Wavelet Packet Transform Research Articles

Health monitoring of CNC machining processes using machine learning and wavelet packet transform

Monitoring the health of a machining process plays a crucial role in advancing fully automated manufacturing. Faulty machining processes (abnormal process) leads to part rejection and can damage the CNC machines. In this context, data-driven machine learning (ML) models with wavelet packet transform (WPT)-based feature extraction method have gained significant importance in health monitoring. The study of different ML models, mother wavelets, and decomposition levels on real production data is important for effective process health monitoring but are not explored well in the literature. This study analyzes the performance of fifty mother wavelets, two decomposition levels (L2 and L3), and five ML models using actual production facility CNC machine dataset to achieve accurate process health monitoring. Various performance indicators obtained from the confusion matrix have been used to evaluate the ML models. The findings indicate that the Random Forest (RF) and Light-Gradient boosting machine (GBM), using the coif8 and db14 mother wavelet, at decomposition level (L3), deliver the best classification performance. Furthermore, the RF model consistently achieves good precision, sensitivity, accuracy, and F1 scores across most classes, making it a reliable and efficient option for the classification of normal and abnormal machining processes. The SVC, MLP, and CNN models, however, also exhibit competitive performance.

SEACKgram: a targeted method of optimal demodulation-band selection for compound faults diagnosis of rolling bearing

Rolling bearing plays an important role in carrying and transmitting power in rotating machinery, and the bearing fault is easy to lead to mechanical accidents, resulting in huge losses and casualties. Therefore, the condition monitoring and diagnosis of rolling bearings are very important to improve the safety of equipment. Compound fault is a common fault evolved from the initial defect, which is characterized by randomness, coupling, concealment, and secondary. The existence of these characteristics brings great challenges to the accurate diagnosis of compound faults. In the diagnosis of compound faults, the traditional methods that select the single optimal demodulation frequency band for analysis and identification sometimes cannot completely extract multiple fault components, which are prone to miss diagnosis and misdiagnosis. In order to solve this problem, the SEACKgram method is proposed by constructing a Square Envelope Unbiased Autocorrelation Correlation Kurtosis (SEACK) index. The frequency band of the original signal is divided by the Maximal Overlap Discrete Wavelet Packet Transform, and the SEACK index is used to quantitatively describe the fault signals of different frequency bands. According to the different fault periods, the resonant frequency bands of the maximum SEACK value are selected, then the resonance band signal is analyzed by square envelope spectrum, and the fault type is identified according to the fault characteristic frequency. The simulated and experimental vibration signals of rolling bearings with compound faults are used to verify the feasibility of the proposed method. The results show that the proposed SEACKgram can improve the accuracy of compound faults identification and would be applied in engineering practice to a certain extent.

A Novel Approach for Denoising ECG Signals Corrupted with White Gaussian Noise Using Wavelet Packet Transform and Soft-Thresholding

A Novel Approach for Denoising ECG Signals Corrupted with White Gaussian Noise Using Wavelet Packet Transform and Soft-Thresholding

Proficiency evaluation of shape and WPT radiomics based on machine learning for CT lung cancer prognosis

BackgroundLung cancer is a fatal disease which has high occurrence and mortality rates, worldwide. Computed tomography imaging is being widely used by clinicians for detection of lung cancer. Radiomics extracted from medical images together with machine learning platform has enabled automated lung cancer diagnosis. Therefore, this study is proposed with the aim to efficiently apply radiomics and ML techniques to classify pulmonary nodules in CT images. Lung Image Data Consortium is utilized which contains 1018 CT lung cancer cases.ResultsRadiomics are extracted using Shape, Gray Level Co-occurrence Method, Gray Level Difference Method, and Gray Level Run Length Matrix along with Wavelet Packet Transform. To select a relevant set of features two techniques, Analysis of variance and Chi-square test, are applied. The classification of nodule into benign or malignant is evaluated by using state-of-art models: Support vector machine, Decision Trees, Ensemble Trees (BOCET, BACET, RUSBOCET), Ensemble Subspace KNN and Ensemble Subspace Discriminant. The results show that, BACET gives best AUROC (92.9%), MGSVM gives best accuracy (90.4%), FGSVM yields the best sensitivity (97.8%), MGSVM gives best precision (94.1%) and RUSBOCET gives best specificity (84%).ConclusionsThe results show that the proposed methodology can be successfully used for the classification of pulmonary nodules based on CT images. The outcome thus can help clinicians to reach better decision, treatments and early diagnosis.

