Wavelet Packet Coefficients Research Articles

A note on wavelet packet summation methods

The wavelet summation method is a method to obtain a non-linear approximation with ‘nice properties’ for a given signal. This technique has been shown to be effective in non-parametric regression and other fields, including signal denoising. By utilizing a shrinkage rule on the empirical wavelet packet coefficients, wavelet packet summation methods can be obtained. In this paper, we show that the wavelet packet expansion of any finite energy function converges pointwise almost everywhere under the wavelet packet projection, hard sampling, and soft sampling methods.

Rolling element bearing fault diagnosis under time-varying speed conditions based on improved wavelet packet transform and envelope order tracking

Abstract Rolling element bearings (REBs) are crucial components of rotating machinery and play an important role in industrial production. Failure of REBs can lead to significant economic losses and catastrophic accidents. In order to ensure their safe and stable operation, we propose a novel approach called EOT-IWPT which combines the envelope order tracking (EOT) with an improved wavelet packet transform algorithm (IWPT) for diagnosing failures in REBs under time-varying speed conditions. First, the time- domain vibration signal is resampled at constant angle intervels according to the phase of the rotating shaft to obtain the angle-domian signal. Next, the resampled signal is decomposed to sub-band signals using IWPT. Third, the squared envelope spectra (also called envelope order spectra) of the last layer wavelet packet coefficients are obtained by the Hilbert transform and the Fourier transform. Finally, the diagnostic results can be easily determined based on the squared envelope spectra. The procedure and performance of the proposed approach are illustrated and evaluated through simulation analysis, proving that the proposed method can effectively extract the fault features. Furthermore, experimental analysis results indicate that the proposed method outperforms both EOT-WPT and SK-EOT-BPF.

Image Enhancement Using Bidimensional Empirical Mode Decomposition and Morphological Operations for Brain Tumor Detection and Classification.

The three steps of brain image processing – preprocessing, segmentation, and classification are becoming increasingly important in patient care. The aim of this article is to present a proposed method in the mentioned three-steps, with emphasis on the preprocessing step, which includes noise removal and contrast enhancement. The fast and adaptive bidimensional empirical mode decomposition and the anisotropic diffusion equation as well as the modified combination of top-hat and bottom-hat transforms are used for noise reduction and contrast enhancement. Fast C-means clustering with enhanced image is used to detect tumors and the tumor cluster corresponds to the maximum centroid. Finally, Ensemble learning is used for classification. The Figshare brain tumor dataset contains magnetic resonance images used for data selection. The optimal parameters for both noise reduction and contrast enhancement are investigated using a tumor contaminated with Gaussian noise. The results are evaluated against state-of-the-art results and qualitative performance metrics to demonstrate the dominance of the proposed approach. The fast C-means algorithm is applied to detect tumors using twelve enhanced images. The detected tumors were compared to the ground truth and showed an accuracy and specificity of 99% each, and a sensitivity and precision of 90% each. Six statistical features are retrieved from 150 enhanced images using wavelet packet coefficients at level 4 of the Daubechies 4 wavelet function. These features are used to develop the classifier model using ensemble learning to create a model with training and testing accuracy of 96.7% and 76.7%, respectively. When this model is applied to classify twelve detected tumor images, the accuracy is 75%; there are three misclassified images, all of which belong to the pituitary disease group. Based on the research, it appears that the proposed approach could lead to the development of computer-aided diagnosis (CADx) software that physicians can use as a reference for the treatment of rain tumor.

Adaptive spectrum amplitude modulation method for rolling bearing fault frequency determination

