Point Interpolation Research Articles

Dynamic response of a MEMS electrothremal actuator by the local radial point interpolation method

Dynamic response of a MEMS electrothremal actuator by the local radial point interpolation method

Applying fractional calculus to malware spread: A fractal-based approach to threat analysis.

Malware is a common word in modern era. Everyone using computer is aware of it. Some users have to face the problem known as Cyber crimes. Nobody can survive without use of modern technologies based on computer networking. To avoid threat of malware, different companies provide antivirus strategies on a high cost. To prevent the data and keep privacy, companies using computers have to buy these antivirus programs (software). Software varies due to types of malware and is developed on structure of malware with a deep insight on behavior of nodes. We selected a mathematical malware propagation model having variable infection rate. We were interested in examining the impact of memory effects in this dynamical system in the sense of fractal fractional (FF) derivatives. In this paper, theoretical analysis is performed by concepts of fixed point theory. Existence, uniqueness and stability conditions are investigated for FF model. Numerical algorithm based on Lagrange two points interpolation polynomial is formed and simulation is done using Matlab R2016a on the deterministic model. We see the impact of different FF orders using power law kernel. Sensitivity analysis of different parameters such as initial infection rate, variable adjustment to sensitivity of infected nodes, immune rate of antivirus strategies and loss rate of immunity of removed nodes is investigated under FF model and is compared with classical. On investigation, we find that FF model describes the effects of memory on nodes in detail. Antivirus software can be developed considering the effect of FF orders and parameters to reduce persistence and eradication of infection. Small changes cause significant perturbation in infected nodes and malware can be driven into passive mode by understanding its propagation by FF derivatives and may take necessary actions to prevent the disaster caused by cyber crimes.

An efficient electromagnetic scattering character restoration solution for UAV swarm targets

ABSTRACT Swarm formulations are new UAV (unmanned aerial vehicle) derivations with high application significances. UAV swarms are nonrigid, deformable, extended targets with multimodality property in radar viewpoint. This brings higher radar cross section (RCS) variety and statistical uncertainty. Conventional full-wave electromagnetic solvers are not applicable for massive UAV swarm RCS simulation. This paper introduces an efficient RCS restoration solution using EPA (equivalent principle algorithm) and EIM (empirical interpolation method). Parameter and solution spaces are constructed to extract interpolation points and basis functions. Specific parameter selection and solution initialization methods enable solution restoration. The quadcopter drone swarm model is developed for numerical verification. RCS restoration accuracy and efficiency evaluation results indicate that the proposed method enables the possibility for massive UAV swarm RCS simulations with prominent efficiency advantages.

Variability of Interpolation Errors and Mutual Enhancement of Different Interpolation Methods

Data interpolation methods are important statistical analysis tools that can fill in data gaps and missing areas by predicting and estimating unknown data points, thereby improving the accuracy and credibility of data analysis and research. Different interpolation methods are widely used in related fields, but the error between different interpolation methods and their interpolation fusion optimization have a significant impact on the interpolation accuracy, which still deserves further exploration. This study is based on two different types of point data: PM2.5 (PM2.5 refers to particulate matter in the atmosphere with a diameter of 2.5 μm or less, also known as inhalable particles or fine particulate matter) in Xinyang City, Henan Province, and the elevation of typical gullies in Yuanmou County, Yunnan Province. Using relative difference coefficients and hotspot analysis methods, the differences in error characteristics among four interpolation methods, ordinary kriging (OK), universal kriging (UK), inverse distance weighted (IDW), and radial basis functions (RBFs), were compared, and the influence of interpolation fusion methods on the accuracy of interpolation results was explored. The results show that after interpolation of PM2.5 concentration and gully elevation, the error difference between OK and UK is the smallest in both datasets. For PM2.5 concentration data, IDW and UK interpolation errors have the largest difference; for elevation data, the differences between RBF and UK interpolation are the largest. The weighted fusion results show that the interpolation error accuracy of PM2.5 concentration data with an interpolation point density of 0.009 points per square kilometer is improved, and the root mean square error (RMSE) after fusion is reduced from 0.374 μg/m3 to 0.004 μg/m3. However, the error accuracy of the elevation data of the gully with an interpolation point density of 0.76 points/m2 did not improve significantly. This indicates that characteristics such as the density of the original data are important factors that affect the accuracy of interpolation. In the case of sparse interpolation points, it is possible to consider fusing the interpolation results with different error patterns to improve their accuracy. This study provides a new idea for improving the accuracy of interpolation errors.

Post-Processing Kalman Filter Application for Improving Cooperative Awareness Messages' Position Data Accuracy.

Cooperative intelligent transportation systems continuously send self-referenced data about their current status in the Cooperative Awareness Message (CAM). Each CAM contains the current position of the vehicle based on GPS accuracy, which can have inaccuracies in the meter range. However, a high accuracy of the position data is crucial for many applications, such as electronic toll collection or the reconstruction of traffic accidents. Kalman filters are already frequently used today to increase the accuracy of position data. The problem with applying the Kalman filter to the position data within the Cooperative Awareness Message is the low temporal resolution (max. 10 Hz) and the non-equidistant time steps between the messages. In addition, the filter can only be applied to the data retrospectively. To solve these problems, an Extended Kalman Filter and an Unscented Kalman Filter were designed and investigated in this work. The Kalman filters were implemented with two kinematic models. Subsequently, driving tests were conducted with two V2X vehicles to investigate and compare the influence on the accuracy of the position data. To address the problem of non-equidistant time steps, an iterative adjustment of the Process Noise Covariance Matrix Q and the introduction of additional interpolation points to equidistance the received messages were investigated. The results show that without one of these approaches, it is impossible to design a generally valid filter to improve the position accuracy of the CAM position data retrospectively. The introduction of interpolation points did not lead to a significant improvement in the results. With the Q matrix adaptation, an Unscented Kalman Filter could be created that improves the longitudinal position accuracy of the two vehicles under investigation by up to 80% (0.54 m) and the lateral position accuracy by up to 72% (0.18 m). The work thus contributes to improving the positioning accuracy of CAM data for applications that receive only these data retrospectively.

