Search Results (94)

The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed phase shift, information loss for real-valued spectral components, and the absence of tunable parameters. The graph fractional Fourier transform introduces domain flexibility through a fractional order parameter $\alpha$ but does not resolve the issues of phase rigidity and information loss. Inspired by the dual-parameter fractional Hilbert transform (FRHT) in classical signal processing, we propose the graph FRHT (GFRHT). The GFRHT incorporates a dual-parameter framework: the fractional order $\alpha$ enables analysis across arbitrary fractional domains, interpolating between vertex and spectral spaces, while the angle parameter $\beta$ provides adjustable phase shifts and a non-zero real-valued response ($cos\beta$) for real eigenvalues, thereby eliminating information loss. We formally define the GFRHT, establish its core properties, and design a method for graph analytic signal construction, enabling precise envelope extraction and demodulation. Experiments on anomaly identification, speech classification and edge detection demonstrate that GFRHT outperforms GHT, offering greater flexibility and superior performance in graph signal processing. Full article

Micro-expression recognition (MER) is challenged by a brief duration, low intensity, and heterogeneous spatial frequency patterns. This study introduces a novel MER architecture that reduces computational cost by fine-tuning a large feature extraction model with LoRA, while integrating frequency-domain transformation and graph-based temporal modeling to minimize preprocessing requirements. A Spatial Frequency Adaptive (SFA) module decomposes high- and low-frequency information with dynamic weighting to enhance sensitivity to subtle facial texture variations. A Dynamic Graph Attention Temporal (DGAT) network models video frames as a graph, combining Graph Attention Networks and LSTM with frequency-guided attention for temporal feature fusion. Experiments on the SAMM, CASME II, and SMIC datasets demonstrate superior performance over existing methods. On the SAMM 5-class setting, the proposed approach achieves an unweighted F1 score (UF1) of 81.16% and an unweighted average recall (UAR) of 85.37%, outperforming the next best method by 0.96% and 2.27%, respectively. Full article

Parkinson’s Disease (PD) is a neurodegenerative disorder in which gait abnormalities serve as key indicators of motor impairment and disease progression. Although wearable sensor-based gait analysis has advanced, existing methods still face challenges in modeling multi-sensor spatial relationships, extracting adaptive multi-scale temporal features, and effectively integrating time–frequency information. To address these issues, this paper proposes a multi-sensor gait neural network that integrates biomechanical priors with time–frequency collaborative learning for the automatic assessment of PD gait severity. The framework consists of three core modules: (1) BGS-GAT (Biomechanics-Guided Graph Attention Network), which constructs a sensor graph based on plantar anatomy and explicitly models inter-regional force dependencies via graph attention; (2) AMS-Inception1D (Adaptive Multi-Scale Inception-1D), which employs dilated convolutions and channel attention to extract multi-scale temporal features adaptively; and (3) TF-Branch (Time–Frequency Branch), which applies Real-valued Fast Fourier Transform (RFFT) and frequency-domain convolution to capture rhythmic and high-frequency components, enabling complementary time–frequency representation. Experiments on the PhysioNet multi-channel foot pressure dataset demonstrate that the proposed model achieves 0.930 in accuracy and 0.925 in F1-score for four-class severity classification, outperforming state-of-the-art deep learning models. Full article

This paper presents new fast algorithms for the type VII discrete cosine transform (DCT-VII) applied to input data sequences of lengths ranging from 3 to 8. Fast algorithms for small-sized trigonometric transforms enable the processing of small data blocks in image and video coding with low computational complexity. To process the information in image and video coding standards, the fast DCT-VII algorithms can be used, taking into account the relationships between the DCT-VII and the type II discrete cosine transform (DCT-II). Additionally, such algorithms can be used in other digital signal processing tasks as components for constructing algorithms for large-sized transforms, leading to reduced system complexity. Existing fast odd DCT algorithms have been designed using relationships among discrete cosine transforms (DCTs), discrete sine transforms (DSTs), and the discrete Fourier transform (DFT); among different types of DCTs and DSTs; and between the coefficients of the transform matrix. However, these algorithms require a relatively large number of multiplications and additions. The process of obtaining such algorithms is difficult to understand and implement. To overcome these shortcomings, this paper applies a structural approach to develop new fast DCT-VII algorithms. The process begins by expressing the DCT-VII as a matrix-vector multiplication, then reshaping the block structure of the DCT-VII matrix to align with matrix patterns known from the basic papers in which the structural approach was introduced. If the matrix block structure does not match any known pattern, rows and columns are reordered, and sign changes are applied as needed. If this is insufficient, the matrix is decomposed into the sum of two or more matrices, each analyzed separately and transformed similarly if required. As a result, factorizations of DCT-VII matrices for different input sequence lengths are obtained. Based on these factorizations, fast DCT-VII algorithms with reduced arithmetic complexity are constructed and presented with pseudocode. To illustrate the computational flow of the resulting algorithms and their modular design, which is suitable for VLSI implementation, data-flow graphs are provided. The new DCT-VII algorithms reduce the number of multiplications by approximately 66% compared to direct matrix-vector multiplication, although the number of additions decreases by only about 6%. Full article

