Optimal Wavelet Decomposition Research Articles

A Bayesian Optimized Variational Mode Decomposition-Based Denoising Method for Measurement While Drilling Signal of Down-the-Hole Drilling

Measurement while drilling (MWD) emerges as a reliable technique for assessing rock mass properties. However, the measured MWD signals are often contaminated with noise, leading to distorted signals. To address this issue, this paper proposes a denoising method that utilizes variational mode decomposition (VMD) and wavelet soft thresholding (WST). The proposed method employs Bayesian optimization to adaptively determine the optimal VMD parameters. The decomposed modes are then further denoised using WST with appropriate thresholding and optimal wavelet decomposition levels. To validate the effectiveness of the proposed method, four synthetic signals with varying input signal-to-noise ratios (SNR) and two sets of measured MWD signals were evaluated. The results demonstrate the surpassing denoising efficiency of the proposed technique in terms of higher output SNR, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and lower RMSE values. Moreover, the denoised MWD signals show promising results, with reduced amplitude and volatility while preserving the characteristics of the original signals.

A deep learning method for predicting lead content in oilseed rape leaves using fluorescence hyperspectral imaging

The purpose of this study was to develop a deep learning method involving wavelet transform (WT) and stacked denoising autoencoder (SDAE) for extracting deep features of heavy metal lead (Pb) detection of oilseed rape leaves. Firstly, the standard normalized variable (SNV) algorithm was established as the best preprocessing algorithm, and the SNV-treated fluorescence spectral data was used for further data analysis. Then, WT was used to decompose the SNV-treated fluorescence spectra of oilseed rape leaves to obtain the optimal wavelet decomposition layers using different wavelet basis functions, and SDAE was used for deep feature learning under the optimal wavelet decomposition layer. Finally, the best established support vector machine regression (SVR) model prediction set parameters Rp2, RMSEP and RPD were 0.9388, 0.0199 mg/kg and 3.275 using sym7 as the wavelet basis function. The results of this study verified that the huge potential of fluorescence hyperspectral technology combined with deep learning algorithms to detect heavy metals.

Field measurement analysis of wind parameters and nonstationary characteristics in mountainous terrain: Focusing on cooling windstorms

Cold fronts passing through the mountain areas may produce continuous windstorm and cooling processes, potentially impacting the mountain areas' infrastructure. Cooling windstorms belong to the dynamically-driven wind in the mountain wind system. To accurately estimate the wind field parameters of these storms and provide a basis for structural wind resistance design, cooling windstorms should be extracted and analyzed separately from the wind field observation data. Based on the long-term field measurement in complex mountain terrain, a framework for identifying cooling windstorms is established according to temperature and wind speed features. The mean and fluctuating wind parameters of these intense winds are then obtained. Strong nonstationary is detected for cooling windstorms. This paper focuses on the time-varying regularity of fluctuating parameters during intense wind with cooling based on the evolutionary power spectral density. From the perspective of turbulent energy, the basis for selecting the optimal wavelet decomposition levels is put forward when extracting the time-varying mean wind through discrete wavelet transform in the nonstationary wind speed model. This investigation can provide a reference for studying the nonstationary wind field.

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.

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.

Demarcation of Gear Defect from Roller Bearing Defect Based on Optimized Wavelet Decomposition Technique

Demarcation of Gear Defect from Roller Bearing Defect Based on Optimized Wavelet Decomposition Technique

Fault line selection in\xa0cooperation with multi-mode grounding control for the\xa0floating nuclear power plant grid

The Floating nuclear power plant grid is composed of power generation, in-station power supply and external power delivery. To ensure the safety of the nuclear island, the in-station system adopts a special power supply mode, while the external power supply needs to be adapted to different types of external systems. Because of frequent single phase-ground faults and various fault forms, the fault line selection protection should be accurate, sensitive and adaptive. This paper presents a fault line selection method in cooperation with multi-mode grounding control. Based on the maximum united energy entropy ratio (MUEER), the optimal wavelet basis function and decomposition scale are adaptively chosen, while the fault line is selected by wavelet transform modulus maxima (WTMM). For high-impedance faults (HIFs), to enlarge the fault feature, the system grounding mode can be switched by the multi-mode grounding control. Based on the characteristic of HIFs, the fault line can be selected by comparing phase differences of zero-sequence current mutation and fault phase voltage mutation before and after the fault. Simulation results using MATLAB/Simulink show the effectiveness of the proposed method in solving the protection problems.

