Multiresolution Wavelet Research Articles

Diagnosis of faults using a new VMD-WMRA approach, optimized by a new criterion: Industrial application

This paper proposes a new criterion for selecting the optimum number of Intrinsic Mode Functions (IMFs) from vibration signals measured on rotating machines. The criterion is based on calculating the variation of normalized Shannon entropy ([Formula: see text]) between two successive IMFs, enabling the optimization of the number of processed IMFs. The method combines Variational Mode Decomposition (VMD) with Wavelet Multi-Resolution Analysis (WMRA) using the newly introduced criterion. The key steps involve determining the optimal number of IMFs, decomposing the vibration signals using VMD, and applying WMRA to the selected IMFs. Numerical simulations and experimental results demonstrate its effectiveness in identifying various faults, including gear defects, shaft misalignment, insufficient backlash, and belt defects. These latter flaws are the primary cause of the elevated noise levels in the measured signals. Finally, to validate our approach in an industrial setting, we diagnosed a turbofan, which revealed the presence of several typical faults for this type of installation. The proposed approach addresses a critical industry need by increasing fault diagnosis accuracy in noisy environments. Its practical impact stems from its ability to improve early fault detection, which is critical for predictive maintenance strategies aimed at reducing equipment downtime and extending its lifespan.

The multi-resolution Haar wavelets collocation procedure for fractional Riccati equations

The multi-resolution Haar wavelets collocation procedure for fractional Riccati equations

Multiresolution cascaded attention U-Net for localization and segmentation of optic disc and fovea in fundus images

Identification of retinal diseases in automated screening methods, such as those used in clinical settings or computer-aided diagnosis, usually depends on the localization and segmentation of the Optic Disc (OD) and fovea. However, this task is difficult since these anatomical features have irregular spatial, texture, and shape characteristics, limited sample sizes, and domain shifts due to different data distributions across datasets. This study proposes a novel Multiresolution Cascaded Attention U-Net (MCAU-Net) model that addresses these problems by optimally balancing receptive field size and computational efficiency. The MCAU-Net utilizes two skip connections to accurately localize and segment the OD and fovea in fundus images. We incorporated a Multiresolution Wavelet Pooling Module (MWPM) into the CNN at each stage of U-Net input to compensate for spatial information loss. Additionally, we integrated a cascaded connection of the spatial and channel attentions as a skip connection in MCAU-Net to concentrate precisely on the target object and improve model convergence for segmenting and localizing OD and fovea centers. The proposed model has a low parameter count of 0.8 million, improving computational efficiency and reducing the risk of overfitting. For OD segmentation, the MCAU-Net achieves high IoU values of 0.9771, 0.945, and 0.946 for the DRISHTI-GS, DRIONS-DB, and IDRiD datasets, respectively, outperforming previous results for all three datasets. For the IDRiD dataset, the MCAU-Net locates the OD center with an Euclidean Distance (ED) of 16.90 pixels and the fovea center with an ED of 33.45 pixels, demonstrating its effectiveness in overcoming the common limitations of state-of-the-art methods.

Underwater acoustic target recognition based on multi-resolution wavelet feature deep learning

The application of underwater acoustic target recognition is extensive, exploration of marine resources, submarine vehicle detection and so on. However, traditional feature extraction methods are susceptible to the influence of complex marine environments and target operating conditions, leading to a significant reduction in the correct recognition rate. This paper introduces an underwater acoustic target recognition method that integrates multi-resolution wavelet features with deep learning algorithms, aiming to overcome the limitations of traditional time-frequency analysis techniques, which are unable to extract multiple signal characteristics simultaneously due to the trade-off between time and frequency resolution. Specifically, the essence of this technique is twofold: (1) Selecting suitable wavelet bases and decomposition levels to capture signal characteristics at different resolutions, effectively seizing the signal's local features within the time-frequency domain; (2) Fusing signal features across different resolutions to optimize the feature extraction process and enhance the distinguishability of target features. Finally, by applying deep learning algorithms to experimentally measured underwater acoustic data, the results demonstrate that this method can effectively enhance the accuracy of underwater acoustic target recognition.

