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Keywords = model-based FDE

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38 pages, 6851 KB  
Article
FGFNet: Fourier Gated Feature-Fusion Network with Fractal Dimension Estimation for Robust Palm-Vein Spoof Detection
by Seung Gu Kim, Jung Soo Kim and Kang Ryoung Park
Fractal Fract. 2025, 9(8), 478; https://doi.org/10.3390/fractalfract9080478 - 22 Jul 2025
Viewed by 397
Abstract
The palm-vein recognition system has garnered attention as a biometric technology due to its resilience to external environmental factors, protection of personal privacy, and low risk of external exposure. However, with recent advancements in deep learning-based generative models for image synthesis, the quality [...] Read more.
The palm-vein recognition system has garnered attention as a biometric technology due to its resilience to external environmental factors, protection of personal privacy, and low risk of external exposure. However, with recent advancements in deep learning-based generative models for image synthesis, the quality and sophistication of fake images have improved, leading to an increased security threat from counterfeit images. In particular, palm-vein images acquired through near-infrared illumination exhibit low resolution and blurred characteristics, making it even more challenging to detect fake images. Furthermore, spoof detection specifically targeting palm-vein images has not been studied in detail. To address these challenges, this study proposes the Fourier-gated feature-fusion network (FGFNet) as a novel spoof detector for palm-vein recognition systems. The proposed network integrates masked fast Fourier transform, a map-based gated feature fusion block, and a fast Fourier convolution (FFC) attention block with global contrastive loss to effectively detect distortion patterns caused by generative models. These components enable the efficient extraction of critical information required to determine the authenticity of palm-vein images. In addition, fractal dimension estimation (FDE) was employed for two purposes in this study. In the spoof attack procedure, FDE was used to evaluate how closely the generated fake images approximate the structural complexity of real palm-vein images, confirming that the generative model produced highly realistic spoof samples. In the spoof detection procedure, the FDE results further demonstrated that the proposed FGFNet effectively distinguishes between real and fake images, validating its capability to capture subtle structural differences induced by generative manipulation. To evaluate the spoof detection performance of FGFNet, experiments were conducted using real palm-vein images from two publicly available palm-vein datasets—VERA Spoofing PalmVein (VERA dataset) and PLUSVein-contactless (PLUS dataset)—as well as fake palm-vein images generated based on these datasets using a cycle-consistent generative adversarial network. The results showed that, based on the average classification error rate, FGFNet achieved 0.3% and 0.3% on the VERA and PLUS datasets, respectively, demonstrating superior performance compared to existing state-of-the-art spoof detection methods. Full article
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22 pages, 2193 KB  
Article
Novel Hybrid Function Operational Matrices of Fractional Integration: An Application for Solving Multi-Order Fractional Differential Equations
by Seshu Kumar Damarla and Madhusree Kundu
AppliedMath 2025, 5(2), 55; https://doi.org/10.3390/appliedmath5020055 - 10 May 2025
Viewed by 1044
Abstract
Although fractional calculus has evolved significantly since its origin in the 1695 correspondence between Leibniz and L’Hôpital, the numerical treatment of multi-order fractional differential equations remains a challenge. Existing methods are often either computationally expensive or reliant on complex operational frameworks that hinder [...] Read more.
