Search Results (130)

Controlled bridge simulation and laboratory damage identification require models that can simulate structural responses and infer localized stiffness loss from limited measurements. Existing Fourier Neural Operator (FNO)-based vehicle–bridge interaction (VBI) models provide efficient surrogates for these mappings, but the global Fourier representation can smooth localized damage transitions and introduce boundary-related errors for finite-span bridge responses. This study adapts the Wavelet Neural Operator (WNO) to the VBI setting and develops the Vehicle–Bridge Interaction Wavelet Neural Operator (VIWNO), an application-oriented framework for wavelet-domain operator learning between structural response fields and damage fields. VIWNO is pre-trained on a numerical VBI finite-element dataset (VBI-FE) and fine-tuned using only healthy-state measurements from a scaled VBI experimental dataset (VBI-EXP), before being evaluated on unseen laboratory damage scenarios. Under the controlled VBI-FE setting, where bridge, vehicle, speed, and measured road-profile parameters are fixed and the main variation is the damage field, VIWNO reduces forward response errors by 20–30% and inverse damage-estimation errors by 26–32% relative to the FNO-based Vehicle–Bridge Interaction Neural Operator (VINO) baseline. Additional morphology and operating-condition stress tests show that the error increases under sharper damage fields and perturbed VBI conditions, but VIWNO remains more accurate than VINO and the added convolutional or frequency-domain baselines in the tested cases. On VBI-EXP, projection-only healthy-state fine-tuning reduces intact false-damage levels and yields sharper damage estimates than VINO under both displacement and acceleration inputs. Stability checks over five initializations and repeated vehicle passages show limited variation in the reported inverse metrics. These results support the feasibility of wavelet-domain neural operators for calibrated VBI simulation and scaled laboratory damage identification, while field-scale bridge health monitoring still requires validation under broader traffic, environmental, support, and damage-morphology variability. Full article

We consider the estimation of partial derivatives of multivariate regression-type functionals from incomplete observations generated by a discrete-time strictly stationary ergodic process. The response variable is subject to a missing-at-random (MAR) mechanism, whereas the covariates are fully observed. Building upon the complete-data wavelet methodology developed in Didi and Bouzebda (2025), we construct inverse-probability-weighted empirical wavelet estimators that compensate for the selection bias induced by missing responses. When the propensity score is unknown, a feasible estimator is obtained by replacing the oracle weights with a nonparametric Nadaraya–Watson estimator. The analysis is carried out under stationary ergodicity without imposing mixing assumptions. The estimation error is decomposed into three analytically distinct components: the deterministic multiresolution approximation error, the stochastic fluctuation of the oracle inverse-probability-weighted estimator, and the additional error arising from propensity score estimation. This decomposition makes it possible to isolate the respective effects of approximation, dependence, and missingness within a unified asymptotic framework. Under explicit assumptions on the multiresolution approximation, missingness mechanism, conditional density stabilization, moment conditions, and accuracy of the propensity estimator, we establish non-asymptotic integrated mean squared error bounds together with their asymptotic rates. We further prove almost-sure uniform consistency over compact subsets of the interior of the support and derive a pointwise central limit theorem for both the oracle and feasible estimators. The limiting variance explicitly reflects the information loss induced by inverse probability weighting, and for general orthogonal projection kernels is formulated under the corresponding dyadic-phase condition. The general methodology is specialized to the estimation of first- and second-order derivatives of ordinary regression functions. A finite-sample simulation study investigates the empirical behavior of the proposed estimators under stationary ergodic dependence and MAR missingness, examines the influence of both the wavelet resolution level and the propensity-score bandwidth, evaluates the finite-sample performance of the asymptotic confidence intervals, and compares the proposed procedure with oracle, complete-case, and competing nonparametric estimators. The numerical results are consistent with the theoretical analysis and illustrate the respective contributions of wavelet approximation, inverse probability weighting, and propensity score estimation to the overall estimation error. When the propensity score is identically equal to one, the proposed methodology reduces to the corresponding complete-data wavelet estimator. Full article