Baseline offset correction technique for terahertz signals based on improved wavelet multiresolution analysis

During the terahertz nondestructive testing of bonded structures, the incomplete discharge of the capacitance in the photoconductive antenna within the terahertz time-domain spectroscopy system results in a shift of the terahertz baseline produced by the antenna. This baseline shift causes variations in the amplitude information of the detected signals. Consequently, when feature imaging of the detection waveforms is performed, the baseline shift can lead to erroneous detection results. In this study, an improved wavelet multiresolution analysis method was used to eliminate high-frequency noise and baseline offset in terahertz detection. The method is based on the frequency characteristics of the detection waveforms, setting thresholds and using similarity as a measurement standard to determine the number of decomposition layers. Ultimately, this achieves the correction of the baseline offset in terahertz signals. Compared with other baseline correction methods, the method presented in this paper achieves the lowest root mean square error of 0.57%, the highest signal-to-noise ratio of 12.64%, and a defect identification accuracy of 96.27% in two-dimensional visualization results.

Non-separable multidimensional multiresolution wavelets: A Douglas-Rachford approach

After re-casting the wavelet construction problem as a feasibility problem with constraints arising from the requirements of compact support, smoothness and orthogonality, the Douglas–Rachford algorithm is employed in the search for multi-dimensional, non-separable, compactly supported, smooth, orthogonal, multiresolution wavelets in the case of translations along the integer lattice and isotropic dyadic dilations. An algorithm for the numerical construction of such wavelets is described. By applying the algorithm, new one-dimensional wavelets are produced as well as genuinely non-separable two-dimensional wavelets.

Advanced feature extraction for the characterization of impact events on composites using multiresolution wavelet-based simulations

The detection and characterization of impact events on composite structures from the induced wave responses, involves many challenges. Coexisting guided waves of high dispersive nature propagate after impact, entailing continuous time variations in their wavenumber, frequency and group velocity content, which complicate the exact estimation of the time-of-flight and the extraction of impact characteristics. A multiresolution finite wavelet domain computational method, combined with appropriate contact laws, is presented to provide enhanced simulation and characterization capabilities of impact events. An explicit multiresolution time integration scheme involves a coarse solution, followed by finer solutions that are sequentially added to the coarse one, until convergence is achieved. The hierarchical character of the approach makes the impact simulation very fast and accurate. Moreover, due to the filtering properties of Daubechies wavelet functions, each resolution component effectively models and isolates specific wavenumber spectra, providing the capability to separate coexisting wave modes, and to overcome difficulties imposed by the dispersive nature of the resultant guided waves. It is demonstrated that the multiresolution simulation can reveal wave characteristics and time-of-flight features that no other traditional single-resolution method can do, and provides the basis for the development of powerful inverse methods that can localize the impact and characterize the impactor parameters. The method is first applied on impacted composite strips and the structural responses of each resolution component are assessed in order to obtain the desired features for impact location estimation and characterization. Finally, the method is implemented on an impacted composite plate structure and the various wave characteristics simulated by the fine components are presented, evincing the advanced features that the proposed method provides.

Analysis of medical images super-resolution via a wavelet pyramid recursive neural network constrained by wavelet energy entropy

Recently, multi-resolution pyramid-based techniques have emerged as the prevailing research approach for image super-resolution. However, these methods typically rely on a single mode of information transmission between levels. In our approach, a wavelet pyramid recursive neural network (WPRNN) based on wavelet energy entropy (WEE) constraint is proposed. This network transmits previous-level wavelet coefficients and additional shallow coefficient features to capture local details. Besides, the parameter of low- and high-frequency wavelet coefficients within each pyramid level and across pyramid levels is shared. A multi-resolution wavelet pyramid fusion (WPF) module is devised to facilitate information transfer across network pyramid levels. Additionally, a wavelet energy entropy loss is proposed to constrain the reconstruction of wavelet coefficients from the perspective of signal energy distribution. Finally, our method achieves the competitive reconstruction performance with the minimal parameters through an extensive series of experiments conducted on publicly available datasets, which demonstrates its practical utility.

Prediction intervals for concrete face sandy gravel dam settlement using Kalman filter-based kernel extreme learning machine

Accurately predicting settlement of concrete face sandy gravel dams is a crucial yet challenging task. The conventional approach of point forecasting can hardly describe the uncertainties inherent in the complex dam system. Hence, a hybrid prediction interval (PI) method using Kalman filter-based kernel extreme learning machine (KELM) is proposed to quantify the uncertain information associated with dam settlement prediction. The Kalman Filter (KF) is integrated into the original KELM by incorporating real-time actual measurement. The wavelet multiresolution analysis is employed to eliminate irrelevant information from historical settlement time series for more accurate prediction. Additionally, a Bayesian method is used to detect change points in the KF modified-KELM model. The proposed method is demonstrated in the settlement monitoring of the Nazixia dam and is compared with three popular machine learning methods. Results indicate that the PI constructed by the proposed method can exhibit better interval coverage and a comprehensive index.

