Continuous Wavelet Transform Research Articles

Heisenberg-Type Inequality and Localization Operators Associated to the Continuous Laguerre-Bessel Wavelet Transform

Heisenberg-Type Inequality and Localization Operators Associated to the Continuous Laguerre-Bessel Wavelet Transform

Hyperspectral Estimation of Chlorophyll Content in Wheat under CO2 Stress Based on Fractional Order Differentiation and Continuous Wavelet Transforms

The leaf chlorophyll content (LCC) of winter wheat, an important food crop widely grown worldwide, is a key indicator for assessing its growth and health status in response to CO2 stress. However, the remote sensing quantitative estimation of winter wheat LCC under CO2 stress conditions also faces challenges such as an unclear spectral sensitivity range, baseline drift, overlapping spectral peaks, and complex spectral response due to CO2 stress changes. To address these challenges, this study introduced the fractional order derivative (FOD) and continuous wavelet transform (CWT) techniques into the estimation of winter wheat LCC. Combined with the raw hyperspectral data, we deeply analyzed the spectral response characteristics of winter wheat LCC under CO2 stress. We proposed a stacking model including multiple linear regression (MLR), decision tree regression (DTR), random forest (RF), and adaptive boosting (AdaBoost) to filter the optimal combination from a large number of feature variables. We use a dual-band combination and vegetation index strategy to achieve the accurate estimation of LCC in winter wheat under CO2 stress. The results showed that (1) the FOD and CWT methods significantly improved the correlation between the raw spectral reflectance and LCC of winter wheat under CO2 stress. (2) The 1.2-order derivative dual-band index (RVI (R720, R522)) constructed by combining the sensitive spectral bands of the CO2 response of winter wheat leaves achieved a high-precision estimation of the LCC under CO2 stress conditions (R2 = 0.901). Meanwhile, the red-edged vegetation stress index (RVSI) constructed based on the CWT technique at specific scales also demonstrated good performance in LCC estimation (R2 = 0.880), verifying the effectiveness of the multi-scale analysis in revealing the mechanism of the CO2 impact on winter wheat. (3) By stacking the sensitive spectral features extracted by combining the FOD and CWT methods, we further improved the LCC estimation accuracy (R2 = 0.906). This study not only provides a scientific basis and technical support for the accurate estimation of LCC in winter wheat under CO2 stress but also provides new ideas and methods for coping with climate change, optimizing crop-growing conditions, and improving crop yield and quality in agricultural management. The proposed method is also of great reference value for estimating physiological parameters of other crops under similar environmental stresses.

Transfer Learning and Deep Neural Networks for Robust Intersubject Hand Movement Detection from EEG Signals

In this research, five systems were developed to classify four distinct motor functions—forward hand movement (FW), grasp (GP), release (RL), and reverse hand movement (RV)—from EEG signals, using the WAY-EEG-GAL dataset where participants performed a sequence of hand movements. During preprocessing, band-pass filtering was applied to remove artifacts and focus on the mu and beta frequency bands. The initial system, a preliminary study model, explored the overall framework of EEG signal processing and classification, utilizing time-domain features such as variance and frequency-domain features such as alpha and beta power, with a KNN model for classification. Insights from this study informed the development of a baseline system, which innovatively combined the common spatial patterns (CSP) method with continuous wavelet transform (CWT) for feature extraction and employed a GoogLeNet classifier with transfer learning. This system classified six unique pairs of events derived from the four motor functions, achieving remarkable accuracy, with the highest being 99.73% for the GP–RV pair and the lowest 80.87% for the FW–GP pair in intersubject classification. Building on this success, three additional systems were developed for four-way classification. The final model, ML-CSP-OVR, demonstrated the highest intersubject classification accuracy of 78.08% using all combined data and 76.39% for leave-one-out intersubject classification. This proposed model, featuring a novel combination of CSP-OVR, CWT, and GoogLeNet, represents a significant advancement in the field, showcasing strong potential as a general system for motor imagery (MI) tasks that is not dependent on the subject. This work highlights the prominence of the research contribution by demonstrating the effectiveness and robustness of the proposed approach in achieving high classification accuracy across different motor functions and subjects.

