Wavelet Reconstruction Research Articles

Study on Fluctuating Wind Characteristics and Non-Stationarity at U-Shaped Canyon Bridge Site

To investigate the non-stationary characteristics of the wind field at the U-shaped canyon bridge site and its impact on fluctuating wind characteristics, a wind observation tower was installed near a cable-stayed bridge. The Augmented Dickey–Fuller (ADF) test was employed to assess the stationarity of wind speed series, while the discrete wavelet transform (DWT) was applied to reconstruct the time-varying mean wind and analyze its effect on fluctuating wind characteristics. Results indicate that wind speeds in this region exhibit bimodal distribution characteristics, with the Weibull-Gamma mixed distribution model providing the best fit. The proportion of non-stationary samples increases with height. Autocorrelation function (ACF), partial autocorrelation function (PACF) tests, and power spectral density (PSD) analysis determined the optimal wavelet decomposition level for wind speed in this region. Analysis of non-stationary samples using db10 wavelet reconstruction reveals that the stationary wind speed model overestimates turbulence intensity but underestimates the turbulence integral scale. The downwind spectrum deviates from the Kaimal spectrum in both low- and high-frequency bands, whereas the vertical spectrum aligns well with the Panofsky spectrum. The findings demonstrate that the wavelet reconstruction method more accurately captures fluctuating wind characteristics under the complex terrain conditions of this canyon area.

Enhanced heart sound anomaly detection via WCOS: a semi-supervised framework integrating wavelet, autoencoder and SVM

Anomaly detection is a typical binary classification problem under the condition of unbalanced samples, which has been widely used in various fields of data mining. For example, it can help detect heart murmurs when the heart is structurally abnormal, to tell if a newborn has congenital heart disease. Due to the low time and high efficiency, most work focuses on the semi- supervised anomaly detection method. However, the anomaly detection effect of this method is not high because of massive data with uneven samples and different noise. To improve the accuracy of anomaly detection under unbalanced sample conditions, we propose a new semi-supervised anomaly detection method (WCOS) based on semi-supervised clustering, which combines wavelet reconstruction, convolutional autoencoder, and one classification support vector machine. In this way, we can not only distinguish a small proportion of abnormal heart sounds in the huge data scale but also filter the noise through the noise reduction network, thus significantly improving the detection accuracy. In addition, we evaluated our method using real datasets. When the noise of sigma = 0.5, the AUC standard deviation of the WR-CAE-OCSVM is 19.2, 54.1, and 29.8% lower than that of WR-OCSVM, CAE-OCSVM and OCSVM, respectively. The results confirmed the higher accuracy of anomaly detection in WCOS compared to other state-of-the-art methods.

LCRTR-Net: A low-cost real-time recognition network for rail corrugation in railway transportation

Rail corrugation has a significant impact on the safety of high-speed railway operations, making its identification particularly important. Traditional manual inspection methods are infeasible for large-scale identification within limited time frames, while existing methods based on machine vision or axle box acceleration face challenges such as high costs, complex equipment installation and maintenance, as well as difficulties in achieving real-time performance. To address these challenges, this study proposes an innovative low-cost real-time recognition network (LCRTR-Net), which utilizes accelerometers installed on the underside of the train body and combines wavelet packet decomposition with dilated causal convolution in a residual neural network. Specifically, the approach first extracts the latent features of train body acceleration caused by rail corrugation through wavelet packet decomposition and reconstruction. Next, dilated causal convolution is employed to capture the temporal causal relationships and long-term dependencies of these latent features. Finally, the integration of residual connections further enhances the feature extraction performance and computational efficiency of LCRTR-Net. Experimental results demonstrate that LCRTR-Net exhibits significant generalization ability and real-time performance, achieving an average recognition accuracy exceeding 97.0%, with a recognition time of only 0.17 ms per rail corrugation sample, significantly outperforming existing rail corrugation recognition methods. This indicates that LCRTR-Net has broad application potential in practical railway operations. Future research directions will focus on unsupervised or few-shot learning algorithms and multi-sensor integration to further improve recognition accuracy and real-time performance, promoting the practical application of this technology.