Although fractional calculus has evolved significantly since its origin in the 1695 correspondence between Leibniz and L’Hôpital, the numerical treatment of multi-order fractional differential equations remains a challenge. Existing methods are often either computationally expensive or reliant on complex operational frameworks that hinder their broader applicability. In the present study, a novel numerical algorithm is proposed based on orthogonal hybrid functions (HFs), which were constructed as linear combinations of piecewise constant sample-and-hold functions and piecewise linear triangular functions. These functions, belonging to the class of degree-1 orthogonal polynomials, were employed to obtain the numerical solution of multi-order fractional differential equations defined in the Caputo sense. A generalized one-shot operational matrix was derived to explicitly express the Riemann–Liouville fractional integral of HFs in terms of the HFs themselves. This allowed the original multi-order fractional differential equation to be transformed directly into a system of algebraic equations, thereby simplifying the solution process. The developed algorithm was then applied to a range of benchmark problems, including both linear and nonlinear multi-order FDEs with constant and variable coefficients. Numerical comparisons with well-established methods in the literature revealed that the proposed approach not only achieved higher accuracy but also significantly reduced computational effort, demonstrating its potential as a reliable and efficient numerical tool for fractional-order modeling. Full article
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21 pages, 3508 KB  
Article
Pedestrian Trajectory Prediction Based on Dual Social Graph Attention Network
by Xinhai Li, Yong Liang, Zhenhao Yang and Jie Li
Appl. Sci. 2025, 15(8), 4285; https://doi.org/10.3390/app15084285 - 13 Apr 2025
Viewed by 1030
Abstract
Pedestrian trajectory prediction poses significant challenges for autonomous systems due to the intricate nature of social interactions in densely populated environments. While the existing methods frequently encounter difficulties in effectively quantifying the nuanced social relationships, we propose a novel dual social graph attention [...] Read more.
Pedestrian trajectory prediction poses significant challenges for autonomous systems due to the intricate nature of social interactions in densely populated environments. While the existing methods frequently encounter difficulties in effectively quantifying the nuanced social relationships, we propose a novel dual social graph attention network (DSGAT) that systematically models multi-level interactions. This framework is specifically designed to enhance the extraction of pedestrian interaction features within the environment, thereby improving the trajectory prediction accuracy. The network architecture consists of two primary branches, namely an individual branch and a group branch, which are responsible for modeling personal and collective pedestrian behaviors, respectively. For individual feature modeling, we propose the Spatio-Temporal Weighted Graph Attention Network (STWGAT) branch, which incorporates a newly developed directed social attention function to explicitly capture both the direction and intensity of pedestrian interactions. This mechanism enables the model to more effectively represent the fine-grained social dynamics. Subsequently, leveraging the STWGAT’s processing of directed weighted graphs, the network’s ability to aggregate spatiotemporal information and refine individual interaction representations is further strengthened. To effectively account for the critical group dynamics, a dedicated group attention function is designed to identify and quantify the collective behaviors within pedestrian crowds. This facilitates a more comprehensive understanding of the complex social interactions, leading to an enhanced trajectory prediction accuracy. Extensive comparative experiments conducted on the widely used ETH and UCY benchmark datasets demonstrate that the proposed network consistently surpasses the baseline methods across the key evaluation metrics, including the Average Displacement Error (ADE) and Final Displacement Error (FDE). These results confirm the effectiveness and robustness of the DSGAT-based approach in handling complex pedestrian interaction scenarios. Full article
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22 pages, 677 KB  
Article
The LDG Finite-Element Method for Multi-Order FDEs: Applications to Circuit Equations
by Mohammad Izadi, Hari Mohan Srivastava and Mahdi Kamandar
Fractal Fract. 2025, 9(4), 230; https://doi.org/10.3390/fractalfract9040230 - 5 Apr 2025
Viewed by 500
Abstract
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the [...] Read more.
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the Liouville–Caputo fractional derivative and upwind numerical fluxes to discretize governing equations while preserving stability. The method was validated through benchmark test cases, including comparisons with analytical solutions and established numerical techniques (e.g., Gegenbauer wavelets and Dickson collocation). The results demonstrate that the LDG method achieves high-accuracy solutions (e.g., with a relatively large time step size) and reduced computational costs, which are attributed to its element-wise formulation. These findings position LDG as a promising tool for complex scientific and engineering applications, particularly in modeling fractional-order systems such as RL, RLC circuits, and other electrical circuit equations. Full article
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22 pages, 2946 KB  
Article
Fast Multimodal Trajectory Prediction for Vehicles Based on Multimodal Information Fusion
by Likun Ge, Shuting Wang and Guangqi Wang
Actuators 2025, 14(3), 136; https://doi.org/10.3390/act14030136 - 10 Mar 2025
Viewed by 1507
Abstract
Trajectory prediction plays a crucial role in level autonomous driving systems, as real-time and accurate trajectory predictions can significantly enhance the safety of autonomous vehicles and the robustness of the autonomous driving system. We propose a novel trajectory prediction model that adopts the [...] Read more.
