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Keywords = power-series theory

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23 pages, 4929 KB  
Article
Research on the Coordination of Surge Protectors in Communication Power Systems
by Kang Yang, Hongyan Xing, Zhoulong Wang and Linlong Shi
Energies 2026, 19(10), 2454; https://doi.org/10.3390/en19102454 - 20 May 2026
Abstract
To address the issue of coordination failure in multi-stage surge protective devices (SPDs) under lightning surges in communication power systems, this study employs traveling wave propagation theory and electromagnetic transient simulations using the PSCAD/EMTDC platform. It systematically evaluates how lightning strike location, interstage [...] Read more.
To address the issue of coordination failure in multi-stage surge protective devices (SPDs) under lightning surges in communication power systems, this study employs traveling wave propagation theory and electromagnetic transient simulations using the PSCAD/EMTDC platform. It systematically evaluates how lightning strike location, interstage cable length, and load type affect energy coordination and overvoltage response in a two-stage SPD configuration. By combining time-domain and frequency-domain analysis, the coupling mechanism of SPD conduction timing is revealed. There exists a critical length for the interstage cable to ensure coordinated operation of the SPDs. This critical length decreases with increasing surge intensity but increases significantly with greater lightning strike distance. Incorporating an appropriate series inductor can provide the necessary time delay, serving as an alternative to using a long cable. For capacitive loads, although an excessively short cable can reduce the amplitude of oscillatory voltage spikes, it aggravates the surge steepness, thereby stressing the SPD. These oscillations can be effectively suppressed by installing a damping resistor in front of the SPD2. Furthermore, the study reveals a strong coupling between energy coordination and overvoltage behavior under capacitive load conditions, indicating that the two must be jointly optimized. The parameter configurations and practical recommendations presented offer quantitative design guidance for SPD selection, cable layout, and resonance suppression in communication power systems. Full article
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24 pages, 4226 KB  
Article
Day-Ahead Optimal Scheduling for Electric Bus PV-Storage Charging Station Under Uncertainty: An IGDT-Based Approach
by Tao Xin, Senyong Fan, Peixin Chang, Qing Yang, Yan Bao, Weige Zhang and Peng Liu
Batteries 2026, 12(5), 167; https://doi.org/10.3390/batteries12050167 - 12 May 2026
Viewed by 266
Abstract
Efficient scheduling of electric bus (EB) photovoltaic-storage charging stations (PSCSs) is essential for ensuring the operational economy of public transit and the security of the power grid. Existing scheduling studies generally simplify charging and storage efficiencies as fixed constants, neglecting their dynamic dependence [...] Read more.
Efficient scheduling of electric bus (EB) photovoltaic-storage charging stations (PSCSs) is essential for ensuring the operational economy of public transit and the security of the power grid. Existing scheduling studies generally simplify charging and storage efficiencies as fixed constants, neglecting their dynamic dependence on power levels. Meanwhile, the stochasticity of photovoltaic (PV) generation further complicates scheduling decisions. To address these issues, this paper proposes a day-ahead robust scheduling method for EB PSCSs that incorporates dynamic charging efficiency. First, the dynamic battery efficiency model is reasonably simplified and reformulated, and the big-M method is employed to transform the nonlinear efficiency model into an equivalent set of linear constraints, thereby effectively integrating dynamic efficiency characteristics into the day-ahead optimization framework. Then, information gap decision theory (IGDT) is adopted to model PV output uncertainty, establishing a risk-averse decision optimization model. On this basis, a two-stage solution algorithm integrated with the bisection method is designed to decompose the IGDT optimization problem into a series of linear programming subproblems, balancing solution accuracy and computational efficiency. Case studies validate the effectiveness of the proposed method. The results demonstrate that the dynamic efficiency model significantly improves scheduling accuracy, and the IGDT framework provides a reliable, robust scheduling strategy for PSCSs under limited information conditions. Full article
(This article belongs to the Section Energy Storage System Aging, Diagnosis and Safety)
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21 pages, 8078 KB  
Article
Damage-Softening Model and Shear Behavior of Geosynthetic–Calcareous Sand Interface Based on Large-Scale Monotonic Shear Tests
by Liangjie Xu, Xinzhi Wang, Ren Wang and Jicheng Zhang
J. Mar. Sci. Eng. 2026, 14(9), 836; https://doi.org/10.3390/jmse14090836 - 30 Apr 2026
Viewed by 230
Abstract
Geosynthetics-reinforced soil technology represents an innovative reinforcement method for calcareous sand foundations and revetment engineering in coral reef areas. The interaction response at the reinforced soil interface directly influences the safety and stability of reinforced soil structures. However, research on the interaction mechanisms [...] Read more.
