Search Results (55)

We investigate invariant finite-dimensional linear spaces for a class of nonlinear evolution equations with second-order time dependence of the type ${\partial }_{tt}u=-{\partial }_x\left(A(x,u)u\right)+{\partial }_{xx}\left(B(x,u)u\right)+f\left(u\right),$ where the coefficients may depend nonlinearly on the solution. Using direct algebraic verification and invariant subspace reductions, we derive several exact solutions and reduce the governing equations to finite-dimensional systems of ordinary differential equations. Various examples are presented to illustrate the applicability of the method to nonlinear transport, diffusion, and reaction models. Full article

Air pollution is primarily caused by human activities such as industrial emissions, road traffic, waste incineration, and fossil fuel power plants. Pollution refers to the presence of harmful substances in the air, such as nitrogen dioxide (NO₂), sulfur dioxide (SO₂), ozone (O₃), carbon monoxide (CO), and other environmental pollutants. Some pollutants pose health risks even at low doses. Given the critical importance of air quality, monitoring air pollution has become an urgent and essential subject. Air quality monitoring relies on accurate data, so changeable environments and sensor issues make using interval diagnostic techniques for addressing uncertainty in systems interesting. In this article, we focus on three key aspects to achieve precise and efficient results: (1) the use of an accurate fault detection method that accounts for data uncertainty while maintaining model symmetry, (2) the implementation of a reliable detection index invariant to symmetric sensor behaviors, and (3) the combination of both to improve fault localization accuracy. This paper presented a fault detection and localization framework designed for uncertain and nonlinear monitoring environments. A novel fault-sensitive detection index was developed and integrated into an elimination-based localization strategy within a reduced-rank interval kernel PCA (RR-IKPCA) model. By exploiting information contained in modified residual subspaces and explicitly accounting for measurement uncertainty, the proposed approach enhances fault sensitivity while preserving robust localization capability, as validated on the AIRLOR air quality monitoring network. Full article

In this paper, the uniform approximation of continuous functions on $[0,1]$ by rational functions with prescribed poles and bounded multiplicities is studied. A classical theorem of Fichera characterizes density in $C\left(\right[0,1\left]\right)$ through the divergence of a conformally invariant series involving the pole distribution. A modern reformulation of this result is developed and it is given an operator-theoretic interpretation in which the approximation property is equivalent to cyclicity and to the absence of nontrivial invariant subspaces in an associated Hardy-space model. In this framework, the classical Blaschke condition emerges as the fundamental obstruction to density, linking rational approximation to the structure of model spaces and non-selfadjoint operator algebras. The density criterion is interpreted in terms of symmetry: divergence corresponds to a balanced distribution of poles compatible with the conformal geometry of the slit domain, while convergence induces symmetry breaking and the emergence of invariant structures. Numerical models illustrate the sharpness of the criterion and provide a concrete manifestation of the Blaschke obstruction and cyclicity mechanism. This new approach places Fichera’s theorem within a broader operator-theoretic and spectral framework, connecting classical approximation theory with Hardy spaces, invariant subspace theory, and modern rational approximation methods. Full article

A piezoelectric actuator (PEA) is a fundamental part of a high-precision motion system, yet its performance is critically constrained by inherent nonlinearities such as the velocity dead zone and hysteresis. To overcome these limitations and the associated time-varying dynamics, this study introduces a novel control framework for a dual-mode standing wave PEA. The framework integrates a Global Linearized Sparse Prediction (GLSP) model with an Adaptive Kalman Observer-based Model Predictive Control (AKOBMPC) strategy, specifically designed for velocity dead-zone compensation. The GLSP model employs Koopman operator theory to lift the complex, nonlinear electromechanical and contact dynamics into a linear invariant subspace. Incorporated with a deep learning-based structured pruning mechanism, the model achieves an effective balance between prediction accuracy and computational efficiency, facilitating real-time implementation. Leveraging this high-fidelity model, the AKOBMPC algorithm is developed to estimate unmeasurable disturbances and optimize the control sequence for precise velocity tracking. Experimental results demonstrate the GLSP model’s accurate prediction of system behavior under varying loads and excitation frequencies. The proposed controller effectively suppresses the velocity dead zone, achieving tracking errors within ±0.35 mm/s for a 40.00 mm/s trapezoidal reference and within ±0.50 mm/s for sinusoidal tracking. These results confirm the superior performance of the AKOBMPC scheme over conventional methods, offering a robust solution for high-precision velocity regulation in PEA system and contributing to the advancement of next-generation precision actuator. Full article