A Partial-Label U-Net Learning Method for Compound-Fault Diagnosis With Fault- Sample Class Imbalance

In the operation process of the rotating machinery, compound faults have various combination forms and are difficult to reproduce, which results in the scarcity of training samples of various compound faults. In this paper, a method of partial-label learning and classification fusion is proposed to investigate the above problems. Wavelet packet transformation (WPT) and dimensionless parameterization (DP) are utilized to extract features in high-dimensional space. A label-specific feature learning architecture is proposed to make up for the shortage of handcrafted features. An improved focal loss is exploited for learning prominent compound-fault characteristics and imbalanced fault samples. Basic probability assignments (BPA) about fault classes are generated from each partial classifier and combined to obtain a final inference about fault types. Experimental results of single-fault and compound-fault classification illustrate the effectiveness of the proposed method.

Wavelet Packet Transform and Deep Learning-based Fusion of Audio-Visual Signals: A Novel Approach for Enhancing Laser Cleaning Effect Evaluation

Wavelet Packet Transform and Deep Learning-based Fusion of Audio-Visual Signals: A Novel Approach for Enhancing Laser Cleaning Effect Evaluation

Effect of Ground Motion Time–Frequency Non-Stationarity on Seismic Response of High-Speed Railway Simply Supported Bridge Based on Wavelet Packet Transform

Time–frequency non-stationarity is a ground motion characteristic which is frequently neglected in current seismic design and research. This paper studies its impact on the seismic response of high-speed railway simply supported bridge (HSRSSB). A method for generating time–frequency stationary earthquakes (TFSEs) and time–frequency non-stationary earthquakes (TFNSEs) using wavelet packet transform is proposed. A finite element model of a three-span HSRSSB is established using OpenSees. The seismic response is obtained through non-linear dynamic time history analysis, and the fragility curves of bridge components and system are calculated through incremental dynamic analysis. Finally, the reasons for the differences are analyzed by comparing the differences in seismic response of bridge, component fragility and system fragility under two groups of ground motion. The results show that the time–frequency non-stationarity of ground motion has an effect on the bridge response and fragility under strong earthquakes. TFNSE will lead to larger ground motion response, and the damage probability of bridge components and systems is higher. The reason is related to the damage and period extension of bridges under ground motion. Structures with prolonged period anti-seismic measures need to pay attention to this effect.

Abnormal noise identification of engines based on wavelet packet transform and bispectrum analysis

Abnormal noise is the most prominent problem for motorcycles and affects the consumers’ purchasing desire and driving experience and the enterprise’s competitiveness. Usually, the noise from a newly assembled engine is detected by manual auscultation (MA) to determine if the engine is operating normally. However, MA is also affected by subjective and objective factors with severe labor intensity, and its accuracy greatly fluctuates. Importantly, MA cannot be applied in a corporation with mass production and high-quality requirements. To improve the efficiency and accuracy of motorcycle engine quality inspection and achieve intelligent production, an online engine abnormal noise detection method was proposed based on wavelet packet transform (WPT) and bispectrum analysis (BA); this method improved the accuracy and stability of the identification of the abnormal noise engine and reduced the cost of the check. First, the acoustic signal of the engine of the motorcycle was acquired by using a free-field microphone. Second, the background noise of signals was eliminated by using the wavelet correlation coefficient (WCC) theory, and the signal features were extracted by applying WPT and BA. Third, the feature vectors were normalized before being used as support vector machine (SVM) samples. Fourth, an appropriate kernel function and parameters were selected to train the vector machine using the training sets. Finally, the testing sets were used to inspect the accuracy of the vector machines. The result showed that the training accuracy is 95% and the testing accuracy is 97.5 of the samples were suitable by using the method of wavelet packet transform-bispectrum analysis-support vector machines (WPT-BA-SVM). WPT-BA-SVM effectively identified engine fault types and provided the theoretical foundation for the establishment of an engine abnormal noise online detection system.