Abstract Signal preprocessing and feature extraction are decisive factors in determining the frequency of bearing faults. The presence of noise interference in the status signal of rolling bearings often hampers accurate fault detection. Although there are various methods for preprocessing vibration signals in rolling bearings, they need further improvement in terms of enhancing fault feature expression and localizing fault frequency bands. This limitation significantly hinders the accuracy of fault frequency determination. In order to enhance the representation of fault information on the frequency spectrum, this study proposes a combined approach that incorporates sparse stacked autoencoder (SSAE), wavelet packet decomposition (WPD), and adaptive spectrum amplitude modulation (ASAM). The resulting method is referred to as SSAE-WPD-ASAM. Firstly, the bearing vibration signal is decomposed by wavelet packet according to the scale and frequency band of the signal. On this basis, the signal reconstruction is realized based on the wavelet packet coefficient and energy distribution in different frequency bands. Secondly, for the whole life cycle signal, the reconstructed signal is self-encoded by sparse stacked autoencoder to achieve dimensionality reduction of the reconstructed signal. Then, the spare reconstructed signal is subjected to ASAM. Finally, through envelope demodulation, peak detection of fault frequency and empirical fault frequency comparison, the specific fault types of rolling bearings are determined. The proposed method is verified by theoretical simulation and three groups of practical experiments. The results show that the proposed method has a significant improvement in diagnostic efficiency and accuracy compared with traditional diagnostic methods.

Cutting state recognition of spiral bevel gear face hobbing

Abstract To investigate the issue of chatter vibration during the face hobbing process of spiral bevel gears, this study conducted experiments on the YKA2260 gear hobbing machine, collecting 142 sets of vibration acceleration signals. The optimal combination for wavelet threshold denoising was determined based on the signal-to-noise ratio (SNR), and preprocessing of the raw signals was performed. Utilizing wavelet packet decomposition, the energy entropy of wavelet packet coefficients was extracted as feature values. A recognition model for the cutting state during the face hobbing process of spiral bevel gears was established using a Support Vector Machine, achieving a recognition accuracy of up to 98.0769%. Furthermore, the model’s high recognition accuracy for small training samples in engineering applications was validated.

Accurate gain method for ground-penetrating radar signals based on stationary wavelet packet transform

In this study, we propose an accurate gain method for ground-penetrating radar (GPR) signals based on the characteristics of refined time-frequency analysis and translation invariance offered by the Stationary Wavelet Packet Transform (SWPT), combined with the conventional signal gain approach. This method aims to address the issue of low signal resolution resulting from the direct gain processing of GPR signals with a low signal-to-noise ratio (SNR). Specifically, the GPR signals are initially decomposed into appropriate wavelet packet coefficients using SWPT, wherein only those coefficients with high SNR undergo gain processing, followed by reconstruction of the signals through SWPT. By employing accurate gain processing on low SNR GPR signals acquired during concrete crack detection tests, we have confirmed that the proposed method effectively distinguishes the target reflected signals from most noise, thereby achieving accurate amplification of the desired reflected signals and significantly enhancing the GPR signals resolution under low SNR conditions.

Application of emotion recognition technology in psychological counseling for college students

Abstract In traditional psychological counseling, limitations of patients’ subjective feelings and expressive abilities, as well as the varying levels of professional skills and conversation skills of counselors, make it difficult to properly solve psychological problems. Emotional recognition technology can help psychological counselors better understand the inner world of patients, thereby providing more targeted psychological counseling services for college students. 2D convolutional neural network-long short-term memory (2DCNN-LSTM) and 1D convolutional neural network-long short-term memory network (1DCNN-LSTM) were used for emotion recognition. Wavelet packet coefficient sequences were utilized to analyze multimodal data; multi-core convolutional neural network models were applied for multimodal feature layer fusion, and LSTM recurrent neural networks were used to effectively identify valence and college student emotions. The experimental results showed that under multimodal recognition, the average recognition accuracy of 2DCNN-LSTM for fourth-year university students was 18.7% higher than that of 1DCNN-LSTM for fourth-year university students. Compared with 1DCNN-LSTM, 2DCNN-LSTM can achieve better recognition accuracy. The research results can help psychological counselors better understand the emotional state and needs of students and provide more personalized and targeted counseling services.