Combined acoustic emission and electrochemical methods for analyzing the uniform corrosion behavior of X90 high-grade steel pipelines

Long-distance, large-diameter, and high-pressure pipelines represent the future of oil and gas pipeline construction. X90 pipeline steel is expected to become the standard steel due to its high transmission efficiency and lower cost in the future, yet corrosion poses the most significant challenge to the development of high-strength pipelines. This study focuses on monitoring the uniform corrosion process of X90 steels using acoustic emission (AE) and electrochemical testing systems. The AE signals from corrosion were processed using wavelet de-noising, decomposition, and reconstruction to extract signal characteristics. Experimental results reveal that the corrosion process of X90 steel can be categorized into three stages: initial metal dissolution, corrosion product accumulation, and corrosion stabilization. Signal activity and strength follow normal distributions throughout these stages. During metal dissolution and corrosion stabilization, AE signals exhibit a frequency range of 100–200 kHz with relatively low amplitude. Conversely, during corrosion product accumulation, signals display a narrow frequency range with higher amplitudes, typically around 3 × 10-4V. Moreover, the appearance of a double-peak signal suggests the presence of two distinct AE sources.

The edge artifact extraction method for Si3N4 ceramic bearing rolling element microcracks characterization

Aiming at the problem that the edge artifacts of Si3N4 ceramic bearing rolling element microcracks have low contrast, contain noise, and easily merge with the background, making it difficult to segment. A method based on 2D discrete wavelet transform and Otsu threshold segmentation is designed to achieve the extraction of microcrack edge artifact features. Wavelet decomposition is used to remove noise, while wavelet reconstruction features are used to restore lost details. Creation of 2D discrete wavelet transform functional equations combining wavelet reconstruction and wavelet decomposition to improve contrast and eliminate noise in images featuring edge artifacts. For the problem of feature edge artifacts that are difficult to remove, the threshold segmentation function equation is designed to maximize the interclass variance, and the optimal threshold value is selected to remove the edge artifacts. The experimental results show that the average PSNR of the Si3N4 ceramic bearing rolling body point, line, and surface microcrack edge artifact feature images enhanced by the method in this paper is close to 62.69 dB, and the average SSIM is about 0.77. The method in this paper improves the contrast of microcrack edge artifact features of Si3N4 ceramic bearing rolling bodies and makes the feature extraction effect of point, line, and surface microcrack edge artifacts more complete.

A Novel Fault Diagnosis Method for Rolling Bearings Based on Multi-Domain Adaptation Neural Network

In recent years, data-driven approaches have shown promise in fault diagnosis. However, in practical industrial applications, challenges such as discrepancies between source domain and target domain data distributions, coupled with limited labeled fault data, have hindered the performance of traditional domain adaptation algorithms in bearing fault diagnosis. To address this issue, this study introduces a novel method based on MDANN (Multi Domain Adaptation Neural Network) for diagnosing rolling bearing faults using unlabeled data. Initially, the raw vibration signals are preprocessed using wavelet packet decomposition and reconstruction (WPT), which helps minimize signal redundancy while preserving critical features. Following this, the multi-kernel maximum mean discrepancy (MK-MMD) algorithm is employed to compute the differences in input feature values, and the MDANN network parameters are adjusted via backpropagation, allowing the network to extract domain-invariant features. To ensure the unlabeled target domain data can be effectively used in training, a pseudo-labeling strategy is applied, where the label with the highest probability is treated as the true label, thereby enabling the model to learn from the target domain data and improve the acquisition of reliable diagnostic knowledge. The method is validated using two publicly available datasets, CWRU and PU, with experimental results demonstrating that it outperforms conventional domain adaptation techniques in terms of diagnostic accuracy. This indicates the proposed approach is highly effective in capturing transferable features and addressing the distributional differences between datasets.

Diagnosis of Schizophrenia Using EEG Sensor Data: A Novel Approach with Automated Log Energy-Based Empirical Wavelet Reconstruction and Cepstral Features.

Schizophrenia (SZ) is a severe mental disorder characterised by disruptions in cognition, behaviour, and perception, significantly impacting an individual's life. Traditional SZ diagnosis methods are labour-intensive and prone to errors. This study presents an innovative automated approach for detecting SZ acquired through electroencephalogram (EEG) sensor signals, aiming to improve diagnostic efficiency and accuracy. We utilised Fast Independent Component Analysis to remove artefacts from raw EEG sensor data. A novel Automated Log Energy-based Empirical Wavelet Reconstruction (ALEEWR) technique was introduced to reconstruct decomposed modes based on their variability, ensuring effective extraction of meaningful EEG signatures. Cepstral-based features-cepstral activity, cepstral mobility, and cepstral complexity-were used to capture the power, rate of change, and irregularity of the cepstrum of preprocessed EEG signals. ANOVA-based feature selection was applied to refine these features before classification using the K-Nearest Neighbour (KNN) algorithm. Our approach achieved an exceptional accuracy of 99.4%, significantly surpassing previous methods. The proposed ALEEWR and cepstral analysis demonstrated high precision, sensitivity, and specificity in the automated diagnosis of schizophrenia. This study introduces a highly accurate and efficient method for SZ detection using EEG technology. The proposed techniques offer significant improvements in diagnostic accuracy, with potential implications for enhancing SZ diagnosis and patient care through automated systems.