Cross-site transfer learning is a promising approach to address data scarcity at newly deployed photovoltaic (PV) stations by leveraging knowledge from data-rich source sites. However, existing domain adaptation methods align feature representations without distinguishing physically meaningful causal relationships from site-specific spurious correlations, leading to negative transfer when local environmental conditions differ substantially between stations. This paper proposes CausalTransPV, a causal invariant representation learning framework that integrates explicit temporal causal discovery with selective domain alignment for cross-site PV power forecasting. The framework comprises three synergistic modules: (i) a multi-station temporal causal discovery module that jointly learns shared and station-specific causal graphs through differentiable acyclicity-constrained optimization with a cross-station invariance regularizer; (ii) a causal-guided disentangled encoder that decomposes representations into causal-invariant and site-specific subspaces using the discovered causal graph as a structural prior; and (iii) a causal-subspace transfer and prediction module that performs maximum mean discrepancy (MMD)-based domain alignment exclusively on the causal subspace. Experiments on the Desert Knowledge Australia Solar Centre (DKASC) multi-station dataset under varying target label ratios (0–50%) demonstrate that CausalTransPV achieves relative mean absolute error (MAE) reductions of 6.9–9.9% over the strongest baseline. Ablation studies, causal graph analysis, feature space visualization, and weather-conditioned case studies further validate the contribution of each component. These results suggest that causal-guided selective transfer offers an effective paradigm for reliable PV forecasting under data-scarce cross-site scenarios. Full article

Few-shot classification aims to generalize from very limited samples, providing an effective solution for data-scarce scenarios. From a symmetry viewpoint, an ideal Few-Shot classifier should be invariant to class permutations and treat support and query features in a balanced manner, preserving intra-class cohesion while enlarging inter-class separation in the embedding space. However, existing methods often violate this symmetry because prototypes are estimated from few noisy samples, which induces asymmetric representations and task-dependent biases under complex inter-class relations. To address this, we propose FC-SBAAT, feature collaboration, and Sparse Bias-Aware Attention Transformer, a framework that explicitly leverages symmetry in feature collaboration and prototype construction. First, we enhance symmetric interactions between support and query samples in both attention and contrastive subspaces and adaptively fuse these complementary representations via learned weights. Second, we refine prototypes by symmetrically aggregating intra-class features with learned importance weights, improving prototype quality while maintaining intra-class symmetry and increasing inter-class discrepancy. For matching, we introduce a Sparse Bias-Aware Attention Transformer that corrects asymmetric task bias through bias-aware attention with a low computational overhead. Extensive experiments show that FC-SBAAT achieves 55.71% and 73.87% accuracy for 1-shot and 5-shot tasks on MiniImageNet and 70.37% and 83.86% on CUB, outperforming prior methods. Full article

In this paper, we present rigorous asymptotic componentwise perturbation bounds for regular Hermitian indefinite matrix eigendecompositions, obtained via the method of splitting operators. The asymptotic bounds are derived from exact nonlinear expressions for the perturbations and allow each entry of every matrix eigenvector to be bounded in the case of distinct eigenvalues. In contrast to the perturbation analysis of the Schur form of a nonsymmetric matrix, the bounds obtained here do not rely on the Kronecker product, which significantly reduces both memory requirements and computational cost. This enables efficient sensitivity analysis of high-order problems. The eigenvector perturbation bounds are further applied to estimate the angles between perturbed and unperturbed one-dimensional invariant subspaces spanned by the corresponding eigenvectors. To reduce conservatism in the case of high-order problems, we propose the use of probabilistic perturbation bounds based on the Markov inequality. The analysis is illustrated by two numerical experiments of order 5000. Full article

This paper introduces an innovative rapid algorithm for estimating two-dimensional direction of arrival (2D-DOA) with randomly arranged electromagnetic vector sensor (EMVS) arrays under nonuniform noise conditions. The approach begins by forming the covariance matrix of the received signal matrix, after which elements affected by noise are removed based on the characteristics of nonuniform noise to reduce its disruptive effects. Subsequently, the pure covariance matrix is filled using a matrix completion algorithm and then reconstructed into a new matrix. Finally, the signal subspace is extracted by the propagator method (PM) algorithm, and the 2D-DOA is estimated via a method analogous to the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). Theoretical analyses confirm the high degrees of freedom of the algorithm, low computational complexity, and accuracy of the estimation. Simulation results validate that the proposed algorithm exhibits remarkable resilience against nonuniform noise. When compared with conventional algorithms such as ESPRIT, ESPRIT-like, and improved ESPRIT (IESPRIT), it also shows better performance in terms of estimation speed and accuracy. Full article