To address the limitations of one-dimensional vibration signals in convolutional neural networks and the insufficient feature extraction capability of traditional single data processing methods under complex operating conditions, this paper proposes a novel fault diagnosis method that integrates dual-graph transformation and an improved residual network. Firstly, the one-dimensional vibration signals are converted into time–frequency representations using the short-time Fourier transform (STFT) and the synchrosqueezed wavelet transform (SWT). Subsequently, these dual-domain representations are fed in parallel into a customized parallel two-dimensional residual network (P2D-Sk-ResNet), which incorporates the selective kernel network (SKNet) mechanism into a ResNet architecture. This design enables adaptive multi-scale feature extraction. Finally, the features from the fully connected layer are classified using the extreme gradient boosting (XGBoost) algorithm to complete the fault diagnosis task. Comparative experiments demonstrate that the proposed STFT-SWT-P2D-Sk-ResNet-XGBoost achieves a diagnostic accuracy of 98.51% under constant load conditions, significantly outperforming several baseline models. Furthermore, the model exhibits superior generalization capability under varying load conditions and strong robustness in noisy environments. The proposed method provides a valuable and practical reference for intelligent fault diagnosis in industrial applications. Full article

In this study, we propose a simple and effective method for gas analysis by establishing a correlation between residual gas analyzer (RGA) intensity and gas concentration. To achieve this, we focused on CF₄ and NF₃, two high-global warming potential (GWP) gases commonly used in industrial applications. The experiment was conducted in four key steps: identifying gas species using optical emission spectroscopy (OES), calibrating RGA with a quadrupole mass spectrometer (QMS), constructing a five-point calibration graph to correlate RGA and Fourier-transform infrared spectroscopy (FT-IR) data, and estimating the concentration of unknown samples using the calibration graph. The results under plasma-on conditions demonstrated correlation and accuracy, confirming the reliability of our approach. In other words, the method effectively captured the relationship between RGA intensity and gas concentration, providing valuable insights into concentration trends. Thus, our approach serves as a useful tool for estimating gas concentrations and understanding the correlation between RGA intensity and gas composition. Full article

CFRP is extensively utilized in the manufacturing of aerospace equipment owing to its distinctive properties, and hole-making processing continues to be the predominant processing method for this material. However, due to the anisotropy of CFRP, in its processing process, processing damage appears easily, such as stratification, fiber tearing, burrs, etc. These damages will seriously affect the performance of CFRP components in the service process. This work employs acoustic emission (AE) and infrared thermography (IT) techniques to analyze the characteristics of AE signals and temperature signals generated during the CFRP drilling process. Fast Fourier transform (FFT) and short-time Fourier transform (STFT) are used to process the collected AE signals. And in combination with the actual damage morphology, the material removal behavior during the drilling process and the AE signal characteristics corresponding to processing defects are studied. The results show that the time-frequency graph and root mean square (RMS) curve of the AE signal can accurately distinguish the different stages of the drilling process. Through the analysis of the frequency domain characteristics of the AE signal, the specific frequency range of the damage mode of the CFRP composite material during drilling is determined. This paper aims to demonstrate the feasibility of real-time monitoring of the drilling process. By analyzing the relationship between the RMS values of acoustic emission signals and hole surface topography under different drilling parameters, it provides a new approach for the research on online monitoring of CFRP drilling damage and improvement of CFRP machining quality. Full article

Rolling bearings are prone to failure, meaning that research on intelligent fault diagnosis is crucial in relation to this key transmission component in rotating machinery. The application of deep learning (DL) has significantly advanced the development of intelligent fault diagnosis. This paper proposes a novel method for rolling bearing fault diagnosis based on the fractional constant Q non-stationary Gabor transform (FCO-NSGT) and VMamba-Conv. Firstly, a rolling bearing fault experimental platform is established and the vibration signals of rolling bearings under various working conditions are collected using an acceleration sensor. Secondly, a kurtosis-to-entropy ratio (KER) method and the rotational kernel function of the fractional Fourier transform (FRFT) are proposed and applied to the original CO-NSGT to overcome the limitations of the original CO-NSGT, such as the unsatisfactory time–frequency representation due to manual parameter setting and the energy dispersion problem of frequency-modulated signals that vary with time. A lightweight fault diagnosis model, VMamba-Conv, is proposed, which is a restructured version of VMamba. It integrates an efficient selective scanning mechanism, a state space model, and a convolutional network based on SimAX into a dual-branch architecture and uses inverted residual blocks to achieve a lightweight design while maintaining strong feature extraction capabilities. Finally, the time–frequency graph is inputted into VMamba-Conv to diagnose rolling bearing faults. This approach reduces the number of parameters, as well as the computational complexity, while ensuring high accuracy and excellent noise resistance. The results show that the proposed method has excellent fault diagnosis capabilities, with an average accuracy of 99.81%. By comparing the Adjusted Rand Index, Normalized Mutual Information, F1 Score, and accuracy, it is concluded that the proposed method outperforms other comparison methods, demonstrating its effectiveness and superiority. Full article

