Search Results (125)

Multi-agent systems (MAS) typically model interaction topologies using directed or undirected graphs when analyzing consensus convergence rates. However, as system complexity increases, purely directed or undirected networks may be insufficient to capture interaction heterogeneity. This paper adopts hybrid networks as interaction topology to investigate strategies for improving consensus convergence rates. We propose the Hermitian Kirchhoff index, a novel metric based on resistance distance, to quantify the consensus convergence rates and establish its theoretical justification. We then examine how adding or removing edges/arcs affects the Hermitian Kirchhoff index, employing first-order eigenvalue perturbation analysis to relate these changes to algebraic connectivity and its associated eigenvectors. Numerical simulations corroborate the theoretical findings and demonstrate the effectiveness of the proposed approach. Full article

This research aims to actively suppress vibrations at the end-effector of a flexible manipulator. When configured in a locked state, the system behaves as a two-link manipulator subjected to disturbances on the first link. To analyze its behavior, Finite Element Analysis (FEA) is employed to extract the natural frequencies (eigenvalues) and corresponding mode shapes (eigenvectors) of a two-link, two-joint flexible manipulator (2L2JM). The obtained eigenvectors are transformed into uncoupled state-space equations using balanced realization and the Match-DC-Gain model reduction algorithm. An H-infinity controller is then designed and applied to both the full-order and reduced-order models of the manipulator. The objective of this study is to validate an analytical framework through FEA, demonstrating its applicability to complex manipulators with multiple joints and flexible links. Given that the full state-space representation typically results in high-dimensional matrices, model reduction enables effective vibration control with a minimal number of states. The derivation of the 2L2JM state space, its model reduction, and a subsequent control strategy have not been previously addressed in this manner. Simulation results showcasing vibration suppression of a cantilever beam are presented and benchmarked against two alternative modeling approaches. Full article

Breeding improvement in alfalfa (Medicago sativa L.) is often constrained by the complexity of agronomic traits and trade-offs among yield-related characteristics. Conventional single-trait selection rarely captures the full range of phenotypic variation or the interactions among traits. To address this, we developed a principal component analysis (PCA)-based framework for multivariate selection in hybrid breeding. Six yield-related traits—plant height, branch number, fresh/hay yield ratio (FHR), leaf/stem ratio (LSR), multifoliolate leaf frequency, and dry weight per plant—were quantified in two parental lines and their F₁/F₂ generations. PCA identified three principal components (PC1–PC3) with eigenvalues >1, explaining 71.14% of the total phenotypic variance: PC1 (32.43% variance) was predominantly loaded with positive contributions from dry weight per single plant, height, and branches, biologically representing overall plant vigor and biomass accumulation; PC2 (21.77% variance) showed strong negative loadings for LSR, capturing architectural trade-offs between stem dominance and leaf production; PC3 (16.94% variance) had positive loadings on multifoliolate leaf rate and fresh/dry ratio, embodying quality and physiological resilience traits. Based on PCA scores, a composite selection index was constructed, and the top 31.1% of F1 hybrids were selected. Their F₂ progeny showed significant improvements in dry weight (+15.56%, p < 0.01), multifoliolate leaf frequency (+74.78%, p < 0.001), and reduced FHR (–8.2%, p < 0.05), accompanied by lower yield decline (−7.2% versus −14.1% in controls). These results show that PCA-based multivariate selection effectively balances trait trade-offs, enhances intergenerational stability, and improves selection efficiency. This framework offers a practical tool for alfalfa breeding. Full article

The basic theoretical properties of the approximate symmetric chordal metric (ASCM) for two real or complex numbers are studied, and reliable, accurate, and efficient algorithms are proposed for its computation. ASCM is defined as the minimum between the moduli of the differences of the two numbers and of their reciprocals. It differs from the chordal metric by including the modulus of the difference of the numbers. ASCM is not a true mathematical distance, but is a useful replacement for a distance in some applications. For instance, sensitivity analysis or block diagonalization of matrix pencils benefit from a measure of closeness of eigenvalues and also of their reciprocals; ASCM is ideal for this purpose. The proposed algorithms can be easily implemented on various architectures and compilers. Extensive numerical tests were performed to assess the performance of the associated implementation. The results were compared to those obtained in MATLAB, but with appropriate modifications for numbers very close to the bounds of the range of representable values, where the usual formulas give wrong results. Full article