Method of feature extraction of abnormal communication signal in network based on nonlinear technology

Abstract Accurate extraction of abnormal communication signal features in the network is the basis to ensure the completion of network communication. Therefore, a method of feature extraction of abnormal communication signal in network based on nonlinear technology is proposed. In this method, wavelet transform is adopted to decompose the abnormal network communication signals in the high- and low-frequency bands. According to the distribution characteristics of noise and signal in the frequency band, the corresponding parameters are selected for phase space reconstruction and nonlinear dimension reduction of local tangent space mainstream shape recognition algorithm, and the decomposition coefficients of wavelet packet after noise reduction are reconstructed to realize the nonlinear noise reduction of abnormal signal; the denoised abnormal communication signal in network is mapped to the high-dimensional feature space. The principal component is analyzed in accordance with the nonlinear function in the mapped feature space, and the nonlinear function is solved by self-organizing neural network to output the principal component extraction result. According to test results, this method has a significant signal noise reduction effect, results are more than 92% for different abnormal communication signals, and the features of abnormal signals are accurately extracted.

High imbalance fault diagnosis of aviation hydraulic pump based on data augmentation via local wavelet similarity fusion

Data augmentation methods, such as SMOTE and deep generative networks, have the potential to solve class-imbalance issue in aviation hydraulic pump fault diagnosis. Nevertheless, the scarcity of faulty samples often leads augmented samples generated using such methods suffer from blurred category boundaries, limited diversity, and mode collapse. To avoid these issues, a new data augmentation method namely Local Wavelet Similarity Fusion (LWSF) is proposed, which augments faulty samples by preserving and distorting the wavelet packet coefficients (WPCs) of the original faulty samples. An important property is that LWSF can generate high-quality synthesis samples without complex model training. First, faulty samples are decomposed into a series of frequency bands using wavelet packet decomposition. Second, the amplitudes of WPCs at a few randomly selected frequency bands are distorted, which is accomplished through a similarity-weighted fusion of the target WPCs with the closest related WPCs matched from reference samples, with the goal of keeping distortion within an appropriate range. Third, these WPCs are used to reconstruct the samples, which serve as the augmented samples. Besides, to enhance diversity, normal samples are also employed to assist in the distortion. Finally, the effectiveness of LWSF is validated by a series of experimental comparisons. In an imbalanced fault diagnosis task, the accuracy and F1-score obtained by LWSF are 97.16 % and 97.35 %, respectively, which are 3.59 % and 7.30 % higher than the best one among the five compared methods.

Research on Vertical SEC Centrifugal Pump Multi-Fault Diagnosis Based on WPT–SVM

To diagnose common failures in vertical Essential Service Water Pumps (SEC), a method combining the wavelet packet transform (WPT) and the support vector machine (SVM) was adopted. This allowed us to construct a diagnostic model capable of classifying multiple states, including the six types of faults and normal conditions in SEC pumps. The diagnostic model utilized the wavelet packet coefficients to capture sub-bands with a higher energy share and reconstruct the signals. The model inputs the 12 frequency features into the support vector machine to analyze the vibration signals gathered from the SEC pump benchmark. The study illustrates that the proposed method can accurately differentiate between various fault conditions when compared to the WPT method, combined with the artificial neural network (ANN) approach. It attains a superior overall precision of up to 94%, and it displays excellent generalization and strong adaptability.

An image zooming method based on the coupling threshold in the wavelet packet transform domain

Aiming at the problem of blurring edge and detail information in the process of image zooming, this paper proposes a new method of image zooming based on wavelet packet transform by combining the characteristics of anisotropic diffusion. First, the initial zoomed image with higher resolution is obtained by wavelet transform, and the wavelet packet decomposition is performed to obtain more high-frequency wavelet packet coefficients reflecting image details. Second, due to the existence of noise, the relationship between wavelet packet transform and anisotropic diffusion is obtained by studying the process of wavelet packet threshold denoising, and the expression of coupling threshold based on diffusion function is given and applied to the high-frequency wavelet packet coefficients. Finally, the original image is used as the low-frequency part after passing the soft threshold, and reconstructed with the denoised high-frequency part to obtain the final zoomed image. The traditional zooming algorithms as well as the learning-based zooming algorithms are selected for comparison. The results show that the algorithm in this paper effectively avoids the blurring of edges and details under the premise of ensuring the similarity between the zoomed image and the original image, so that the zoomed image can obtain more high-frequency information, and achieves the purpose of removing the noise as well as enhancing the detailed information of the image. The effectiveness of this paper’s algorithm in edge protection can be seen from the results of the comparison with the deep learning-based zooming algorithms.

