ABSTRACT Robust bearing fault diagnosis in electric motor‐driven electromechanical systems remains challenging under varying operating conditions, where changes in speed, load, and torque induce substantial distribution shifts in vibration signals. This study presents an end‐to‐end deep learning framework that integrates learnable multi‐band FIR decomposition, a Dynamic Phase Event Encoder (DPEE), and a Selective state space model–convolutional (SSM–Conv) hybrid backbone within a unified differentiable architecture. Unlike conventional approaches that mainly rely on amplitude‐ or spectrum‐oriented representations, the proposed method introduces a phase‐driven intermediate representation designed to capture both localized fault‐related irregularities and longer‐range temporal dependencies. To reflect more realistic monitoring conditions, evaluation was performed using a condition‐based leave‐one‐operating‐condition‐out protocol, ensuring strict separation between training and test conditions and reducing condition‐level data leakage. On the Case Western Reserve University (CWRU) dataset, the framework achieved consistently strong performance across unseen load conditions, while on the more challenging Paderborn dataset, the results varied depending on the severity of the condition shift. Ablation studies further supported the contribution of both the learnable FIR decomposition and the DPEE module. Additional analyses were also conducted to assess robustness and transferability. Under additive white Gaussian noise, the model remained comparatively stable at mild‐to‐moderate SNR levels but showed noticeable degradation under severe noise. Cross‐dataset experiments between CWRU and Paderborn, including target‐domain fine‐tuning with 5%, 10%, and 20% labeled target data, indicated that limited target supervision can substantially improve adaptation. Overall, the results suggest that the proposed framework is a promising approach for reliability‐oriented bearing condition monitoring under variable operating regimes.

This paper presents an energy-efficient photoplethysmography (PPG) sensor IC with adaptive windowing for low-power wearable monitoring. By utilizing the first derivative of the PPG signal (i.e., the velocity of PPG, VPG), the proposed algorithm tracks the PPG peaks and valleys (PAVs), enabling higher sampling rates only when necessary. Validated on the BIDMC dataset, the proposed VPG-based method reduces the PAV missing rate from 9.90% to 3.81% compared with the period-based algorithm. Additional BIDMC evaluations under additive noise and periodic artifact injection characterize its operating boundary, while representative walking examples from the PTT dataset illustrate PAV tracking under real motion-degraded conditions. The proposed IC, fabricated in a 180-nm CMOS process, is validated through in vivo measurements against a clinical-grade reference device. The system achieves mean absolute errors (MAEs) of 0.73 bpm for heart rate and 0.53% for SpO2, while reducing the total power consumption to 10.42 μW per channel, corresponding to a 53% reduction. These results demonstrate a practical low-power PPG sensing solution for wearable monitoring.

Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical nonlinearities inherent in real-world systems including water, energy, agriculture, and financial networks. Here, we present a unified framework for solving discrete-time optimal control with higher order state and control costs of power-law form. By building convex-completion techniques, we derive semi-explicit expressions for control laws, cost-to-go functions, and recursive coefficient dynamics across deterministic and stochastic system settings. Key contributions include variance-aware solutions under additive and multiplicative noise, extensions to mean-field-type-dependent dynamics, and conditions that ensure the positivity of recursive coefficients. In particular, we establish that higher order costs induce less aggressive control policies (lower action changes) compared to quadratic formulations, a finding that is validated through numerical analyses.

Laser active polarization imaging is susceptible to coherent speckle noise, which severely degrades both image quality and the accuracy of polarization parameter estimation. Existing polarimetric denoising methods, predominantly designed for additive noise models, struggle to handle speckle noise due to its complex statistical characteristics while failing to fully exploit the structural correlations among multi-channel polarization images. To address these limitations, this study proposes a polarimetric speckle suppression network named PoDeFormer, which achieves effective speckle removal by establishing the intrinsic connection between incoherent illumination and coherent speckle in laser active polarization imaging. Experimental results demonstrate that the network not only effectively removes speckle noise while preserving polarization information integrity but also enables fast inference with minimal computational overhead, providing an efficient and reliable solution for real-time denoising in laser active polarization imaging applications.

