Wavelet Threshold De-noising Method Research Articles

Traffic Flow Prediction by an Ensemble Framework with Data Denoising and Functional Principal Components Analysis

Accurate traffic flow data are important for congestion identification and real-time traffic control. Raw traffic flow data may be disturbed by different noises during the acquisition process, which leads to the degradation of model prediction performance. To address this problems, this paper proposes a data denoising method based on the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) combined with wavelet threshold denoising (WTD) to suppress potential outliers in the data, and then introduces functional principal component analysis to accomplish the traffic forecasting task. We use the proposed framework for real traffic flow prediction and validate the prediction performance of the proposed framework using root mean square error and mean absolute error. In the prediction performance comparison, five denoising methods are considered: empirical mode decomposition (EMD), ensemble empirical mode decomposition, complete ensemble empirical mode decomposition with adaptive noise, ICEEMDAN, and WTD. The prediction results show that the model combined with the denoising method outperforms the model without the denoising method. ICEEMDAN combined with WTD’s denoising method improves prediction performance more than other methods. Furthermore, the WTD method with dmey type achieves higher accuracy than other types.

EMD-based noise reduction study of steel cored conveyor belt containing slag signal

This paper proposes a noise reduction technique that combines empirical mode decomposition (EMD) and wavelet thresholding to eliminate the noise interference caused by metal slag in the steel cord conveyor belt damage signal. Initially, the original signal undergoes decomposition by EMD into high- and low-frequency intrinsic mode function (IMF) components based on metal slag signal feature analysis. The wavelet threshold de-noising method is then applied to filter out the high-frequency noise while preserving the low-frequency IMF components. The IMF components containing slag noise are discarded, and the filtered signal and the low-frequency IMF components are used for signal reconstruction to obtain an optimal noise reduction effect. The study demonstrates that this method is more effective in suppressing metal slag noise, environmental noise, and other noise interferences than traditional EMD decomposition noise reduction and wavelet threshold noise reduction methods. This research provides a valuable reference for noise reduction in steel cord conveyor belt detection data.

A new underwater acoustic signal denoising method based on modified uniform phase empirical mode decomposition, hierarchical amplitude-aware permutation entropy, and optimized improved wavelet threshold denoising

Underwater acoustic signal (UAS) denoising is base and prerequisite for UAS detection, recognition and classification. In order to perform UAS denoising effectively, a new UAS denoising method based on modified uniform phase empirical mode decomposition (MUPEMD), hierarchical amplitude-aware permutation entropy (HAAPE), and improved wavelet threshold denoising (IWTD) method optimized by sand cat swarm optimization (SCSO) (SIWTD), named MUPEMD-HAAPE-SIWTD, is proposed. Firstly, decompose original signal into a battery of intrinsic mode functions (IMFs) by MUPEMD. Secondly, determine the double threshold by HAAPE to classify signal into pure signal, mixed signal and noisy signal. Then, optimize IWTD by SCSO, so that it can adaptively select the optimal wavelet basis function to achieve the denoising of mixed signal. Finally, the denoised mixed signal is reconstructed with pure signal to obtain ultima denoised signal. The denoising experiments on Lorenz signal and Duffing signal demonstrate that signal-to-noise ratio can be improved by 9 dB–13 dB by the proposed method. The denoising experiments on simulating ship radiated noise signals and four kinds of actual ship radiated noise signals (https://www.aigei.com/, accessed on June 1, 2023) demonstrate that the proposed method makes phase diagram smoother and clearer, and makes the ability of suppressing noise higher.