Research on Fault Diagnosis of Drilling Pump Fluid End Based on Time-Frequency Analysis and Convolutional Neural Network

Operating in harsh environments, drilling pumps are highly susceptible to failure and challenging to diagnose. To enhance the fault diagnosis accuracy of the drilling pump fluid end and ensure the safety and stability of drilling operations, this paper proposes a fault diagnosis method based on time-frequency analysis and convolutional neural networks. Firstly, continuous wavelet transform (CWT) is used to convert the collected vibration signals into time-frequency diagrams, providing a comprehensive database for fault diagnosis. Next, a SqueezeNet-based fault diagnosis model is developed to identify faults. To validate the effectiveness of the proposed method, fault signals from the fluid end were collected, and fault diagnosis experiments were conducted. The experimental results demonstrated that the proposed method achieved an accuracy of 97.77% in diagnosing nine types of faults at the fluid end, effectively enabling precise fault diagnosis, which is higher than the accuracy of a 1D convolutional neural network by 14.55%. This study offers valuable insights into the fault diagnosis of drilling pumps and other complex equipment.

The Development of a Novel Transient Signal Analysis: A Wavelet Transform Approach

This paper presents a new method for the analysis of transient signals in the frequency domain based on the Continuous Wavelet Transform (CWT). The proposed case study involves test signals measured from an electronic switch considering open and close operations. The source is connected to inductive, resistive, and capacitive loads. Resonance behaviors are introduced and compared with the Discrete Fourier Transform (DFT). Multiple factors, such as reliability, repeatability, high noise attenuation, and the smoothing of the analyzed spectrum, are considered in this study. This proposed study highlights the effectiveness of CWT in signal processing, especially in obtaining a detailed spectrum that reveals the behavior of electrical circuits. Resonance behaviors were analyzed, demonstrating that the signal processing performed by CWT is better for spectrum analysis than DFT. This study shows the potential of CWT to analyze transient electrical signals, specifically for identifying and characterizing the behavior of load connections and disconnections.

Detection of ultra-low concentration NH3, SO2, and NO using UV-DOAS combined with multidimensional spectral fusion

Since nitric oxide (NO), sulfur dioxide (SO2), and ammonia (NH3) in flue gas cause severe air pollution, accurate measurements of their concentrations are crucial for optimizing the efficiency of flue gas denitrification in coal-fired power plants and protecting the atmosphere. Due to their large absorption cross sections in the ultraviolet (UV) band, NH3, SO2, and NO in flue gas can be detected by UV Differential Optical Absorption Spectroscopy (UV-DOAS) techniques. However, spectral overlap and noise caused by short optical path limitations in the measurement are the main obstacles to achieve concentration inversion. Here, we propose a multidimensional spectral fusion method one-dimensional convolutional neural network combined with two-dimensional convolutional neural network (1D-2D-CNN) with the ability to invert concentration of NH3, SO2 and NO at ppb level with 0.5 m optical-length. To separate the absorption features, one-dimensional spectra are converted into two-dimensional time-frequency plots by continuous wavelet transform (CWT). After denoising the spectra by wavelet thresholding, one-dimensional and two-dimensional spectral features are extracted by 1D-2D-CNN model and fused for inversion. The experimental results show that the proposed system can effectively eliminate interferences from NH3, SO2, and NO, significantly improving the concentration inversion accuracy. The detection limits for NH3, SO2 and NO in the mixture are 0.95 ppb∙m, 6.31 ppb∙m, and 2.53 ppb∙m, respectively, demonstrating that our approach outperforms other reported methods for flue gas analysis. The proposed system is expected to be applied to ammonia slip monitoring of Selective Catalytic Reduction (SCR) in power plants.

