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18 pages, 3505 KB  
Article
Online Robust Detection of Structural Anomaly Under Environmental Variability via Orthogonal Projection and Noisy Low-Rank Matrix Completion
by Peng Ren, Le Zhou, Heng Zhang, Xiaochu Wang, Wei Li and Peng Niu
Buildings 2025, 15(20), 3749; https://doi.org/10.3390/buildings15203749 - 17 Oct 2025
Abstract
A long-standing challenge for the structural health monitoring (SHM) community is the masking effect of environmental variability, typically addressed by orthogonal projection (OP)-based data normalization to isolate the influence of environmental variability and enable structural anomaly detection. However, conventional OP techniques, such as [...] Read more.
A long-standing challenge for the structural health monitoring (SHM) community is the masking effect of environmental variability, typically addressed by orthogonal projection (OP)-based data normalization to isolate the influence of environmental variability and enable structural anomaly detection. However, conventional OP techniques, such as principal component analysis, rely on clean and complete data, and their performance degrades in the presence of outliers or missing entries. To overcome this limitation, this paper proposes an integrated approach that combines OP with noisy low-rank matrix completion (NLRMC). The main advantage of NLRMC is its ability to couple low-rank and sparse decomposition with matrix completion, simultaneously handling data corruption and missingness to recover incomplete datasets and enable robust anomaly detection. By incorporating novelty-indicator extraction, a fully online, unsupervised anomaly-detection procedure is established. Validation on a vibration-based SHM dataset from the KW51 railway bridge confirms that the NLRMC-OP approach achieves reliable detection of operational state changes before and after retrofitting, even under both data corruption and missing scenarios. This study advances the usability of SHM data and facilitates efficient decision-making, while also highlighting the broader significance of leveraging the low-rank data structure in AI-enabled operation and maintenance of civil infra-structure. Full article
(This article belongs to the Section Building Structures)
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22 pages, 4783 KB  
Article
Underwater Target Search Path Planning Based on Sound Speed Profile Clustering and Improved Ant Colony Optimization
by Wenjun Wang, Yuhao Liu, Wenbin Xiao and Longquan Shang
J. Mar. Sci. Eng. 2025, 13(10), 1983; https://doi.org/10.3390/jmse13101983 - 16 Oct 2025
Viewed by 121
Abstract
To address the problems of low efficiency and poor real-time performance in underwater acoustic modeling, as well as the requirement of maximizing search coverage for underwater target search path planning, this paper proposed an efficient path planning method based on Sound Speed Profile [...] Read more.
To address the problems of low efficiency and poor real-time performance in underwater acoustic modeling, as well as the requirement of maximizing search coverage for underwater target search path planning, this paper proposed an efficient path planning method based on Sound Speed Profile (SSP) clustering. Firstly, the SSPs were dimensionally reduced via Empirical Orthogonal Function (EOF) decomposition, and the sea area was divided into 10 acoustic sub-areas using K-means clustering after fusing geographic coordinates and terrain information, thereby constructing a block-wise sound field model. Secondly, with the active sonar equation as the core, sonar parameters such as the noise level and target strength were solved, respectively, to generate a spatial distribution matrix of search distances. Finally, an Improved Ant Colony Optimization (IACO) algorithm was modified by dynamically setting the pheromone evaporation rate and improving the heuristic information for search path optimization. Numerical experiments showed that clustering significantly improves the efficiency of sound field modeling, reducing the time consumption of the transmission loss calculation from 24.74 h to 10.84 min. The IACO increased the average search coverage from 47.96% to 86.01%, with an improvement of 79.34%. The performance of IACO is superior to those of the compared algorithms, providing support for efficient underwater target search. Full article
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24 pages, 7771 KB  
Article
Cross-Domain OTFS Detection via Delay–Doppler Decoupling: Reduced-Complexity Design and Performance Analysis
by Mengmeng Liu, Shuangyang Li, Baoming Bai and Giuseppe Caire
Entropy 2025, 27(10), 1062; https://doi.org/10.3390/e27101062 - 13 Oct 2025
Viewed by 175
Abstract
In this paper, a reduced-complexity cross-domain iterative detection for orthogonal time frequency space (OTFS) modulation is proposed that exploits channel properties in both time and delay–Doppler domains. Specifically, we first show that in the time-domain effective channel, the path delay only introduces interference [...] Read more.