Background/Objectives: An ASD diagnosis from EEG is challenging due to non-stationary, low-SNR signals and small cohorts. We propose a compact, interpretable pipeline that pairs a shift-invariant Stationary Wavelet Transform (SWT) with Fisher’s Linear Discriminant (FLDA) as a supervised projection method, delivering band-level insight and subject-wise evaluation suitable for resource-constrained clinics. Methods: EEG from the KAU dataset (eight ASD, eight controls; 256 Hz) was decomposed with SWT (db4). We retained levels 3, 4, and 6 (γ/β/θ) as features. FLDA learned a low-dimensional discriminant subspace, followed by a linear decision rule. Evaluation was conducted using a subject-wise 70/30 split (no subject overlap) with accuracy, precision, recall, F1, and confusion matrices. Results: The β band (Level 4) achieved the best performance (accuracy/precision/recall/F1 = 0.95), followed by γ (0.92) and θ (0.85). Despite partial overlap in FLDA scores, the projection maximized between-class separation relative to within-class variance, yielding robust linear decisions. Conclusions: Unlike earlier FLDA-only pipelines and wavelet–entropy–ANN approaches, our study (1) employs SWT (undecimated, shift-invariant) rather than DWT to stabilize sub-band features on short resting segments, (2) uses FLDA as a supervised projection to mitigate small-sample covariance pathologies before classification, (3) provides band-specific discriminative insight (β > γ/θ) under a subject-wise protocol, and (4) targets low-compute deployment. These choices yield a reproducible baseline with competitive accuracy and clear clinical interpretability. Future work will benchmark kernel/regularized discriminants and lightweight deep models as cohort size and compute permit. Full article

This study proposes a parallel model reduction method for two-dimensional discrete-time systems, utilizing Krawtchouk moments and equivalent transformation. This work makes two significant contributions. First, we introduce a projection subspace that is independent of the input as well as of the Krawtchouk parameters, thus ensuring robustness. Second, we propose an efficient parallel algorithm for computing the basis of the projection subspace. With the difference relation of Krawtchouk polynomials and the analytic identity theorem, we obtain the explicit formula for the Krawtchouk moments of the state, which is input-dependent and Krawtchouk-parameter-dependent. We derive a projection subspace that is independent of both input and Krawtchouk parameter, such that it is equivalent to the subspace spanned by the Krawtchouk moments. Further, we propose a parallel strategy based on the equivalent transformation of the block bi-diagonal Toeplitz matrices with bi-diagonal blocks to compute the basis of the projection subspace, facilitating acceleration of the model reduction process on high-performance computers. Moreover, we analyze the Krawtchouk moment invariants of the proposed parallel method. Finally, the effectiveness of the proposed method is illustrated by two numerical examples. Full article

Remaining useful life (RUL) prediction of rolling bearings is of significance for improving the reliability and durability of rotating machinery. Aiming at the problem of suboptimal RUL prediction precision under cross-working conditions due to distribution discrepancies between training and testing data, enhanced cross-working condition RUL prediction for rolling bearings via an initial degradation detection-enabled joint transfer metric network is proposed. Specifically, the health indicator, called reconstruction along projection pathway (RAPP), is calculated for initial degradation detection (IDD), in which RAPP is obtained from a novel deep adversarial convolution autoencoder network (DACAEN) and compares discrepancies between the input and the reconstruction by DACAEN, not only in the input space, but also in the hidden spaces, and then RUL prediction is triggered after IDD via RAPP. After that, a joint transfer metric network is proposed for cross-working condition RUL prediction. Joint domain adaptation loss, which combines representation subspace distance and variance discrepancy representation, is designed to act on the final layer of the mapping regression network to decrease data distribution discrepancies and ultimately obtain cross-domain invariant features. The experimental results from the PHM2012 dataset show that the proposed method has higher prediction accuracy and better generalization ability than typical and advanced transfer RUL prediction methods under cross-working conditions, with improvements of 0.047, 0.053, and 0.058 in the MSE, RMSE, and Score. Full article

Phase space methods, particularly Wigner functions, provide intuitive tools for representing and analyzing quantum states. We focus on systems with SU(2) dynamical symmetry, which naturally describes spin and a wide range of two-mode quantum models. We present a unified phase space framework tailored to these systems, highlighting its broad applicability in quantum optics, metrology, and information. After reviewing the core SU(2) phase-space formalism, we apply it to states designed for optimal quantum sensing, where their nonclassical features are clearly revealed in the Wigner representation. We then extend the approach to systems with an indefinite number of excitations, introducing a generalized framework that captures correlations across multiple SU(2)-invariant subspaces. These results offer practical tools for understanding both theoretical and experimental developments in quantum science. Full article