Trajectory prediction plays a crucial role in level autonomous driving systems, as real-time and accurate trajectory predictions can significantly enhance the safety of autonomous vehicles and the robustness of the autonomous driving system. We propose a novel trajectory prediction model that adopts the encoder–decoder paradigm. In the encoder, we introduce a dual-thread interaction relationship encoding method based on a sparse graph attention mechanism, which allows our model to aggregate richer multimodal interaction information. Additionally, we introduce a non-autoregressive query generation method that reduces the model’s inference time by approximately 80% through the parallel generation of decoding queries. Finally, we propose a multi-stage decoder that generates more accurate and reasonable predicted trajectories by predicting trajectory reference points and performing spatial and posture optimization on the predicted trajectories. Comparative experiments with existing advanced algorithms demonstrate that our method improves the minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR) by 10.3%, 10.3%, and 14.5%, respectively, compared to the average performance. Lastly, we validate the effectiveness of the various modules proposed in this paper through ablation studies. Full article
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14 pages, 1136 KB  
Article
Generating Realistic Vehicle Trajectories Based on Vehicle–Vehicle and Vehicle–Map Interaction Pattern Learning
by Peng Li, Biao Yu, Jun Wang, Xiaojun Zhu, Hui Zhang, Chennian Yu and Chen Hua
World Electr. Veh. J. 2025, 16(3), 145; https://doi.org/10.3390/wevj16030145 - 4 Mar 2025
Viewed by 891
Abstract
Diversified and realistic traffic scenarios are a crucial foundation for evaluating the safety of autonomous driving systems in simulations. However, a considerable number of current methods generate scenarios that lack sufficient realism. To address this issue, this paper proposes a vehicle trajectory generation [...] Read more.
Diversified and realistic traffic scenarios are a crucial foundation for evaluating the safety of autonomous driving systems in simulations. However, a considerable number of current methods generate scenarios that lack sufficient realism. To address this issue, this paper proposes a vehicle trajectory generation method based on vehicle–vehicle and vehicle–map interaction pattern learning. By leveraging a multihead self-attention mechanism, the model efficiently captures complex dependencies among vehicles, enhancing its ability to learn realistic traffic dynamics. Moreover, the multihead cross-attention mechanism is also used to learn the interaction features between the vehicles and the map, addressing the challenge of trajectory generation’s difficulty in perceiving static environments. This proposed method enhances the model’s ability to learn natural traffic sequences, enable the generation of more realistic traffic flow, and provide strong support for the testing and optimization of autonomous driving systems. Experimental results show that compared to the Trafficgen baseline model, the proposed method achieves a 26% improvement in ADE and a 20% improvement in FDE. Full article
(This article belongs to the Special Issue Recent Advances in Autonomous Vehicles)
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32 pages, 4386 KB  
Article
Multi-Source, Fault-Tolerant, and Robust Navigation Method for Tightly Coupled GNSS/5G/IMU System
by Zhongliang Deng, Zhichao Zhang, Zhenke Ding and Bingxun Liu
Sensors 2025, 25(3), 965; https://doi.org/10.3390/s25030965 - 5 Feb 2025
Viewed by 1418
Abstract
The global navigation satellite system (GNSS) struggles to deliver the precision and reliability required for positioning, navigation, and timing (PNT) services in environments with severe interference. Fifth-generation (5G) cellular networks, with their low latency, high bandwidth, and large capacity, offer a robust communication [...] Read more.
