Search Results (20)

This study proposes a novel fuzzy disturbance observer (FDO)-augmented adaptive nonsingular terminal sliding mode control (NTSMC) framework for multi-joint robotic manipulators, addressing critical challenges in trajectory tracking precision and disturbance rejection. Unlike conventional disturbance observers requiring prior knowledge of disturbance bounds, the proposed FDO leverages fuzzy logic principles to dynamically estimate composite disturbances—including unmodeled dynamics, parameter perturbations, and external torque variations—without restrictive assumptions about disturbance derivatives. The control architecture achieves rapid finite-time convergence by integrating the FDO with a singularity-free terminal sliding manifold and an adaptive exponential reaching law while significantly suppressing chattering effects. Rigorous Lyapunov stability analysis confirms the uniform ultimate boundedness of tracking errors and disturbance estimation residuals. Comparative simulations on a 2-DOF robotic arm demonstrate a 97.28% reduction in root mean square tracking errors compared to PD-based alternatives and a 73.73% improvement over a nonlinear disturbance observer-enhanced NTSMC. Experimental validation on a physical three-joint manipulator platform reveals that the proposed method reduces torque oscillations by 58% under step-type disturbances while maintaining sub-millimeter tracking accuracy. The framework eliminates reliance on exact system models, offering a generalized solution for industrial manipulators operating under complex dynamic uncertainties. Full article

This paper presents a physics-informed training framework for projection-based Reduced-Order Models (ROMs). We extend the original PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual loss, bridging the gap between traditional projection-based ROMs and physics-informed neural networks (PINNs). Unlike conventional PINNs that rely on analytical PDEs, our approach leverages FEM residuals to guide the learning of the ROM approximation manifold. Our key contributions include the following: (1) a parameter-agnostic, discrete residual loss applicable to nonlinear problems, (2) an architectural modification to PROM-ANN improving accuracy for fast-decaying singular values, and (3) an empirical study on the proposed physics-informed training process for ROMs. The method is demonstrated on a nonlinear hyperelasticity problem, simulating a rubber cantilever under multi-axial loads. The main accomplishment in regards to the proposed residual-based loss is its applicability on nonlinear problems by interfacing with FEM software while maintaining reasonable training times. The modified PROM-ANN outperforms POD by orders of magnitude in snapshot reconstruction accuracy, while the original formulation is not able to learn a proper mapping for this use case. Finally, the application of physics-informed training in ANN-PROM modestly narrows the gap between data reconstruction and ROM accuracy; however, it highlights the untapped potential of the proposed residual-driven optimization for future ROM development. This work underscores the critical role of FEM residuals in ROM construction and calls for further exploration on architectures beyond PROM-ANN. Full article

In this article, we consider the singular $p$-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold. Then, we investigate the least-energy sign-changing solutions by considering the Nehari nodal set. In both cases, the critical Sobolev exponent is of great importance as the solutions exists only if we are below the critical Sobolev exponent. Full article

Wildfires increasingly threaten ecosystems and infrastructure, making accurate burn severity mapping (BSM) essential for effective disaster response and environmental management. Machine learning (ML) models utilizing satellite-derived vegetation indices are crucial for assessing wildfire damage; however, incorporating many indices can lead to multicollinearity, reducing classification accuracy. While principal component analysis (PCA) is commonly used to address this issue, its effectiveness relative to other feature extraction (FE) methods in BSM remains underexplored. This study aims to enhance ML classifier accuracy in BSM by evaluating various FE techniques that mitigate multicollinearity among vegetation indices. Using composite burn index (CBI) data from the 2014 Carlton Complex fire in the United States as a case study, we extracted 118 vegetation indices from seven Landsat-8 spectral bands. We applied and compared 13 different FE techniques—including linear and nonlinear methods such as PCA, t-distributed stochastic neighbor embedding (t-SNE), linear discriminant analysis (LDA), Isomap, uniform manifold approximation and projection (UMAP), factor analysis (FA), independent component analysis (ICA), multidimensional scaling (MDS), truncated singular value decomposition (TSVD), non-negative matrix factorization (NMF), locally linear embedding (LLE), spectral embedding (SE), and neighborhood components analysis (NCA). The performance of these techniques was benchmarked against six ML classifiers to determine their effectiveness in improving BSM accuracy. Our results show that alternative FE techniques can outperform PCA, improving classification accuracy and computational efficiency. Techniques like LDA and NCA effectively capture nonlinear relationships critical for accurate BSM. The study contributes to the existing literature by providing a comprehensive comparison of FE methods, highlighting the potential benefits of underutilized techniques in BSM. Full article