Image steganography is an information-hiding technique, aiming to achieve confidentiality and data privacy while transmitting the data in a digital environment. Over the last two decades, steganography has evolved from classical spatial domain embedding to intelligent and adaptive steganographic systems capable of balancing imperceptibility, embedding capacity, robustness and security. This paper presents a review by categorizing the existing techniques into spatial domain-based, transform domain-based, hybrid and adaptive intelligent techniques. The review follows the PRISMA approach to make the selection process transparent for the inclusion and exclusion of papers in the study. Initially, the reviews include the spatial domain-based methods focusing on higher embedding capacity and simple embedding strategy, followed by transform-domain based techniques, including discrete cosine transform, discrete wavelet transform, and other multi-resolution wavelet transforms aiming to enhance robustness and imperceptibility by embedding the data into frequency coefficients. This paper further explores the methods that combine these techniques with other recent trends to develop adaptive and hybrid techniques. These techniques mainly integrate chaotic theory to enhance the security of secret data before embedding and optimization algorithms such as genetic algorithm, particle swarm optimization, Firefly, etc., for adaptive embedding to achieve an improved tradeoff. Finally, intelligent and adaptive techniques based on deep learning models such as convolutional neural networks, autoencoders, and generative adversarial networks are examined, highlighting their ability to learn intelligent embedding strategies and resist modern steganalysis. A comparative analysis is presented, including the technique, strengths, and limitations, together with the discussion of performance evaluation metrics and vulnerability analysis under image processing attacks. The review highlights the current trends and outlines the future direction to develop next-generation secure image steganographic systems. Full article

Millimeter-wave radar enables non-contact monitoring of cardiac activity and therefore has the potential to reconstruct electrocardiogram signals without surface electrodes. However, existing radar-based electrocardiogram reconstruction methods still suffer from incomplete extraction of heartbeat-related information and insufficient modeling of electrocardiogram-related features, which limits reconstruction accuracy. To address these issues, this study proposes a millimeter-wave radar-based electrocardiogram reconstruction method that integrates a respiratory-harmonic-suppressed multi-channel signal-processing frontend with the proposed CA-WTBNet deep reconstruction network. First, based on maximal overlap discrete wavelet transform-based multi-resolution analysis, respiratory harmonics mixed into heartbeat-related components are suppressed by combining respiratory harmonic detection with a heart-rate frequency protection strategy, while cardiac-related information is preserved as much as possible. A multi-channel input representation is then constructed. Meanwhile, the proposed deep reconstruction network is developed to jointly model complementary channel-wise features, local waveform morphology, and temporal dependencies by integrating channel-attention mechanisms, convolutional residual modules, window-based Transformer blocks, and bidirectional long short-term memory. Experiments conducted on the public dataset show that our method achieves an average Pearson correlation coefficient of 0.9641, a mean normalized root mean square error of 0.0458, an average R-peak F1 score of 0.9956, and an average R-peak timing error of 3.13 ms on the test set. In comparison with related studies on the same public Resting dataset, the proposed method achieves the best overall performance among the compared methods, with a 0.53% improvement in Pearson correlation coefficient and a 10.20% reduction in normalized root mean square error over the best-performing compared method. Full article

High-dynamic amusement ride conditions involving impacts, rapid rotations, and abrupt posture changes introduce severe motion artifacts that degrade vital sign quality and destabilize physiological state recognition. This study aims to develop an engineering-ready closed-loop framework for robust passenger monitoring and intelligent diagnosis. A multimodal sensing and modeling pipeline was designed to jointly leverage physiological signals such as heart rate and SpO₂ and kinematic measurements, including acceleration, angular rate, velocity, and attitude. Inertial and PPG signals were preprocessed into supervised samples through wavelet multiresolution denoising and coordinate frame unification, while a strapdown inertial navigation system was used to propagate a 12-channel physical quantity sequence. To ensure interpretability and standards compliance, constraints from GB 8408-2018 were translated into executable threshold rules, enabling standards-driven auto-labeling and rule-based early warning. Building on this foundation, three learning modules were developed: a fusion model for high-dynamic heart rate estimation, a CNN–LSTM dynamic-threshold-enhanced network TAPNet for rapid kinematic anomaly screening, and an attention-augmented hybrid model HS-BANet integrating one-dimensional residual blocks, bidirectional LSTM, and multi-head attention for fine-grained arrhythmia classification. Experimental results demonstrated accurate and consistent heart rate estimation with RMSE of 1.18 bpm on HSSH-I and 1.24 bpm on the independent HSSH-II set, strong agreement with training and testing correlations of 0.9928 and 0.9865, and near-zero bias in Bland–Altman analysis. TAPNet achieved 96.9% validation accuracy and 98.2% test accuracy for kinematic anomaly recognition, maintaining robust generalization under class imbalance. HS-BANet enabled multi-class identification of PVC, PAC, VT, SVT, and AF, achieving an accuracy of 92.37%, an F1-score of 86.87%, a precision of 88.45%, a sensitivity of 88.14%, and a specificity of 89.42%. Overall, the proposed two-stage multimodal closed-loop—fast, interpretable early warning based on physical quantity thresholds followed by fine-grained diagnosis from physiological signals—supports stable feature extraction and reliable decision-making under strong motion artifacts and non-stationary dynamics, balancing responsiveness and diagnostic credibility, while showing potential for practical safety early warning and future deployment-oriented operational support in amusement ride scenarios. Full article