Research on capacitance-coupled electrical impedance imaging fusion algorithm based on wavelet transform.

Capacitively Coupled Electrical Impedance Tomography (CCEIT), as a new electrical tomography method, effectively overcomes the drawbacks of traditional electrical resistance tomography that requires direct contact with liquids, so as to achieve non-contact measurement. In order to make full use of the complete electrical impedance information (real and imaginary) obtained by CCEIT and further improve the quality of image reconstruction, an image fusion algorithm based on wavelet transform was proposed. First, the Landweber algorithm is used to image the real part information and the imaginary part information, and the wavelet transform algorithm is used to decompose the two images at multiple scales, in which the low-frequency coefficient is fused by the improved logic filter algorithm based on the adaptive threshold, the high-frequency coefficient is selected based on the absolute value maximum method for fusion, and finally, the fused image is obtained by wavelet reconstruction. Numerical simulations and experiments verify the feasibility of the proposed method, and the results show that the relative error is reduced by up to 17% and the correlation coefficient is increased by up to 10%.

WPConvNet: An Interpretable Wavelet Packet Kernel-Constrained Convolutional Network for Noise-Robust Fault Diagnosis.

Deep learning (DL) has present great diagnostic results in fault diagnosis field. However, the poor interpretability and noise robustness of DL-based methods are still the main factors limiting their wide application in industry. To address these issues, an interpretable wavelet packet kernel-constrained convolutional network (WPConvNet) is proposed for noise-robust fault diagnosis, which combines the feature extraction ability of wavelet bases and the learning ability of convolutional kernels together. First, the wavelet packet convolutional (WPConv) layer is proposed, and constraints are imposed to convolutional kernels, so that each convolution layer is a learnable discrete wavelet transform. Second, a soft threshold activation is proposed to reduce the noise component in feature maps, whose threshold is adaptively learned by estimating the standard deviation of noise. Third, we link the cascaded convolutional structure of convolutional neutral network (CNN) with wavelet packet decomposition and reconstruction using Mallat algorithm, which is interpretable in model architecture. Extensive experiments are carried out on two bearing fault datasets, and the results show that the proposed architecture outperforms other diagnosis models in terms of interpretability and noise robustness.

Bowel Sounds Detection Method Based on ResNet-BiLSTM and Attention Mechanism

Bowel sounds can reflect the movement and health status of the gastrointestinal tract. However, the traditional manual auscultation method has subjective deviation and is time-consuming and labor-intensive. In order to better assist doctors in diagnosing bowel sounds and improve the reliability and efficiency of bowel sound detection, this study proposed a deep neural network model that combines a residual neural network (ResNet), a bidirectional long short-term memory network (BiLSTM), and an attention mechanism. Firstly, a large number of labeled clinical data was collected using the self-developed multi-channel bowel sound acquisition system, and the multi-scale wavelet decomposition and reconstruction method was used to preprocess the bowel sounds. Then, log Mel spectrogram features were extracted and sent to the network for training. Finally, the performance and effectiveness of the model were evaluated and verified by 10-fold cross-validation and an ablation experiment. The experimental results showed that the precision, recall, and F 1 score of the model reached 83%, 76%, and 79%, respectively, and it could effectively detect bowel sound segments and locate their start and end times, performing better than previous algorithms. This algorithm can not only provide auxiliary information for doctors in clinical practice but also offer technical support for further analysis and research of bowel sounds.