In this paper, we prove the existence of at least two weak solutions to a class of singular two-phase problems with variable exponents involving a ψ-Hilfer fractional operator and Dirichlet-type boundary conditions when the term source is dependent on one parameter. Here, we use the fiber method and the Nehari manifold to prove our results. Full article

This paper explores solitary wave solutions arising in the deformations of a hyperelastic compressible plate. Explicit traveling wave solution expressions with various parameters for the hyperelastic compressible plate are obtained and visualized. To analyze the perturbed equation, we employ geometric singular perturbation theory, Melnikov methods, and invariant manifold theory. The solitary wave solutions of the hyperelastic compressible plate do not persist under small perturbations for wave speed $c>-\beta k^2$. Further exploration of nonlinear models that accurately depict the persistence of solitary wave solution on the significant physical processes under the K-S perturbation is recommended. Full article

This work presents a finite-time robust path-following control scheme for perturbed autonomous ground vehicles. Specifically, a novel self-tuning nonsingular fast-terminal sliding manifold that further enhances the convergence rate and tracking accuracy is proposed. Then, uncertain dynamics and external disturbances are estimated by a high-gain disturbance observer to compensate for the designed control input. Successively, a super-twisting algorithm is incorporated into the final control law, significantly mitigating the chattering phenomenon of both the input control signal and the output trajectory. Furthermore, the global finite-time convergence and stability of the whole proposed control algorithm are proven by the Lyapunov theory. Finally, the efficacy of the proposed method is validated with comparisons in a numerical example. It obtains high control performance, reduced chattering, fast convergence rate, singularity avoidance, and robustness against uncertainties. Full article

Amid the challenges posed by the COVID-19 pandemic, this study conducts a rigorous analysis of the online learning landscape within higher education. It scrutinizes the manifold issues that emerged during the era of quarantine restrictions, investigating the perspectives and experiences of students and academic staff in this transformative educational paradigm. Employing a comprehensive suite of research methodologies, including content analysis, observation, comparative analysis, questionnaires, correlation studies, and statistical and graphical methods, this research unearths the substantial challenges faced by participants in online learning. It meticulously evaluates the advantages and limitations of this pedagogical shift during the pandemic, probing into satisfaction levels regarding the quality of online instruction and the psychological aspects of adapting to new learning environments. Moreover, this study offers practical recommendations to address the identified challenges and proposes solutions. The findings serve as invaluable insights for higher education management, particularly within the framework of quality assurance, equipping administrators with the requisite tools and strategies to confront the extraordinary challenges that have arisen in contemporary higher education. These lessons gleaned from the crucible of the pandemic’s trials also hold a unique promise. The results of this research are not confined to a singular crisis but carry a profound implication: the effective application of online learning, even under the most arduous conditions. These ‘pandemic lessons’ become the guiding light for resilient education in the face of any adversity. Full article

This paper examines the use of manifold learning in the context of electric power system transient stability analysis. Since wide-area monitoring systems (WAMSs) introduced a big data paradigm into the power system operation, manifold learning can be seen as a means of condensing these high-dimensional data into an appropriate low-dimensional representation (i.e., embedding) which preserves as much information as possible. In this paper, we consider several embedding methods (principal component analysis (PCA) and its variants, singular value decomposition, isomap and spectral embedding, locally linear embedding (LLE) and its variants, multidimensional scaling (MDS), and others) and apply them to the dataset derived from the IEEE New England 39-bus power system transient simulations. We found that PCA with a radial basis function kernel is well suited to this type of power system data (where features are instances of three-phase phasor values). We also found that the LLE (including its variants) did not produce a good embedding with this particular kind of data. Furthermore, we found that a support vector machine, trained on top of the embedding produced by several different methods was able to detect power system disturbances from WAMS data. Full article