Smart Grids rely on robust communication infrastructures to monitor, control, and stabilize information in real time across geographically distributed energy resources. Trellis Coded Modulation (TCM) is a well-established technique for improving spectral efficiency and reliability, particularly in bandwidth-constrained and noisy channels. By combining convolutional coding with multilevel modulation, TCM achieves significant coding gains without increasing bandwidth, making it well suited for Smart Grid communication links. Turbo Trellis Coded Modulation (TTCM) extends TCM by incorporating parallel concatenated trellis encoders with iterative decoding, further enhancing performance and robustness under a wide range of channel distortions, including additive noise and fading. In this paper, we present the underlying mathematical framework for TCM and TTCM, simulation results under AWGN and Rayleigh fading channels, and comparisons to uncoded transmission. We also discuss future prospects of TCM, including integration with AI-driven adaptive coding and 5G-enabled Smart Grid infrastructures, highlighting the critical role of high-reliability communication systems in next-generation energy networks. Consequently, TTCM offers a hybrid solution that combines strong error correction with efficient bandwidth utilization, ensuring dependable communication for reliability-critical Smart Grid applications.

High-resolution range profile (HRRP) target recognition has advanced with deep learning, yet most existing methods rely primarily on data-driven feature extraction and still face challenges in physical interpretability and noise robustness. To address these issues, this paper proposes a physics-guided dual-branch fusion (PGDBF) model. It consists of two parallel branches: a data-driven branch extracts discriminative features from raw HRRPs, while a physics-guided branch estimates sparse peak parameters (position and intensity) and reconstructs the signal envelope under sparsity constraints. Cross-attention adaptively fuses the two branches. Experiments on measured ten-class aircraft HRRP data show that PGDBF achieves higher accuracy and improved robustness under additive Gaussian noise in the evaluated fixed-route scenario. Visualizations confirm that the estimated peaks align with dominant HRRP energy, linking model variables to physically meaningful peak locations and intensities. These results suggest that integrating explicit peak parameter estimation with data-driven learning is a promising direction for improving HRRP recognition robustness and interpretability under low-SNR conditions.

Early stopping is a standard form of implicit regularization in neural sequence models, but criteria based solely on validation loss can become unstable or weakly informative in noisy, non-stationary, or weakly separated regimes. We propose Symbolic Early Stopping (SES), a representation-aware hybrid stopping criterion that monitors the evolution of validation hidden-state organization during training. At each epoch, SES constructs a Mapper-based symbolic abstraction of hidden representations extracted from a fixed monitored layer, transforms latent trajectories into symbol sequences, and summarizes them through a compact set of symbolic–dynamic descriptors capturing sequential complexity, transition uncertainty, and geometric dispersion. These descriptors are aggregated into a single symbolic stability score, which is combined with validation-loss monitoring to detect convergence of the learned representation. We evaluate SES on recurrent, bidirectional recurrent, and encoder-only Transformer architectures across multiple time-series regimes with different levels of structural regularity and noise. The results indicate that SES frequently terminates training substantially earlier than conservative loss-based baselines while preserving a competitive quality–efficiency trade-off relative to oracle validation-based stopping. Robustness experiments under additive input noise show that the symbolic monitoring signal remains informative under moderate perturbations, although its advantage is not uniform across all datasets and model classes. A layer-wise analysis further suggests that useful stopping signals may emerge before the final validation curve fully stabilizes, reflecting earlier organization of latent representations. Overall, SES provides an interpretable and computationally tractable framework for representation-level early stopping in neural sequence modeling.