Accurate forecasting of tropical cyclone (TC) tracks is critical for disaster preparedness and risk mitigation. While traditional numerical weather prediction (NWP) systems have long served as the backbone of operational forecasting, they face limitations in computational cost and sensitivity to initial conditions. In recent years, deep learning (DL) has emerged as a promising alternative, offering data-driven modeling capabilities for capturing nonlinear spatiotemporal patterns. This paper presents a comprehensive review of DL-based approaches for TC track forecasting. We categorize all DL-based TC tracking models according to the architecture, including recurrent neural networks (RNNs), convolutional neural networks (CNNs), Transformers, graph neural networks (GNNs), generative models, and Fourier-based operators. To enable rigorous performance comparison, we introduce a Unified Geodesic Distance Error (UGDE) metric that standardizes evaluation across diverse studies and lead times. Based on this metric, we conduct a critical comparison of state-of-the-art models and identify key insights into their relative strengths, limitations, and suitable application scenarios. Building on this framework, we conduct a critical cross-model analysis that reveals key trends, performance disparities, and architectural tradeoffs. Our analysis also highlights several persistent challenges, such as long-term forecast degradation, limited physical integration, and generalization to extreme events, pointing toward future directions for developing more robust and operationally viable DL models for TC track forecasting. To support reproducibility and facilitate standardized evaluation, we release an open-source UGDE conversion tool on GitHub. Full article

To address the challenge of incomplete fault feature extraction in rolling bearing fault diagnosis under small-sample conditions, this paper proposes a Temporal-Graph Convolutional Fusion Network (T-GCFN). The method enhances diagnostic robustness through collaborative extraction and dynamic fusion of features from time-domain and frequency-domain branches. First, Variational Mode Decomposition (VMD) was employed to extract time-domain Intrinsic Mode Functions (IMFs). These were then input into a Temporal Convolutional Network (TCN) to capture multi-scale temporal dependencies. Simultaneously, frequency-domain features obtained via Fast Fourier Transform (FFT) were used to construct a K-Nearest Neighbors (KNN) graph, which was processed by a Graph Convolutional Network (GCN) to identify spatial correlations. Subsequently, a channel attention fusion layer was designed. This layer utilized global max pooling and average pooling to compress spatio-temporal features. A shared Multi-Layer Perceptron (MLP) then established inter-channel dependencies to generate attention weights, enhancing critical features for more complete fault information extraction. Finally, a SoftMax classifier performed end-to-end fault recognition. Experiments demonstrated that the proposed method significantly improved fault recognition accuracy under small-sample scenarios. These results validate the strong adaptability of the T-GCFN mechanism. Full article

This paper introduces a novel approach to hand motion gesture recognition by integrating the Fourier transform with hypergraph convolutional networks (HGCNs). Traditional recognition methods often struggle to capture the complex spatiotemporal dynamics of hand gestures. HGCNs, which are capable of modeling intricate relationships among joints, are enhanced by Fourier transform to analyze gesture features in the frequency domain. A hypergraph is constructed to represent the interdependencies among hand joints, allowing for dynamic adjustments based on joint movements. Hypergraph convolution is applied to update node features, while the Fourier transform facilitates frequency-domain analysis. The T-Module, a multiscale temporal convolution module, aggregates features from multiple frames to capture gesture dynamics across different time scales. Experiments on the dynamic hypergraph (DHG14/28) and shape retrieval contest (SHREC’17) datasets demonstrate the effectiveness of the proposed method, achieving accuracies of 96.4% and 97.6%, respectively, and outperforming traditional gesture recognition algorithms. Ablation studies further validate the contributions of each component in enhancing recognition performance. Full article

