Abstract In angles-only initial relative orbit determination for non-cooperative targets, many existing methods require multiple angle measurements over a long time span or rely on iterative optimization. As a result, it is difficult to achieve fast initialization from a small number of measurements at the beginning of on-orbit navigation. To address this issue, this paper proposes a non-iterative initial relative orbit determination algorithm in a spherical coordinate framework. First, the relative motion equations are derived in detail in a spherical coordinate system centered on the line-of-sight direction, including the exact nonlinear two-body model and a linear time-invariant model applicable to near-circular orbits. Second, a non-iterative estimation algorithm that requires no prior state information is developed. The algorithm only needs to perform singular value decomposition on a single $6 \times 6$ matrix and solve a univariate polynomial. In the absence of camera offsets or orbital maneuvers, the initial relative state of the target can be obtained rapidly using only four angle measurements. Simulation results show that, compared with the classical iterative method, the proposed algorithm significantly improves computational efficiency while maintaining comparable or even superior estimation accuracy. It also exhibits excellent numerical stability and noise robustness, making it suitable for fast initialization in angles-only relative navigation of non-cooperative targets.


Abstract Bearing fault diagnosis is essential to the operational reliability of rotating machinery. Sparse low-rank (SLR) representation has found widespread application in fault diagnosis. However, existing SLR methods suffer from amplitude underestimation, singular value estimation bias, and insufficient sparsity in applications, leading to fault extraction error. To address this issue, this paper proposes an enhanced periodic group sparse low rank method (EPSLR) with non-convex regularization. The proposed method integrates singular value non-convex penalty, periodic group overlap shrinkage strategy and generalized minimum maximum concave (GMC) penalty function to construct a non-convex optimization problem. Combining the derivation of the convexity conditions and convex optimization algorithms, the non-convex optimization problem is solved and the global optimum is derived. The EPSLR can clearly reveal that the low-rank property and sparsity can be enhanced and fault feature extraction capability improved. The effectiveness of the EPSLR is validated using simulations and real-world rolling bearing signals.

FA-GCL: Feature-augmented graph contrastive learning method.

Entropy-based methods have gained increasing prominence in analyzing and detecting patterns in complex systems data. Key aspects such as fractality, time reversibility, and nonlinearity are commonly characterized using these methods, often in conjunction with techniques like wavelets and empirical modeling. The goal is to extract complexity indices and identify patterns that traditional methods struggle to capture. Shannon entropy obtains information from data by, e.g., extracting hidden information by removing noisy components. However, its applicability can be limited for data of short length. Approximate, sample and permutation entropies offer more flexible approaches, but their parameter dependence can complicate the interpretation of results. Singular value decomposition (SVD) entropy provides a framework for assessing pattern diversity in terms of an entropy index, reflecting an approximate dimensionality of a given dataset. This review focuses on recent SVD entropy applications across various fields and explores its potential in nonlinearity detection and transfer entropy analysis for time series, illustrated through select cases.

Spatio-temporal registration of multi-perspective 3D echocardiography for improved strain estimation.

Rapid factorization of single EEM for dissolved organic matter analysis.

Singular Value Decomposition-based lightweight LSTM for time series forecasting

Singular Value Inequalities related to PPT

This study presents a comparative analysis of the novel guided-wave-based imaging method that integrates variational Bayesian principal component analysis with time-delay strategy for detecting internal and external defects in plate-like structures. The performance of the conventional delay-and-sum imaging method deteriorates when the signal-to-noise ratio of signals is low or when other wave packets overlap with the defect scattering signal. The imaging method based on variational Bayesian principal component analysis analyzes the principal components and corresponding singular values of the time-delayed signal array, and the maximum singular value represents the contribution of the most principal component, serving as an indicator of the coherent defect-related wave packets. Thus, the defect can be highlighted by accounting for the effect of noise and wave packet interference on the time-delayed signal array. However, when defects are located outside the sensor network, the limited information available may reduce the imaging performance. Numerical simulations and experimental studies conducted on plate-like structures demonstrate the proposed method achieves higher imaging clarity and localization accuracy for the internal defect compared with the external defect, with the former exhibiting mm-level absolute localization errors.