Synthetic mammography (SM) derived from digital breast tomosynthesis differs fundamentally from conventional digital mammography (DM) in noise characteristics; however, these differences remain poorly understood. This study aimed to comprehensively characterize the noise structures unique to SM and to clarify their physical origins through comparison with DM. SM and DM images were analyzed using a multi-perspective framework that integrated the normalized noise power spectrum (NPS), noise factor analysis based on the relative standard deviation method, subtraction-based analysis, and pixel-wise signal-to-noise ratio (SNR) maps. Directional NPS was evaluated to assess anisotropy, while subtracted images were used to distinguish fixed-pattern noise from processing-related noise. Noise factor analysis was applied to quantify Poisson, multiplicative, and additive noise contributions, and SNR maps derived from repeated acquisitions were used to evaluate pixel-level reproducibility. Compared with DM, SM images exhibited pronounced anisotropy and stronger spatial correlation in the NPS, reflecting structural noise introduced during image synthesis. The NPS of subtracted images closely matched that of the original SM images, indicating that the dominant noise components were not spatially fixed patterns but rather randomly generated structural texture noise. Noise factor analysis demonstrated that multiplicative noise dominated SM images across all dose levels. No clear differences were observed in the SNR maps, whereas the non-stationary nature of SM noise was confirmed. These results demonstrate that SM noise is dominated by randomly generated structural textures with strong spatial correlations. The findings further emphasize the need for multi-perspective and task-based approaches for accurate assessment and effective clinical utilization of SM images.

Orthogonal Frequency Division Multiplexing (OFDM) plays a vital role in both present and emerging communication systems. Despite its advantages, one major limitation of OFDM is the issue of a high peak-to-average power ratio (PAPR). Signal distortion schemes, along with the implications of the signal distribution transformation approach, are effective mechanisms to reduce the PAPR in OFDM systems. The proposed method utilizes the transformation of the OFDM signal's amplitude distribution to lower the PAPR. This is achieved by compressing high-amplitude peaks and expanding lower-amplitude components, while carefully selecting transformation parameters to preserve the average signal power. The proposed algorithm is formulated in accordance with a universal design criterion of the companding scheme, derived through a comprehensive analysis of signal distribution transformation and the associated signal distortion. Based on the constraints imposed by this criterion, a novel companding algorithm is subsequently developed to achieve optimal performance. The graph for the probability density function of the amplitude of the original OFDM signal, along with the signal generated after employing the proposed algorithm, is compared. Theoretical analysis and simulation results confirm that the suggested scheme exhibits a good ability to reduce PAPR and a good bit error rate performance through a solid-state power amplifier over an additive white Gaussian noise channel. Moreover, the power spectral density (PSD) analysis confirms that the proposed scheme exhibits favorable spectral properties, showing minimal spectral regrowth in the compressed OFDM signals. It is also versatile, making it suitable for use with various modulation formats and subcarrier configurations.

This study proposes a novel double-slope chirp symbol, termed double–slope start zero stop minimum (DSSZ–SM), for efficient data communication. Unlike conventional chirp coding, which often involves complex generation and synchronization, the DSSZ–SM provides a simpler structure with inherent clock synchronization using a PWM-based generator. System performance is evaluated through analysis and simulations over additive white Gaussian noise (AWGN) and Rayleigh fading channels. Two asynchronous decoding methods, with and without an integrator, are compared. Results show that the non-integrator approach achieves lower error rates under both channel conditions. The proposed DSSZ–SM offers a simplified and robust alternative for efficient data communication. Keywords: Double-slope chirp, chirp encoding, asynchronous decoding, data communication

Indirect time-of-flight (IToF) cameras reconstruct scene distance from modulated light reflections, but their raw measurements are strongly affected by photon and thermal shot noise, as well as ambient illumination. Thus, the theoretical ability for the sensor's distance map to resolve millimeter-level distance details is not attainable without noise suppression. Due to a highly nonlinear relationship between the temporally modulated light measurements and the phase, however, modeling the stochastic nature of the output distance value is very challenging. For this reason, existing denoising algorithms-including deep neural networks and optimization-based schemes-have relied on simplified noise models (such as additive white Gaussian noise) or learned noise models instead of explicit structure-aware designs tailored to IToF physics, making it difficult to achieve true robustness in real-world scenarios. In this work, we derive an IToF structure-aware Bayesian denoising framework that mathematically propagates the physics-based likelihood model to address corruption of raw IToF sensor measurements by photon and thermal noise to the latent distance value. Our contributions are the physics-motivated mathematical insights and innovations that enable a multi-resolution hierarchical Bayesian minimum-mean-square-error (MMSE) estimator: (i) the underlying statistical joint distribution of distance signal and noise interferometric measurements becomes analytically tractable when modeled as a multinomial-Poisson process; (ii) a logarithmic function linearizes the multinomial data, solving the mathematical challenge of combining this likelihood function with a Gaussian-scale-mixture prior model in linearly transformed feature representation. The resulting BayesToF denoising method is a "coring" rule-based estimation technique that adapts automatically to photon and thermal shot noise and spatial frequency, enabling robust noise suppression without any network training. Experiments on both public and a new noisy IToF sensor dataset (UDayton-IToF2025) demonstrate high-quality distance reconstruction of BayesToF with superior accuracy and generalization over the state-of-the-art IToF denoising techniques.