Performance Comparison of Image Fusion Alternatives Combining PCA with Multi-resolution Wavelet Transforms

Performance Comparison of Image Fusion Alternatives Combining PCA with Multi-resolution Wavelet Transforms

DEW: A wavelet approach of rare sound event detection.

This paper presents a novel sound event detection (SED) system for rare events occurring in an open environment. Wavelet multiresolution analysis (MRA) is used to decompose the input audio clip of 30 seconds into five levels. Wavelet denoising is then applied on the third and fifth levels of MRA to filter out the background. Significant transitions, which may represent the onset of a rare event, are then estimated in these two levels by combining the peak-finding algorithm with the K-medoids clustering algorithm. The small portions of one-second duration, called 'chunks' are cropped from the input audio signal corresponding to the estimated locations of the significant transitions. Features from these chunks are extracted by the wavelet scattering network (WSN) and are given as input to a support vector machine (SVM) classifier, which classifies them. The proposed SED framework produces an error rate comparable to the SED systems based on convolutional neural network (CNN) architecture. Also, the proposed algorithm is computationally efficient and lightweight as compared to deep learning models, as it has no learnable parameter. It requires only a single epoch of training, which is 5, 10, 200, and 600 times lesser than the models based on CNNs and deep neural networks (DNNs), CNN with long short-term memory (LSTM) network, convolutional recurrent neural network (CRNN), and CNN respectively. The proposed model neither requires concatenation with previous frames for anomaly detection nor any additional training data creation needed for other comparative deep learning models. It needs to check almost 360 times fewer chunks for the presence of rare events than the other baseline systems used for comparison in this paper. All these characteristics make the proposed system suitable for real-time applications on resource-limited devices.

Evidence of Excited-State Vibrational Mode Governing the Photorelaxation of a Charge-Transfer Complex.

Modern, nonlinear, time-resolved spectroscopic techniques have opened new doors for investigating the intriguing but complex world of photoinduced ultrafast out-of-equilibrium phenomena and charge dynamics. The interaction between light and matter introduces an additional dimension, where the complex interplay between electronic and vibrational dynamics needs the most advanced theoretical-computational protocols to be fully understood on the molecular scale. In this study, we showcase the capabilities of ab initio molecular dynamics simulation integrated with a multiresolution wavelet protocol to carefully investigate the excited-state relaxation dynamics in a noncovalent complex involving tetramethylbenzene (TMB) and tetracyanoquinodimethane (TCNQ) undergoing charge transfer (CT) upon photoexcitation. Our protocol provides an accurate description that facilitates a direct comparison between transient vibrational analysis and time-resolved spectroscopic signals. This molecular level perspective enhances our understanding of photorelaxation processes confined in the adiabatic regime and offers an improved interpretation of vibrational spectra. Furthermore, it enables the quantification of anharmonic vibrational couplings between high- and low-frequency modes, specifically the TCNQ "rocking" and "bending" modes. Additionally, it identifies the primary vibrational mode that governs the adiabaticity between the ground state and the CT state. This comprehensive understanding of photorelaxation processes holds significant importance in the rational design and precise control of more efficient photovoltaic and sensor devices.

Money supply and inflation in Algeria : a Wavelet Based Analysis

The purpose of this study is to examine the relationship between money supply and inflation in Algeria using wavelet analysis. In this study, we have applied Maxima Overlap Discrete Wavelet Transform (MODWT), Multiresolution Analysis (MRA), wavelet correlation, Wavelet Coherence, and wavelet-based Granger causality test to analyze the relationship between the two variables during the period from January 2010 to November 2019. Our findings show strong links between money supply and inflation in both the short and long run, which supports both the traditional and modern quantity theories of money. Additionally, the time scale Granger causality analysis indicates the existence of causality from money supply to inflation over different time horizons. The outcomes of the current study should be of interest to Algerian monetary policymakers as they decide to sustain growth using unconventional monetary policy.