State of charge estimation of lithium-ion battery based on improved adaptive boosting algorithm

State of charge (SOC) is a crucial battery state to calibrate the remaining charge of lithium-ion batteries in electric vehicles. Accurate battery SOC estimation is one of the keys and difficult issues for lithium-ion batteries. To achieve SOC estimation accurately, an improved adaptive boosting algorithm called AdaBoost.RT algorithm, which is a regression ensemble algorithm and uses the extreme learning machine (ELM) as weak learners, is applied to estimate the SOC of lithium-ion batteries in this paper. And a two-step method is also proposed to denoise experimental data, which are used as the input data of the proposed SOC estimation method, to further enhance the accuracy of SOC estimation. Firstly, a complementary ensemble empirical mode decomposition with adaptive noise method (CEEMDAN) is utilized to decompose the experimental data including battery voltage and current according to the frequency of the signals to form different frequency components. Secondly, a wavelet threshold denoising method (WTD) is combined to denoise these components. The denoised components trend to form a new battery signal by the linear superposition principle and input into the proposed SOC method in this paper. The combined SOC estimation method can be called CEEMDAN-WTD-AdaBoost-ELM (CWAELM) method. To verify the proposed method, experiments are conducted under Beijing dynamic stress test (BJDST), dynamic stress test (DST), federal urban driving schedule (FUDS), and highway driving schedule (US06) conditions at 0 °C, 25 °C and 45 °C temperatures, respectively. The results show that the proposed model has good robustness and accuracy in the SOC estimation of lithium-ion batteries under various working conditions at different temperatures.

Research on Improved Wavelet Threshold Denoising Method for Non-Contact Force and Magnetic Signals

In order to solve the problem of noise interference in the collected magneto mechanical signals, a new wavelet shrinkage threshold based on adaptive estimation is proposed. Based on the shortcomings of the traditional threshold function, an improved threshold function is proposed, and the parameters of the threshold function are solved by the improved genetic algorithm, and the optimal denoising effect is finally obtained. The new threshold function can not only make up the defects of each threshold function, ensure the continuity of threshold function, but also flexibly adjust the threshold to adapt to different noise conditions, and solve the deviation caused by inherent threshold function, and protect the useful information with noise signals.

Fast Sleep Stage Classification Using Cascaded Support Vector Machines with Single-Channel EEG Signals.

Long-term sleep stage monitoring is very important for the diagnosis and treatment of insomnia. With the development of wearable electroencephalogram (EEG) devices, we developed a fast and accurate sleep stage classification method in this study with single-channel EEG signals for practical applications. The original sleep recordings were collected from the Sleep-EDF database. The wavelet threshold denoising (WTD) method and wavelet packet transformation (WPT) method were applied as signal preprocessing to extract six kinds of characteristic waves. With a comprehensive feature system including time, frequency, and nonlinear dynamics, we obtained the sleep stage classification results with different Support Vector Machine (SVM) models. We proposed a novel classification method based on cascaded SVM models with various features extracted from denoised EEG signals. To enhance the accuracy and generalization performance of this method, nonlinear dynamics features were taken into consideration. With nonlinear dynamics features included, the average classification accuracy was up to 88.11% using this method. In addition, with cascaded SVM models, the classification accuracy of the non-rapid eye movement sleep stage 1 (N1) was enhanced from 41.5% to 55.65% compared with the single SVM model, and the overall classification time for each epoch was less than 1.7 s. Moreover, we demonstrated that it was possible to apply this method for long-term sleep stage monitor applications.

An Improved Wavelet Threshold Denoising Method for Health Monitoring Data: A Case Study of the Hong Kong-Zhuhai-Macao Bridge Immersed Tunnel

Tunnels generally operate underground or underwater in a complex environment. As a result, the health monitoring system is inevitably affected by various environmental factors, which introduces noise to the system. However, the noise contained in the monitoring sequence may disrupt structural damage identification and health state assessment as the real structural response may be overwhelmed by the noise. To properly eliminate the noise in an objective way, this study proposed an improved wavelet threshold denoising method. Firstly, it adopts a quantitative factor, namely the Sparse Index, to assist the selection of the best wavelet basis in numerous wavelet packages. Then, the decomposition layer and threshold are optimized by a comprehensive evaluation based on a variation coefficient method. At last, the application of the concrete strain health monitoring data of the Hong Kong-Zhuhai-Macao Bridge immersed tunnel verified the effectiveness of the proposed method. It is found that the combination of sym12 and five decomposition layers can obtain the best denoising results within the selected wavelet families and decomposition levels. Moreover, the proposed method achieves good denoising results under different fluctuation levels. Thus, the proposed method is reliable, can solve the problem of optimal parameter selection such as decomposition level and wavelet basis in wavelet denoising, and can be applied in the structural health monitoring of critical infrastructures.