The thermal runaway propagation (TRP) model of energy storage batteries can provide solutions for the safety protection of energy storage systems. Traditional TRP models are solved using the finite element method, which can significantly consume computational resources and time due to the large number of elements and nodes involved. To ensure solution accuracy and improve computational efficiency, this paper transforms the heat transfer problem in finite element calculations into a state-space equation form based on the reduced-order theory of linear time-invariant (LTI) systems; a simplified method is proposed to solve the heat flow changes in the battery TRP process, which is simple, stable, and computationally efficient. This study focuses on a four-cell 100 Ah lithium iron phosphate battery module, and module experiments are conducted to analyze the TRP characteristics of the battery. A reduced-order model (ROM) of module TRP is established based on the Arnoldi method for Krylov subspace, and a comparison of simulation efficiency is conducted with the finite element model (FEM). Finally, energy flow calculations are performed based on experimental and simulation data to obtain the energy flow rule during TRP process. The results show that the ROM achieves good accuracy with critical feature errors within 10%. Compared to the FEM, the simulation duration is reduced by 40%. The model can greatly improve the calculation efficiency while predicting the three-dimensional temperature distribution of the battery. This work facilitates the efficient computation of TRP simulations for energy storage batteries and the design of safety protection for energy storage battery systems. Full article

In orthodontics, the manual tracing of cephalometric radiographs is a common practice, where the Sella Turcica (ST) serves as a reference point. The radiologist often manually traces the outline of the sella using manual tools (e.g., calipers on radiographs). Perhaps the inherent complexity and variability in the shapes of sella and the lack of advanced assessment tools make the classification of sella challenging, as it requires extensive training, skills, time, and manpower to detect subtle changes that often may not be apparent. Moreover, existing semi-supervised learning (SSL) methods face key limitations such as shift invariance, inadequate feature representation, overfitting on small datasets, and a lack of generalization to unseen variations in ST morphology. Medical imaging data are often unlabeled, limiting the training of automated classification systems for ST morphology. To address these limitations, a novel semi-supervised deep subspace embedding (SSLDSE) framework is proposed. This approach integrates real-time stochastic augmentation to significantly expand the training dataset and introduce natural variability in the ST morphology, overcoming the constraints of small and non-representative datasets. Non-linear features are extracted and mapped to a non-linear subspace using Kullback–Leibler divergence, which ensures that the model remains consistent despite image transformations, thus resolving issues related to shift invariance. Additionally, fine-tuning the Inception-ResNet-v2 network on these enriched features reduces retraining costs when new unlabeled data becomes available. t-distributed stochastic neighbor embedding (t-SNE) is employed for effective feature representation through manifold learning, capturing complex patterns that previous methods might miss. Finally, a zero-shot classifier is utilized to accurately categorize the ST, addressing the challenge of classifying new or unseen variations. Further, the proposed SSLDSE framework is evaluated through comparative analysis with the existing methods (Active SSL, GAN SSL, Contrastive SSL, Modified Inception-ResNet-v2) for ST classification using various evaluation metrics. The SSLDSE and the existing methods are trained on our dataset (sourced from PGI Chandigarh, India), and a blind test is conducted on the benchmark dataset (IEEE ISBI 2015). The proposed method improves classification accuracy by 15% compared to state-of-the-art models and reduces retraining costs. Full article

Operational modal analysis (OMA) is essential for long-term health monitoring of offshore wind turbines (OWTs), helping identifying changes in structural dynamic characteristics. OMA has been applied under parked or idle states for OWTs, assuming a linear and time-invariant dynamic system subjected to white noise excitations. The impact of complex operating environmental conditions on structural modal identification therefore requires systematic investigation. This paper studies the applicability of OMA based on covariance-driven stochastic subspace identification (SSI-COV) under various non-white noise excitations, using a DTU 10 MW jacket OWT model as a basis for a case study. Then, a scaled (1:75) 10 MW jacket OWT model test is used for the verification. For pure wave conditions, it is found that accurate identification for the first and second FA/SS modes can be achieved with significant wave energy. Under pure wind excitations, the unsteady servo control behavior leads to significant identification errors. The combined wind and wave actions further complicate the picture, leading to more scattered identification errors. The SSI-COV based modal identification method is suggested to be reliably applied for wind speeds larger than the rated speed and with sufficient wave energy. In addition, this method is found to perform better with larger misalignment of wind and wave directions. This study provides valuable insights in relation to the engineering applications of in situ modal identification techniques under operating conditions in real OWT projects. Full article