Biomimetic underwater acoustic communication is attractive for covert military operations because it disguises communication signals as marine-mammal whistles, but in modification-type whistle-mimicking schemes, concealment and communication reliability are tightly coupled and often trade off against each other. The proposed method addresses this problem by establishing a whale-whistle waveform-learning framework that extracts baseband pulses from real false killer whale whistles, learns Nyquist-constrained representative symbol waveforms through an autoencoder, and combines them with envelope-driven adaptive symbol durations to preserve whale-like waveform statistics while equalizing symbol energy. The proposed method is evaluated in terms of mimicry using Evaluation of Covertness of Sound Mimicking Marine Mammals (ECSM3) and higher-order cumulants, and in terms of communication performance using Bit Error Rate (BER) under Additive White Gaussian Noise, a simulated underwater channel, and 1.5 km sea trials against BOK, continuous varying carrier frequency modulation (CV-CFM), Hybrid Orthogonal Division Frequency Modulation (HODFM), and Variable Duartion Phase Shift Keying (V-DPSK) at matched data rates. The proposed method achieves the highest mean ECSM3 score with the smallest variation and the lowest BER among the same-rate schemes; in the 1.5 km sea trial at 250 bps, it attains a BER of 0.0245, which corresponds to about 72.8%, 79.4%, and 87.4% lower BER than V-DPSK, HODFM, and CV-CFM, respectively, demonstrating that learned whale-like pulses can simultaneously improve covertness and reliable underwater acoustic communication.

Analytical evaluation of the estimation accuracy in the LS-Prony method for natural frequency estimation under sampling jitter and additive noise

Invariant measure of non-autonomous stochastic reaction-diffusion equations with infinite delay and additive white noise

Long time stability and strong convergence of an efficient tamed scheme for stochastic Allen-Cahn equation driven by additive white noise

Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate. Here, we address this issue within a scattering-matrix formalism for sensing with coherent light, which allows the quantum Fisher information (QFI) to be evaluated directly from experimentally accessible scattering data without introducing additional noise channels beyond those inherent to the scattering process. We analyze both nondegenerate and degenerate scattering-matrix poles, including EPs of arbitrary order, and show that the QFI per incoming photon flux is bounded and controlled by three key factors: the decay rate of the resonant mode, the strength of the spectral response associated with non-normality, and the adjustment between the scattering states and the information source. For spatially localized perturbations, this implies that the maximal QFI achievable by wavefront shaping is fully determined by the local density of states at the perturbation site. Within this framework, we demonstrate that EPs can enhance the QFI compared to isolated modes or diabolic points with identical decay rates, and that the QFI can be further increased by moving away from the EP toward parameter regimes where non-Hermitian linewidth splitting reduces the decay rate of one mode. We further show that sufficiently small additional internal losses do not alter this overall picture, thereby providing a unified and experimentally relevant perspective on the design of quantum-limited non-Hermitian sensors.

Low-light object detection remains challenging because insufficient illumination obscures visual features and increases the discrepancy between training and testing conditions. Existing approaches often rely on detector redesign, image enhancement, or target-domain data, which may introduce additional complexity during training or inference. This paper presents Exposure-Aware Training (EAT), a lightweight degradation-based training strategy that applies illumination attenuation and additive Gaussian noise to normal-light images during training. The degradation parameters are estimated from real low-light image pairs, while the detector architecture remains unchanged. Our experimental results show that moderate degradation consistently improves low-light detection performance, whereas excessively strong degradation may damage semantic information, especially for small objects. Under both cross-domain and mixed-training settings, EAT achieves stable improvements on YOLOv8 and Faster R-CNN, with more noticeable gains for illumination-sensitive categories. These results indicate that exposing detectors to task-oriented illumination degradation during training can effectively improve low-light detection performance without additional inference overhead.