The Spillover Effects among Crude Oil Future Markets under High-Frequency Data Environment: Trivariate VAR-BEKK-GARCH Model Based on Wavelet Multiresolution Analysis

With the rapid development of financial globalization, the interconnection of international financial markets has deepened, and the relationship between domestic and international crude oil futures market price fluctuations has been increasingly strengthened. This paper utilizes 1-minute high-frequency price data of INE, WTI, and BRENT crude oil. By employing wavelet multiresolution analysis to address the ‘Calendar Effect’ present in intraday high-frequency data, and decomposing financial time series into different hierarchy of time scales. On this basis, the VAR-BEKK-GARCH model is established to study the spillover effect among the three crude oil future markets from the perspective of different trading cycles. The main conclusions of this paper are as follows: (1) The energy spectrum of wavelet multiresolution analysis shows that the price fluctuations of domestic and international crude oil futures are mainly reflected in the short-term trading cycles of 1-4 minutes; (2) The empirical results of the VAR-BEKK-GARCH model indicate that there are significant bidirectional mean and volatility spillover effects among INE, WTI, and BRENT crude oil in each trading cycle. Specifically, the mean spillover effect between INE and WTI markets shows that the short-term mean spillover effect of INE crude oil on WTI crude oil is larger, which is contrast to the medium- and long-term effect, and there is no significant pattern in the volatility spillover effect. The overall mean and volatility spillover effects of INE crude oil on BRENT crude oil are relatively larger. The overall mean and volatility spillover effects of WTI crude oil on BRENT crude oil are also relatively larger.

Discrete wavelet transform based processing of embroidered textile-electrode electromyography signal acquired with load and pressure effect

The diagnosis of neuromuscular diseases is complicated by overlapping symptoms from other conditions. Textile-based surface electromyography (sEMG) of skeletal muscles, offer promising potential in diagnosis, treatment, and rehabilitation of various neuromuscular disorders. However, it is important to consider the impact of load and pressure on EMG signals, as this can significantly affect the signal’s accuracy. This study seeks to investigate the influence of load and pressure on EMG signals and establish a processing framework for these signals in the diagnosis of neuromuscular diseases. The sEMG data were collected from healthy subjects using a textile electrode developed from polyester multi-filament conductive hybrid thread (CleverTex). The textrode was embroidered directly on an elastic bandage (Velcro® strap) placed on volunteer’s muscles while different activities were performed with varying loads and pressure. The collected data were pre-processed using standard techniques of the discrete wavelet transform to remove noise and artifacts. The performance of the proposed denoising algorithm was evaluated using the signal-to-noise ratio (SNR), percentage root mean square difference (PRD), and root mean square error (RMSE). Various signal processing approaches (filters) were considered and the results were compared with the proposed EMG noise reduction algorithms. Based on the experimental results, the fourth level of decomposition for the sym5 wavelets with the Rigrsure threshold method achieved the highest signal-to-noise ratio (SNR) values of 16.69 and 21.91, for soft and hard thresholding functions, respectively. The SNR values of 22.11, 21.54, and 2.78 at three different pressure levels 5 mmHg, 10 mmHg, and 20 mmHg, respectively, indicate the superior performance of wavelet multiresolution filter in de-noising applications. The results of this study suggest that our methodology is effective, precise, and reliable for analysing sEMG data and provide insights into both physiological and pathological neuromuscular conditions.

Unraveling Multi-Scale dynamics of estuarine wetland vegetation using the multi-resolution analysis wavelet transform and the Landsat time-series

Estuarine wetland vegetation (EWV) serves as a critical indicator of ecosystem health but is increasingly threatened by human activities and climate change. Though remote sensing (RS) data provide a holistic view of vegetation change with sufficient spatial resolution, temporal changes in EWV are still ambiguous because of the twisted signals between phenological dynamics and multi-scale external disturbances. To address these knowledge gaps, a method integrated with multi-resolution analysis wavelet transform (MRA-WT) and time-series RS images were utilized in this study to uncover detailed multiple-scale EWV dynamics from the perspectives of vegetation phenology and evolution trends. Our results showed that: 1) The MRA-WT effectively decomposes NDVI at multiple scales, revealing intra- and inter-annual dynamics of EWV in complex environments. 2) In the Jiuduansha (JDS) wetland, the phenological characteristics and evolution processes of EWV are determined by vegetation type and geographical location. 3) The EWV in the JDS wetland remained stable with gradual growth from 2000 to 2021, despite the impacts of sediment reduction, estuarine projects, and invasive species. However, a declining trend post-2018 serves as a warning sign of potential ecosystem issues. Moreover, higher spatial and temporal resolutions enable more precise tracking of fine-scale details in the dynamics of EWV with the proposed method.