Transitioning predictive maintenance from expensive, high-frequency piezoelectric sensors to affordable, edge-deployed MEMS sensors poses a significant challenge in industrial tool condition monitoring (TCM). Both technologies differ in signal quality, frequency capability, robustness, and reliability, which would affect how accurately machine faults can be detected. This work presents a systematic framework to bridge this gap, enabling real-time tool wear prediction and cross-sensor transferability. The methodology employs unsupervised Wavelet Packet Decomposition (WPD) and dynamic programming on high-resolution vibration signals to establish ground-truth wear phases: initial, steady-state, and accelerated. Multi-resolution time-frequency features are extracted and globally ranked using a multi-metric scoring system. A multi-task Bidirectional Long Short-Term Memory (Bi-LSTM) network is then trained to simultaneously predict a continuous wear index and classify discrete wear zones. To ensure model portability, Canonical Correlation Analysis (CCA) is utilised to align the high-fidelity piezoelectric feature space with the lower-frequency MEMS domain. The optimised multi-task Bi-LSTM architecture achieved up to 97.9% zone classification accuracy and a mean absolute error of 0.042 for wear index regression. Furthermore, CCA-based domain adaptation successfully transferred a model trained on piezoelectric data to classify unseen low-cost MEMS sensor data, maintaining a robust 87% accuracy. Combining optimised WPD features with CCA effectively overcomes hardware and sampling rate discrepancies, proving the viability of using low-cost sensors for reliable industrial retrofitting and real-time degradation tracking. Full article

Accurate crack severity classification in rotating shafts remains a challenging task due to the strong spectral overlap between adjacent damage levels and the absence of distinct fault-specific frequency components. In such conditions, conventional vibration-based approaches relying on global spectral descriptors often fail to provide sufficient discriminatory information. This work proposes a stability-driven multi-resolution framework for crack severity classification based on the Wavelet Packet Transform (WPT). The approach aims to identify frequency bands that exhibit consistent diagnostic relevance across multiple decomposition levels while maintaining a monotonic relationship with crack severity. To this end, an interpretability-driven analysis based on Random Forest feature importance is combined with a frequency stability criterion and a monotonicity constraint, enabling the selection of physically meaningful and consistent spectral regions. The proposed framework has been evaluated on vibration data acquired from a rotating shaft test bench under multiple operating speeds and damage conditions. The results have shown that crack progression is characterised by distributed energy variations across specific frequency regions rather than by the emergence of isolated spectral peaks. It can be concluded that the proposed stability-driven band selection approach enables the identification of these regions in a consistent manner across spectral resolutions and operating conditions. Furthermore, the integration of WPT-based features with conventional time- and frequency-domain descriptors leads to a hybrid multi-scale representation that improves classification performance, particularly in intermediate severity regimes where spectral overlap is most pronounced. Overall, the proposed methodology provides a physically interpretable and consistent framework for vibration-based crack severity classification, with potential applicability to a wide range of rotating machinery diagnostics problems. Full article

Extracting evoked potentials (EPs) from single trials in electroencephalography (EEG) remains a major challenge due to a characteristically low signal-to-noise ratio (SNR). This paper presents an enhanced denoising framework that combines multiresolution wavelet transform (MWT) with a statistical resampling technique. A key contribution is the introduction of an SNR-based preprocessing step that assesses individual trials and discards those with an SNR below 0 dB to prevent heavily corrupted data from degrading the analysis. Unlike traditional methods that rely on Gaussian noise assumptions, our approach utilizes empirical resampling to estimate optimal wavelet coefficient thresholds in a fully data-driven manner. Hard thresholding is subsequently applied to isolate transient neural events from background fluctuations. The method was validated using synthetic signals and real EEG recordings from ten subjects (aged 20–31 years) performing an Eriksen flanker task. Results from simulations demonstrated a significant mean SNR improvement of 13 dB. In real data applications, the error-monitoring components (Ne and Pe) were clearly identified at the single-trial level, with peak latencies observed at approximately 180 ms and 220 ms, respectively. This approach enables reliable single-trial EP analysis without the need for templates or multichannel recordings, offering a robust tool for brain–computer interfaces and clinical diagnostics. Full article