DENOISING DIFFUSION PROBABILISTIC MODEL WITH WAVELET PACKET TRANSFORM FOR FINGERPRINT GENERATION

The majority of contemporary fingerprint synthesis is based on the Generative Adversarial Network (GAN). Recently, the Denoising Diffusion Probabilistic Model (DDPM) has been demonstrated to be more effective than GAN in numerous scenarios, particularly in terms of diversity and fidelity. This research develops a model based on the enhanced DDPM for fingerprint generation. Specifically, the image is decomposed into sub-images of varying frequency sub-bands through the use of a wavelet packet transform (WPT). This method enables DDPM to operate at a more local and detailed level, thereby accurately obtaining the characteristics of the data. Furthermore, a polynomial noise schedule has been designed to replace the linear noise strategy, which can result in a smoother noise addition process. Experiments based on multiple metrics on the datasets SOCOFing and NIST4 demonstrate that the proposed model is superior to existing models.

A novel design employing arbitrary tree structure for adaptive thrsholding discrete wavelet packet transformation

A novel design employing arbitrary tree structure for adaptive thrsholding discrete wavelet packet transformation

Comparison of the Packet Wavelet Transform Method for Medical Image Compression

Medical images are often used for educational, analytical, and medical diagnostic purposes. Medical image data requires large amounts of storage on computers. Three types of codecs, namely Haar, Daubechies, and Biorthogonal, were used in this study. This study aims to find the best wavelet method of the three tested wavelet methods (Haar, Daubechies, and Biorthogonal). This study uses medical images representing USG and CT-scan images as testing data. The first test is carried out by comparing the threshold ratio. Three threshold values are used, namely 30, 40, and 50. The second test looks for PSNR values with different thresholds. The third test looks for a comparison of the rate (image size) to the PSSR value. The final test is to find each medical image's compression and decompression times. The first compression ratio test results on both medical images showed that CT scan images on Haar and Biorthogonal wavelets were the best, with an average compression ratio of 40.76% and a PSNR of 33.77. The PSNR obtained is also getting more significant for testing with a larger image size. The average compression time is 0.52 seconds, and the decompression time is 2.27 seconds. Based on the test results, this study recommends that the Daubechies wavelet method is very good for compression, which is 0.51 seconds, and the Biorthogonal wavelet method is very good for medical image decompression, which is 1.69 seconds.

Comparison of the Packet Wavelet Transform Method for Medical Image Compression

Medical images are often used for educational, analytical, and medical diagnostic purposes. Medical image data requires large amounts of storage on computers. Three types of codecs, namely Haar, Daubechies, and Biorthogonal, were used in this study. This study aims to find the best wavelet method of the three tested wavelet methods (Haar, Daubechies, and Biorthogonal). This study uses medical images representing USG and CT-scan images as testing data. The first test is carried out by comparing the threshold ratio. Three threshold values are used, namely 30, 40, and 50. The second test looks for PSNR values with different thresholds. The third test looks for a comparison of the rate (image size) to the PSSR value. The final test is to find each medical image's compression and decompression times. The first compression ratio test results on both medical images showed that CT scan images on Haar and Biorthogonal wavelets were the best, with an average compression ratio of 40.76% and a PSNR of 33.77. The PSNR obtained is also getting more significant for testing with a larger image size. The average compression time is 0.52 seconds, and the decompression time is 2.27 seconds. Based on the test results, this study recommends that the Daubechies wavelet method is very good for compression, which is 0.51 seconds, and the Biorthogonal wavelet method is very good for medical image decompression, which is 1.69 seconds.