This paper presents a formulation for the dynamic analysis of dam–reservoir–foundation systems, employing a coupled finite element model that integrates displacements and reservoir pressures. An innovative coupled approach, without separating the solid and fluid equations, is proposed to directly solve the single non-symmetrical governing equation for the whole system with non-proportional damping. For the modal analysis, a state–space method is adopted to solve the coupled eigenproblem, and complex eigenvalues and eigenvectors are computed, corresponding to non-stationary vibration modes. For the seismic analysis, a time-stepping method is applied to the coupled dynamic equation, and the stress–transfer method is introduced to simulate the nonlinear behavior, innovatively combining a constitutive joint model and a concrete damage model with softening and two independent scalar damage variables (tension and compression). This formulation is implemented in the computer program DamDySSA5.0, developed by the authors. To validate the formulation, this paper provides the experimental and numerical results in the case of the Cahora Bassa dam, instrumented in 2010 with a continuous vibration monitoring system designed by the authors. The good comparison achieved between the monitoring data and the dam–reservoir–foundation model shows that the formulation is suitable for simulating the modal response (natural frequencies and mode shapes) for different reservoir water levels and the seismic response under low-intensity earthquakes, using accelerograms measured at the dam base as input. Additionally, the dam’s nonlinear seismic response is simulated under an artificial accelerogram of increasing intensity, showing the structural effects due to vertical joint movements (release of arch tensions near the crest) and the concrete damage evolution. Full article

We present an advanced restrictively preconditioned biconjugate gradient-stabilized (RPBiCGSTAB) algorithm specifically designed to improve the convergence speed of Krylov subspace methods for nonlinear systems characterized by a structured 5-by-5 block configuration. This configuration frequently arises from cell-centered finite difference discretizations employed in solving image deblurring problems governed by mean curvature dynamics. The RPBiCGSTAB method is crafted to exploit this block structure, thereby optimizing both computational efficiency and convergence behavior in complex image processing tasks. Analyzing the spectral characteristics of preconditioned matrices often reveals a beneficial distribution of eigenvalues, which plays a critical role in accelerating the convergence of the RPBiCGSTAB algorithm. Furthermore, our numerical experiments validate the computational efficiency and practical applicability of the method in addressing nonlinear systems commonly encountered in image deblurring. Our analysis also extends to the spectral properties of the preconditioned matrices, noting a pronounced clustering of eigenvalues around 1, which contributes to enhanced stability and convergence performance.Through numerical simulations that focus on mean curvature-driven image deblurring, we highlight the superior performance of the RPBiCGSTAB method in comparison to other techniques in this specialized field. Full article

This study investigated the squeal noise characteristics of the in-plane mode of the disc in a disc brake system as influenced by the temperature of the brake pad. The temperature range of the brake pad was set between 50 °C and 300 °C, and the squeal noise was analyzed by calculating the complex eigenvalues using the finite element method (FEM). The FEM analysis indicated that instability was most sensitive near 80 °C, and it was observed that instability exhibited mode exchange from the disc’s in-plane mode to the out-of-plane mode in a nearby frequency band due to thermal deformation of the pad. A reproduction test was conducted using a brake dynamometer, where the main squeal noise was found to be approximately 10,000 Hz, consistent with the FEM analysis. Additionally, the squeal noise occurred most near 100 °C, and the noise disappeared after 250 °C. These results largely align with the FEM analysis model, validating the suitability of the analysis approach. Full article

In complex underwater environments, the stability of navigation for autonomous underwater vehicles (AUVs) is critical for mission success. To enhance the reliability of the AUV-integrated navigation system, fault detection technology was investigated. Initially, the causes and classifications of faults within the integrated navigation system were analyzed in detail, and these faults were categorized as either abrupt or gradual, based on variations in sensor output characteristics under fault conditions. To overcome the limitations of the residual chi-square method in detecting gradual faults, a cumulative residual detection approach with error coefficient amplification was proposed. The algorithm enhances gradual fault detection by using eigenvalue analysis and constructing fault-frequency-based error amplification coefficients with non-parametric techniques. Furthermore, to improve the detection of gradual faults, artificial intelligence-based fault detection methods were also explored. Specifically, the particle swarm optimization (PSO) algorithm was employed to optimize the hyperparameters of a long short-term memory (LSTM) neural network, leading to the development of a PSO-LSTM fault detection model. In this model, the fault detection function was formulated by comparing the predictions generated by the PSO-LSTM model with those derived from the Kalman filter. The experimental results demonstrated that the fault detection function formulated by PSO-LSTM exhibited enhanced sensitivity to gradual faults and enabled the timely isolation of faulty sensors. In unfamiliar marine regions, the PSO-LSTM method demonstrates greater stability and avoids the need to recalibrate detection thresholds for each sea area—an important advantage for AUV autonomous navigation in complex environments. Full article