Missing values in nuclear magnetic resonance metabolomics data compromise downstream clinical interpretation. Here, we present MetImputBERT, an imputation method based on a pretrained BERT framework. MetImputBERT uses the masks in the masked language model to simulate missing values and leverages predictions and reconstructions to these positions to simulate the imputation process. The learning of MetImputBERT is driven by minimizing the reconstruction error. MetImputBERT was pretrained on the largest metabolomics dataset to date, comprising data from over 230 000 individuals in the UK Biobank. When new datasets with missing values were encountered, MetImputBERT loaded the pretrained parameters and directly imputed the missing values by inferring their reconstructed estimates. MetImputBERT outperformed commonly used methods—K-nearest neighbors, multiple imputation by chained equations, and singular value decomposition—in imputation performance on two independent test sets. We provide an open-source Python tool that allows users to quickly impute missing values in their own NMR metabolomics data without any additional training.

Modern energy and electronic systems comprise a large number of nonlinear elements operating in dynamic modes. Accurate modeling of such systems requires proper consideration of nonlinear current-voltage characteristics (CVC) and transient processes, which is especially important when designing rectifiers, inverters, control systems and other power electronics devices. Existing electrical circuit simulators do not always provide users with the necessary flexibility, scalability, or compatibility with enterprise safety standards, and may have legal restrictions. Custom effective modeling methods for such systems allow for creating specialized software solutions to analyze dynamic modes of electrical circuits, free from the limitations of commercial simulators and tailored to specific engineering and scientific tasks. The purpose of the work is to develop a method for numerical modeling of dynamic modes of electrical circuits comprising semiconductor diodes or other elements with nonlinear CVC, described by nodal equations. The scientific novelty lies in the development of a homotopy approach to overcoming high condition number of the Jacobian matrix when solving nonlinear differential-algebraic equations (DAEs) of electrical circuits, based on deformation of CVC with adaptation of the deformation parameter depending on the residual norm and condition number of the matrix; in the development of a method for extracting linearly independent differential equations from DAEs of electrical circuits without preliminary analysis of their topology; in the development of a universal stamp of a nonlinear element, based on linearization of the functional in the vicinity of the current approximation, allowing for integration of diode models with various CVCs into nodal equations. Materials and methods. Theoretical electrical engineering methods were used in the work, including the modified nodal potential method. The proposed numerical modeling method involves integration of elements with nonlinear CVC into nodal equations; extraction of differential and algebraic parts from DAEs, based on singular value decomposition of the matrix standing before the derivative vector; transformation of DAEs into a nonlinear system of algebraic equations using backward differentiation formulas (BDF) with variable time step. Initial points for BDF were determined by the diagonally implicit Runge–Kutta method of second order accuracy. Numerical solution of the obtained nonlinear equations was performed by the damped Newton–Raphson method. To reduce the condition number of the Jacobian matrix in transient modes, when the spread of differential conductivities reaches 12 orders and higher, a homotopy approach was proposed, consisting of gradual deformation of the diode CVC from a smoothed to the original curve during convergence, while maintaining a given value of the condition number. Results. To demonstrate the proposed solutions, computer simulation of a bridge rectifier operating on an active-inductive load with two types of diode CVC was performed: piecewise-linear and smooth, corresponding to the Shockley equation with series resistance. The deformation parameter and damping coefficient were adaptively changed depending on the residual norm of the functional and the condition number of the Jacobian matrix. Comparison of simulation results with different methods of specifying diode CVC showed that differences appear predominantly in transient processes of switching diode operation modes. It has been found that to ensure convergence of numerical solution in diode switching modes, characterized by high condition number of the Jacobian matrix, the homotopy approach is more effective than diagonal regularization. The proposed method for numerical modeling of dynamic modes of electrical circuits with nonlinear elements has a natural algorithmic structure, allowing for simple software implementation. Conclusions. 1. The most universal diode stamp, obtained on the basis of linearization of the functional derived from the CVC equation in the vicinity of the current approximation, has been identified. 2. A method for extracting linearly independent differential equations from DAEs of electrical circuits without preliminary analysis of circuit topology has been proposed. 3. A method for calculating the Jacobian matrix for solving nonlinear DAE has been proposed. 4. To ensure convergence of numerical solution with high condition number of the Jacobian matrix, it is preferable to apply the homotopy approach.

This study investigates the kinematic behavior of a reconfigurable Delta parallel robot aiming to enhance its performance in real industrial applications such as high-speed packaging, precision pick-and-place operations, automated inspection, and lightweight assembly tasks. While Delta robots are widely recognized for their speed and accuracy, their practical use is often limited by workspace constraints and singularities that compromise motion stability and control safety. Through a detailed analysis, it is shown that classical Jacobian-based performance indices are unsuitable for resolving the redundancy introduced by geometric reconfiguration, as they may lead the system toward singular or ill-conditioned configurations. To overcome these limitations, this work introduces an adjustable singularity-sensitive performance index designed to penalize extreme velocity and force singular values and enables tuning between velocity and force performance. Simulation results demonstrate that optimizing the reconfiguration parameter using this index increases the usable workspace by approximately 82% and improves the uniformity of manipulability across the workspace. These findings suggest that the proposed approach provides a robust framework for enhancing the operational range and kinematic safety of reconfigurable Delta robots, while remaining adaptable to different design priorities.