In this paper, a reduced-complexity cross-domain iterative detection for orthogonal time frequency space (OTFS) modulation is proposed that exploits channel properties in both time and delay–Doppler domains. Specifically, we first show that in the time-domain effective channel, the path delay only introduces interference among samples in adjacent time slots, while the Doppler becomes a phase term that does not affect the channel sparsity. This investigation indicates that the effects of delay and Doppler can be decoupled and treated separately. This “band-limited” matrix structure further motivates us to apply a reduced-size linear minimum mean square error (LMMSE) filter to eliminate the effect of delay in the time domain, while exploiting the cross-domain iteration for minimizing the effect of Doppler by noticing that the time and Doppler are a Fourier dual pair. Furthermore, we apply eigenvalue decomposition to the reduced-size LMMSE estimator, which makes the computational complexity independent of the number of cross-domain iterations, thus significantly reducing the computational complexity. The bias evolution and variance evolution are derived to evaluate the average MSE performance of the proposed scheme, which shows that the proposed estimators suffer from only negligible estimation bias in both time and DD domains. Particularly, the state (MSE) evolution is compared with bounds to verify the effectiveness of the proposed scheme. Simulation results demonstrate that the proposed scheme achieves almost the same error performance as the optimal detection, but only requires a reduced complexity. Full article
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23 pages, 11346 KB  
Article
Polarmetric Consistency Assessment and Calibration Method for Quad-Polarized ScanSAR Based on Cross-Beam Data
by Di Yin, Jitong Duan, Jili Sun, Liangbo Zhao, Xiaochen Wang, Songtao Shangguan, Lihua Zhong and Wen Hong
Remote Sens. 2025, 17(20), 3420; https://doi.org/10.3390/rs17203420 - 13 Oct 2025
Viewed by 158
Abstract
The range-dependence on polarization distortion of spaceborne polarimetric synthetic aperture radar (SAR) affects the accuracy of wide-swath polarization applications, such as environmental monitoring, sea ice classification and ocean wave inversion. Traditional calibration methods, assessing the distortion mainly based on ground experiments, suffer from [...] Read more.
The range-dependence on polarization distortion of spaceborne polarimetric synthetic aperture radar (SAR) affects the accuracy of wide-swath polarization applications, such as environmental monitoring, sea ice classification and ocean wave inversion. Traditional calibration methods, assessing the distortion mainly based on ground experiments, suffer from tedious active calibrator deployment work, which are time-consuming and cost-intensive. This paper proposes a novel polarimetric assessment and calibration method for the quad-polarized wide-swath ScanSAR imaging mode. Firstly, by using distributed target data that satisfy the system reciprocity requirement, we assess the polarization distortion matrices for a single beam in the mode. Secondly, we transfer the matrix results from one beam to another by analyzing data from the overlapping region between beams. Thirdly, we calibrate the quad-polarized data and achieve an overall assessment and calibration results. Compared to traditional calibration methods, the presented method focuses on using cross-beam (overlapping area) data to reduce the dependence on active calibrators and avoid conducting calibration work beam-by-beam. The assessment and calibration experiment is conducted on Gaofen-3 quad-polarized ScanSAR experiment mode data. The calibrated images and polarization decomposition results are compared with those from well-calibrated quad-polarized Stripmap mode data located in the same region. The results of the comparison revealed the effectiveness and accuracy of the proposed method. Full article
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16 pages, 1619 KB  
Article
Effect of Mixing Time on the Thermal Stability and Activation Energies of NiO/PMMA Nanocomposites
by Aytekin Ulutaş
J. Compos. Sci. 2025, 9(10), 557; https://doi.org/10.3390/jcs9100557 - 11 Oct 2025
Viewed by 305
Abstract
In this study, NiO nanoparticle–reinforced PMMA nanocomposites were fabricated by melt blending, and the influence of extrusion mixing time on structural and thermal properties was examined. Mixing durations of 6 and 12 min were applied, and the materials were characterized by X-ray diffraction [...] Read more.