Reliable detection of internal defects in pressure vessel structures remains essential for structural safety and condition-based maintenance. This study presents a low-complexity structural health monitoring framework based on fiber Bragg grating (FBG) sensing and multiresolution wavelet analysis for void detection in curved pressure vessel structures under guided wave excitation. Guided waves are introduced using piezoelectric actuators, while the FBG sensors capture the resulting strain-induced wavelength variations. Due to the limited bandwidth of the optical interrogator, the recorded signals represent the strain envelope response associated with guided wave interaction rather than the resolved ultrasonic carrier waveform. To characterize defect-induced changes, the acquired signals are analyzed using continuous wavelet transform (CWT) for time–frequency interpretation, and discrete wavelet transform (DWT) and wavelet packet transform (WPT) for energy-based multiresolution feature extraction. Experimental results show that void defects lead to consistent redistribution of wavelet-domain energy and increased non-stationarity in the measured strain responses. These trends are further supported by finite-element simulations, which reproduce similar energy redistribution patterns between intact and damaged cases. The proposed framework provides a physically interpretable and computationally efficient approach for defect detection using low-bandwidth FBG sensing, without reliance on high-speed acquisition or data-intensive learning models. The results demonstrate the feasibility of using energy-based multiresolution analysis of FBG strain signals for practical and scalable structural health monitoring of pressure vessel systems. Full article

The mathematical characterization of non-stationary signals remains a significant challenge, particularly when impulsive components are obscured by high-dimensional noise and structural coupling. This paper proposes an application-driven mathematical methodology for a learnable discrete wavelet transform (LDWT) that combines classical multi-resolution analysis with task-optimized data-driven adaptivity. Rather than introducing entirely new foundational theory, our approach strategically relaxes constraints from orthogonal wavelet theory within the non-perfect reconstruction filter bank framework, enabling controlled spectral decomposition optimized for supervised fault diagnosis. We introduce a specialized regularization term based on the half-band property to ensure spectral complementarity and minimize cross-band correlation, while a Jacobian-based stabilization approach is formulated to ensure the convergence of filter coefficients during optimization. The proposed algorithmic architecture, LDBRFnet, features a dual-branch encoder system designed to capture the mathematical synergy between sub-band-level global statistics and time-domain local morphology. This dual-view representation effectively mitigates feature leakage and overconfidence in classification. Theoretical analysis and numerical experiments demonstrate that the learned filters satisfy the frequency-shift property and maintain robust spectral partitioning even under low signal-to-noise ratios. Validation on complex vibration datasets confirms that the framework achieves superior diagnostic accuracy (over 95.5%) and computational efficiency, reducing model parameters by 96.7% compared to state-of-the-art baselines. This work provides a generalizable mathematical approach for adaptive signal decomposition and robust pattern recognition in interdisciplinary applications. Full article

The minimum fuel transfer problem in low-thrust trajectory optimization remains a major challenge and is typically addressed using bang-bang control. A novel methodology integrating Adaptive Multiresolution Collocation (AMRC) and Sequential Convex Programming (SCP) to solve the minimum-fuel low-thrust trajectory optimization problem is proposed. First, the approach employs the cubic spline wavelet-like transform for mesh refinement, where wavelet coefficients serve as error indicators to dynamically concentrate nodes in regions of rapid state variation. Then, the nonlinear programming problem is convexified via control variable relaxation and small-perturbation linearization, reformulated as a second-order cone programming (SOCP) problem, and efficiently solved using convex optimization tools. Subsequently, progressive selection of the location points ensures rapid and accurate convergence to the optimal trajectory. Finally, numerical simulations of Earth–Mars and Earth–Venus transfer validate the effectiveness and accuracy of the AMRC-based method. Compared with conventional approaches, the proposed method achieves comparable optimality while markedly improving computational efficiency, precisely localizing switching times, and improving numerical precision, requiring only 29.7% of the nodes and 14.7% of the computation time of uniform-grid convex optimization, achieving fuel-optimal deviations within 0.07% of the indirect method and demonstrating accuracy improvements of 2–3 orders of magnitude over GPOPS. Full article