Comparison of the Packet Wavelet Transform Method for Medical Image Compression

Medical images are often used for educational, analytical, and medical diagnostic purposes. Medical image data requires large amounts of storage on computers. Three types of codecs, namely Haar, Daubechies, and Biorthogonal, were used in this study. This study aims to find the best wavelet method of the three tested wavelet methods (Haar, Daubechies, and Biorthogonal). This study uses medical images representing USG and CT-scan images as testing data. The first test is carried out by comparing the threshold ratio. Three threshold values are used, namely 30, 40, and 50. The second test looks for PSNR values with different thresholds. The third test looks for a comparison of the rate (image size) to the PSSR value. The final test is to find each medical image's compression and decompression times. The first compression ratio test results on both medical images showed that CT scan images on Haar and Biorthogonal wavelets were the best, with an average compression ratio of 40.76% and a PSNR of 33.77. The PSNR obtained is also getting more significant for testing with a larger image size. The average compression time is 0.52 seconds, and the decompression time is 2.27 seconds. Based on the test results, this study recommends that the Daubechies wavelet method is very good for compression, which is 0.51 seconds, and the Biorthogonal wavelet method is very good for medical image decompression, which is 1.69 seconds.

A Technique for Bearing Fault Diagnosis Using Novel Wavelet Packet Transform-Based Signal Representation and Informative Factor LDA

This paper proposes a new method for bearing fault diagnosis using wavelet packet transform (WPT)-based signal representation and informative factor linear discriminant analysis (IF-LDA). Time–frequency domain approaches for analyzing bearing vibration signals have gained wide acceptance due to their effectiveness in extracting information related to bearing health. WPT is a prominent method in this category, offering a balanced approach between short-time Fourier transform and empirical mode decomposition. However, the existing methods for bearing fault diagnosis often overlook the limitations of WPT regarding its dependence on the mother wavelet parameters for feature extraction. This work addresses this issue by introducing a novel signal representation method that employs WPT with a new rule for selecting the mother wavelet based on the power spectrum energy-to-entropy ratio of the reconstructed coefficients and a combination of the nodes from different WPT trees. Furthermore, an IF-LDA feature preprocessing technique is proposed, resulting in a highly sensitive set of features for bearing condition assessment. The k-nearest neighbors algorithm is employed as the classifier, and the proposed method is evaluated using datasets from Paderborn and Case Western Reserve universities. The performance of the proposed method demonstrates its effectiveness in bearing fault diagnosis, surpassing existing techniques in terms of fault identification and diagnosis performance.

Iterative singular value decomposition-based in-band denoising approach with envelope order analysis for sun gear fault diagnosis of planetary system under varying speed

The vibration signal of the planetary gear train is easily disturbed by the background noise, so the measured signal is complicated. In order to accurately extract the fault features, the resonance method has been widely used. However, even if the optimal resonance frequency band is found, the in-band noise still exists, so it is necessary to study an effective in-band denoising method. In this paper, an in-band denoising method based on Iterative Singular Value Decomposition (ISVD) is proposed for the fault diagnosis of the secondary sun gear of a planetary gear train, combined with the envelope order spectrum analysis. This method uses the enhanced Wavelet Packet Transform Spectral Kurtosis (WPTSK) to determine the best frequency band for the signal, and uses the ISVD method to realize the signal denoising. It sets a threshold to avoid the destruction of the useful information caused by the excessive iteration, and uses the relationship between the singular values and frequency components to reconstruct the denoised signal. Finally, the signal is converted to the fault characteristic order domain by resampling to identify the fault type of the sun gear from the envelope order spectrum. The simulation and experimental results show that compared with the Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD), the ISVD can effectively suppress the in-band noise and more accurately extract the fault characteristic order of the secondary sun gear under varying speed.

Optimizing the performance of machine learning algorithms for the condition assessment of utility timber poles

ABSTRACT This study focuses on evaluating several machine learning algorithms for the condition assessment of utility timber poles. An efficient feature extraction technique combining Hilbert Huang transform (HHT) and wavelet packet transform (WPT) is adopted from the authors’ previous work and implemented to determine damage-sensitive features from vibration data related to five serviceable and eight unserviceable in-situ timber poles. Then, these features are pre-processed using correlation heat map analysis for feature selection. Principal component analysis (PCA) is adopted as the final step of pre-processing for reducing noise interference and enhancing classification accuracy. Afterwards, a feature matrix is formed, which is fed into the selected classifiers for pattern recognition. In addition, the information gain method is also implemented and compared against PCA to examine the effect of feature selection. Finally, selected classifiers are employed using those dominant features, and their performance is evaluated based on six parameters – accuracy, precision, recall, F1-score, confusion matrix and Receiver Operating Characteristic (ROC) curve. It was found that choosing the best feature set related to the health state helps to improve the performance of the pattern recognition algorithms to a great extent.