Optimized Wavelet Decomposition and Gaussian interpolation based Satellite Image Enhancement

Satellite images (SI) play a vital role in various remote sensing applications like geoscience, geographical studies, observing the earth's atmosphere, monitoring natural disasters, etc. The SI are used in these applications require high-resolution. The performance of the wavelet transforms based resolution enhancement methods depends on the type of the mother wavelet used and it varies with image to image. The novel robust SI resolution enhancement technique including Optimized wavelet transform based image decomposition and Gaussian interpolation is proposed in this paper. Optimized wavelet decomposition is obtained using the Stochastic Diffusion Search algorithm and the Gaussian distribution function is used for interpolation. The proposed method is compared with the Discrete wavelet decomposition and Gaussian interpolation resolution enhancement method and proved that the proposed method gives the best results for any image.

Hyperspectral technique combined with deep learning algorithm for detection of compound heavy metals in lettuce

The aim of this research was to develop a deep learning method which involved wavelet transform (WT) and stack convolution auto encoder (SCAE) for extracting compound heavy metals detection deep features of lettuce leaves. WT was used to decompose the visible-near infrared (400.68–1001.61 nm) hyperspectral image of lettuce sample in the multi-scale transform to acquire the optimal wavelet decomposition layers of cadmium (Cd) and lead (Pb) content prediction, and then using SCAE to perform deep feature learning on spectral data under optimal wavelet decomposition layer. Support vector machine regression (SVR) models established by the deep features obtained by WT-SCAE achieved reasonable performance with coefficient of determination for prediction (Rp2) of 0.9319, root mean square error for prediction (RMSEP) of 0.04988 mg/kg and the relative percent different (RPD) of 3.187 for Cd content, and with Rp2 of 0.9418, RMSEP of 0.04123 mg/kg and RPD of 3.214 for Pb content. The results of this study confirmed the great potential for detecting compound heavy metals by the combination of hyperspectral technique and deep learning algorithm.

Satellite Image Enhancement using Optimized Wavelet Decomposition and Bicubic Interpolation

Satellite Images (SI) play a vital role in various civilian and military applications for weather forecasting, monitoring of resources of the earth, environmental studies, observing natural disasters and natural calamities, etc. When these SI are used in military applications and almost all other applications for efficient study, the big challenge is its resolution. In wavelet transforms based satellite image enhancement techniques, choosing a proper wavelet transform plays a key role and vary with the image to image. To improve the resolution, a novel robust optimized wavelet decomposition and a bicubic interpolation-based satellite image enhancement method is proposed. In this method, the Stochastic Diffusion Search (SDS) algorithm is used to get the optimized wavelet decomposition of the image into different subbands and bicubic interpolation is used to improve the resolution. Image is decomposed using the optimized wavelet filter bank based on the SDS algorithm, decomposed sub-bands are interpolated with bicubic interpolation and inverse wavelet transform is applied to compose the interpolated sub-bands into a high-resolution image. The proposed method is tested on satellite images and other images also. Compared to the proposed method with the existing methods and proved that the proposed method is superior to existing methods and applicable to any type of image.

An Adaptive Matrix Pencil Algorithm Based-Wavelet Soft-Threshold Denoising for Analysis of Low Frequency Oscillation in Power Systems

One of the main reasons that affecting the stability of power systems is low frequency oscillation (LFO). The existence of noise influences the accuracy of LFO mode identification extracted from wide-area measurement system (WAMS). The wavelet threshold de-noising is widely used in signal processing. In this paper, wavelet soft threshold is illustrated to attenuate the noise of LFO signal, the optimal wavelet basis and decomposition level for de-noising LFO signal with noise are obtained and verified by experiments. Following the signal de-noising, an improved Matrix Pencil (MP) algorithm is used for mode identification of LFO. This improvement particularly lies in the ratio of adjacent singular entropy increment difference (RASEID) designed as an adaptive order determination method in the MP algorithm proposed in the paper. RASEID not only makes the MP algorithm adaptive, but also enhances the stability of the order determination in the mode identification process. The proposed method ensures the accuracy of mode identification with lower sensitivity to noise interference. Finally, the validity of the proposed method is verified by three cases studies. The first study is on the analysis of synthetic signal typically performed in many literatures. The second study is to identify the mode of active power LFO signal which is generated by IEEE four-generator and two-area system given with disturbance on RT-LAB experimental platform. The third study is the oscillation analysis of the actual LFO data in the North American power grid. The results validate the feasibility of the proposed method for mode identification of noisy LFO.