Identifying Halos in Cosmological Simulations with Continuous Wavelet Analysis: The 2D Case

Continuous wavelet analysis is gaining popularity in science and engineering for its ability to analyze data across both spatial and scale domains simultaneously. In this study, we introduce a wavelet-based method for halo identification and assess its feasibility in two-dimensional (2D) scenarios. We begin by generating four pseudo-2D data sets from the SIMBA dark matter simulation by compressing thin slices of three-dimensional (3D) data into 2D. Subsequently, we calculate the continuous wavelet transform (CWT) directly from the particle distributions, identify local maxima that represent actual halos, and segment the CWT to delineate halo boundaries. A comparison with the traditional friends-of-friends (FOF) method shows that while our CWT-identified halos contain slightly fewer particles, they have smoother boundaries and are more compact in dense regions. In contrast, the CWT method can link particles over greater distances to form halos in sparse regions due to its spatial segmentation scheme. The spatial distribution and halo power spectrum of both CWT and FOF halos demonstrate substantial consistency, validating the 2D applicability of CWT for halo detection. While our identification scheme has been tested solely in a limited 2D context and has shown some performance limitations, its linear time complexity of O(N) and consistency with the FOF method suggest its suitability for analyzing significantly larger data sets in the future and its potential to be extended to the 3D case.

Intra-pulse modulation discrimination using a self-supervised attention-driven CNN-BiLSTM-VAE combination

Identification of intra-pulse modulation (IPM) of radar signals is a crucial part of contemporary electronic support systems and electronic intelligence reconnaissance. Artificial intelligence (AI)-based methods can be very effective in recognising the IPM of radar signals. In this direction, an automatic method is proposed for recognising a few IPMs of radar signals based on continuous wavelet transform (CWT) and a hybrid model of self-attention (SA)-aided convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM). Firstly, time–frequency attributes of different radar signals are obtained using CWT, and thereafter CNN-SA-BiLSTM is utilised for feature extraction from the 2D scalograms formed by the time–frequency components. The CNN extracts features from the scalograms, SA enhances the discriminative power of the feature map, and BiLSTM detects radar signals based on these features. Additionally, the study addresses real-world data imbalance issues by incorporating a generative AI model, namely the Variational Autoencoder (VAE). The VAE-based approach effectively mitigates challenges arising from data imbalance situations. This method is tested at varying noise levels to give a proper representation of the actual electronic warfare environment. The simulation results demonstrate that the best overall recognition accuracy of the proposed method is 98.4%, even at low signal-to-noise ratios (SNR).

Support Vector Machine Framework for Detecting Ambiguous Contours of Space Debris Cloud

Operational spacecraft are prepared for collisions with space debris by installing protective walls (bumpers). A group of vaporized and liquefied microparticles generated by debris collisions is called a debris cloud. To evaluate the protective performance of bumpers, it is important to measure the spread velocity and angle of the debris cloud. However, debris cloud images exhibit ambiguous contours of debris clouds. Consequently, measurement errors in the spread velocity and spread angles occur because of the observer’s subjectivity. Commonly used derivative-based methods can detect steep contours; however, they cannot detect ambiguous contours such as those of debris clouds. In this study, a method for uniquely detecting the ambiguous contours of a debris cloud based on supervised machine learning and a continuous wavelet transform (CWT) is proposed. Feature points that indicate candidate points of the debris cloud contour are extracted using a method based on CWT. Four types of specific features for debris cloud contours were assigned to the feature points. Supervised machine learning using a support vector machine can detect the debris cloud contours. The proposed method enables the evaluation of the ambiguous contours of a debris cloud and the protection performance of a bumper without observer subjectivity.

SFNet: Stellar Feature Network with CWT for Stellar Spectra Recognition

Stellar spectral classification is crucial in astronomical data analysis. However, existing studies are often limited by the uneven distribution of stellar samples, posing challenges in practical applications. Even when balancing stellar categories and their numbers, there is room for improvement in classification accuracy. This study introduces a Continuous Wavelet Transform using the Super Morlet wavelet to convert stellar spectra into wavelet images. A novel neural network, the Stellar Feature Network, is proposed for classifying these images. Stellar spectra from Large Sky Area Multi-Object Fiber Spectroscopic Telescope DR9, encompassing five equal categories (B, A, F, G, K), were used. Comparative experiments validate the effectiveness of the proposed methods and network, achieving significant improvements in classification accuracy.