The global navigation satellite system (GNSS) struggles to deliver the precision and reliability required for positioning, navigation, and timing (PNT) services in environments with severe interference. Fifth-generation (5G) cellular networks, with their low latency, high bandwidth, and large capacity, offer a robust communication infrastructure, enabling 5G base stations (BSs) to extend coverage into regions where traditional GNSSs face significant challenges. However, frequent multi-sensor faults, including missing alarm thresholds, uncontrolled error accumulation, and delayed warnings, hinder the adaptability of navigation systems to the dynamic multi-source information of complex scenarios. This study introduces an advanced, tightly coupled GNSS/5G/IMU integration framework designed for distributed PNT systems, providing all-source fault detection with weighted, robust adaptive filtering. A weighted, robust adaptive filter (MCC-WRAF), grounded in the maximum correntropy criterion, was developed to suppress fault propagation, relax Gaussian noise constraints, and improve the efficiency of observational weight distribution in multi-source fusion scenarios. Moreover, we derived the intrinsic relationships of filtering innovations within wireless measurement models and proposed a time-sequential, observation-driven full-source FDE and sensor recovery validation strategy. This approach employs a sliding window which expands innovation vectors temporally based on source encoding, enabling real-time validation of isolated faulty sensors and adaptive adjustment of observational data in integrated navigation solutions. Additionally, a covariance-optimal, inflation-based integrity protection mechanism was introduced, offering rigorous evaluations of distributed PNT service availability. The experimental validation was carried out in a typical outdoor scenario, and the results highlight the proposed method’s ability to mitigate undetected fault impacts, improve detection sensitivity, and significantly reduce alarm response times across step, ramp, and multi-fault mixed scenarios. Additionally, the dynamic positioning accuracy of the fusion navigation system improved to 0.83 m (1σ). Compared with standard Kalman filtering (EKF) and advanced multi-rate Kalman filtering (MRAKF), the proposed algorithm achieved 28.3% and 53.1% improvements in its 1σ error, respectively, significantly enhancing the accuracy and reliability of the multi-source fusion navigation system. Full article
(This article belongs to the Section Navigation and Positioning)
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19 pages, 6207 KB  
Article
Machine Learning-Based Fault Detection and Exclusion for Global Navigation Satellite System Pseudorange in the Measurement Domain
by Ma’mon Saeed Alghananim, Cheng Feng, Yuxiang Feng and Washington Yotto Ochieng
Sensors 2025, 25(3), 817; https://doi.org/10.3390/s25030817 - 29 Jan 2025
Cited by 2 | Viewed by 1021
Abstract
Global Navigation Satellite Systems (GNSS) support numerous applications, including mission-critical ones that require a high level of integrity for safe operations, such as air, maritime, and land-based navigation. Fault Detection and Exclusion (FDE) is crucial for mission-critical applications, as faulty measurements significantly impact [...] Read more.
Global Navigation Satellite Systems (GNSS) support numerous applications, including mission-critical ones that require a high level of integrity for safe operations, such as air, maritime, and land-based navigation. Fault Detection and Exclusion (FDE) is crucial for mission-critical applications, as faulty measurements significantly impact system integrity. FDE can be applied within the positioning algorithm in the measurement’s domain and the integrity monitoring domain. Previous research has utilized a limited number of Machine Learning (ML) models and Quality Indicators (QIs) for the FDE process in the measurement domain. It has not evaluated the pseudorange measurement fault thresholds that need to be detected. In addition, ML models were mainly evaluated based on accuracy, which alone does not provide a comprehensive evaluation. This paper introduces a comprehensive framework for traditional ML-based FDE prediction models in the measurement domain for pseudorange in complex environments. For the first time, this study evaluates the fault detection thresholds across 40 values, ranging from 1 to 40 m, using six ML models for FDE. These models include Decision Tree, K-Nearest Neighbors (KNN), Discriminant, Logistic, Neural Network, and Trees (Boosted, Bagged, and Rusboosted). The models are comprehensively assessed based on four key aspects: accuracy, probability of misdetection, probability of fault detection, and the percentage of excluded data. The results show that ML models can provide a high level of performance in the FDE process, exceeding 95% accuracy when the fault threshold is equal to or greater than 4 m, with KNN providing the highest FDE performance. Full article
(This article belongs to the Section Navigation and Positioning)
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41 pages, 3733 KB  
Review
A Comprehensive Survey on the Integrity of Localization Systems
by Elias Maharmeh, Zayed Alsayed and Fawzi Nashashibi
Sensors 2025, 25(2), 358; https://doi.org/10.3390/s25020358 - 9 Jan 2025
Cited by 1 | Viewed by 1464
Abstract
This survey extends and refines the existing definitions of integrity and protection level in localization systems (localization as a broad term, i.e., not limited to GNSS-based localization). In our definition, we study integrity from two aspects: quality and quantity. Unlike existing reviews, this [...] Read more.