Stock Closing Price Interval Prediction Based on CEEMDAN-WTD-Bilstm-Transformer Model

Stock price indices usually contain much noise and exhibit significant non-linearity, non-smoothness, and other complex characteristics. To address the complexity and long-term dependence of financial time series forecasting, a novel stock interval forecasting model based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Analysis (CEEMDAN)-wavelet threshold de-noising (WTD) joint de-noising method and Transformer model improved by a Bi-directional Long Short-Term Memory model (BiLSTM) is proposed in this paper. First, based on CEEMDAN, the WTD method is incorporated to extract features from the basic ticker data of financial time series and use them as the input of the Transformer model. Meanwhile, the BiLSTM provides the time-series relationship among the input stock data for the Transformer to forecast the financial time series. Moreover, a hybrid sliding Kernel Density Interval Estimation (KDE) method to demonstrate the forecasting accuracy of financial time series. Using stock price index data, the prediction results are compared with those of traditional neural networks, and the results show that the stock interval prediction of the CEEMDAN-WTD-BiLSTM-Transformer model has a relatively high prediction accuracy, which achieves an improvement of 0.88%~3.62%.

A method for reducing transient electromagnetic Noise: Combination of variational mode decomposition and wavelet denoising algorithm

The transient electromagnetic method (TEM) is used to detect mineral resources and mined-out areas, to eliminate the secondary field signal noise interference, this paper proposes an algorithm for denoising the TEM signal based on Variational Mode Decomposition (VMD) and Wavelet Threshold Denoising (WTD) methods. The Grey Wolf Optimization (GWO) algorithm solves the parameter combination (K, α) in the VMD, and the K intrinsic mode functions (IMFs) are then obtained using the decomposed TEM signal. Subsequently, all IMFs are analyzed according to the correlation coefficient and divided into signal modes, mixed modes, and invalid modes. Finally, the mixed modes are denoised by WTD, the signal and denoised modes are combined. To validate the effectiveness of the VMD-WTD algorithm, the method was compared in simulations with the Ensemble Empirical Mode Decomposition (EEMD) algorithm and various other methods previously developed to improve the TEM, its performance in a field experiment was also confirmed.

Weak Signal Detection Based on Lifting Wavelet Threshold Denoising and Multi-Layer Autocorrelation Method

To solve the problem that the weak signal is difficult to detect under a strong background noise, a detection method based on lifting wavelet threshold denoising and multi-layer autocorrelation method is proposed. Firstly, the original signal is denoised by lifting wavelet threshold to improve the signal-to-noise ratio. Secondly, the multi-layer autocorrelation function of the noise-reconstructed signal is calculated, and its time-frequency signature are analyzed. Finally, the combined algorithm is used on weak signals with low signal-to-noise ratio to extract weak signal features. Simulation and experimental results demonstrate that the proposed method can detect weak signal features buried in the heavy noise effectively. The proposed method is compared with the traditional noise reduction method, which reflects its effectiveness and superiority.