This article introduces an automaton designed to improve feasible solutions to the Monge–Kantorovich (MK) problem, particularly effective when the cost function is continuous. To enhance its performance, a good initial solution is obtained using the discrete wavelet transform. Specifically, a transportation problem is solved where the cost matrix is composed of the approximation coefficients of the transform, reducing the number of variables to one quarter of the original discrete problem. The solution to this reduced problem is extended using the detail coefficients, yielding a feasible solution to the original problem. This solution serves as the initial state of the tuning automaton, whose final states provide approximations to the optimal solution of the transportation problem. Full article

Accurate and efficient detection is pivotal for tiny objects in remote sensing. However, achieving a favorable accuracy-efficiency trade-off remains challenging due to the few informative pixels of small targets, frequent occlusions, cluttered backgrounds, and detail degradation introduced by downsampling and multi-scale fusion. To address these challenges, we propose WEYOLO, a wavelet-enhanced detector that explicitly models frequency components and adaptively strengthens high-frequency cues to improve tiny-object robustness while maintaining competitive efficiency in inference speed and model size for remote-sensing deployment. To preserve edges and textures when spatial resolution is reduced, we design a Frequency-Aware Lifting Haar (FaLH) backbone that decomposes features into directional sub-bands and retains them during downsampling, preventing the loss of high-frequency information. Next, to address the blurring and detail loss caused by conventional pooling during multi-scale fusion, we introduce a Frequency-Domain Pyramid-Pooling (FDPP) module that performs wavelet-based multi-resolution analysis for frequency-aware feature-pyramid fusion. Additionally, we propose a stable size-aware quality focal regression loss that unifies Focaler-CIoU and size-aware DFL into a single objective, improving robustness and overall accuracy for small objects. Comprehensive experiments show that WEYOLO improves precision and recall over the baseline by 3.2%/4.2% on VisDrone and 2.6%/9.7% on TT100K; on AI-TOD, it achieves 47.5% mAP@0.5 and 21.3% mAP@0.5:0.95. Meanwhile, it reduces the parameter count by 60%, achieving a strong accuracy-efficiency balance for practical aerial sensing deployment. Full article

Characterizing instability in gas–liquid flows is difficult because flow dynamics interact across multiple scales. In this work, we develop an integrated framework that combines multi-resolution analysis with composite multiscale equiprobable symbolic sample entropy (MRA-CMESSE). This combination enables us to examine flow instability from a multistructural and multiscale perspective. A comprehensive evaluation across four distinct metrics shows that our method is more robust to changes in data length than multiscale sample entropy and composite multiscale sample entropy approaches. Furthermore, MRA-CMESSE is applied to analyze differential pressure time series from vertical air–water two-phase flow, providing a quantitative characterization of the instability of three flow patterns. Among these, bubble flow is the most unstable, with energy spread out and high complexity at small scales; slug flow is the most stable, with its energy focused at larger scales with low complexity, and churn flow falls in between. A central finding is that as superficial gas velocity increases, energy and complexity shift to the meso-scale and micro-scale. This quantitative analysis identifies increased agitation at the meso-scale and micro-scale as the primary driver of enhanced overall flow instability. This framework offers a new quantitative basis for analyzing gas–liquid two-phase flows and strengthens the physical foundation for the monitoring and control of related industrial systems. Full article

We study the predictability and cross-market structural similarity of Brent, WTI, and Dubai crude oil futures by means of a wavelet-based Sharma–Mittal energy entropy measure. The proposed framework combines multiresolution wavelet decomposition with a parametric generalised entropy, allowing the characterisation of informational complexity across scales and entropic parameters. We show that predictability is jointly scale- and parameter-dependent. Despite this dependence, the resulting wavelet entropy surfaces exhibit a high degree of geometric similarity across the three benchmarks. A discrepancy analysis further indicates that cross-market differences are localised in restricted regions of the parameter space, whereas intermediate scales are associated with maximal entropy values. Outside such regions, the entropy surfaces converge. Overall, the results provide evidence of a common multi-scale entropic structure underlying crude oil benchmarks, with regional effects affecting predictability without altering the global structural properties. These findings are consistent with the hypothesis of strong informational integration in global oil markets. Full article