This survey extends and refines the existing definitions of integrity and protection level in localization systems (localization as a broad term, i.e., not limited to GNSS-based localization). In our definition, we study integrity from two aspects: quality and quantity. Unlike existing reviews, this survey examines integrity methods covering various localization techniques and sensors. We classify localization techniques as optimization-based, fusion-based, and SLAM-based. A new classification of integrity methods is introduced, evaluating their applications, effectiveness, and limitations. Comparative tables summarize strengths and gaps across key criteria, such as algorithms, evaluation methods, sensor data, and more. The survey presents a general probabilistic model addressing diverse error types in localization systems. Findings reveal a significant research imbalance: 73.3% of surveyed papers focus on GNSS-based methods, while only 26.7% explore non-GNSS approaches like fusion, optimization, or SLAM, with few addressing protection level calculations. Robust modeling is highlighted as a promising integrity method, combining quantification and qualification to address critical gaps. This approach offers a unified framework for improving localization system reliability and safety. This survey provides key insights for developing more robust localization systems, contributing to safer and more efficient autonomous operations. Full article
(This article belongs to the Section Navigation and Positioning)
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35 pages, 4267 KB  
Article
Uncertainty-Aware Multimodal Trajectory Prediction via a Single Inference from a Single Model
by Ho Suk and Shiho Kim
Sensors 2025, 25(1), 217; https://doi.org/10.3390/s25010217 - 2 Jan 2025
Viewed by 2091
Abstract
In the domain of autonomous driving, trajectory prediction plays a pivotal role in ensuring the safety and reliability of autonomous systems, especially when navigating complex environments. Unfortunately, trajectory prediction suffers from uncertainty problems due to the randomness inherent in the driving environment, but [...] Read more.
In the domain of autonomous driving, trajectory prediction plays a pivotal role in ensuring the safety and reliability of autonomous systems, especially when navigating complex environments. Unfortunately, trajectory prediction suffers from uncertainty problems due to the randomness inherent in the driving environment, but uncertainty quantification in trajectory prediction is not widely addressed, and most studies rely on deep ensembles methods. This study presents a novel uncertainty-aware multimodal trajectory prediction (UAMTP) model that quantifies aleatoric and epistemic uncertainties through a single forward inference. Our approach employs deterministic single forward pass methods, optimizing computational efficiency while retaining robust prediction accuracy. By decomposing trajectory prediction into velocity and yaw components and quantifying uncertainty in both, the UAMTP model generates multimodal predictions that account for environmental randomness and intention ambiguity. Evaluation on datasets collected by CARLA simulator demonstrates that our model not only outperforms Deep Ensembles-based multimodal trajectory prediction method in terms of accuracy such as minFDE and miss rate metrics but also offers enhanced time to react for collision avoidance scenarios. This research marks a step forward in integrating efficient uncertainty quantification into multimodal trajectory prediction tasks within resource-constrained autonomous driving platforms. Full article
(This article belongs to the Section Vehicular Sensing)
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21 pages, 3566 KB  
Article
Rapid Vehicle Trajectory Prediction Based on Multi-Attention Mechanism for Fusing Multimodal Information
by Likun Ge, Shuting Wang and Guangqi Wang
Electronics 2024, 13(23), 4806; https://doi.org/10.3390/electronics13234806 - 5 Dec 2024
Cited by 1 | Viewed by 1496
Abstract
Trajectory prediction plays a crucial role in autonomous driving tasks, as accurately and rapidly predicting the future trajectories of traffic participants can significantly enhance the safety and robustness of autonomous driving systems. This paper presents a novel trajectory prediction model that follows the [...] Read more.