Automated Crack Detection in Monolithic Zirconia Crowns Using Acoustic Emission and Deep Learning Techniques.

Monolithic zirconia (MZ) crowns are widely utilized in dental restorations, particularly for substantial tooth structure loss. Inspection, tactile, and radiographic examinations can be time-consuming and error-prone, which may delay diagnosis. Consequently, an objective, automatic, and reliable process is required for identifying dental crown defects. This study aimed to explore the potential of transforming acoustic emission (AE) signals to continuous wavelet transform (CWT), combined with Conventional Neural Network (CNN) to assist in crack detection. A new CNN image segmentation model, based on multi-class semantic segmentation using Inception-ResNet-v2, was developed. Real-time detection of AE signals under loads, which induce cracking, provided significant insights into crack formation in MZ crowns. Pencil lead breaking (PLB) was used to simulate crack propagation. The CWT and CNN models were used to automate the crack classification process. The Inception-ResNet-v2 architecture with transfer learning categorized the cracks in MZ crowns into five groups: labial, palatal, incisal, left, and right. After 2000 epochs, with a learning rate of 0.0001, the model achieved an accuracy of 99.4667%, demonstrating that deep learning significantly improved the localization of cracks in MZ crowns. This development can potentially aid dentists in clinical decision-making by facilitating the early detection and prevention of crack failures.

Blood Pressure Estimation from Wavelet Scalogram of PPG signals using Convolutional Neural Networks

Introduction In this work, calibration-free blood pressure estimation using wavelet scalograms of PPG signals using Convolutional Neural Network (CNN) has been proposed. The PPG signal, easily obtained from a subject, serves as a reliable indicator for predicting blood pressure (BP). Methods The proposed methodology involves employing Continuous Wavelet Transform (CWT) scalograms of the PPG signal as inputs for the CNN. Two distinct architectures for BP estimation are explored: one employing regression with a fully connected neural network and another utilizing CNN with Support Vector Regression (SVR). Results The results demonstrate superior BP estimation with the CNN-SVR architecture. With the CNN-SVR model, the Systolic Blood Pressure (SBP) and Diastolic Blood Pressure (DBP) are estimated with a Root Mean Square Error (RMSE) of 6.7 mmHg and 8.9 mmHg, respectively. Conclusion The proposed CNN-SVR model gives 52% better estimation error performance in SBP estimation compared to a machine learning model reported in a previous work.

Quantifying spatial interaction centrality in urban population mobility: A mobility feature- and network topology-based locational measure

Spatial interaction centrality reflects the relative importance of population mobility within a location in urban population mobility. Population mobility networks visually represent urban population mobility, with mobility features and network topology contributing to the quantification of spatial interaction centrality of locations (i.e., geographical nodes). However, existing centrality measures rarely consider mobility features and network topology simultaneously. Centrality quantification also ignores the differences in distance effects between long- and short-distance trips. These factors have led to the inaccurate quantification of centrality. We propose an algorithm called k-dis-weight-shell that quantifies the spatial interaction centrality of geographical nodes at different spatiotemporal scales. Considering the different effects of distance on long- and short-distance trips, we use a spatial continuous wavelet transformation to estimate the radiation radius of geographical nodes. Then, by combining network topology with mobility features (mobility distance and flow), the algorithm transforms them into a ranked order of spatial interaction centrality. Tested in Wuhan and Chengdu, our algorithm outperforms six existing benchmarks. For cases in urban planning and epidemic management, results show that k-dis-weight-shell effectively distinguishes similarities and differences between the distribution of population mobility's spatial interaction centrality and the urban center hierarchy at a coarse spatiotemporal scale. Additionally, it reveals a double wave phenomenon of spatiotemporal correlation between population mobility and COVID-19 transmission before and after lockdown at a fine spatiotemporal scale.