In this study, NiO nanoparticle–reinforced PMMA nanocomposites were fabricated by melt blending, and the influence of extrusion mixing time on structural and thermal properties was examined. Mixing durations of 6 and 12 min were applied, and the materials were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). These analyses confirmed the presence of NiO within the PMMA matrix and indicated that prolonged mixing promoted particle agglomeration. Thermal behavior was assessed by thermogravimetric analysis (TGA) at heating rates of 5, 10, 15, and 20 K·min−1, and activation energies of decomposition were calculated using the Kissinger, Takhor, and Augis–Bennett methods. The results showed that extended mixing reduced composite homogeneity and adversely affected thermal stability. Incorporation of NiO nanoparticles decreased both the onset decomposition temperature and the activation energy compared to pure PMMA, facilitating earlier degradation. At 620 K, pure PMMA exhibited ~8% mass loss, whereas the 12 min blend showed ~12% loss. These findings highlight the importance of nanoparticle dispersion and processing parameters in governing the degradation behavior of PMMA/NiO nanocomposites. Full article
(This article belongs to the Section Polymer Composites)
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26 pages, 2902 KB  
Article
Distributed Phased-Array Radar Mainlobe Interference Suppression and Cooperative Localization Based on CEEMDAN–WOBSS
by Xiang Liu, Huafeng He, Ruike Li, Yubin Wu, Xin Zhang and Yongquan You
Sensors 2025, 25(20), 6277; https://doi.org/10.3390/s25206277 - 10 Oct 2025
Viewed by 383
Abstract
Mainlobe interference can severely degrade the performance of distributed phased-array radar systems in the presence of strong jamming or low-reflectivity targets. This paper introduces a signal–data dual-domain cooperative antijamming and localization (SDCAL) framework that integrates adaptive complete ensemble empirical mode decomposition with improved [...] Read more.
Mainlobe interference can severely degrade the performance of distributed phased-array radar systems in the presence of strong jamming or low-reflectivity targets. This paper introduces a signal–data dual-domain cooperative antijamming and localization (SDCAL) framework that integrates adaptive complete ensemble empirical mode decomposition with improved blind source separation and wavelet optimization (CEEMDAN-WOBSS) for signal-level denoising and separation. Following source separation, CFAR-based pulse compression is applied for precise range estimation, and multi-node data fusion is then used to achieve three-dimensional target localization. Under low signal-to-noise ratio (SNR) conditions, the adaptive CEEMDAN–WOBSS approach reconstructs the signal covariance matrix to preserve subspace rank, thereby accelerating convergence of the separation matrix. The subsequent pulse compression and CFAR detection steps provide reliable inter-node distance measurements for accurate fusion. The simulation results demonstrate that, compared to conventional blind-source-separation methods, the proposed framework markedly enhances interference suppression, detection probability, and localization accuracy—validating its effectiveness for robust collaborative sensing in challenging jamming scenarios. Full article
(This article belongs to the Special Issue Radar Target Detection, Imaging and Recognition)
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102 pages, 1631 KB  
Review
A Comprehensive Review on the Generalized Sylvester Equation AXYB = C
by Qing-Wen Wang and Jiale Gao
Symmetry 2025, 17(10), 1686; https://doi.org/10.3390/sym17101686 - 8 Oct 2025
Viewed by 403
Abstract
Since Roth’s work on the generalized Sylvester equation (GSE) AXYB=C in 1952, related research has consistently attracted significant attention. Building on this, this review systematically summarizes relevant research on GSE from five perspectives: research methods, constrained solutions, [...] Read more.
Since Roth’s work on the generalized Sylvester equation (GSE) AXYB=C in 1952, related research has consistently attracted significant attention. Building on this, this review systematically summarizes relevant research on GSE from five perspectives: research methods, constrained solutions, various generalizations, iterative algorithms, and applications. Furthermore, we provide comments on current research, put forward several intriguing questions, and offer prospects for future research trends. We hope this work can fill the gap in the review literature on GSE and offer some inspiration for subsequent studies in the field. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2025)
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17 pages, 3752 KB  
Article
Operating State Analysis of Asymmetric Reactive Power Compensator via Data Mining
by Yunfei Chen and Yi Zhang
Symmetry 2025, 17(10), 1676; https://doi.org/10.3390/sym17101676 - 7 Oct 2025
Viewed by 218
Abstract
Given the inadequacies in the management of reactive power compensation equipment in distribution networks and insufficient power data mining, existing studies pay little attention to asymmetric reactive power compensation equipment and face pain points such as difficult quantification of nonlinear relationships and challenging [...] Read more.