Zeroing neural network (ZNN) is an effective alternative to gradient neural networks for time-varying problems. However, when applied to complex-domain time-varying matrix inversion, existing ZNNs still employ fixed convergence factors and ignore noises, leading to slow response and potential divergence. To fill this gap, we propose an adaptive noise-tolerant ZNN (ANT-ZNN). Specifically, a noise-tolerant integral ZNN is embedded to reject disturbances, while a fuzzy controller dynamically adjusts an adaptive convergence factor, increasing proportionally with the instantaneous error magnitude and gradually diminishing upon convergence. These designs are synthesised into the ANT-ZNN model that guarantees global stability, finite-time convergence, and robustness against additive noises, as rigorously proved via Lyapunov theory. Comparative simulations further verify that the ANT-ZNN outperforms fixed-parameter models in both noise-free and noisy environments.

Hybrid brain–computer interfaces (BCIs) have attracted growing research attention because they combine the millisecond-level temporal resolution of electroencephalography (EEG) with the spatially informative hemodynamic responses of functional near-infrared spectroscopy (fNIRS). However, most existing deep fusion methods rely on static late-fusion strategies, which tend to underexploit latent cross-modal dependencies and are vulnerable to modality-specific signal degradation. To address these limitations, we propose MGFNet, a multi-granularity fusion network for hybrid BCI decoding. MGFNet contains three components: (1) intra-modal encoders that learn modality-specific spatiotemporal representations from EEG, oxygenated hemoglobin (HbO), and deoxygenated hemoglobin (HbR) signals; (2) cross-modal interaction encoders that temporally align paired modalities and use dilated convolutions to capture long-range EEG-fNIRS dependencies; and (3) a Coupling-Guided Sparse Component Routing (CGSCR) module that estimates sample-specific cross-modal coupling and performs adaptive discrete routing. We further introduce a deep supervision strategy to stabilize optimization and improve branch-level discriminability. Under a within-subject held-out evaluation protocol on a public benchmark dataset, MGFNet achieved classification accuracies of 99.40% on the n-back task and 99.03% on the word generation (WG) task, outperforming representative comparison methods evaluated under a matched protocol. Ablation studies further confirmed the contributions of the intra-modal encoders, the cross-modal interaction encoders, and the CGSCR module. Under controlled EEG corruption with additive white Gaussian noise at −10 dB, MGFNet outperformed a static-fusion variant by 9.23 percentage points on the n-back task and 6.31 percentage points on the WG task. These results support the effectiveness of MGFNet in the present offline within-subject setting and indicate improved robustness under controlled single-modality degradation.

Sensorless permanent magnet synchronous motor (PMSM) drives rely on accurate rotor electrical angle and speed estimation, vulnerable to noisy currents, quantization, and sensor biases. Fixed-bandwidth phase-locked loops (PLLs) entail an intrinsic trade-off between fast transient tracking and high-frequency noise rejection. This paper proposes an adaptive PLL based on linear active disturbance rejection control (LADRC), where a virtual coordinate formulation treats electrical-angle mismatch as a lumped disturbance estimated online by a linear extended state observer (LESO). The observer bandwidth dynamically adapts to the LESO innovation. To optimize performance, adaptive-law parameters are tuned offline via success-history adaptive differential evolution with linear population size reduction (L-SHADE). Comparative simulations against a proportional-integral PLL indicate substantially improved robustness to measurement noise, analog-to-digital quantization, and current-sensor DC offset. Specifically, the speed root-mean-square error decreases from to under additive noise, and from to under 12-bit quantization at . These enhancements reduce reliance on high-precision sensing hardware, offering a practical solution for low-cost, highly reliable motor control in complex industrial environments.