Continuous Wavelet Transform Analysis of Climate Variability, Resiliency, and Restoration Strategies in Mesohaline Tidal Creeks

This research article employs the continuous wavelet transform analysis to identify the climatological effects among various water quality parameters to identify the successfulness of upland stream restoration on the receiving mesohaline tidal creeks. Estuaries and their corresponding tidal creeks have been impacted by human anthropogenic influences for decades, allowing a variety of restoration practices to be implemented in upland streams. In the face of climate variability and continuous human development pressures, this research performs statistical analysis and a wavelet coherence on, before, and after stream restoration for water quality changes in Chesapeake Bay’s tidal tributaries in the Lower Western Shore to identify if the restoration strategies have been effective in the mesohaline tidal creeks. Statistical analysis showed that currently, the receiving tidal basins are not seeing the required positive improvements in water quality after years of upland stream restoration. Compounding this is the fact climate variability cannot be ignored. Results indicate that the North Atlantic Oscillation (NAO) has significant wavelet coherence with bottom dissolved oxygen, precipitation, and nutrients. This suggests that current restoration efforts may not be able to keep up with climate variability, and other techniques (restoration or policies) may need to be implemented.

Deep Learning-Based Flood Detection for Bridge Monitoring Using Accelerometer Data

Flooding and consequential scouring are the primary causes of bridge failures, making the detection of such events crucial for structural safety. This study investigates the characteristics of accelerometer data from bridge pier vibrations and proposes a flood detection method with deep learning-based models based on ResNet18 and 1D Convolution architectures. These models were comprehensively evaluated for (1) detecting vehicles passing on bridges and (2) detecting flood events based on axis-specific accelerometer data under various traffic conditions. Continuous Wavelet Transform (CWT) was employed to convert the accelerometer data into richer time-frequency representations, enhancing the detection of passing vehicles. Notably, when vehicles are passing over bridges, the vertical direction exhibits a magnified and more sustained energy distribution across a wider frequency range. Additionally, under flooding conditions, time-frequency representations from the bridge direction reveal a significant increase in energy intensity and continuity compared with non-flooding conditions. For detection of vehicles passing, ResNet18 outperformed the 1D Convolution model, achieving an accuracy of 97.2% compared with 91.4%. For flood detection without vehicles passing, the two models performed similarly well, with accuracies of 97.3% and 98.3%, respectively. However, in scenarios with vehicles passing, the 1D Convolution model excelled, achieving an accuracy of 98.6%, significantly higher than that of ResNet18 (81.6%). This suggests that high-frequency signals, such as vertical vibrations induced by passing vehicles, are better captured by more complex representations (CWT) and models (e.g., ResNet18), while relatively low-frequency signals, such as longitudinal vibrations caused by flooding, can be effectively captured by simpler 1D Convolution over the original signals. Consequentially, the two model types are deployed in a pipeline where the ResNet18 model is used for classifying whether vehicles are passing the bridge, followed by two 1D Convolution models: one trained for detecting flood events under vehicles-passing conditions and the other trained for detecting flood events under no-vehicles-passing conditions. This hierarchical approach provides a robust framework for real-time monitoring of bridge response to vehicle passing and timely warning of flood events, enhancing the potential to reduce bridge collapses and improve public safety.

Research on vibration signal decomposition of cracked rotor-bearing system with double-disk based on CEEMDAN-CWT

In the actual working process, the source of vibration signal is not only the rotor itself, so the detected vibration signal will become complicated. This complex signal makes it difficult to accurately measure the existence of crack. In this paper, a novel method, which includes complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and continuous wavelet transform (CWT), is proposed to analyze the cracked rotor-rolling bearing system. The CEEMDAN-CWT successfully separates the vibration signal of the rotor itself from the original signal and provides results similar to the simulation signal. At the speed below 2000 rpm, the 2X frequency difference between cracked rotor and healthy rotor in CEEMDAN-CWT spectrum is about 1, while the difference of FFT spectrum of original signal is about 0.6, which shows the superiority of the novel method in extracting rotor vibration signals from complex vibration signals.