Conditional simulation of spatially correlated earthquake accelerograms based on wavelet packet coefficients

Herein, a method is developed, within the framework of the multivariate linear prediction (MLP), for conditionally simulating spatially correlated nonstationary ground motions at unobserved points measured in this local region. Given the limitation of recognizing the characteristics of the original signal, this scheme is based on the extension of the MLP to the wavelet packet transform (WPT). In this process, the WPT algorithm is used to estimate the corresponding wavelet packet coefficients from the decomposed orthogonal component time-histories corresponding to nonoverlapping frequency bands, which can accurately describe the time-varying nonstationary characteristics of the original signals. The original signal used in the MLP is replaced; instead, the wavelet packet coefficients are regarded as signals and are decomposed into different nonoverlapping subfrequency bands. Subsequently, this simulating process is transformed into a solution of the wavelet packet coefficients at the target points. Finally, an inverse WPT is added to obtain the corresponding ground motions. In addition to matching the specified coherency values, the earthquake time-histories generated by the proposed scheme inherit the physical properties of the predefined recordings well, including the waveform, cumulative energy, response spectrum, and nonstationary characteristics. Two numerical examples and blind tests are employed to simulate an ensemble of spatially correlated ground motions using data from the SMART-1 array. The proposed method will have a significant influence on engineering applications and regional hazard analyses.

A Data-Driven Approach Using Enhanced Bayesian-LSTM Deep Neural Networks for Picks Wear State Recognition

Picks are key components for the mechanized excavation of coal by mining machinery, with their wear state directly influencing the efficiency of the mining equipment. In response to the difficulty of determining the overall wear state of picks during coal-mining production, a data-driven wear state identification model for picks has been constructed through the enhanced optimization of Long Short-Term Memory (LSTM) networks via Bayesian algorithms. Initially, a mechanical model of pick and coal-rock interaction is established through theoretical analysis, where the stress characteristic of the pick is analyzed, and the wear mechanism of the pick is preliminarily revealed. A method is proposed that categorizes the overall wear state of picks into three types based on the statistical relation of the actual wear amount and the limited wear amount. Subsequently, the vibration signals of the cutting drum from a bolter miner that contain the wear information of picks are decomposed and denoised using wavelet packet decomposition, with the standard deviation of wavelet packet coefficients from decomposed signal nodes selected as the feature signals. These feature signals are normalized and then used to construct a feature matrix representing the vibration signals. Finally, this constructed feature matrix and classification labels are fed into the Bayesian-LSTM network for training, thus resulting in the picks wear state identification model. To validate the effectiveness of the Bayesian-LSTM deep learning algorithm in identifying the overall picks wear state of mining machinery, vibration signals from the X, Y, and Z axes of the cutting drum from a bolter miner at the C coal mine in Shaanxi, China, are collected, effectively processed, and then input into deep LSTM and Back-Propagation (BP) neural networks respectively for comparison. The results showed that the Bayesian-LSTM network achieved a recognition accuracy of 98.33% for picks wear state, showing a clear advantage over LSTM, BP network models, thus providing important references for the identification of picks wear state based on deep learning algorithms. This method only requires the processing and analysis of the equipment parameters automatically collected from bolter miners or other mining equipment, offering the advantages of simplicity, low cost, and high accuracy, and providing a basis for a proper picks replacement strategy.

A structural model of teachers’ teaching competencies based on multimodal affective features of support vector machines

Abstract Based on big data technology, this paper first proposes to study and analyze the structural model of teachers’ teaching ability based on multimodal sentiment features of support vector machines. Then the Mel inverse spectral coefficients, wavelet packet coefficients, Fourier coefficient features, dynamic features, and global features are extracted respectively, and the features are dimensionalized using linear support vector machine and Lagrangian function, and the dimensionalized feature parameters are sent to the classifier for emotion recognition. Finally, the structural model evaluation index system of teachers’ teaching ability is constructed, and the current teaching ability development of college teachers in a province is studied and analyzed from two perspectives of teachers’ self-assessment and students’ evaluation based on multimodal emotional features of support vector machine. The results showed that in terms of teaching ability dimensions, teachers had the highest expectation of their teaching ability (4.38) in each dimension, followed in order by teachers’ self-evaluation of teaching ability (4.15), students’ expectation (4.05), and students’ evaluation of teachers’ teaching ability (3.56) was the lowest. This study reveals that teachers’ perceptions of the teaching competencies they should have are biased, and their awareness of self-development is insufficient from the emotional characteristics.