Fault signature extraction of rolling bearings under variable speed via time–frequency overlap group sparse representation

The high-fidelity extraction of the nonperiodic fault transients of rolling bearings under variable speed is of significant importance, while still a challenge for early-stage fault diagnosis of major equipment such as aero engines and wind turbines. A method termed continuous symmetric Laplace wavelet transform (CSLWT) enhanced time–frequency overlap group sparse (OGS) representation is proposed in this paper. A symmetric Laplace mother wavelet function is proposed which could satisfy the admissibility condition of wavelet decomposition and reconstruction, upon which the CSLWT is fabricated and adopted as the sparse representation dictionary to match the nonperiodic fault transients. Since the decomposition coefficients of nonperiodic fault impulses via the CSLWT exhibit group sparsity on the time–frequency plane with unknown intervals, the time–frequency OGS model is adopted and then solved for extraction of the nonperiodic fault transients. Moreover, a data driven, multi-objective optimization strategy is presented for determining the hyper-parameters of the sparse model. The correlated kurtosis of angular envelope signal (CK-AE) and harmonic-to-noise energy ratio of the order spectrum (HNR-OS) are introduced as the optimization objectives, and the Pareto front is solved based on the NSGA-II algorithm, upon which the acceptable solutions set is chosen from the Pareto front, and the proper hyper-parameters are further determined via proposed normalized solutions distance density sorting of the acceptable solutions set. The performance of the proposed method is validated via processing both simulated and experimental vibration signals, as well as compared with some tradition fault diagnosis methods.

Short-Term Traffic Flow Prediction Based on Wavelet Analysis and XGBoost

Traffic flow prediction is of great significance for urban planning and alleviating traffic congestion. Due to the randomness and high volatility of urban road network short-term traffic flow, it is difficult for a single model to accurately estimate traffic flow and travel time. In order to obtain more ideal prediction accuracy, a combined prediction model based on wavelet decomposition and reconstruction (WDR) and the extreme gradient boosting (XGBoost) model is developed in this paper. Firstly, the Mallat algorithm is applied to perform multi-scale wavelet decomposition on the average travel time series of the original traffic data, and single branch reconstruction is performed on the components at each scale. Secondly, XGBoost is used to predict each reconstructed single-branch sequence, so as to obtain multiple sub-models, and the Bayesian algorithm is used to optimize the hyperparameters of the sub-models. Finally, the algebraic sum of the predicted values of all sub-models is used to obtain the overall traffic prediction result. To test the performance of the proposed model, actual traffic flow data has been collected from a certain link of the Brooklyn area in New York, USA. The performance of proposed WDR-XGBoost model has been compared with other existing machine learning models, e.g., support vector regression model (SVR) and single XGBoost model. Experimental findings demonstrated that the proposed WDR-XGBoost model performs better on multiple evaluation indicators and has significantly outperformed the other models in terms of accuracy and stability.

Multi-Scale Marine Object Detection in Side-Scan Sonar Images Based on BES-YOLO.

Aiming at the problem of low accuracy of multi-scale seafloor target detection in side-scan sonar images with high noise and complex background texture, a model for multi-scale target detection using the BES-YOLO network is proposed. First, an efficient multi-scale attention (EMA) mechanism is used in the backbone of the YOLOv8 network, and a bi-directional feature pyramid network (Bifpn) is introduced to merge the information of different scales, finally, a Shape_IoU loss function is introduced to continuously optimize the model and improve its accuracy. Before training, the dataset is preprocessed using 2D discrete wavelet decomposition and reconstruction to enhance the robustness of the network. The experimental results show that 92.4% of the mean average accuracy at IoU of 0.5 (mAP@0.5) and 67.7% of the mean average accuracy at IoU of 0.5 to 0.95 (mAP@0.5:0.95) are achieved using the BES-YOLO network, which is an increase of 5.3% and 4.4% compared to the YOLOv8n model. The research results can effectively improve the detection accuracy and efficiency of multi-scale targets in side-scan sonar images, which can be applied to AUVs and other underwater platforms to implement intelligent detection of undersea targets.

Information Entropy Analysis of a PIV Image Based on Wavelet Decomposition and Reconstruction.

In particle image velocimetry (PIV) experiments, background noise inevitably exists in the particle images when a particle image is being captured or transmitted, which blurs the particle image, reduces the information entropy of the image, and finally makes the obtained flow field inaccurate. Taking a low-quality original particle image as the research object in this research, a frequency domain processing method based on wavelet decomposition and reconstruction was applied to perform particle image pre-processing. Information entropy analysis was used to evaluate the effect of image processing. The results showed that useful high-frequency particle information representing particle image details in the original particle image was effectively extracted and enhanced, and the image background noise was significantly weakened. Then, information entropy analysis of the image revealed that compared with the unprocessed original particle image, the reconstructed particle image contained more effective details of the particles with higher information entropy. Based on reconstructed particle images, a more accurate flow field can be obtained within a lower error range.