Given the inadequacies in the management of reactive power compensation equipment in distribution networks and insufficient power data mining, existing studies pay little attention to asymmetric reactive power compensation equipment and face pain points such as difficult quantification of nonlinear relationships and challenging evaluation of mechanical switches. First, this paper proposes a data mining-based diagnostic method for the operating status of asymmetric reactive power compensation equipment: it preprocesses data via singular value decomposition and matrix approximation. Second, it classifies load types with K-means clustering, defines “health degree” by introducing mutual information and a reliability coefficient, constructs dual switching criteria, and defines the switching qualification rate. Third, the TOPSIS method is employed for dual-index comprehensive evaluation, and equipment status levels are classified with statistical analysis. Finally, the case analysis demonstrates that the proposed method is accurate, applicable, and easy to implement, which can serve as a basis for equipment troubleshooting and maintenance, thereby filling the relevant research gap. Full article
(This article belongs to the Section Engineering and Materials)
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13 pages, 379 KB  
Article
Nyström-Based 2D DOA Estimation for URA: Bridging Performance–Complexity Trade-Offs
by Liping Yuan, Ke Wang and Fengkai Luan
Mathematics 2025, 13(19), 3198; https://doi.org/10.3390/math13193198 - 6 Oct 2025
Viewed by 227
Abstract
To address the computational efficiency challenges in two-dimensional (2D) direction-of-arrival (DOA) estimation, a two-stage framework integrating the Nyström approximation with subspace decomposition techniques is proposed in this paper. The methodology strategically integrates the Nyström approximation with subspace decomposition techniques to bridge the critical [...] Read more.
To address the computational efficiency challenges in two-dimensional (2D) direction-of-arrival (DOA) estimation, a two-stage framework integrating the Nyström approximation with subspace decomposition techniques is proposed in this paper. The methodology strategically integrates the Nyström approximation with subspace decomposition techniques to bridge the critical performance–complexity trade-off inherent in high-resolution parameter estimation scenarios. In the first stage, the Nyström method is applied to approximate the signal subspace while simultaneously enabling construction of a reduced rank covariance matrix, which effectively reduces the computational complexity compared with eigenvalue decomposition (EVD) or singular value decomposition (SVD). This innovative approach efficiently derives two distinct signal subspaces that closely approximate those obtained from the full-dimensional covariance matrix but at substantially reduced computational cost. The second stage employs a sophisticated subspace-based estimation technique that leverages the principal singular vectors associated with these approximated subspaces. This process incorporates an iterative refinement mechanism to accurately resolve the paired azimuth and elevation angles comprising the 2D DOA solution. With the use of the Nyström approximation and reduced rank framework, the entire DOA estimation process completely circumvents traditional EVD/SVD operations. This elimination constitutes the core mechanism enabling substantial computational savings without compromising estimation accuracy. Comprehensive numerical simulations rigorously demonstrate that the proposed framework maintains performance competitive with conventional high-complexity estimators while achieving significant complexity reduction. The evaluation benchmarks the method against multiple state-of-the-art DOA estimation techniques across diverse operational scenarios, confirming both its efficacy and robustness under varying signal conditions. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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23 pages, 5971 KB  
Article
Improved MNet-Atten Electric Vehicle Charging Load Forecasting Based on Composite Decomposition and Evolutionary Predator–Prey and Strategy
by Xiaobin Wei, Qi Jiang, Huaitang Xia and Xianbo Kong
World Electr. Veh. J. 2025, 16(10), 564; https://doi.org/10.3390/wevj16100564 - 2 Oct 2025
Viewed by 320
Abstract
In the context of low carbon, achieving accurate forecasting of electrical energy is critical for power management with the continuous development of power systems. For the sake of improving the performance of load forecasting, an improved MNet-Atten electric vehicle charging load forecasting based [...] Read more.