The application of ceramic particle-reinforced metal matrix composites (CPRMMCs) in the nuclear power sector is primarily dependent on their mechanical and thermal properties. A comprehensive understanding of the structure–property (SP) linkages between microstructures and macroscopic properties is critical for optimizing material properties. However, traditional studies on SP linkages generally rely on experimental methods, theoretical analysis, and numerical simulations, which are often associated with high time and economic costs. To address this challenge, this study proposes a novel method based on Materials Informatics (MI), combining the finite element method (FEM), graph Fourier transform, principal component analysis (PCA), and machine learning models to establish the SP linkages between the microstructure and thermodynamic properties of CPRMMCs. Specifically, FEM is used to model the microstructures of CPRMMCs with varying particle volume fractions and sizes, and their elastic modulus, thermal conductivity, and coefficient of thermal expansion are computed. Next, the statistical features of the microstructure are captured using graph Fourier transform based on two-point spatial correlations, and PCA is applied to reduce dimensionality and extract key features. Finally, a polynomial kernel support vector regression (Poly-SVR) model optimized by Bayesian methods is employed to establish the nonlinear relationship between the microstructure and thermodynamic properties. The results show that this method can effectively predict FEM results using only 5–6 microstructure features, with the R² values exceeding 0.91 for the prediction of thermodynamic properties. This study provides a promising approach for accelerating the innovation and design optimization of CPRMMCs. Full article

Coal-fired boilers significantly contribute to nitrogen oxides (NOx) emissions, posing critical environmental and health risks. Effective prediction of NOx emissions is essential for optimizing control measures and achieving stringent emission standards. This study applies a Multiscale Graph Convolutional Network (MSGNet) designed to capture multiscale dynamic relationships among operational parameters of a 660 MW coal-fired boiler. MSGNet employs Fast Fourier Transform (FFT) for automatic periodic pattern recognition, adaptive graph convolution for dynamic inter-variable relationships, and a multihead attention mechanism to assess temporal dependencies comprehensively. Compared with the existing state of the art, the proposed structure achieves a good performance of 2.176 mg/m³, 1.652 mg/m³, and 0.988 of RMSE, MAE, and $R^2$. Experimental evaluations demonstrate that MSGNet achieves superior predictive performance compared with traditional methods such as LSTM, BiLSTM, and GRU. Results underscore MSGNet’s robust accuracy, stability, and generalization capability, highlighting its potential for advanced emission control and environmental management applications in thermal power generation. Full article

In this paper, a numerical study of two-phase flow instability in parallel rectangular channels is presented. Using the homogeneous flow model, marginal stability boundaries (MSBs) are derived in the parameter space defined by the phase change number (N_pch) and subcooling number (N_sub) under various operating conditions. Comparison with experimental data shows that the model predicts stability trends with a deviation of ±12.5%. The study reveals that, under constant mass flux conditions, stability decreases as the equivalent diameter (De) of the channels increases. Additionally, the exit area ratio of the two parallel tubes has minimal effect on the MSB, indicating that exit geometry does not significantly influence system stability. However, an increase in the inlet area ratio, from 0.1 to 1, reduces system stability, suggesting that larger inlet areas relative to tube cross-sectional areas may lead to greater flow disturbances, thereby decreasing stability. Moreover, increasing the length of the tubes enhances system stability, which may be attributed to the extended development length allowing for dissipation of flow disturbances. The study further demonstrates that higher flow rates, between 0.15 kg/s and 0.25 kg/s, enhance stability, while increasing the outlet flow resistance coefficient reduces stability. Conversely, increasing the inlet flow resistance coefficient improves stability. At system pressures of 3 MPa, 6 MPa, and 9 MPa, it is observed that higher pressures shift the boundary of complete vaporization (X_e = 1) to the left on the N_pch and N_sub graph, reducing the region susceptible to instability. The study also employs Fast Fourier Transform (FFT) analysis to identify peak frequencies across different parameter ranges. By examining the stability map and frequency spectra, the study provides deeper insights into two-phase flow instabilities in parallel channels. Full article

The wet chemical auto-combustion technique was used to synthesize barium zirconate ceramic (BaZrO₃). Many strategies were applied to regulate the functional properties of the perovskite-structured sample which was calcinated at 800 °C for 9 h. A Fourier-transform IR spectrometer, an X-ray diffractometer, a scanning electron microscope (SEM)-EDAX, an LCR meter, and a UV–visible spectrometer were employed to study the structural, morphological, optical, and electrical properties of the prepared barium zirconate sample. Using data derived from XRD, the perovskite phase was confirmed, and the average value of the crystallite size was found to be 17.68 nm. The lattice constant, crystallinity, unit cell volume, tolerance factor, and X-ray density were also calculated. SEM-EDAX confirmed the elemental composition of the product and verified that it contained only the major constituents (Ba, Zr, and O). The vibrational modes of the prepared sample were investigated using FTIR in wavelengths ranging from 400 to 4000 cm⁻¹. Energy bandgap was observed using Tauc’s plot, where a graph was prepared for photon energy (hυ) and (αhυ)². The powder sample was blended with PVA and made into pellets of 13 mm diameter using a pelletizer to explore dielectric parameters like the dielectric constant, while the loss factor was recorded at a frequency ranging from 100 Hz to 4 MHz at room temperature. With its high dielectric constant and low dielectric loss factor, barium zirconate ceramic stands as an excellent material for several microwave applications. Full article