (EMG) has become an interesting domain for many researchers. In this paper, we present an approach to evaluate and classify the non-stationary EMG signals based on discrete wavelet transform (DWT). Most often researches did not consider the effect of DWT factors on the performance of EMG signals classification. This problem is still an interesting unsolved challenge. However, the selection of appropriate mother wavelet and related level decomposition is an essential issue that should be addressed in DWT-based EMG signals classification. The proposed method consists of decomposing a raw EMG signal into different sub-bands. Several statistical features were extracted from each sub-band and six wavelet families were investigated. The feature vector was used as inputs to support vector machine (SVM) classifier for the diagnosis of neuromuscular disorders. The obtained results achieve satisfactory performances with optimal DWT factors using 10-fold cross-validation. From the classification performances, it was found that sym14 is the most suitable mother wavelet at the 8th optimal wavelet level of decomposition. These simulation results demonstrated that the proposed method is very reliable for reducing cost computational time of automated neuromuscular disorders system and removing the redundancy information.

Removal algorithm of horizontal noise for echoes in mine geological radar

In view of the problems of inaccurate echo signal caused by noise interference in mine geological radar echo detection, a method for eliminating horizontal noise of radar echo signal based on wavelet threshold is proposed. In this method, binomial function is selected as the Morlet wavelet basis function. According to the wavelet threshold algorithm, the optimal decomposition level is adaptively selected and the wavelet threshold is determined. The sqtwolog criterion is selected to remove the horizontal noise in the mine geological radar echo. The hard threshold method is used to detect the echo signal. Finally, the simulation experiment is carried out. The results show that the method of determining the optimal decomposition level based on wavelet decorrelation whitening test is feasible and effective. The optimal decomposition level of mine geological radar echo signal is between 4 and 5, and the effect of denoising is the best.