Trajectory prediction plays a crucial role in autonomous driving tasks, as accurately and rapidly predicting the future trajectories of traffic participants can significantly enhance the safety and robustness of autonomous driving systems. This paper presents a novel trajectory prediction model that follows the encoder–decoder paradigm, achieving precise and rapid predictions of future vehicle trajectories by efficiently aggregating the spatiotemporal and interaction information of agents in traffic scenarios. We propose an agent–agent interaction information extraction module based on a sparse graph attention mechanism, which enables the efficient aggregation of interaction information between agents. Additionally, we introduce a non-autoregressive query generation method that accelerates the model inference speed by generating the decoding queries in parallel. Comparative experiments with the existing advanced algorithms show that our method improves the multimodal trajectory prediction metrics for the Minimum Average Displacement Error (minADE), the Minimum Final Displacement Error (minFDE), and the Miss Rate (MR) by an average of 9.1%, 11.8%, and 14.6%, respectively, while the inference time is only 33.7% of the average time taken by the other algorithms. Finally, we demonstrate the effectiveness of the various modules proposed in this paper through ablation studies. Full article
(This article belongs to the Section Electrical and Autonomous Vehicles)
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24 pages, 6958 KB  
Article
Ship Trajectory Prediction in Complex Waterways Based on Transformer and Social Variational Autoencoder (SocialVAE)
by Pengyue Wang, Mingyang Pan, Zongying Liu, Shaoxi Li, Yuanlong Chen and Yang Wei
J. Mar. Sci. Eng. 2024, 12(12), 2233; https://doi.org/10.3390/jmse12122233 - 5 Dec 2024
Viewed by 1333
Abstract
Ship trajectory prediction plays a key role in the early warning and safety of maritime traffic. It is a necessary assistant tool that can forecast a ship’s trajectory in a certain period to prevent ship collision. However, highly precise prediction of long-term ship [...] Read more.
Ship trajectory prediction plays a key role in the early warning and safety of maritime traffic. It is a necessary assistant tool that can forecast a ship’s trajectory in a certain period to prevent ship collision. However, highly precise prediction of long-term ship trajectories is still a challenge. This study proposes a ship trajectory prediction model called ShipTrack-TVAE, which is based on a Variational Autoencoder (SocialVAE) and Transformer architecture. It aims to address ship trajectory prediction tasks in complex waterways. To enable the model to avoid potential collision risks, this study designs a collision avoidance mechanism, which comprehensively incorporates safety constraints related to the distance between ships into the loss function. The experimental results show that on the Qiongzhou Strait ship AIS dataset, the Average Displacement Error (ADE) of ShipTrack-TVAE improved by 21.85% compared to the current state-of-the-art trajectory prediction model, SocialVAE, while the Final Displacement Error (FDE) improved by 17.83%. The experimental results demonstrate that the ShipTrack-TVAE model can effectively improve the prediction accuracy of short-term, medium-term, and long-term ship trajectories. It has excellent performance and provides a certain reference value for advancing unmanned ship collision avoidance. Full article
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11 pages, 2721 KB  
Article
A High-Transferability Adversarial Sample Generation Method Incorporating Frequency Domain Transformations
by Sijian Yan, Zhengjie Deng, Jiale Dong and Xiyan Li
Electronics 2024, 13(22), 4480; https://doi.org/10.3390/electronics13224480 - 15 Nov 2024
Viewed by 1276
Abstract
Adversarial attack methods have achieved satisfactory results in white-box attack scenarios, but their performance declines when transferred to other deep neural network (DNN) models. Currently, there are many methods to improve the transferability of adversarial samples, and enhancing transferability through input transformations is [...] Read more.