Geosynthetics-reinforced soil technology represents an innovative reinforcement method for calcareous sand foundations and revetment engineering in coral reef areas. The interaction response at the reinforced soil interface directly influences the safety and stability of reinforced soil structures. However, research on the interaction mechanisms between geosynthetics and calcareous sand interfaces remains insufficient. Therefore, this paper investigates the effects of different normal stresses and various interface types on the shear characteristics of the geosynthetics–calcareous sand interface through a series of large-scale monotonic direct shear tests. By integrating statistical damage theory and accounting for the influence of residual strength, we establish the constitutive relation for interface damage. The results indicate that the shear stress–displacement curves for both the geosynthetics–calcareous sand interface and the unreinforced calcareous sand exhibit softening behavior. Furthermore, the relationship between the interface shear modulus and horizontal displacement for the geogrid–calcareous sand and unreinforced calcareous sand adheres to a power function model, while the relationship for the geotextile–calcareous sand follows a logarithmic function model. In the structural design of geosynthetics-reinforced calcareous sand, it is crucial to consider the influence of residual shear strength on structural stability. This study proposes a statistical damage constitutive model that accounts for the strain-softening characteristics of the geosynthetics–calcareous sand interface, while also considering the impact of residual strength. The findings provide a theoretical basis for the stability analysis of geosynthetics-reinforced calcareous sand structures in coral reefs with significant engineering implications for island reef construction, coastal development, and bank slope protection projects. Full article
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21 pages, 1899 KB  
Article
Risk Assessment of Distribution Network Based on Dirichlet Process Mixture Model and the Cumulant Method
by Yuxuan Huang, Yuwei Chen, Zhenguo Shao, Feixiong Chen, Yunting Shao, Yifan Zhang and Changming Chen
Inventions 2026, 11(2), 42; https://doi.org/10.3390/inventions11020042 - 21 Apr 2026
Viewed by 254
Abstract
To address the increased operational risk in distribution network caused by the grid integration of distributed wind power, a distribution network risk assessment method that combines a Dirichlet process mixture model (DPMM) with the cumulant method (CM) is proposed, to achieve effective quantification [...] Read more.
To address the increased operational risk in distribution network caused by the grid integration of distributed wind power, a distribution network risk assessment method that combines a Dirichlet process mixture model (DPMM) with the cumulant method (CM) is proposed, to achieve effective quantification of operational risk. Firstly, a DPMM is employed to cluster wind power output data, and adaptive kernel density estimation is introduced to construct a probabilistic model of wind power output, thereby improving local fitting accuracy. Secondly, uncertainties arising from wind generation and load are considered, and a probabilistic power flow model for the distribution network is established based on the CM and the Gram–Charlier series expansion, in order to obtain the probability distributions of state variables and branch power flows. Then, distribution entropy theory is introduced to quantify the severity of limit violations for state variables such as voltage and power, so that operational risk assessment is enabled. Finally, simulations are conducted on a modified IEEE 34-bus distribution test system, and the results demonstrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Recent Advances and Challenges in Emerging Power Systems: 3rd Edition)
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22 pages, 4371 KB  
Article
Efficiency-Based CLLC Bidirectional DC-DC Converter Using Copolar Switching
by Yueh-Tsung Hsieh, Chun-Hao Chen, Wen-Yuh Shieh, Chi-Chun Haung, Wei-Hua Chieng and Edward Yi Chang
Energies 2026, 19(8), 1820; https://doi.org/10.3390/en19081820 - 8 Apr 2026
Viewed by 482
Abstract
This paper introduces a novel switching method called copolar switching, designed to maintain high power efficiency in CLLC bidirectional chargers across different modes of operation. The proposed method sets the switching frequency close to the resonance of the LC tank within the CLLC [...] Read more.