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.

Cross-scale data-based damage identification of CFRP laminates using acoustic emission and deep learning

Damage characterization of laminated composites has undergone extensive research, leading to the development of several damage models that incorporate acoustic emission (AE). However, feature extraction from AE data will cause the loss of certain information in the construction of damage models, which manifestly falls short of feature analysis in the frequency domain. In this study, a novel cross-scale data-based damage identification methodology for carbon fiber-reinforced polymer (CFRP) laminates is proposed by combining the AE technique with deep learning approach. Elementary experiments involved with single damage mode are designed to avoid blind inference, and the cross-scale correlation of AE features between component materials and CFRP laminates is established by wavelet packet transform (WPT). The time–frequency spectrums of AE signals of CFRP laminates by continuous wavelet transform (CWT), which adequately preserve the frequency domain information, are adopted as inputs to the convolutional neural network (CNN) model. The proposed methodology achieves a high accuracy of 96.3% in detecting and classifying damage modes (i.e., matrix cracking, matrix/fiber debonding, and fiber breakage) in unidirectional CFRP laminates.

Optimized Wavelet and Wavelet Packet Transform Techniques for Assessing Crack Behavior in Curved Segments of Arched Beam Bridges Spanning Rivers

Our study focuses on the dynamic transient analysis of arched beam bridges over rivers, which face unique geohazards and challenges, including vibrations and dynamic loads that can affect structural integrity. The finite element software ANSYS v. 19.3 was employed to assess acceleration time histories at various bridge positions. Using MATLAB, we conducted wavelet packet decomposition to extract insights from the data, specifically isolating river-induced influences. In this article, the introduction of the wavelet packet rate index (WPERI) is presented as a novel metric for the detection of cracks in the curved bridge segments over rivers. The WPERI proves reliable in accounting for the river environment’s impact on structural integrity. Our findings highlight the sensitivity and precision of the WPERI in accurately detecting cracks and vulnerabilities in these riverine bridges. By combining WPT, finite element analysis, and signal decomposition, our research offers insights into tailored crack detection methods for riverine bridges. This study underscores the potential of WPT as a tool for identifying and characterizing cracks in curved bridge elements over rivers. The innovative WPERI provides a holistic approach to addressing structural issues, thus enhancing bridge durability amid changing environmental conditions. It contributes significantly to structural engineering and paves the way for the further exploration of river-specific crack detection techniques.

A Technique for Centrifugal Pump Fault Detection and Identification Based on a Novel Fault-Specific Mann-Whitney Test.

This work presents a technique for fault detection and identification in centrifugal pumps (CPs) using a novel fault-specific Mann-Whitney test (FSU Test) and K-nearest neighbor (KNN) classification algorithm. Traditional fault indicators, such as the mean, peak, root mean square, and impulse factor, lack sensitivity in detecting incipient faults. Furthermore, for defect identification, supervised models rely on pre-existing knowledge about pump defects for training purposes. To address these concerns, a new centrifugal pump fault indicator (CPFI) that does not rely on previous knowledge is developed based on a novel fault-specific Mann-Whitney test. The new fault indicator is obtained by decomposing the vibration signature (VS) of the centrifugal pump hierarchically into its respective time-frequency representation using the wavelet packet transform (WPT) in the first step. The node containing the fault-specific frequency band is selected, and the Mann-Whitney test statistic is calculated from it. The combination of hierarchical decomposition of the vibration signal for fault-specific frequency band selection and the Mann-Whitney test form the new fault-specific Mann-Whitney test. The test output statistic yields the centrifugal pump fault indicator, which shows sensitivity toward the health condition of the centrifugal pump. This indicator changes according to the working conditions of the centrifugal pump. To further enhance fault detection, a new effect ratio (ER) is introduced. The KNN algorithm is employed to classify the fault type, resulting in promising improvements in fault classification accuracy, particularly under variable operating conditions.