In the context of low carbon, achieving accurate forecasting of electrical energy is critical for power management with the continuous development of power systems. For the sake of improving the performance of load forecasting, an improved MNet-Atten electric vehicle charging load forecasting based on composite decomposition and the evolutionary predator–prey and strategy model is proposed. In this light, through the data decomposition theory, each subsequence is processed using complementary ensemble empirical mode decomposition and filters out high-frequency white noise by using singular value decomposition based on matrix operation, which improves the anti-interference ability and computational efficiency of the model. In the model construction stage, the MNet-Atten prediction model is developed and constructed. The convolution module is used to mine the local dependencies of the sequences, and the long term and short-term features of the data are extracted through the loop and loop skip modules to improve the predictability of the data itself. Furthermore, the evolutionary predator and prey strategy is used to iteratively optimize the learning rate of the MNet-Atten for improving the forecasting performance and convergence speed of the model. The autoregressive module is used to enhance the ability of the neural network to identify linear features and improve the prediction performance of the model. Increasing temporal attention to give more weight to important features for global and local linkage capture. Additionally, the electric vehicle charging load data in a certain region, as an example, is verified, and the average value of 30 running times of the combined model proposed is 117.3231 s, and the correlation coefficient PCC of the CEEMD-SVD-EPPS-MNet-Atten model is closer to 1. Furthermore, the CEEMD-SVD-EPPS-MNet-Atten model has the lowest MAPE, RMSE, and PCC. The results show that the model in this paper can better extract the characteristics of the data, improve the modeling efficiency, and have a high data prediction accuracy. Full article
(This article belongs to the Section Charging Infrastructure and Grid Integration)
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27 pages, 860 KB  
Article
LP-Based Leader-Following Positive Consensus of T-S Fuzzy Multi-Agent Systems
by Qingbo Li, Haoyue Yang and Chongxiang Yu
Mathematics 2025, 13(19), 3146; https://doi.org/10.3390/math13193146 - 1 Oct 2025
Viewed by 236
Abstract
This paper investigates the leader–follower consensus problem for T-S fuzzy multi-agent systems with positive constraints by designing observer-based control protocols, where the T-S fuzzy model is mainly used to characterize the nonlinearity in the system. First, a stable system is chosen as the [...] Read more.
This paper investigates the leader–follower consensus problem for T-S fuzzy multi-agent systems with positive constraints by designing observer-based control protocols, where the T-S fuzzy model is mainly used to characterize the nonlinearity in the system. First, a stable system is chosen as the leader. Then, a fuzzy observer that satisfies the positivity condition is constructed for follower agents. Meanwhile, an observer-based fuzzy controller design is proposed using a matrix decomposition approach. On this basis, the positivity and asymptotic consensus of the system are achieved by a set of sufficient conditions in the form of linear programming. Subsequently, an unstable system is chosen as the leader. A virtual target is introduced. By means of the co-positive Lyapunov function and linear programming approach, an observer and controller are designed to ensure both positivity and practical consensus of systems. Compared to existing literature, the consideration of positivity constraints and the linear programming-based observation-control scheme expand the application scope of multi-agent systems while reducing the computational burden. Finally, two illustrative examples are provided to verify the effectiveness of the obtained results. Full article
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33 pages, 5470 KB  
Article
Geochemical Characterization of Kupferschiefer in Terms of Hydrocarbon Generation Potential and Hydrogen Content
by Irena Matyasik, Małgorzata Kania, Małgorzata Labus and Agnieszka Wciślak-Oleszycka
Molecules 2025, 30(19), 3886; https://doi.org/10.3390/molecules30193886 - 25 Sep 2025
Viewed by 276
Abstract
The Permian Kupferschiefer shale, a key stratigraphic unit within the Zechstein sequence of the Fore-Sudetic Monocline, represents both a metal-rich lithofacies and a potential source rock for hydrocarbon generation. This study presents a comprehensive geochemical characterization of selected Kupferschiefer samples obtained from the [...] Read more.