This paper introduces a novel switching method called copolar switching, designed to maintain high power efficiency in CLLC bidirectional chargers across different modes of operation. The proposed method sets the switching frequency close to the resonance of the LC tank within the CLLC circuit, ensuring efficient power conversion in both the forward (charging) and reverse (discharging) modes. Using Fourier series analysis and circuit theory, the necessary duty cycle for achieving the target efficiency is derived and applied to the full bridge on the high-voltage side in reverse mode. Copolar switching ensures that the entire CLLC circuit operates at a single resonant frequency, addressing the conventional issue of unbalanced efficiency between forward and reverse power conversions. A prototype circuit was designed for power conversion between 400 V and 48 V. Experimental results demonstrate 1 kW power conversion with 97% efficiency in forward mode and 800 W conversion with the same efficiency in reverse mode. Additionally, the copolar switching method shows potential for applications requiring voltage output adjustments, such as converting between 400 V and 50 V. Full article
(This article belongs to the Section F1: Electrical Power System)
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40 pages, 6580 KB  
Article
Self-Organized Criticality and Multifractal Characteristics of Power-System Blackouts: A Long-Term Empirical Study of China’s Power System
by Qun Yu, Zhiyi Zhou, Jiongcheng Yan, Weimin Sun and Yuqing Qu
Fractal Fract. 2026, 10(4), 239; https://doi.org/10.3390/fractalfract10040239 - 3 Apr 2026
Viewed by 463
Abstract
Power system blackouts represent typical manifestations of instability in complex systems, whose evolution often exhibits non-stationarity, long-range correlations, and nonlinear scaling behavior. Most reliability assessment methods widely used in engineering practice are built on the core assumptions of event independence and light-tailed distribution, [...] Read more.
Power system blackouts represent typical manifestations of instability in complex systems, whose evolution often exhibits non-stationarity, long-range correlations, and nonlinear scaling behavior. Most reliability assessment methods widely used in engineering practice are built on the core assumptions of event independence and light-tailed distribution, which will inevitably lead to systematic underestimation of extreme tail risks when blackouts actually present long-range memory and power-law heavy-tailed characteristics. Based on long-cycle historical blackout records of China’s power grid spanning 1981–2025, this paper develops an integrated framework combining Self-Organized Criticality (SOC) theory, Hurst exponent analysis, symbolic time-series methods, and Multifractal Detrended Fluctuation Analysis (MFDFA). This study systematically characterizes the evolution law and inherent dependence structure of blackout events from four dimensions: statistical scaling, temporal correlation, nonlinear structure, and multi-scale fractal spectrum. The results show that both the load-loss magnitudes and inter-event intervals of blackouts follow strict power-law distributions, with the system exhibiting scaling behavior consistent with SOC theory. The blackout event sequence presents significant long-range positive correlation and self-similarity, confirming a persistent long-term memory effect in the system evolution. Symbolic analysis further reveals the nonlinear fluctuation patterns and burst clustering behavior of the blackout process, reflecting the intermittency and complexity of blackout risks. MFDFA results verify that the blackout sequence has a broad-spectrum multifractal structure across different temporal scales, and Monte Carlo shuffle tests demonstrate that this multifractality mainly arises from intrinsic long-range temporal correlations, rather than being driven solely by heavy-tailed distribution. This study confirms that blackouts in China’s power grid are not random independent events, but present fractal statistical characteristics consistent with the self-organized critical mechanism. The findings provide a novel fractal perspective and quantitative framework for the statistical characterization, operational security assessment, and multi-scale early-warning modeling of blackout risks in China’s large-scale power systems. Full article
(This article belongs to the Special Issue Multifractal Analysis and Complex Systems)
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21 pages, 1203 KB  
Article
Performance in Action and Textual Re-Creation: A Study of the Dual Performativity in Hyakuzahōdan Kikigakishō (百座法談聞書抄)
by Ziqi Zhang, Kehua Liu and Yingbo Zhao
Religions 2026, 17(4), 410; https://doi.org/10.3390/rel17040410 - 24 Mar 2026
Viewed by 853
Abstract
The Hyakuzahōdan Kikigakishō (百座法談聞書抄, hereafter Hyakuza 百座), compiled in the late Heian period, is an important Buddhist document that records a hundred-day lecture series on the Lotus Sutra (法華経). While previous scholarship has recognized the constructed nature of the text as a kikigaki [...] Read more.