In the digital era, protecting the integrity and ownership of digital content is increasingly crucial, particularly against unauthorized copying and tampering. Traditional watermarking techniques often struggle to remain robust under various image manipulations, leading to a need for more resilient methods. To address this challenge, we propose a novel watermarking technique that integrates the Discrete Wavelet Transform (DWT), Singular Value Decomposition (SVD), and Schur matrix factorization to embed a QR code as a watermark into digital images. Our method was rigorously tested across a range of common image attacks, including histogram equalization, salt-and-pepper noise, ripple distortions, smoothing, and extensive cropping. The results demonstrate that our approach significantly outperforms existing methods, achieving high normalized correlation (NC) values such as 0.9949 for histogram equalization, 0.9846 for salt-and-pepper noise (2%), 0.96063 for ripple distortion, 0.9670 for smoothing, and up to 0.9995 under 50% cropping. The watermark consistently maintained its integrity and scannability under all tested conditions, making our method a reliable solution for enhancing digital copyright protection.

Five-axis precision dispensing machines are employed for semiconductor packaging. The dispensing accuracy is significantly affected by multiple geometric errors among the five axes. This paper proposes a vision-based measurement (VBM) system for identifying geometric errors and calibrating kinematics. The VBM system is also employed to complete the detection of the workpiece. A kinematic model of the machine was established using a local product-of-exponential formulation of screw theory. A geometric error identification algorithm was designed. Eight position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) were involved. The system of overdetermined equations was solved. Combining the singular value decomposition and regularization, eight PIGEs in the A and C axes were identified. Comprehensive error measurement results verified the proposed approach. The VBM system measured a mean spatial position error of approximately 59.9 μm and a mean orientation error of about 160 arcsec for the end-effector, reflecting the geometric error level of the prototype machine. The proposed approach provides a feasible and automated calibration solution for five-axis precision dispensing machines.

Electromagnetic ultrasonic testing technology, owing to its couplant-free, high-temperature-resistant, and non-contact characteristics, exhibits unique advantages for thickness measurement in harsh industrial environments. However, its accuracy is fundamentally limited by inherent constraints in signal bandwidth and low signal-to-noise ratio. To address these challenges, this work proposes an electromagnetic ultrasonic thickness measurement method that integrates Adaptive Denoising with Bayesian Vector Autoregressive (AD-BVAR) spectral extrapolation. The approach employs Particle Swarm Optimization (PSO) and automatically determines the optimal parameters for Variational Mode Decomposition (VMD), followed by integration with Singular Value Decomposition (SVD) to achieve the adaptive denoising of signals. Subsequently, the BVAR model incorporating prior constraints performs robust extrapolation of the effective frequency band spectrum, ultimately achieving high measurement accuracy signal reconstruction. The experimental results demonstrate that on step blocks with thicknesses of 3 mm and 12.5 mm, the proposed method achieved significantly reduced error rates of 0.267% and 0.240%, respectively. This performance markedly surpasses that of the conventional Autoregressive (AR) method, which yielded errors of 0.767% and 0.560% under identical conditions, while maintaining stable performance across different thicknesses.

ABSTRACT Background With the global popularity of the Internet since the twenty-first century, the amount of data information has increased exponentially. Data mining and application have become one of the focuses of all circles. Data information can help users quickly find products that meet their interest needs through personalized recommendation, precision marketing, and other ways, so as to improve the shopping experience. It can also optimize the allocation of learning resources through data analysis, so that learners can acquire the required knowledge more effectively and improve learning efficiency. As a widely used algorithm in data utilization, recommenda-tion algorithms can make accurate recommendations to users based on their past historical data. Previous recommendation algorithms, such as user-based collaborative filtering and item-based collaborative filtering, content-based recommendation technology, and matrix decomposition-based methods, have insufficient accuracy and slow computing speed, which cannot meet the needs of platforms and users. Method Therefore, this paper proposes an online shopping platform product recommendation model to make the recommendation more accurate. This is a combination of the attention mechanism and GRU (Gated Recurrent Unit, GRU) algorithm. Result Through the test on a real data set, the recognition rate of this research-proposed algorithm reaches 90.2% in 15 iterations, the average time of a single iteration is 21 s, and the accuracy range is 95.32 ~ 96.03%. Compared with Singular Value Decomposition, the Non-negative Matrix Factorization recommendation algorithm, and the Personal Rank algo-rithm based on random walk, the research method has better performance in the aspects of recommendation accuracy and recall rate. Conclusion The attention-based GRU recommendation model effectively improves the accuracy and efficiency of recommendation systems. It outperforms traditional methods and is well-suited for large-scale, high-concurrency scenarios in online shopping platforms.