A lightweight fetal distress-assisted diagnosis model based on a cross-channel interactive attention mechanism.

Fetal distress is a symptom of fetal intrauterine hypoxia, which is seriously harmful to both the fetus and the pregnant woman. The current primary clinical tool for the assessment of fetal distress is Cardiotocography (CTG). Due to subjective variability, physicians often interpret CTG results inconsistently, hence the need to develop an auxiliary diagnostic system for fetal distress. Although the deep learning-based fetal distress-assisted diagnosis model has a high classification accuracy, the model not only has a large number of parameters but also requires a large number of computational resources, which is difficult to deploy to practical end-use scenarios. Therefore, this paper proposes a lightweight fetal distress-assisted diagnosis network, LW-FHRNet, based on a cross-channel interactive attention mechanism. The wavelet packet decomposition technique is used to convert the one-dimensional fetal heart rate (FHR) signal into a two-dimensional wavelet packet coefficient matrix map as the network input layer to fully obtain the feature information of the FHR signal. With ShuffleNet-v2 as the core, a local cross-channel interactive attention mechanism is introduced to enhance the model's ability to extract features and achieve effective fusion of multichannel features without dimensionality reduction. In this paper, the publicly available database CTU-UHB is used for the network performance evaluation. LW-FHRNet achieves 95.24% accuracy, which meets or exceeds the classification results of deep learning-based models. Additionally, the number of model parameters is reduced many times compared with the deep learning model, and the size of the model parameters is only 0.33M. The results show that the lightweight model proposed in this paper can effectively aid in fetal distress diagnosis.

A weak fault identification method of micro-turbine blade based on sound pressure signal with LSTM networks

The working condition of micro-turbine blades is very harsh, which is easy to cause blade faults such as fouling, cracks, and fractures. Therefore, it is of great significance to accurately and timely identify the early faults of turbine blades. In this paper, an early weak fault identification method of micro-turbine blade based on sound pressure signal and long short-term memory (LSTM) networks is proposed. Firstly, the sound pressure signals generated by different turbine structures are analyzed by frequency spectrum. Then, the wavelet packet decomposition method is adopted to extract wavelet packet coefficient energy as the fault feature vector, and the weak fault identification model of the turbine blade is established based on LSTM networks. Finally, different faults of turbine blades under different working conditions are identified and tested by using the sound pressure test platform of the micro-turbine. The results show that it is feasible to identify turbine blade faults based on sound pressure signals. Through multiple test results, it can be seen that the identification accuracy of the proposed method for turbine blade faults reaches more than 98%, indicating that it is effective for weak fault identification of turbine blades under complex working conditions, which can provide reference and guidance for the identification and warning of early weak faults of micro turbine blades.

Transformer Aging Diagnosis Method Based on Raman Spectroscopy Wavelet Packet-SPCA Feature Extraction

Ensuring the safety and reliable operation of a power transformer is a top priority in grid work. There is an urgent need to study methods for measuring and evaluating the aging state of oil–paper insulation in older transformers. Raman spectroscopy is widely used in material detection; the spectra can represent the inner components of transformer oil and help diagnose the aging states of the transformer efficiently. In this article, thermal accelerated aging experiments were conducted, and oil–paper insulation samples with different aging states were obtained. The aging states of oil–paper insulation were tagged by the degree of polymerization (DP) value of the paper. Four wavelet packet decompositions were used for the Raman spectra, and sparse principal component analysis was used to extract the features in the wavelet packet coefficients. A 14-D feature was built and trained with a multiclassification support vector machine (SVM), and a diagnosis model for aging states was established. The results show that the accuracy of the diagnosis model reaches 94.9%. Seven samples of transformers in operation also verify the method’s effectiveness. This method has practical significance for quickly detecting the aging states of operating transformers.