Enhancing data sparsity in spectral signals using wavelet decomposition for improved compression and storage efficiency

Wavelet decomposition (WD) is integrated into the Compressive Sensing (CS) model to enhance data sparsity. This approach aims to ensure efficiency and quality in the received data after compression and reconstruction processes. The proposed WD-CS model is developed for reflected spectra signals from Fiber Bragg Gratings-based extensometers, which were subjected to induced deflections simulating the underground soil movement. WD decomposes the input signal before compressive measurement, followed by transferring and storing the compressed data in the cloud. The spectral data were reconstructed using Orthogonal Matching Pursuit (OMP) followed by wavelet reconstruction. The impact of wavelet decomposition on the quality of compression and reconstruction is assessed and compared against that of the standard CS model. The findings indicate that the WD-CS model can improve data sparsity by a factor of three and compressibility by a factor of ten without degenerating the reconstructed data quality. The error in the Bragg wavelength shift of the reconstructed spectra is minimal extracted using Pseudo-high Resolution Interrogation (PHRI) method. The proposed WD-CS model is useful in improving data compression for FBG spectra as well as storage efficiency, which make it potentially applicable in FBG-based sensor networks for long-term structural health monitoring applications.

Intelligent fault diagnosis and security early warning method of new power system based on system network situation

In the past few decades, China’s power demand has been increasing, and the power fiber plays a key role in ensuring the orderly dispatching of all links of the power system. The study used a wavelet decomposition and reconstruction method, which is a signal processing technique used to decompose complex optical power data into low-frequency and high-frequency signals with different frequency components. Through this decomposition, we can more clearly observe periodic fluctuations, trend changes, and noise components in optical power data. The study also examined different prediction models, including GRU, LSTM, ARMA), etc. The performance of these models in predicting optical power trends is then analyzed, taking into account their accuracy, stability, and computational efficiency. Finally, we carefully evaluated the GRU-ARMA combined prediction model and determined its superior performance in predicting optical power trends. The outcomes show that after adjusting the input data length of the gating cycle cell model and the relevant parameters of the autoregressive sliding mean model, the residual mean value was 0.0141. At the same time, the root mean square error calculated by the combined prediction model of the gating cycle unit-autoregressive moving mean model was 0.000618, which successfully improved the accuracy of predicting the optical power trend of power fiber. This research result provides an important reference for the aging state assessment of power fiber lines, and has an important practical application value for the maintenance of power fiber lines.

Generalized Shannon entropy sparse wavelet packet transform for fault detection of traction motor bearings in high-speed trains

An effective structural health monitoring method of traction motor bearings is a powerful guarantee for the safety operation of high-speed trains. However, it is exceptionally difficult to detect bearing fault characteristics from the vibration signals of traction motor bearings operating at high rotational speeds. In this scenario, a generalized Shannon entropy sparse wavelet packet transform (GSWPT) for fault detection of motor bearings is proposed in this paper. Firstly, a generalized Shannon entropy sparse regularization method is proposed to obtain sparse wavelet reconstruction coefficients by extending the definition of the Shannon information entropy, and the non-convex sparse regularization function is minimized by synergistic swarm optimization algorithm. Then, the wavelet node coefficients are weighted according to the second-order cyclostationarity index of the wavelet packet node to further enhance the sparsity of the reconstructed signal. Moreover, the optimal decomposition level of GSWPT is adaptively selected by the maximum sparsity and cyclostationarity criterion. Particularly, in order to verify the bearing fault detection performance of GSWPT in practical engineering, a bearing fault dynamic model of traction motor in high-speed train was established based on Hertz contact theory and the fourth-order Runge-Kutta method to obtain simulated data under strong Gaussian white noise, and a corresponding test platform was constructed to collect experimental data under different operating conditions. Finally, the applications on the simulated and experimental signals of traction motor bearings in high-speed trains demonstrate that GSWPT significantly outperforms the conventional wavelet packet transform, dual-tree complex wavelet packet transform, blind deconvolution, modal decomposition, and Infogram methods to some extent for fault detection.