Analysis of Cosmic Ray Fluxes at Different Stations during Geomagnetic Storms using Wavelet Based Approaches: Continuous Wavelet Transform and Multi-Resolution Analysis

Analysis of Cosmic Ray Fluxes at Different Stations during Geomagnetic Storms using Wavelet Based Approaches: Continuous Wavelet Transform and Multi-Resolution Analysis

High-order adaptive multiresolution wavelet upwind schemes for hyperbolic conservation laws

We present a novel system of high-order adaptive multiresolution wavelet collocation upwind schemes, implemented in a meshfree framework, for solving hyperbolic conservation laws. Our approach constructs asymmetrical wavelet bases with interpolation properties to achieve the upwind property and address nonlinearities in hyperbolic problems. An adaptive algorithm based on multiresolution analysis in wavelet theory is designed to capture moving shock waves and identify new localized steep regions. To suppress the Gibbs phenomenon, we propose an integration average reconstruction method based on the Lebesgue differentiation theorem. These numerical techniques enable the wavelet collocation upwind scheme to provide a general framework for devising satisfactory adaptive wavelet upwind methods with high-order accuracy. We perform several benchmark tests for 1D hyperbolic problems to verify the accuracy and efficiency of the proposed wavelet schemes. Notably, our wavelet collocation upwind schemes successfully solve the two interacting blast waves problem when discretizing the spatial derivatives in the physical space directly. This is in contrast to classical high-order schemes that usually involve transforming variables back and forth between physical and characteristic spaces with many local projections. Our results indicate the robustness, stability, and efficiency of our proposed schemes for strong shock wave interaction problems.

Micro-flow structure at regime transition from bubbling to turbulent fluidization in a fluidized bed

Gas-solid fluidized beds have found extensive utilization in frontline manufacturing, in particular as low-velocity beds. The fluidization status, the bubbling or turbulent flow regime and the transition in between, determine the system performance in practical applications. Though the convoluted hydrodynamics are quantitively evaluated through numerous data-processing methodologies, none of them alone can reflect all the critical information to identify the transition from the bubbling to the turbulent regime. Accordingly, this study was to exploit a coupling data processing methodology, in the combination of standard deviation, power spectrum density, probability density function, wavelet transform, and wavelet multiresolution method, to jointly explain the micro-flow structure at the regime transition from bubbling to turbulent fluidization. The transient differential pressure fluctuation was measured for the evaluation in a fluidized bed (0.267 m i.d. × 2.5 m height) with FCC catalysts (d¯p=65μm, ρp=1780kg/m3) at different superficial gas velocities (0.02–1.4 m/s). The results show that the onset of turbulent fluidization starts earlier in the top section of the bed than in the bottom section. The wavelet decomposition displays that the fluctuation of differential pressure mainly concentrates on the sub-signals with an intermediate frequency band. These sub-signals could be synthesized into three types of scales (micro-scale, meso-scale, and macro-scale), representing the multi-scale hydrodynamics in the fluidized bed. The micro-scale signal has the characteristic information of bubbling fluidization, and the characteristic information of turbulent fluidization is mainly represented by the meso-scale signal. This work provides a systematic comprehension of fluidization status assessment and serves as an impetus for more coupling analysis in this sector.

Application of Wavelet Transform for Bias Correction and Predictor Screening of Climate Data

Climate model (CM) statistical downscaling requires quality and quantity modifications of the CM’s outputs to increase further modeling accuracy. In this respect, multi-resolution wavelet transform (WT) was employed to determine the hidden resolutions of climate signals and eliminate bias in a CM. The results revealed that the newly developed discrete wavelet transform (DWT)-based bias correction method can outperform the quantile mapping (QM) method. In this study, wavelet coherence analysis was utilized to assess the high common powers and the multi-scale correlation between the predictors and predictand as a function of time and frequency. Thereafter, to rate the most contributing predictors based on potential periodicity, the average variance was calculated, which is named the Scaled Average (SA) measure. Consequently, WT along with Artificial Neural Network (ANN) were applied for bias correction and identifying the dominant predictors for statistical downscaling. The CAN-ESM5 data of Canadian climate models and INM-CM5 data of Russian climate models over two climatic areas of Iran with semi-arid (Tabriz) and humid (Rasht) weather were applied. The projection of future precipitation revealed that Tabriz will experience a 3.4–6.1% decrease in precipitation, while Rasht’s precipitation will decrease by 1.5–2.5%. These findings underscore the importance of refining CM data and employing advanced techniques to assess the potential impacts of climate change on regional precipitation patterns.