Accurate and early prediction of the wound healing outcome of burn injuries using the wavelet Shannon entropy of terahertz time-domain waveforms.

Severe burn injuries cause significant hypermetabolic alterations that are highly dynamic, hard to predict, and require acute and critical care. The clinical assessments of the severity of burn injuries are highly subjective and have consistently been reported to be inaccurate. Therefore, the utilization of other imaging modalities is crucial to reaching an objective and accurate burn assessment modality. We describe a non-invasive technique using terahertz time-domain spectroscopy (THz-TDS) and the wavelet packet Shannon entropy to automatically estimate the burn depth and predict the wound healing outcome of thermal burn injuries. We created 40 burn injuries of different severity grades in two porcine models using scald and contact methods of infliction. We used our THz portable handheld spectral reflection (PHASR) scanner to obtain the in vivo THz-TDS images. We used the energy to Shannon entropy ratio of the wavelet packet coefficients of the THz-TDS waveforms on day 0 to create supervised support vector machine (SVM) classification models. Histological assessments of the burn biopsies serve as the ground truth. We achieved an accuracy rate of 94.7% in predicting the wound healing outcome, as determined by histological measurement of the re-epithelialization rate on day 28 post-burn induction, using the THz-TDS measurements obtained on day 0. Furthermore, we report the accuracy rates of 89%, 87.1%, and 87.6% in automatic diagnosis of the superficial partial-thickness, deep partial-thickness, and full-thickness burns, respectively, using a multiclass SVM model. The THz PHASR scanner promises a robust, high-speed, and accurate diagnostic modality to improve the clinical triage of burns and their management.

Improving purity of blasting vibration signals using advanced Empirical Mode Decomposition and Wavelet packet technique

The study proposes a denoising method based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Wavelet packet threshold denoising (WPTD) to reduce the noise of blasting vibration signals. CEEMDAN is first employed to decompose noisy blasting vibration signals into different intrinsic mode functions (IMFs), i.e., different frequencies of subcomponents. By using correlation coefficients, all of IMFs are automatically categorized as the dominant IMFs with higher portions of vibration components and the secondary IMFs with less vibration contents. Then, with further decomposing two groups of IMFs into different scales of Wavelet packet coefficient series, WPTD based on the fixed-threshold technique and the soft threshold function method is applied to minimize the level of noise in two groups of IMFs. Two groups of denoised IMFs are finally reconstructed as the pure blasting vibration waveform. Numerical waveforms with different types and intensities of noise and measured blasting vibration signals with different main frequency bands are used to verify the accuracy and capability of the proposed method. The numerical and field results show that the proposed method can not only effectively reduce noise components, but also well remain components of blasting vibrations.

Abnormal Properties of Cortical Functional Brain Network in Major Depressive Disorder: Graph Theory Analysis Based on Electroencephalography-Source Estimates

Studies of scalp electroencephalography (EEG) had shown altered topological organization of functional brain networks in patients with major depressive disorder (MDD). However, most previous EEG-based network analyses were performed at sensor level, while the interpretation of obtained results was not straightforward due to volume conduction effect. To reduce the impact of this defect, the whole cortical functional brain networks of MDD patients were studied during resting state based on EEG-source estimates in this paper. First, scalp EEG signals were recorded from 19 patients with MDD and 20 normal controls under resting eyes-closed state, and cortical neural signals were estimated by using sLORETA method. Then, the correntropy coefficient of wavelet packet coefficients was performed to calculate functional connectivity (FC) matrices in four different frequency bands: δ, θ, α, β, respectively. Afterwards, topological properties of brain networks were analyzed by graph theory approaches. The results showed that the global FC strength of MDD patients was significantly higher than that of healthy subjects in α band. Also, it was found that MDD patients have abnormally increased clustering coefficient and local efficiency in both α and β bands compared to normal people. Furthermore, patients with MDD exhibited increased nodal clustering coefficients in the left lingual gryus and left precuneus in α band. In addition, β band global clustering coefficient was positively correlated with the scores of depression severity. Therefore, the findings indicated the cortical functional brain networks in MDD patients were disruptions, which suggested it would be one of potential causes of depression.