A multi-layer extreme learning machine refined by sparrow search algorithm and weighted mean filter for short-term multi-step wind speed forecasting

With a rapidly growing wind power capacity, wind speed forecasting is of great importance for secure and economical operation of power systems. Nonetheless, due to the volatility of wind speed, its prediction has always been a challenging task. Although utilization of promising noise reduction techniques can mitigate this problem to some extent, wavelet threshold denoising methods (WTDs) suffer from their boundary effects in practice. To address this issue, weighted mean filtering (WMF) is adopted as an alternative of WTDs to reduce the information redundancy of wind speed time series. Furthermore, multi-layer extreme learning machine (MLELM) is combined with WMF to form an ensemble model for one-step and multi-step wind speed forecasting. Besides, as a novel swarm algorithm, the sparrow search algorithm (SSA), is utilized to improve the performance of MLELM. Finally, a data-driven ensemble model WMF-SSA-MLELM is proposed herein, which can be divided into three blocks, data preprocessing, optimization, and prediction. In the first block, WMF suppresses redundant noise in wind speed time series and makes it easier to extract essential features of wind speed. In the second block, SSA optimizes input weights and biases of hidden layers in the optimization stage. In the prediction block, MLELM with two hidden layers optimized by SSA provides the prediction of future wind speed by using denoised wind speed series obtained in the first two steps. The test results on four datasets demonstrate superior accuracy and efficiency of the proposed model WMF-SSA-MLELM, via comparison with all candidate models in both one-step and multi-step wind speed forecasting.

Data-driven early fault diagnostic methodology of permanent magnet synchronous motor

Permanent magnet synchronous motor (PMSM) is one of the common core power components in modern industrial systems. Early fault diagnosis can avoid major accidents and plan maintenance in advance. However, the features of early faults are weak, and the symptoms are not obvious. Meanwhile, the fault signal is often overwhelmed by noise. Accordingly, fault diagnosis for early faults is difficult, and the diagnostic accuracy is generally low. A Bayesian-network-based data-driven early fault diagnostic methodology of PMSM is proposed with vibration and acoustic emission data. The wavelet threshold denoising and minimum entropy deconvolution methods are used to improve the signal-to-noise ratio. The complementary ensemble empirical mode decomposition method is used to extract signal eigenvalues, and Bayesian networks are applied to identify the early, middle, and permanent faults. Experimental data carried out with Tyco ST8N80P100V22E medium PMSM are used to train the fault diagnostic model and validate the proposed fault diagnostic methodology. Result shows that the accuracy for early faults is more than 90% when acoustic emission signal is used, and it is higher than the accuracy with vibration signal. The influence of load on diagnostic accuracy is also investigated, and it indicates that the accuracy with acoustic emission signal is higher than that with vibration signal under different loads.

Accuracy improvement of quantitative LIBS analysis of coal properties using a hybrid model based on a wavelet threshold de-noising and feature selection method.

A hybrid model based on a wavelet threshold de-noising (WTD) and recursive feature elimination with cross-validation (RFECV) method was proposed to improve the measurements in quantitative analysis of coal properties using laser-induced breakdown spectroscopy (LIBS). First, a modified threshold of WTD was proposed based on wavelet coefficient theory. Interference of noise in the LIBS spectrum was reduced by using this modified method. Then, the RFECV method was applied to extract effective features from the de-noised LIBS spectrum. Finally, support vector regression (SVR) models of coal properties were established by the selected features. A validation set was used to verify the effectiveness and robustness of the hybrid model. The improvement of the hybrid model on the quantitative analysis of each index of coal properties (heat value, ash, volatile content) was studied and discussed. By using the proposed model, the determination coefficient (R2), root mean square error of prediction, average relative error, and relative standard deviation were all significantly improved over the original spectra model. The results demonstrated that the proposed model could effectively improve the accuracy and precision of LIBS quantitative analysis for coal properties.

A novel bat algorithm with double mutation operators and its application to low-velocity impact localization problem

The low-velocity impact localization in the plate structure of the ship is a critical problem which can be considered as a nonlinear optimization problem. The bat algorithm (BA) has been widely used to solve nonlinear optimization problems. However, the standard BA exhibits poor performance on complex problems because of its premature convergence. In this study, a novel bat algorithm with double mutation operators (TMBA), in which a modified time factor and two mutation operators are integrated, is proposed to enhance BA’s performance on nonlinear optimization problems. Classical benchmark functions are employed to analyze the contributions of the three modifications and demonstrate the significant improvement of TMBA. For the low-velocity impact localization problem, the low-velocity impact localization system based on fiber Bragg grating (FBG) sensors is utilized to receive the impact signals. The wavelet threshold de-noising method and the generalized cross-correlation method are both applied to the extraction of time differences between the impact signals. Then, the proposed algorithm and several well-known optimization algorithms are adopted to solve the minimization fitness function which is established using the triangulation method. The statistical results indicate that TMBA is more feasible and effective for solving the low-velocity impact localization problem.