The Permian Kupferschiefer shale, a key stratigraphic unit within the Zechstein sequence of the Fore-Sudetic Monocline, represents both a metal-rich lithofacies and a potential source rock for hydrocarbon generation. This study presents a comprehensive geochemical characterization of selected Kupferschiefer samples obtained from the Legnica–Głogów Copper District (LGOM) and exploratory boreholes. Analytical methods included Rock-Eval pyrolysis, Py-GC/FID, elemental analysis, TG-FTIR, biomarker profiling, and stable carbon isotope measurements. Results indicate that the shales contain significant amounts of Type II and mixed Type II/III kerogen, derived primarily from marine organic matter with minor terrestrial input. The organic matter maturity, expressed by Tmax, places most samples within the oil window. Rock-Eval S2 values exceed 60 mg HC/g rock in some samples, confirming excellent generative potential. Py-GC/FID data further support high hydrocarbon yields, particularly in samples from the CG-4 borehole and LGOM mines. The thermal decomposition of kerogen reveals multiple degradation phases, with evolved gas analysis identifying sulfur-containing compounds and hydrocarbons indicative of sapropelic origin. Isotopic compositions of bitumen and kerogen suggest syngenetic relationships and marine depositional settings, with samples from a North Poland borehole showing isotopic enrichment consistent with post-depositional oxidation. Kinetic parameters calculated using the Kissinger–Akahira–Sunose method demonstrate variable activation energies (107–341 kJ/mol), correlating with differences in organic matter composition and mineral matrix. The observed variability in geochemical properties highlights both regional and facies-dependent influences on the shale’s generative capacity. The study concludes that the Kupferschiefer in southwestern and northern Poland exhibits substantial hydrocarbon generation potential. This potential has been previously underestimated due to the unit’s thinness, but localized zones with high TOC, favorable kerogen type, and low activation energy could be viable exploration targets for natural gas. Full article
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20 pages, 5553 KB  
Article
Transmit Power Optimization for Intelligent Reflecting Surface-Assisted Coal Mine Wireless Communication Systems
by Yang Liu, Xiaoyue Li, Bin Wang and Yanhong Xu
IoT 2025, 6(4), 59; https://doi.org/10.3390/iot6040059 - 25 Sep 2025
Viewed by 296
Abstract
The adverse propagation environment in underground coal mine tunnels caused by enclosed spaces, rough surfaces, and dense scatterers severely degrades reliable wireless signal transmission, which further impedes the deployment of IoT applications such as gas monitors and personnel positioning terminals. However, the conventional [...] Read more.
The adverse propagation environment in underground coal mine tunnels caused by enclosed spaces, rough surfaces, and dense scatterers severely degrades reliable wireless signal transmission, which further impedes the deployment of IoT applications such as gas monitors and personnel positioning terminals. However, the conventional power enhancement solutions are infeasible for the underground coal mine scenario due to strict explosion-proof safety regulations and battery-powered IoT devices. To address this challenge, we propose singular value decomposition-based Lagrangian optimization (SVD-LOP) to minimize transmit power at the mining base station (MBS) for IRS-assisted coal mine wireless communication systems. In particular, we first establish a three-dimensional twin cluster geometry-based stochastic model (3D-TCGBSM) to accurately characterize the underground coal mine channel. On this basis, we formulate the MBS transmit power minimization problem constrained by user signal-to-noise ratio (SNR) target and IRS phase shifts. To solve this non-convex problem, we propose the SVD-LOP algorithm that performs SVD on the channel matrix to decouple the complex channel coupling and introduces the Lagrange multipliers. Furthermore, we develop a low-complexity successive convex approximation (LC-SCA) algorithm to reduce computational complexity, which constructs a convex approximation of the objective function based on a first-order Taylor expansion and enables suboptimal solutions. Simulation results demonstrate that the proposed SVD-LOP and LC-SCA algorithms achieve transmit power peaks of 20.8dBm and 21.4dBm, respectively, which are slightly lower than the 21.8dBm observed for the SDR algorithm. It is evident that these algorithms remain well below the explosion-proof safety threshold, which achieves significant power reduction. However, computational complexity analysis reveals that the proposed SVD-LOP and LC-SCA algorithms achieve O(N3) and O(N2) respectively, which offers substantial reductions compared to the SDR algorithm’s O(N7). Moreover, both proposed algorithms exhibit robust convergence across varying user SNR targets while maintaining stable performance gains under different tunnel roughness scenarios. Full article
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30 pages, 668 KB  
Article
Symmetry-Aware Transformers for Asymmetric Causal Discovery in Financial Time Series
by Wenxia Zheng and Wenhe Liu
Symmetry 2025, 17(10), 1591; https://doi.org/10.3390/sym17101591 - 24 Sep 2025
Cited by 1 | Viewed by 639
Abstract
Financial markets exhibit fundamental asymmetries in temporal causality, where policy interventions create asymmetric transmission patterns that traditional symmetric modeling approaches fail to capture. This work introduces a mathematical framework that exploits the inherent symmetries of transformer architectures while preserving essential asymmetric temporal relationships [...] Read more.