The Hyakuzahōdan Kikigakishō (百座法談聞書抄, hereafter Hyakuza 百座), compiled in the late Heian period, is an important Buddhist document that records a hundred-day lecture series on the Lotus Sutra (法華経). While previous scholarship has recognized the constructed nature of the text as a kikigaki (聞書), it has predominantly focused on content analysis, implicitly treating the text as a transparent window into the actual preaching event. To move beyond this limitation, this study proposes the analytical framework of dual performativity and, drawing on Diana Taylor’s theory of the archive and the repertoire, reexamines the text’s generative logic and political implications. This study argues that the Hyakuza embodies two interrelated forms of performance: first, the performativity of the hōdan (法談) as a live ritual, understood as a repertoire performance that constructs immediate authority through body, voice, and situational dynamics; second, the performativity of the kikigaki as textual construction, understood as an archival performance that transforms the ephemeral oral event into an authoritative, transmissible text through formulaic rhetoric, localized adaptation, and systematic arrangement. Integrating methodologies from textual history, rhetorical analysis, ritual theory, and intellectual history, this study demonstrates that the Hyakuza is not a neutral transcript of sermons but a meticulous, intentional act of writing with two fundamental aims: on a cultural level, to hierarchically integrate shinbutsu shūgō (神仏習合) through narrative appropriation; on a social level, to symbolically bind Buddhist merit with the institutional identities of aristocrats such as naishinnō (内親王), ultimately serving the self-affirmation internal cohesion, and cultural demarcation of the elite community from the masses, while simultaneously contributing to the state’s project of constructing a unified ideology in the late Heian period. By examining both cross-civilizational universal logic and specific historical context, this study reveals how the Hyakuza’s dual performativity produces and categorizes knowledge narratives while embedding political power dynamics, offering a critical path for the study of kikigaki-genre literature from discourse analysis to politics of textuality. Full article
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29 pages, 426 KB  
Article
Umbral Theory and the Algebra of Formal Power Series
by Roberto Ricci
Axioms 2026, 15(3), 237; https://doi.org/10.3390/axioms15030237 - 21 Mar 2026
Cited by 1 | Viewed by 445
Abstract
Umbral theory, formulated in its modern version by S. Roman and G. C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special function theory. Concepts [...] Read more.