Transfinite interpolation, originally proposed in the early 1970s as a global interpolation method, was first implemented using Lagrange polynomials and cubic Hermite splines. While initially developed for computer-aided geometric design (CAGD), the method also found application in global finite element analysis. With the advent of isogeometric analysis (IGA), Bernstein–Bézier polynomials have increasingly replaced Lagrange polynomials, particularly in conjunction with tensor product B-splines and non-uniform rational B-splines (NURBSs). Despite its early promise, transfinite interpolation has seen limited adoption in modern CAD/CAE workflows, primarily due to its mathematical complexity—especially when blending polynomials of different degrees. In this context, the present study revisits transfinite interpolation and demonstrates that, in four broad classes, Lagrange polynomials can be systematically replaced by Bernstein polynomials in a one-to-one manner, thus giving the same accuracy. In a fifth class, this replacement yields a robust dual set of basis functions with improved numerical properties. A key advantage of Bernstein polynomials lies in their natural compatibility with weighted formulations, enabling the accurate representation of conic sections and quadrics—scenarios where IGA methods are particularly effective. The proposed methodology is validated through its application to a boundary-value problem governed by the Laplace equation, as well as to the eigenvalue analysis of an acoustic cavity, thereby confirming its feasibility and accuracy. Full article

The understanding and application of fluid-type inerters by scholars have been on the rise. However, due to their intricate multiphase mechanical properties, existing models still have considerable room for improvement. This study presents two fractional-order models and conducts parameter identification by integrating them with classical experimental data. The first model is an independent fractional-order model. In comparison with traditional models, it demonstrates significantly higher fitting accuracy in frequency regions beyond the ultra-low frequency range. The second model is a segmented fractional-order model, which determines segments according to critical frequencies. Although this model enhances the overall fitting accuracy, it also leads to increased complexity. To tackle this complexity issue, a rough design strategy is proposed to minimize the critical frequency. Research indicates that under such a strategy, the inertial effect dominates the behavior of the fluid inerter. Even when the independent fractional-order model is used, a high fitting accuracy can be achieved. Consequently, by designing the structural parameters and fluid medium of the fluid inerter based on the rough design strategy, the model can be simplified. Moreover, compared with traditional nonlinear inerter models, the transfer function and eigenvalue analysis methods can be effectively applied. This enables the acquisition of more comprehensive theoretical research results, thereby greatly facilitating theoretical analysis. Full article

Voltage source converter-based high-voltage direct current (VSC-HVDC) systems integrated into weak AC grids may exhibit oscillation-induced instability, posing significant threats to power system security. With increasing structural complexity and diverse control strategies, the stability characteristics of VSC-HVDC system require further investigation. This paper focuses on the stability of a receiving-end VSC-HVDC system consisting of a DC voltage-controlled VSC parallel-connected to a power-controlled VSC, under various operating conditions. First, small-signal models of each subsystem were developed and a linearized full-system model was constructed based on port relationships. Then, eigenvalue and participation factor analyses were utilized to evaluate the influence of control strategy, asymmetrical grid strength, power flow direction, and tie line on the system’s small-signal stability. A feasible short-circuit ratio (SCR) region was established based on joint power–topology joint, forming a stable operating space for the system. Finally, the correctness of the theoretical analysis was validated via MATLAB/Simulink time-domain simulations. Results indicate that, in comparison to the power control strategy, the DC voltage control strategy was more sensitive to variations in the AC system and demands a strong grid, and this disparity was predominantly caused by the DC voltage control. Furthermore, the feasible region of the short-circuit ratio (SCR) diminished with the increase in the length of the tie-line and alterations in power flow direction under the mutual-support power mode, leading to a gradual reduction in the system’s stability margin. Full article

The homogeneous polynomial defined by a tensor, $\mathcal{A}{\mathbf{x}}^{m-1}$ for $\mathbf{x}\in {\mathbb{R}}^n$, has been used in many recent problems in the context of tensor analysis and optimization, including the tensor eigenvalue problem, tensor equation, tensor complementary problem, tensor eigenvalue complementary problem, tensor variational inequality problem, and least element problem of polynomial inequalities defined by a tensor, among others. However, conventional computation methods use the definition directly and neglect the structural characteristics of homogeneous polynomials involving tensors, leading to a high computational burden (especially when considering iterative algorithms or large-scale problems). This motivates the need for efficient methods to reduce the complexity of relevant algorithms. First, considering the symmetry of each monomial in the canonical basis of homogeneous polynomials, we propose a calculation method using the merge tensor of the involved tensor to replace the original tensor, thus reducing the computational cost. Second, we propose a calculation method that combines sparsity to further reduce the computational cost. Finally, a simplified algorithm that avoids duplicate calculations is proposed. Extensive numerical experiments demonstrate the effectiveness of the proposed methods, which can be embedded into algorithms for use by the tensor optimization community, improving computational efficiency in magnetic resonance imaging, n-person non-cooperative games, the calculation of molecular orbitals, and so on. Full article