Adversarial attack methods have achieved satisfactory results in white-box attack scenarios, but their performance declines when transferred to other deep neural network (DNN) models. Currently, there are many methods to improve the transferability of adversarial samples, and enhancing transferability through input transformations is an effective approach. However, most existing input transformations are performed in the spatial domain, neglecting transformations in the frequency domain. Therefore, this paper proposes a novel input transformation-based attack: the frequency domain enhancement (FDE) method, which performs input transformations in the frequency domain to increase input diversity. Specifically, this method processes input images in the frequency domain, suppresses high-frequency information in the input images, and then randomly amplifies certain frequency domain information, generating adversarial samples with stronger transferability. Experimental results show that adversarial samples generated through FDE demonstrate significant improvement in transferability on both undefended and defended models on the ImageNet dataset. Notably, this method can be combined with many existing techniques to further enhance the transferability of adversarial samples. Full article
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34 pages, 12268 KB  
Article
Novel Fractional Order Differential and Integral Models for Wind Turbine Power–Velocity Characteristics
by Ahmed G. Mahmoud, Mohamed A. El-Beltagy and Ahmed M. Zobaa
Fractal Fract. 2024, 8(11), 656; https://doi.org/10.3390/fractalfract8110656 - 11 Nov 2024
Viewed by 1832
Abstract
This work presents an improved modelling approach for wind turbine power curves (WTPCs) using fractional differential equations (FDE). Nine novel FDE-based models are presented for mathematically modelling commercial wind turbine modules’ power–velocity (P-V) characteristics. These models utilize Weibull and Gamma probability density functions [...] Read more.
This work presents an improved modelling approach for wind turbine power curves (WTPCs) using fractional differential equations (FDE). Nine novel FDE-based models are presented for mathematically modelling commercial wind turbine modules’ power–velocity (P-V) characteristics. These models utilize Weibull and Gamma probability density functions to estimate the capacity factor (CF), where accuracy is measured using relative error (RE). Comparative analysis is performed for the WTPC mathematical models with a varying order of differentiation (α) from 0.5 to 1.5, utilizing the manufacturer data for 36 wind turbines with capacities ranging from 150 to 3400 kW. The shortcomings of conventional mathematical models in various meteorological scenarios can be overcome by applying the Riemann–Liouville fractional integral instead of the classical integer-order integrals. By altering the sequence of differentiation and comparing accuracy, the suggested model uses fractional derivatives to increase flexibility. By contrasting the model output with actual data obtained from the wind turbine datasheet and the historical data of a specific location, the models are validated. Their accuracy is assessed using the correlation coefficient (R) and the Mean Absolute Percentage Error (MAPE). The results demonstrate that the exponential model at α=0.9 gives the best accuracy of WTPCs, while the original linear model was the least accurate. Full article
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21 pages, 4510 KB  
Article
Pedestrian Trajectory Prediction in Crowded Environments Using Social Attention Graph Neural Networks
by Mengya Zong, Yuchen Chang, Yutian Dang and Kaiping Wang
Appl. Sci. 2024, 14(20), 9349; https://doi.org/10.3390/app14209349 - 14 Oct 2024
Cited by 1 | Viewed by 3745
Abstract
Trajectory prediction is a key component in the development of applications such as mixed urban traffic management and public safety. Traditional models have struggled with the complexity of modeling dynamic crowd interactions, the intricacies of spatiotemporal dependencies, and environmental constraints. Addressing these challenges, [...] Read more.
Trajectory prediction is a key component in the development of applications such as mixed urban traffic management and public safety. Traditional models have struggled with the complexity of modeling dynamic crowd interactions, the intricacies of spatiotemporal dependencies, and environmental constraints. Addressing these challenges, this paper introduces the innovative Social Attention Graph Neural Network (SA-GAT) framework. Utilizing Long Short-Term Memory (LSTM) networks, SA-GAT encodes pedestrian trajectory data to extract temporal correlations, while Graph Attention Networks (GAT) are employed to precisely capture the subtle interactions among pedestrians. The SA-GAT framework boosts its predictive accuracy with two key innovations. First, it features a Scene Potential Module that utilizes a Scene Tensor to dynamically capture the interplay between crowds and their environment. Second, it incorporates a Transition Intention Module with a Transition Tensor, which interprets latent transfer probabilities from trajectory data to reveal pedestrians’ implicit intentions at specific locations. Based on AnyLogic modeling of the metro station on Line 10 of Chengdu Shuangliu Airport, China, numerical studies reveal that the SA-GAT model achieves a substantial reduction in ADE and FDE metrics by 34.22% and 38.04% compared to baseline models. Full article
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