An ECG Signal De-Noising Approach Based on Wavelet Energy and Sub-Band Smoothing Filter

Electrocardiographic (ECG) signal is essential to diagnose and analyse cardiac disease. However, ECG signals are susceptible to be contaminated with various noises, which affect the application value of ECG signals. In this paper, we propose an ECG signal de-noising method using wavelet energy and a sub-band smoothing filter. Unlike the traditional wavelet threshold de-noising method, which carries out threshold processing for all wavelet coefficients, the wavelet coefficients that require threshold de-noising are selected according to the wavelet energy and other wavelet coefficients remain unchanged in the proposed method. Moreover, The sub-band smoothing filter is adopted to further de-noise the ECG signal and improve the ECG signal quality. The ECG signals of the standard MIT-BIH database are adopted to verify the proposed method using MATLAB software. The performance of the proposed approach is assessed using Signal-To-Noise ratio (SNR), Mean Square Error (MSE) and percent root mean square difference (PRD). The experimental results illustrate that the proposed method can effectively remove noise from the noisy ECG signals in comparison to the existing methods.

Application of Improved Wavelet Thresholding Method and an RBF Network in the Error Compensating of an MEMS Gyroscope

The large random errors in Micro-Electro-Mechanical System (MEMS) gyros are one of the major factors that affect the precision of inertial navigation systems. Based on the indoor inertial navigation system, an improved wavelet threshold de-noising method was proposed and combined with a gradient radial basis function (RBF) neural network to better compensate errors. We analyzed the random errors in an MEMS gyroscope by using Allan variance, and introduced the traditional wavelet threshold methods. Then, we improved the methods and proposed a new threshold function. The new method can be used more effectively to detach white noise and drift error in the error model. Finally, the drift data was modeled and analyzed in combination with the RBF neural network. Experimental results indicate that the method is effective, and this is of great significance for improving the accuracy of indoor inertial navigation based on MEMS gyroscopes.

Vessel Trajectory Prediction Model Based on AIS Sensor Data and Adaptive Chaos Differential Evolution Support Vector Regression (ACDE-SVR)

There are difficulties in obtaining accurate modeling of ship trajectories with traditional prediction methods. For example, neural networks are prone to falling into local optima and there are a small number of Automatic Identification System (AIS) information samples regarding target ships acquired in real time at sea. In order to improve the accuracy of ship trajectory predictions and solve these problems, a trajectory prediction model based on support vector regression (SVR) is proposed. Ship speed, course, time stamp, longitude and latitude from AIS data were selected as sample features and the wavelet threshold de-noising method was used to process the ship position data. The adaptive chaos differential evolution (ACDE) algorithm was used to optimize the internal model parameters to improve convergence speed and prediction accuracy. AIS sensor data corresponding to a certain section of the Tianjin Port ships were selected, on which SVR, Recurrent Neural Network (RNN) and Back Propagation (BP) neural network model trajectory prediction simulations were carried out. A comparison of the results shows that the trajectory prediction model based on ACDE-SVR has higher and more stable prediction accuracy, requires less time and is simple, feasible and efficient.

LSTM with Wavelet Transform Based Data Preprocessing for Stock Price Prediction

For profit maximization, the model-based stock price prediction can give valuable guidance to the investors. However, due to the existence of the high noise in financial data, it is inevitable that the deep neural networks trained by the original data fail to accurately predict the stock price. To address the problem, the wavelet threshold-denoising method, which has been widely applied in signal denoising, is adopted to preprocess the training data. The data preprocessing with the soft/hard threshold method can obviously restrain noise, and a new multioptimal combination wavelet transform (MOCWT) method is proposed. In this method, a novel threshold-denoising function is presented to reduce the degree of distortion in signal reconstruction. The experimental results clearly showed that the proposed MOCWT outperforms the traditional methods in the term of prediction accuracy.