As the field of deep learning experiences a meteoric rise, the urgency to decipher the complex geometric properties of feature spaces, which underlie the effectiveness of diverse learning algorithms and optimization techniques, has become paramount. In this scholarly review, a comprehensive, holistic outlook on the geometry of feature spaces in deep learning models is provided in order to thoroughly probe the interconnections between feature spaces and a multitude of influential factors such as activation functions, normalization methods, and model architectures. The exploration commences with an all-encompassing examination of deep learning models, followed by a rigorous dissection of feature space geometry, delving into manifold structures, curvature, wide neural networks and Gaussian processes, critical points and loss landscapes, singular value spectra, and adversarial robustness, among other notable topics. Moreover, transfer learning and disentangled representations in feature space are illuminated, accentuating the progress and challenges in these areas. In conclusion, the challenges and future research directions in the domain of feature space geometry are outlined, emphasizing the significance of comprehending overparameterized models, unsupervised and semi-supervised learning, interpretable feature space geometry, topological analysis, and multimodal and multi-task learning. Embracing a holistic perspective, this review aspires to serve as an exhaustive guide for researchers and practitioners alike, clarifying the intricacies of the geometry of feature spaces in deep learning models and mapping the trajectory for future advancements in this enigmatic and enthralling domain. Full article

Graph regularized non-negative matrix factorization (GNMF) is widely used in feature extraction. In the process of dimensionality reduction, GNMF can retain the internal manifold structure of data by adding a regularizer to non-negative matrix factorization (NMF). Because Ga NMF regularizer is implemented by local preserving projections (LPP), there are small sample size problems (SSS). In view of the above problems, a new algorithm named robust exponential graph regularized non-negative matrix factorization (REGNMF) is proposed in this paper. By adding a matrix exponent to the regularizer of GNMF, the possible existing singular matrix will change into a non-singular matrix. This model successfully solves the problems in the above algorithm. For the optimization problem of the REGNMF algorithm, we use a multiplicative non-negative updating rule to iteratively solve the REGNMF method. Finally, this method is applied to AR, COIL database, Yale noise set, and AR occlusion dataset for performance test, and the experimental results are compared with some existing methods. The results indicate that the proposed method is more significant. Full article

In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation. This modification yields the right Lax pair and allows us to implement binary Darboux transformations, which can be used to construct an iterative method to obtain exact solutions. Full article

In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of analyzing large amounts of data has been explored, such as machine learning (ML) algorithms. ML algorithms are being used to analyze and classify biological sequences, despite the intrinsic difficulty in extracting and finding representative biological sequence methods suitable for them. Thereby, extracting numerical features to represent sequences makes it statistically feasible to use universal concepts from Information Theory, such as Tsallis and Shannon entropy. In this study, we propose a novel Tsallis entropy-based feature extractor to provide useful information to classify biological sequences. To assess its relevance, we prepared five case studies: (1) an analysis of the entropic index q; (2) performance testing of the best entropic indices on new datasets; (3) a comparison made with Shannon entropy and (4) generalized entropies; (5) an investigation of the Tsallis entropy in the context of dimensionality reduction. As a result, our proposal proved to be effective, being superior to Shannon entropy and robust in terms of generalization, and also potentially representative for collecting information in fewer dimensions compared with methods such as Singular Value Decomposition and Uniform Manifold Approximation and Projection. Full article

The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester and Hinds method), or are formulated in the tangent bundle of the configuration space. Owing to its interesting relation with general relativity we use a concrete example as a test bed: an extension of the Pontryagin and Husain–Kuchař actions to four dimensional manifolds with boundary. Full article

In this paper, the tracking control problem of underwater robot manipulators is investigated under the influence of the lumped disturbances, including unknown ocean current disturbances and parameter uncertainties. The proposed novel continuous nonsingular finite–time (CNFT) control method is twofold. Firstly, the modified adaptive super–twisting algorithm (ASTA) is proposed with a nonsingular fast terminal sliding mode (NFTSM) manifold to guarantee the finite–time convergence both in the sliding mode phase and the reaching phase. Secondly, a higher–order super–twisting disturbance observer (HOSTDO) is exploited to attenuate the effects of the lumped disturbances. Considering the time–varying gain matrix of the closed–loop control system, the bounded stability is strictly proved via the Lyapunov theory. Hence, the superiority of the proposed controller is singularity–free, fast convergence, chattering–free, high steady–state tracking performance, and good robustness by resorting to the methods of CNFT control and ASTA in combination with a disturbance observer. Finally, numerical simulations are conducted on a two degree–of–freedom (DOF) underwater robot manipulator to demonstrate the effectiveness and high tracking performance of the designed controller. Full article