Sugarcane disease recognition through visible and near-infrared spectroscopy using deep learning assisted continuous wavelet transform-based spectrogram

Utilizing visible and near-infrared (Vis-NIR) spectroscopy in conjunction with chemometrics methods has been widespread for identifying plant diseases. However, a key obstacle involves the extraction of relevant spectral characteristics. This study aimed to enhance sugarcane disease recognition by combining convolutional neural network (CNN) with continuous wavelet transform (CWT) spectrograms for spectral features extraction within the Vis-NIR spectra (380–1400 nm) to improve the accuracy of sugarcane diseases recognition. Using 130 sugarcane leaf samples, the obtained one-dimensional CWT coefficients from Vis-NIR spectra were transformed into two-dimensional spectrograms. Employing CNN, spectrogram features were extracted and incorporated into decision tree, K-nearest neighbour, partial least squares discriminant analysis, and random forest (RF) calibration models. The RF model, integrating spectrogram-derived features, demonstrated the best performance with an average precision of 0.9111, sensitivity of 0.9733, specificity of 0.9791, and accuracy of 0.9487. This study may offer a non-destructive, rapid, and accurate means to detect sugarcane diseases, enabling farmers to receive timely and actionable insights on the crops’ health, thus minimizing crop loss and optimizing yields.

Research on a Bearing Fault Diagnosis Method Based on an Improved Wasserstein Generative Adversarial Network

In this paper, an advanced Wasserstein generative adversarial network (WGAN)-based bearing fault diagnosis approach is proposed to bolster the diagnostic efficacy of conventional WGANs and tackle the challenge of selecting optimal hyperparameters while reducing the reliance on sample labeling. Raw vibration signals undergo continuous wavelet transform (CWT) processing to generate time–frequency images that align with the model’s input dimensions. Subsequently, these images are incorporated into a region-based fully convolutional network (R-FCN), substituting the traditional discriminator for feature capturing. The WGAN model is refined through the utilization of the Bayesian optimization algorithm (BOA) to optimize the generator and discriminator’s semi-supervised learning loss function. This approach is verified using the Case Western Reserve University (CWRU) dataset and a centrifugal pump failure experimental dataset. The results showed improvements in data input generalization and fault feature extraction capabilities. By avoiding the need to label large quantities of sample data, the diagnostic accuracy was improved to 98.9% and 97.4%.

Continuous Wavelet Transform Peak-Seeking Attention Mechanism Conventional Neural Network: A Lightweight Feature Extraction Network with Attention Mechanism Based on the Continuous Wave Transform Peak-Seeking Method for Aero-Engine Hot Jet Fourier Transform Infrared Classification

Continuous Wavelet Transform Peak-Seeking Attention Mechanism Conventional Neural Network: A Lightweight Feature Extraction Network with Attention Mechanism Based on the Continuous Wave Transform Peak-Seeking Method for Aero-Engine Hot Jet Fourier Transform Infrared Classification

A Novel Transformer Network Based on Cross–Spatial Learning and Deformable Attention for Composite Fault Diagnosis of Agricultural Machinery Bearings

Diagnosing agricultural machinery faults is critical to agricultural automation, and identifying vibration signals from faulty bearings is important for agricultural machinery fault diagnosis and predictive maintenance. In recent years, data–driven methods based on deep learning have received much attention. Considering the roughness of the attention receptive fields in Vision Transformer and Swin Transformer, this paper proposes a Shift–Deformable Transformer (S–DT) network model with multi–attention fusion to achieve accurate diagnosis of composite faults. In this method, the vibration signal is first transformed into a time–frequency graph representation through continuous wavelet transform (CWT); secondly, dilated convolutional residual blocks and efficient attention for cross–spatial learning are used for low–level local feature enhancement. Then, the shift window and deformable attention are fused into S–D Attention, which has a more focused receptive field to learn global features accurately. Finally, the diagnosis result is obtained through the classifier. Experiments were conducted on self–collected datasets and public datasets. The results show that the proposed S–DT network performs excellently in all cases. With a slight decrease in the number of parameters, the validation accuracy improves by more than 2%, and the training network has a fast convergence period. This provides an effective solution for monitoring the efficient and stable operation of agricultural automation machinery and equipment.