Loop closure detection is essential for improving the long-term consistency and robustness of simultaneous localization and mapping (SLAM) systems. Existing LiDAR-based loop closure approaches often rely on limited or partial geometric features, restricting their performance in complex environments. To address these limitations, this paper introduces a Density Triangle Descriptor (DTD). The proposed method first extracts keypoints from density images generated from LiDAR point clouds, and then constructs a triangle-based global descriptor that is invariant to rotation and translation, enabling robust structural representation. Furthermore, to enhance local discriminative ability, the neighborhood around each keypoint is modeled as a Gaussian distribution, and a local descriptor is derived from the entropy of its probability distribution. During loop closure detection, candidate matches are first retrieved via hash indexing of triangle edge lengths, followed by entropy-based local verification, and are finally refined by singular value decomposition for accurate pose estimation. Extensive experiments on multiple public datasets demonstrate that compared to STD, the proposed DTD improves the average F1 max score and EP by 18.30% and 20.08%, respectively, while achieving a 50.57% improvement in computational efficiency. Moreover, DTD generalizes well to solid-state LiDAR with non-repetitive scanning patterns, validating its robustness and applicability in complex environments.

Nonlinear signal models are widely used in power amplifier predistortion, full-duplex self-interference cancellation, and other scenarios. The parallel Hammerstein (PH) model is a typical nonlinear signal model, but its serial and parallel hybrid architecture brings difficulties in performance analysis and coefficient estimation. This paper focuses on the performance analysis and coefficient estimation of the PH model for nonlinear systems with memory effects, such as power amplifiers. By comparing the PH model with the memory polynomial (MP) model under identical basis functions, we analyze its performance across varying numbers of parallel branches, nonlinear orders, and memory depths. Using singular value decomposition (SVD), we derive a closed-form expression for the PH model's performance under underdetermined conditions, establishing its relationship to the non-zero singular values of the MP model's coefficient matrix. Based on this, we propose a coefficient generation method combining SVD and least squares (LS), which directly computes coefficients and assesses performance during execution. Simulations confirm the method's effectiveness, showing that selecting branches associated with larger singular values achieves near-optimal performance with reduced complexity.

By using the geometric and algebraic properties of Bernstein polynomials, a composite method for solving the initial value problems (IVP's) with first-order, singular and nonlinear ordinary differential equations (ODE's) has been developed. The Newton’s method is incorporated into the method to solve the resulting system of nonlinear equations. The algorithm of the problem solving is reduced to the calculation of the unknown Bernstein coefficients of the approximate solution. The effectiveness of the proposed method is verified by comparing the present numerical results by other existing ones. The proposed method reduces the computation cost and gives a better approximation to the exact solution even for small degrees of approximation. Another advantage of the present method is the ability to calculate the approximate solution at each point of the solution interval in addition to the grid points.

Short-term weather prediction plays a critical role in supporting decision-making across sectors such as agriculture, transportation, and disaster risk management. This study proposes an interpretable and computationally efficient weather forecasting approach based on linear system modeling combined with Singular Value Decomposition (SVD). Historical meteorological data—including temperature, humidity, air pressure, and wind speed—are represented in matrix form to extract dominant patterns and construct a system of linear equations describing inter-variable relationships. The resulting model is evaluated for short-term forecasting horizons of 24–48 hours using standard performance metrics. Experimental results demonstrate that the proposed SVD-based linear system model outperforms conventional linear regression, achieving lower MAE and RMSE values and higher coefficients of determination (R² = 0.94 for temperature and 0.91 for humidity). While not intended to replace physics-based numerical weather prediction models for long-term forecasting, the proposed approach offers significant advantages in computational speed, interpretability, and applicability in data- and resource-constrained environments. These findings indicate that matrix-based linear system analysis provides a viable alternative for fast and accurate short-term weather prediction and can be further enhanced through integration with non-linear or machine learning-based methods.