Umbral theory, formulated in its modern version by S. Roman and G. C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special function theory. Concepts like the umbral image and umbral vacuum have been introduced as pivotal elements of the discussion which, albeit effective, lack generality. This article is directed towards endowing the formalism with a rigorous formulation within the context of formal power series with complex coefficients (Ct,). The new formulation is founded on the definition of the umbral operator u as a functional in the “umbral ground state” subalgebra of analytically convergent formal series φC{t}. We consider in detail some specific classes of umbral ground states φ and analyse the conditions for analytic convergence of the corresponding umbral identities, defined as formal series resulting from the action on φ of operators of the form f(ζuμ) with fC{t} and μ,ζC. For these umbral states, we exploit the Gevrey classification of formal power series to establish a connection with the theory of Borel–Laplace resummation, allowing us to make rigorous sense of a large class of—even divergent—umbral identities. As an application of the proposed theoretical framework, we introduce and investigate the properties of new umbral images for the Gaussian trigonometric functions, which emphasise the trigonometric-like nature of these functions and enable defining the concept of a “Gaussian Fourier transform”, a potentially powerful tool for applications. Full article
(This article belongs to the Special Issue Applications in Functional Analysis)
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26 pages, 2811 KB  
Article
Love Wave Propagation in a Piezoelectric Composite Structure with an Inhomogeneous Internal Layer
by Yanqi Zhao, Peng Li, Guochao Fan and Chun Shao
Materials 2026, 19(6), 1151; https://doi.org/10.3390/ma19061151 - 16 Mar 2026
Viewed by 450
Abstract
An inhomogeneous thin internal stratum sometimes exists between two dissimilar materials, which is usually caused by non-uniform thermal distribution, interaction of different media, diffusion impurity or material degeneration and damage. In this paper, it is considered as a functional graded (FG) piezoelectric material [...] Read more.
An inhomogeneous thin internal stratum sometimes exists between two dissimilar materials, which is usually caused by non-uniform thermal distribution, interaction of different media, diffusion impurity or material degeneration and damage. In this paper, it is considered as a functional graded (FG) piezoelectric material in surface acoustic wave devices, and we investigate its effect on Love wave propagation within the framework of the linear piezoelectric theory. Correspondingly, the power series technique is presented and applied to solve the dynamic governing equations, i.e., two-dimensional partial differential equations with variable coefficients, with the convergence and correctness being proved. In this method, the material coefficients can change in random functions along the thickness direction, which reveals the generality of this method to some extent. As the numerical case, the elastic coefficient, piezoelectric coefficient, dielectric permittivity, and mass density change in the linear form but with different graded parameters, and the influence of material inhomogeneity on the Love wave propagation is systematically investigated, including the phase velocity, electromechanical coupling factor, and displacement distribution. In addition, the FG piezoelectric material caused by piezoelectric damage and material bonding is discussed. Numerical results demonstrated that both piezoelectric damaged and material bonding can make the higher modes appear earlier for the electrically open case, decrease the initial phase velocity, and limit the existing region of the fundamental Love mode for the electrically shorted case. The qualitative conclusions and quantitative results can provide a theoretical guide for the structural design of surface wave devices and sensors. Full article
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21 pages, 6110 KB  
Article
Stochastic Dynamic Analysis and Vibration Suppression of FG-GPLRC Cylinder–Plate Combined Structures with Distributed Dynamic Vibration Absorbers
by Qingtao Gong, Ai Zhang, Yao Teng and Yuan Wang
Materials 2026, 19(6), 1082; https://doi.org/10.3390/ma19061082 - 11 Mar 2026
Viewed by 410
Abstract
Cylinder–plate combined structures (CPCS) are widely used in aerospace, marine engineering, and offshore platform systems. During service, they are frequently subjected to stochastic excitations induced by turbulent boundary layers, acoustic loads, hydrodynamic disturbances, and broadband operational vibrations. Excessive random vibration responses may significantly [...] Read more.