Research on moldy tea feature classification based on WKNN algorithm and NIR hyperspectral imaging

In order to identify the moldy tea leaves in a fast and nondestructive way, a method involving wavelet coupled with k-nearest neighbor (WKNN) was proposed to select effective characteristic wavelengths in this paper. The hyperspectral imaging of 300 dried tea samples with 3 different mildew degrees (contrast check, mild moldy and severe moldy) were obtained using hyperspectral data acquisition device. Besides, food microbiological examination results showed that mold count and total numbers of colony increased with the increase of storage time, temperature and humidity. Roughness penalty smoothing (RPS) algorithm was used to preprocess the raw spectra. Afterwards, WKNN was applied to select the optimal wavelengths of spectral data by using db4, db6, sym5, sym7 as wavelet basis functions, respectively. In addition, five layers of wavelet decomposition were adopted based on different wavelet basis functions. Linear discriminant analysis (LDA) algorithm was used to build the classification models based on preprocessed spectra feature in characteristic wavelengths. The results showed that four optimal prediction models were optimal decomposition level in each wavelet basis function. In addition, the best performance model among all LDA models achieved an identification rate of 100% in the calibration set and 98.33% in the prediction set, in which db4 was used as wavelet basis function and the optimal wavelet decomposition level was 2. WKNN algorithm can effectively achieve the best wavelet decomposition layer and the best wavelengths. WKNN algorithm combined with NIR hyperspectral imaging technology can realize the effective wavelength extraction and classification of dried tea with different mildew degrees.

Identification of Alcoholism Based on Wavelet Renyi Entropy and Three‐Segment Encoded Jaya Algorithm

The alcohol use disorder (AUD) is an important brain disease, which could cause the damage and alteration of brain structure. The current diagnosis of AUD is mainly done manually by radiologists. This study proposes a novel computer‐vision‐based method for automatic detection of AUD based on wavelet Renyi entropy and three‐segment encoded Jaya algorithm from MRI scans. The wavelet Renyi entropy is proposed to provide multiresolution and multiscale analysis of features, describe the complexity of the brain structure, and extract the distinctive features. Grid search method was used to select the optimal wavelet decomposition level and Renyi order. The classifier was constructed based on feedforward neural network and a three‐segment encoded (TSE) Jaya algorithm providing parameter‐free training of the weights, biases, and number of hidden neurons. We have conducted the experimental evaluation on 235 subjects (114 are AUDs and 121 healthy). k‐fold cross validation has been used to avoid overfitting and report out‐of‐sample errors. The results showed that the proposed method outperforms four state‐of‐the‐art approaches in terms of accuracy. The proposed TSE‐Jaya provides a better performance, compared to the conventional approaches including plain Jaya, multiobjective genetic algorithm, particle swarm optimization, bee colony optimization, modified ant colony system, and real‐coded biogeography‐based optimization.

Wavelet Entropy Based Analysis and Forecasting of Crude Oil Price Dynamics

For the modeling of complex and nonlinear crude oil price dynamics and movement, wavelet analysis can decompose the time series and produce multiple economically meaningful decomposition structures based on different assumptions of wavelet families and decomposition scale. However, the determination of the optimal model specification will critically affect the forecasting accuracy. In this paper, we propose a new wavelet entropy based approach to identify the optimal model specification and construct the effective wavelet entropy based forecasting models. The wavelet entropy algorithm is introduced to determine the optimal wavelet families and decomposition scale, that will produce the improved forecasting performance. Empirical studies conducted in the crude oil markets show that the proposed algorithm outperforms the benchmark model, in terms of conventional performance evaluation criteria for the model forecasting accuracy.

Generalized optimal wavelet decomposing algorithm for big financial data

Using big financial data for the price dynamics of U.S. equities, we investigate the impact that market microstructure noise has on modeling volatility of the returns. Based on wavelet transforms (DWT and MODWT) for decomposing the systematic pattern and noise, we propose a new wavelet-based methodology (named GOWDA, i.e., the generalized optimal wavelet decomposition algorithm) that allows us to deconstruct price series into the true efficient price and microstructure noise, particularly for the noise that induces the phase transition behaviors. This approach optimally determines the wavelet function, level of decomposition, and threshold rule by using a multivariate score function that minimizes the overall approximation error in data reconstruction. The data decomposition method enables us to estimate and forecast the volatility in a more efficient way than the traditional methods proposed in the literature. Through the proposed method we illustrate our simulation and empirical results of improving the estimation and forecasting performance.