Financial markets exhibit fundamental asymmetries in temporal causality, where policy interventions create asymmetric transmission patterns that traditional symmetric modeling approaches fail to capture. This work introduces a mathematical framework that exploits the inherent symmetries of transformer architectures while preserving essential asymmetric temporal relationships in financial causal inference. We develop CausalFormer, a symmetry-aware neural architecture that maintains the permutation equivariance properties of self-attention mechanisms while enforcing strict temporal asymmetry constraints for causal discovery. The framework incorporates three mathematically principled components: (1) a symmetric attention matrix construction with asymmetric temporal masking that preserves the mathematical elegance of transformer operations while ensuring causal consistency, (2) a multi-scale convolution module with symmetric kernel initialization but asymmetric temporal receptive fields that captures policy transmission effects across heterogeneous time horizons, and (3) enhanced Nelson–Siegel decomposition that maintains the symmetric factor structure while modeling the evolution dynamics of asymmetric factors. Our mathematical formulation establishes the formal symmetry properties of the attention mechanism under temporal transformations while proving asymmetric convergence behaviors in policy transmission scenarios. The integration of symmetric optimization landscapes with asymmetric causal constraints enables simultaneous achievement of mathematical elegance and economic interpretability. Comprehensive experiments on monetary policy datasets demonstrate that the symmetry-aware design achieves a 15.3% improvement in the accuracy of causal effect estimations and a 12.7% enhancement in the predictive performance compared to those for existing methods while maintaining 91.2% causal consistency scores. The framework successfully identifies asymmetric policy transmission mechanisms, revealing that monetary tightening exhibits 40% faster propagation than easing policies, establishing new mathematical insights into the temporal asymmetries in financial systems. This work demonstrates how principled exploitation of architectural symmetries combined with domain-specific asymmetric constraints opens up new directions for mathematically rigorous yet economically interpretable deep learning in financial econometrics, with broad applications spanning computational finance, economic forecasting, and policy analysis. Full article
(This article belongs to the Section Mathematics)
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20 pages, 2107 KB  
Article
Distribution Dynamic Direct Orthogonal Decomposition Method for Quality-Related Fault Detection
by Jie Yuan, Yue Wang and Hao Ma
Processes 2025, 13(10), 3035; https://doi.org/10.3390/pr13103035 - 23 Sep 2025
Viewed by 227
Abstract
Traditional centralized modeling and fault detection methods for large-scale industrial processes have limitations, including a significant computational load and reduced performance. To address these issues, this paper proposes a distributed dynamic direct orthogonal decomposition method for quality-related fault detection in large-scale industrial processes. [...] Read more.
Traditional centralized modeling and fault detection methods for large-scale industrial processes have limitations, including a significant computational load and reduced performance. To address these issues, this paper proposes a distributed dynamic direct orthogonal decomposition method for quality-related fault detection in large-scale industrial processes. This method first decomposes the industrial process to several subunits based on its inherent mechanism. To fully consider the coupling relationship between subunits and improve the communication efficiency among them, the representative variables within each subunit are first selected based on the cosine function. On this basis, regression equations are established between the representative variables of each local subunit and those of its adjacent subunits using LASSO. Then, relevant adjacent unit variables are selected based on the regression coefficients to achieve effective information exchange between the local and adjacent subunits. For the reconstructed local subunits, a dynamic direct orthogonal decomposition method is proposed to achieve quality-related fault detection. In the proposed fault detection method at the subunit level, to better capture the dynamics within the data, the time-delay factor is first introduced to the process variables and the quality variables, and the load matrix of the process variables and the quality variables is obtained using standard partial least squares. Subsequently, the covariance matrix of the load matrix is decomposed based on singular value decomposition to construct an orthogonal decomposition matrix, thereby achieving orthogonal division of the process variables based on the quality variables within each subunit. To derive a more concise detection logic, the Bayesian fusion strategy is adopted to integrate the statistical indicators corresponding to the same type of faults detected in each subunit. Finally, the effectiveness of this method is verified through an industrial example. Full article
(This article belongs to the Section Process Control and Monitoring)
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