Cylinder–plate combined structures (CPCS) are widely used in aerospace, marine engineering, and offshore platform systems. During service, they are frequently subjected to stochastic excitations induced by turbulent boundary layers, acoustic loads, hydrodynamic disturbances, and broadband operational vibrations. Excessive random vibration responses may significantly reduce structural reliability, accelerate fatigue damage, and compromise operational safety. To address these engineering challenges, a unified stochastic dynamic analysis and vibration suppression framework is established for functionally graded graphene platelet-reinforced composites (FG-GPLRC) CPCS equipped with distributed dynamic vibration absorbers (DVAs). Adopting the First-order Shear Deformation Theory (FSDT), a comprehensive energy functional for the CPCS is established, in which the penalty method is implemented to impose boundary conditions and ensure interface continuity. Subsequently, the Pseudo-excitation Method (PEM) is utilized to convert the stochastic vibration analysis into an equivalent deterministic harmonic problem, and the governing equations are spatially discretized by combining the spectral geometric method (SGM) with the Ritz variational procedure, enabling efficient evaluation of power spectral density (PSD) and root-mean-square (RMS) responses. The reliability of the proposed model is verified through a series of numerical validation comparisons. On this basis, comprehensive parametric investigations are conducted to assess how material properties, structural geometries, and critical DVA parameters influence system behavior. The results demonstrate that the incorporation of distributed DVAs can achieve superior vibration suppression performance. This study provides an efficient and reliable theoretical framework for stochastic vibration analysis and damping design of advanced composite plate–shell coupled structures operating in complex random environments, offering important theoretical support for dynamic optimization design in aerospace and marine engineering applications. Full article
(This article belongs to the Special Issue Research on Vibration of Composite Structures)
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20 pages, 736 KB  
Article
Cognitive Biases in Asset Pricing: An Empirical Analysis of the Alphabet Effect and Ticker Fluency in the US Market
by Antonio Pagliaro
Symmetry 2026, 18(3), 477; https://doi.org/10.3390/sym18030477 - 11 Mar 2026
Viewed by 468
Abstract
Behavioral finance theory predicts that Processing Fluency—the subjective ease of parsing a nominal stimulus—should systematically influence investor attention and asset pricing through heuristic-based decision making. Yet modern equity markets, increasingly dominated by High-Frequency Trading (HFT) and algorithmic execution, provide powerful near-instantaneous arbitrage forces [...] Read more.
Behavioral finance theory predicts that Processing Fluency—the subjective ease of parsing a nominal stimulus—should systematically influence investor attention and asset pricing through heuristic-based decision making. Yet modern equity markets, increasingly dominated by High-Frequency Trading (HFT) and algorithmic execution, provide powerful near-instantaneous arbitrage forces that should neutralize any pricing premium arising from superficial nominal cues. Whether cognitive biases such as the “Ticker Fluency” effect and the “Alphabet Effect” persist in this algorithmic environment or have been fully arbitraged away remains an open empirical question with direct implications for the boundary conditions of Processing Fluency Theory. We address this gap by applying a deterministic Heuristic Fluency Score—based on vowel density and consonant cluster penalties—to all 492 S&P 500 constituents over 752 trading days (January 2021–January 2024), estimating individual stock Fama-French 3-Factor Alphas via daily time-series regressions, and testing whether fluency or alphabetical rank explains cross-sectional variation in abnormal returns after controlling for Liquidity, Amihud illiquidity, and GICS Sector Fixed Effects. To guard against Selection Bias, we explicitly contrast a biased illustrative case study (N=25, 2019–2024) against the rigorous full-market analysis. We find no statistically or economically significant effect: the Fluency Score coefficient is β=0.0036 (p=0.495) and the Alphabet Rank coefficient is β=0.0027 (p=0.642), with the results robust to all tested parameterizations (λ[0.05,0.20]; p>0.50 throughout). These findings establish a boundary condition of Processing Fluency Theory: in algorithm-dominated, highly liquid large-cap markets, cognitive biases in nominal cues are fully absorbed by arbitrage, and ticker symbols function as neutral identifiers rather than heuristic signals. Residual effects, if any, are more likely to manifest in attention-based or volume-related outcomes, or in less institutionalized market segments where algorithmic participation is lower. Full article
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21 pages, 5808 KB  
Article
Gyroscope Denoising Algorithm Based on EMD-SSA-VMD Double-Layer Decomposition
by Chuanqian Lv, Yaohong Zhao, Fangzhou Li and Haibo Luo
Sensors 2026, 26(4), 1367; https://doi.org/10.3390/s26041367 - 21 Feb 2026
Viewed by 1431
Abstract
To reduce random errors effectively and improve measurement precision in MEMS gyroscopes, we establish a dual-layer noise suppression method named EMD-SSA-VMD. The algorithm is grounded in empirical mode decomposition (EMD) and variational mode decomposition (VMD), incorporating the sparrow search algorithm (SSA) and entropy [...] Read more.