Adaptive Algorithm for Determination of Optimal Wavelet Decomposition Level Based on Jarque-Bera Test

Additive Gauss white noise is one of the most commonly observed interferences in practical engineering applications. This paper proposed an algorithm for the adaptive determination of the optimal wavelet decomposition level based on Jarque-Bera test in efforts to solve the filtering problem of additive white Gaussian noise signal. By, The optimal decomposition level of wavelet is determined by testing the white noise which was realized by calculating skewness (S) and kurtosis (K) of the parameters. With signal-to-noise ratio (SNR) as the measurement index, simulation results show that the presented algorithm have higher accuracy, and better filtering effect on low SNR signals compared with nonparametric test methods.

Seismic Data Denoising Simulation Research Based on Wavelet Transform

The wavelet packet transform is a new time-frequency analysis method, and is superior to the traditional wavelet transform and Fourier transform, which can finely do time-frequency dividion on seismic data. A series of simulation experiments on analog seismic signals wavelet packet decomposition and reconstruction at different scales were done by combining different noisy seismic signals, in order to achieve noise removal at optimal wavelet decomposition scale. Simulation results and real data experiments showed that the wavelet packet transform method can effectively remove the noise in seismic signals and retain the valid signals, wavelet packet transform denoising is very effective.

A wavelet-based baseline drift correction method for grounded electrical source airborne transient electromagnetic signals

A grounded electrical source airborne transient electromagnetic (GREATEM) system on an airship enjoys high depth of prospecting and spatial resolution, as well as outstanding detection efficiency and easy flight control. However, the movement and swing of the front-fixed receiving coil can cause severe baseline drift, leading to inferior resistivity image formation. Consequently, the reduction of baseline drift of GREATEM is of vital importance to inversion explanation. To correct the baseline drift, a traditional interpolation method estimates the baseline ‘envelope’ using the linear interpolation between the calculated start and end points of all cycles, and obtains the corrected signal by subtracting the envelope from the original signal. However, the effectiveness and efficiency of the removal is found to be low. Considering the characteristics of the baseline drift in GREATEM data, this study proposes a wavelet-based method based on multi-resolution analysis. The optimal wavelet basis and decomposition levels are determined through the iterative comparison of trial and error. This application uses the sym8 wavelet with 10 decomposition levels, and obtains the approximation at level-10 as the baseline drift, then gets the corrected signal by removing the estimated baseline drift from the original signal. To examine the performance of our proposed method, we establish a dipping sheet model and calculate the theoretical response. Through simulations, we compare the signal-to-noise ratio, signal distortion, and processing speed of the wavelet-based method and those of the interpolation method. Simulation results show that the wavelet-based method outperforms the interpolation method. We also use field data to evaluate the methods, compare the depth section images of apparent resistivity using the original signal, the interpolation-corrected signal and the wavelet-corrected signal, respectively. The results confirm that our proposed wavelet-based method is an effective, practical method to remove the baseline drift of GREATEM signals and its performance is significantly superior to the interpolation method.

An Adaptive Self-Configuration Scheme for Severity Invariant Machine Fault Diagnosis

Vibration signals, used for abnormality detection in machine health monitoring (MHM), exhibit significant variation with varying fault severity. This signal variation causes overlap among the features characterizing different types of faults, which results in severe performance degradation of the fault diagnostic model. In this paper, a wavelet based adaptive training set and feature selection (WATF) self-configuration scheme is presented, which selects the optimum wavelet decomposition level, and employs adaptive selection of the training set and features. Optimal wavelet decomposition level selection is such that the maximum fault signature-signal energy bands are achieved. The severity variant features, which could cause detrimental class overlap for MHM, are avoided using adaptive selection of the training set and features based on the location of a test data in feature space. WATF uses Support Vector Machines (SVM) to build the fault diagnostic model, and its performance and robustness has been tested with data having different severity levels. Comparative studies of WATF with eight existing fault diagnosis schemes show that, for publicly available data sets, WATF achieves higher fault detection accuracy, even when training and testing data sets belong to different severity levels.

A Selective Feature Matching Approach for Iris Recognition

Reliable automatic recognition of persons has long been an attractive goal of many researchers. Thus the recognition of an individual based on iris pattern is gaining more popularity due to the uniqueness of the pattern among the people which are highly stable starting from about one year past the date of birth, until death. The probability for the existence of two irises that are same has been theoretically estimated to be very high, i.e. one in 10 which counts for the unique characterization of the iris. Although many approaches for iris recognition have been proposed by many researchers in the last few years, in this paper a selective iris feature matching method for iris recognition based on optimized wavelet decomposition of normalized iris image has been proposed. Comparing the average normalised correlation of the wavelet coefficients of optimised level and its adjacent levels improved matching is obtained, thus performing uniqueness verification of a person. General Terms Pattern Recognition and Analysis, Security, Proposed Matching Algorithm, Reliable Person Authentication