Terahertz Multivariate Spectral Analysis and Molecular Dynamics Simulations of Three Pyrethroid Pesticides

The terahertz (THz) multivariate spectral characteristics and the molecular dynamics of three pyrethroid pesticides, including deltamethrin, fenvalerate, and beta-cypermethrin, were studied in this paper. THz spectra of the pesticides were measured in frequency range of 0.06–3.5 THz by using THz time-domain spectroscopy (THz-TDS). To improve the THz spectral quality, the wavelet threshold de-noising (WTD) method was used to remove spectral noise and the spectral baseline correction (SBC) method was used to remove baseline drift. Specific absorption peaks were observed in the processed THz spectra of the three pesticides. Deltamethrin showed three peaks at 0.90, 1.49, and 2.32 THz. Fenvalerate had five peaks at 1.13, 1.43, 1.61, 1.98, and 2.58 THz. Beta cypermethrin had four peaks at 1.27, 1.84, 2.12, and 2.92 THz. The density functional theory (DFT) was used to characterize the molecular dynamics and formation mechanism of the absorption peaks. Results showed that there was a good matching effect between the THz experimental spectra and the DFT quantum calculation spectra. Based on the characterized fingerprint absorption peaks, the linear addition model was used to simulate the THz spectra of mixed pesticides. The simulated spectra of multicomponent pesticides were demonstrated to be in good agreement with those obtained by THz-TDS. By analyzing the absorption peaks of THz spectra, the composition and concentration of multicomponent pesticides could be determined. The proposed strategy presented an analytical methodology for studying the THz spectral characteristics of pesticides. In addition, this work provided experimental and theoretical basis for the detection potential of pesticides in agricultural products based on THz technology.

Spectral Characterization and Molecular Dynamics Simulation of Pesticides Based on Terahertz Time-Domain Spectra Analyses and Density Functional Theory (DFT) Calculations.

This work provides the experimental and theoretical fundamentals for detecting the molecular fingerprints of six kinds of pesticides by using terahertz (THz) time-domain spectroscopy (THz-TDS). The spectra of absorption coefficient and refractive index of the pesticides, chlorpyrifos, fipronil, carbofuran, dimethoate, methomyl, and thidiazuron are obtained in frequencies of 0.1–3.5 THz. To accurately describe the THz spectral characteristics of pesticides, the wavelet threshold de-noising (WTD) method with db 5 wavelet fucntion, 5-layer decomposition, and soft-threshold de-noising was used to eliminate the spectral noise. The spectral baseline correction (SBC) method based on asymmetric least squares smoothing was used to remove the baseline drift. Spectral results show that chlorpyrifo had three characteristic absorption peaks at 1.47, 1.93, and 2.73 THz. Fipronil showed three peaks at 0.76, 1.23, and 2.31 THz. Carbofuran showed two peaks at 2.72 and 3.06 THz. Dimethoate showed three peaks at 1.05, 1.89, and 2.92 THz. Methomyl showed five peaks at 1.01, 1.65, 1.91, 2.72, and 3.20 THz. Thidiazuron showed four peaks at 0.99, 1.57, 2.17, and 2.66 THz. The density functional theory (DFT) of B3LYP/6-31G+(d,p) was applied to simulate the molecular dynamics for peak analyzing of the pesticides based on isolated molecules. The theoretical spectra are in good agreement with the experimental spectra processed by WTD + SBC, which implies the validity of WTD + SBC spectral processing methods and the accuracy of DFT spectral peak analysis. These results support that the combination of THz-TDS and DFT is an effective tool for pesticide fingerprint analysis and the molecular dynamics simulations.