To reduce random errors effectively and improve measurement precision in MEMS gyroscopes, we establish a dual-layer noise suppression method named EMD-SSA-VMD. The algorithm is grounded in empirical mode decomposition (EMD) and variational mode decomposition (VMD), incorporating the sparrow search algorithm (SSA) and entropy theory. The process starts by breaking down the signal into a series of intrinsic mode functions (IMFs) and a residual via EMD. By calculating the power spectral entropy (PSE) of IMFs, we can sort the signal components into three categories: noise signals, mixed signals, and effective signals. The mixed signals then undergo VMD processing, where SSA optimizes the key decomposition parameters. The sample entropy (SE) of the IMFs from VMD is computed to distinguish between actual signal components and noise. Finally, we combine all valuable signals to reconstruct the denoising signal. MATLAB(R2024b) simulation results show that this algorithm improves both the Signal-to-Noise Ratio (SNR) and the Root Mean Square Error (RMSE), demonstrating a more efficient removal of noise. Experiments on actual gyroscope data confirm these improvements, yielding higher SNR and a waveform that closely matches the original signal. This proves the algorithm’s practical value in engineering applications. Full article
(This article belongs to the Special Issue Feature Papers in Physical Sensors 2025)
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48 pages, 3619 KB  
Article
Comparative Assessment of the Reliability of Non-Recoverable Subsystems of Mining Electronic Equipment Using Various Computational Methods
by Nikita V. Martyushev, Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Georgy E. Kurdyumov, Viktor V. Kondratiev and Antonina I. Karlina
Mathematics 2026, 14(4), 723; https://doi.org/10.3390/math14040723 - 19 Feb 2026
Cited by 1 | Viewed by 600
Abstract
The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysis of several deterministic approaches for reliability estimation, focusing on their computational efficiency, accuracy, [...] Read more.
The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysis of several deterministic approaches for reliability estimation, focusing on their computational efficiency, accuracy, and applicability. The investigated methods include classical boundary techniques (minimal paths and cuts), analytical decomposition based on the Bayes theorem, the logic–probabilistic method (LPM) employing triangle–star transformations, and the algorithmic Structure Convolution Method (SCM), which is based on matrix reduction of the system’s connectivity graph. The reliability problem is formally represented using graph theory, where each element is modeled as a binary variable with independent failures, which is a standard and practically justified assumption for power electronic subsystems operating without common-cause coupling. Numerical experiments were carried out on canonical benchmark topologies—bridge, tree, grid, and random connected graphs—representing different levels of structural complexity. The results demonstrate that the SCM achieves exact reliability values with up to six orders of magnitude acceleration compared to the LPM for systems containing more than 20 elements, while maintaining polynomial computational complexity. Qualitatively, the compared approaches differ in the nature of the output and practical applicability: boundary methods provide fast interval estimates suitable for preliminary screening, whereas decomposition may exhibit a systematic bias for highly connected (non-series–parallel) topologies. In contrast, the SCM consistently preserves exactness while remaining computationally tractable for medium and large sparse-to-moderately dense graphs, making it preferable for repeated recalculations in design and optimization workflows. The methods were implemented in Python 3.7 using NumPy and NetworkX, ensuring transparency and reproducibility. The findings confirm that the SCM is an efficient, scalable, and mathematically rigorous tool for reliability assessment and structural optimization of large-scale non-repairable systems. The presented methodology provides practical guidelines for selecting appropriate reliability evaluation techniques based on system complexity and computational resource constraints. Full article
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16 pages, 818 KB  
Article
Probabilistic Assume–Guarantee Contracts for Islanded Mission-Critical Power System Operations
by Venkatraman Renganathan and Soham Ghosh
Electronics 2026, 15(4), 855; https://doi.org/10.3390/electronics15040855 - 18 Feb 2026
Viewed by 427
Abstract
Design of large-scale power systems is getting increasingly complex nowadays from an operational and reliability standpoint due to the uncertainties associated with the injection of renewables and consumption of load. These uncertainties pose a great challenge in gauging and subsequently obtaining reliable system-level [...] Read more.