Accurate, real-time, and dynamic monitoring of crop planting distributions in hilly areas with complex terrain and frequent meteorological changes is highly important for agricultural production. Dual-polarization SAR has high application value in the fields of feature classification and crop distribution extraction because of its all-day all-weather operation, large mapping bandwidth, and easy data acquisition. To explore the feasibility and applicability of dual-polarization synthetic-aperture radar (SAR) data in crop monitoring, this study draws on two basic methods of dual-polarization decomposition (eigenvalue decomposition and three-component polarization decomposition) to construct time series of crop dual-polarization radar vegetation indices (RVIs), and it performs a full coverage analysis of crop distribution extraction in dryland mountainous areas of southeastern China. On the basis of the Sentinel-1 dual-polarization RVIs, the time-series classification and rapeseed distribution extraction impacts were compared using southern Hunan Province’s principal rapeseed (Brassica napus L.) production area as the study area. From the comparison results, $RV{I}_{3-c}$ performed better in terms of single-point recognition capability and area extraction accuracy than the other indices did, as verified by sampling points and samples, and the OA and F-1 score of rapeseed extraction based on $RV{I}_{3-c}$ were 74.13% and 81.02%, respectively. Therefore, three-component polarization decomposition is more suitable than other methods for crop information extraction and remote sensing classification applications involving dual-polarized SAR data. Full article

This study focuses on a novel parameterized Wigner distribution, which is an organic integration of the free metaplectic Wigner distribution and the $\mathbf{K}$-Wigner distribution. We style this as the free metaplectic $\mathbf{K}$-Wigner distribution (FMKWD) and investigate its uncertainty principles and related applications. We establish a crucial equivalence relation between the uncertainty product in time-FMKWD and free metaplectic transformation (FMT)-FMKWD domains and those in two FMT domains, from which we derive two types of orthogonality conditions: an orthonormality condition; and two sub-types of minimum or maximum eigenvalue commutativity conditions on the FMKWD. Finally we separately formulate an uncertainty inequality in FMKWD domains for real-valued functions, three kinds of uncertainty inequalities in orthogonal FMKWD domains, an uncertainty inequality in orthonormal FMKWD domains, and four kinds of uncertainty inequalities in the minimum or maximum eigenvalue commutative FMKWD domains for complex-valued functions. The time-frequency resolution of the FMKWD is compared with those of the free metaplectic Wigner distribution, $\mathbf{K}$-Wigner distribution, and N-dimensional Wigner distribution to demonstrate its superiority in super-resolution analysis. For applications, the uncertainty inequalities derived are used to estimate the bandwidth in FMKWD domains, and the FMKWD is applied to detect noisy linear frequency-modulated signals. Full article

The accurate and efficient simulation of seismic wave energy dissipation and phase dispersion during propagation in subsurface media due to inelastic attenuation is critical for the hydrocarbon-bearing distinction and improving the quality of seismic imaging in strongly attenuating geological media. The fractional viscoelastic equation, which quantifies frequency-independent anelastic effects, has recently become a focal point in seismic exploration. We have developed a novel hybrid staggered-grid Grünwald–Letnikov (HSGGL) finite difference method for solving the fractional viscoelastic equation in the time domain. The proposed method achieves accurate and computationally efficient solutions by using a staggered grid to discretize the first-order partial derivatives of the velocity–stress equations, combined with Grünwald–Letnikov finite difference discretization for the fractional-order terms. To improve the computational efficiency, we employ a preset accuracy to truncate the difference stencil, resulting in a compact fractional-order difference scheme. A stability analysis using the eigenvalue method reveals that the proposed method confers a relaxed stability condition, providing greater flexibility in the selection of sampling intervals. The numerical experiments indicate that the HSGGL method achieves a maximum relative error of no more than 0.17% compared to the reference solution (on a finely meshed domain) while being significantly faster than the conventional global FD method (GFD). In a 500 × 500 computational domain, the computation times for the proposed methods, which meet the specified accuracy levels used, are only approximately 4.67%, 4.47%, 4.44%, and 4.42% of that of the GFD method. This indicates that the novel HSGGL method has the potential as an effective forward modeling tool for understanding complex subsurface structures by employing a fractional viscoelastic equation. Full article