The Optimization of LSTM Model by Wavelet Transform and Simulated Annealing Algorithm

The main objective of this paper is to study the integration of data processing methods and intelligent algorithms to optimize the results of LSTM prediction models. In this paper, continuous wavelet transform is used to clean and preprocess time series data and improve data quality. Wavelet reconstruction is used to restore the results. At the same time, the simulated annealing algorithm is introduced as an intelligent algorithm to search globally for the best solution to achieve the optimal prediction result. The application of this comprehensive approach can also improve the quality and precision of data analysis in various fields, such as the parameter estimation of pulse signals in physics. The core challenge of the research is to optimize the data prediction results, and for this purpose, a multi-level method of continuous wavelet transform, deep learning model (LSTM) and simulated annealing algorithm is adopted.

Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms.

In power electronics systems, system design and operation often involve multiple time and space scales, ranging from nanosecond switching dynamics to hour-level system operation behavior. Due to the complexity of these systems and the rise of wide-gap semiconductor technology, a series of multi-scale phenomena have emerged that are difficult to ignore. The high frequency of switching operations makes multi-scale effects particularly significant, including the fast dynamic response of the power loop, EMI, and heat conduction problems. They are key factors that must be considered in the design to ensure the efficient and reliable operation of power electronic devices. This study proposes the construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms to address the multi-scale phenomenon and limitations of single-scale power electronic converters. Firstly, a joint scale model for power electronic converters at both macro and micro-scales was established, targeting both single-scale models and simple combinations of multiple scale models for power electronic converters. The traditional single-scale model is sufficient to describe the average behavior of the converter, but it has serious limitations in capturing fast transient processes and high-frequency switching behavior in power electronic systems. These limitations often manifest themselves when there is a need to capture fine timescales of detail. By transforming between the time domain and the frequency domain, wavelet decomposition enables the model to capture both macroscopic average characteristics and microscopic transient dynamics. The wavelet reconstruction algorithm can simulate all kinds of fast changes in the actual working process more accurately and compress irrelevant information while retaining key signal features, so as to optimize the simulation performance of the model. Secondly, this algorithm is used to analyze BC in short time scale. Finally, the short time scale characteristics of power electronic converters are analyzed. Experimental results show that the fusion of wavelet decomposition and reconstruction algorithm enhances the accuracy of the power electronic converter model and improves the performance of the system. The model achieves an error reduction of nearly 3% in the calculation step size of 10-7s, which has a significant impact on the high precision requirements of high-frequency operations. In addition, the optimal calculation step size of 8×10-8s achieves an error reduction of more than 14%, making an important contribution to the transient analysis and fine structure simulation. The wavelet algorithm can improve the accuracy of multi-scale modeling in power electronic system and reduce the simulation time. The reduction of error not only shows the improvement of the accuracy of the model, but also shows its practical significance in the design and test of the actual power electronic system. The reduction in error reveals the ability to more accurately predict and mitigate potential performance problems in matching tests with actual hardware, as well as its ability to adapt to emerging wide bandgap semiconductor materials and structures.

Predicting resting-state brain functional connectivity from the structural connectome using the heat diffusion model: a multiple-timescale fusion method

Objective. Understanding the intricate relationship between structural connectivity (SC) and functional connectivity (FC) is pivotal for understanding the complexities of the human brain. To explore this relationship, the heat diffusion model (HDM) was utilized to predict FC from SC. However, previous studies using the HDM have typically predicted FC at a critical time scale in the heat kernel equation, overlooking the dynamic nature of the diffusion process and providing an incomplete representation of the predicted FC. Approach. In this study, we propose an alternative approach based on the HDM. First, we introduced a multiple-timescale fusion method to capture the dynamic features of the diffusion process. Additionally, to enhance the smoothness of the predicted FC values, we employed the Wavelet reconstruction method to maintain local consistency and remove noise. Moreover, to provide a more accurate representation of the relationship between SC and FC, we calculated the linear transformation between the smoothed FC and the empirical FC. Main results. We conducted extensive experiments in two independent datasets. By fusing different time scales in the diffusion process for predicting FC, the proposed method demonstrated higher predictive correlation compared with method considering only critical time points (Singlescale). Furthermore, compared with other existing methods, the proposed method achieved the highest predictive correlations of 0.6939 ± 0.0079 and 0.7302 ± 0.0117 on the two datasets respectively. We observed that the visual network at the network level and the parietal lobe at the lobe level exhibited the highest predictive correlations, indicating that the functional activity in these regions may be closely related to the direct diffusion of information between brain regions. Significance. The multiple-timescale fusion method proposed in this study provides insights into the dynamic aspects of the diffusion process, contributing to a deeper understanding of how brain structure gives rise to brain function.