Design of large-scale power systems is getting increasingly complex nowadays from an operational and reliability standpoint due to the uncertainties associated with the injection of renewables and consumption of load. These uncertainties pose a great challenge in gauging and subsequently obtaining reliable system-level assurances from subsystem-level guarantees, particularly in mission-critical systems such as those seen in data centers. We propose a formal and modular framework of probabilistic assume–guarantee contracts (PAGCs) for compositional reasoning and control of uncertain power systems, motivated by the need for resilient and verifiable operation in data center power networks. In contrast to classical contracts, which require absolute satisfaction of assumptions and guarantees, PAGCs allow for high-probability satisfaction under system uncertainty and variability. We formalize the syntax and semantics of PAGCs, develop soundness and compositionality theorems, and demonstrate their applicability to power grid components such as generators, transformers, circuit breakers, and loads. Given the current approval bottlenecks in interconnection requests, a growing number of data center operators are opting for islanded generation configuration. A case study on such a modular islanded data center power system is presented to validate the proposed theory. The proposed PAGC application in power networks is promising in several aspects to solve several existing open problems in distributed systems, particularly in future large-scale smart power networks. Full article
(This article belongs to the Section Systems & Control Engineering)
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47 pages, 645 KB  
Review
A Survey of Lattice-Based Physical-Layer Security for Wireless Systems with p-Modular Lattice Constructions
by Hassan Khodaiemehr, Khadijeh Bagheri, Amin Mohajer, Chen Feng, Daniel Panario and Victor C. M. Leung
Entropy 2026, 28(2), 235; https://doi.org/10.3390/e28020235 - 18 Feb 2026
Viewed by 659
Abstract
Physical-layer security (PLS) provides an information-theoretic framework for securing wireless communications by exploiting channel and signal-structure asymmetries, thereby avoiding reliance on computational hardness assumptions. Within this setting, lattice codes and their algebraic constructions play a central role in achieving secrecy over Gaussian and [...] Read more.
Physical-layer security (PLS) provides an information-theoretic framework for securing wireless communications by exploiting channel and signal-structure asymmetries, thereby avoiding reliance on computational hardness assumptions. Within this setting, lattice codes and their algebraic constructions play a central role in achieving secrecy over Gaussian and fading wiretap channels. This article offers a comprehensive survey of lattice-based wiretap coding, covering foundational concepts in algebraic number theory, Construction A over number fields, and the structure of modular and unimodular lattice families. We review key secrecy metrics, including secrecy gain, flatness factor, and equivocation, and consolidate classical and recent results to provide a unified perspective that links wireless-channel models with their underlying algebraic lattice structures. In addition, we review a newly proposed family of p-modular lattices in Khodaiemehr, H., 2018 constructed from cyclotomic fields Q(ζp) for primes p1(mod4) via a generalized Construction A framework. We characterize their algebraic and geometric properties and establish a non-existence theorem showing that such constructions cannot be extended to prime-power cyclotomic fields Q(ζpn) with n>1. Finally, motivated by the fact that these p-modular lattices naturally yield mixed-signature structures for which classical theta series diverge, we integrate recent advances on indefinite theta series and modular completions. Drawing on Vignéras’ differential framework and generalized error functions, we outline how modularly completed indefinite theta series provide a principled analytic foundation for defining secrecy-relevant quantities in the indefinite setting. Overall, this work serves both as a survey of algebraic lattice techniques for PLS and as a source of new design insights for secure wireless communication systems. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)
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