Direct Taylor Expansion of Substructures Constructed Parametric Reduced-Order Modeling Method

The parametric substructure modeling shows enormous potential for efficiently conducting dynamic reanalysis of large-scale structures with small geometric variability. Parametric substructure mode is a vital component in ensuring the accuracy of the modeling process. This work uses the Craig–Bampton Component Mode Synthesis method to calculate normal and constraint modes of substructures at interpolation points. Instead of using singular value decomposition of augmented fixed-interface modes, the presented approach performs direct Taylor expansion for substructure modes with randomly varying parameters. The parametric substructure modes are approximated by the modes at interpolation points. The global parametric reduced-order model is constructed through the synthesis of parametric substructures. The effectiveness of the proposed approach is validated through 1) a thickness-variable beam, 2) a cantilevered plate with varying thicknesses, and 3) a mistuned blisk. Numerical results demonstrate that the computational accuracy of the parametric reduced-order model aligns closely with a more time-consuming full-order model.

Marine Trajectory Reconstruction Method Based on Navigation State Recognition and Bi-Directional Kinematic Interpolation

The trajectory data mining and analysis of maritime targets are of great significance in furthering the construction of maritime traffic facilities, improving the ability of marine supervision and maintaining national marine security. However, due to factors such as detection means and environmental interference, a large number of trajectory data have problems such as large space-time span, uneven sampling, and poor continuity, which seriously restrict the effect of trajectory mining. Therefore, this paper proposes a method of trajectory reconstruction based on navigation state recognition and bidirectional kinematic interpolation. The method mainly includes three steps: (1) data preprocessing, (2) navigation state recognition, and (3) trajectory interpolation. The method can recognize the navigation state of the targets in different segments, and then adaptively select the interpolation method to reconstruct the trajectories, that is, linear interpolation in the straight segments and bidirectional kinematic interpolation in the turning segments. Among them, bidirectional kinematic interpolation uses the cubic Hermite function to nonlinearly fit the acceleration of the interpolation section, and then calculates the velocity and coordinates of the interpolation points by time weighting from the positive and negative directions. The proposed method is verified and analyzed on the contest dataset of “Intelligent classification and recognition of XX trajectories”. Compared with the existing methods, the reconstruction results of the proposed method are closer to the real trajectories, and it can effectively reconstruct the target trajectories with better accuracy and stability. At the same time, the effect of trajectories classification based on the Long Short-Term Memory (LSTM) model, which uses trajectories before and after reconstruction, is compared and analyzed. The results show that the model has a higher classification accuracy for reconstructed trajectory, which proves the necessity of trajectory reconstruction.

Proficient trigonometrical-fitted two-derivative multistep collocation methods in predictor-corrector approach: Application to perturbed Kepler problem

An efficient trigonometrical-fitted two-derivative multistep collocation (TF-TDMC) method using Legendre polynomials up to order five as the basis functions, has been developed for solving second-order ordinary differential equations with oscillatory solution effectively. Interpolation method of approximated power series and collocation technique of its second and third derivative are implemented in the construction of the methods. Two-derivative multistep collocation methods are developed in predictor and corrector form with varying collocation and interpolation points. Later, trigonometrically-fitting technique is implemented into TF-TDMC method, using the linear combination of trigonometrical functions, to produce frequency-dependent coefficients in TF-TDMC method. The stability of the TF-TDMC method, with fitted parameters, is thoroughly analyzed and has been proven to achieve zero stability. Stability polynomials and regions for predictor and corrector of TF-TDMC method are developed and plotted. In the operation of the TF-TDMC method, initial conditions and the frequency for each problem (based on the exact solutions) are identified. The frequency-dependent coefficients are then adjusted according to the identified frequency. Predictor and corrector steps are implemented to estimate and refine the values of the dependent variable and its derivative, ensuring that convergence is achieved.A numerical experiment demonstrates that the proposed method significantly outperforms other existing methods in the literature, achieving the lowest maximum global error with moderate computational time across all step sizes for solving second-order ordinary differential equations with oscillatory solutions. Additionally, it effectively addresses real-world perturbed Kepler problems. The results include a detailed discussion and analysis of the numerical performance.•An efficient two-derivative multistep collocation method in predictor-corrector mode with trigonometrically-fitting technique (TF-TDMC) is developed for direct solving second-order ordinary differential equations with oscillatory solution.•TF-TDMC method has been proved to acquire zero-stability and its stability region is analyzed.•TF-TDMC method is the best among all selected methods in solving second-order ordinary differential equations with oscillatory solution, including perturbed Kepler problem.

Trajectory Planning and Adaptive Fuzzy PID Control for Precision in Robotic Vertebral Plate Cutting: Addressing Force Dynamics and Deformation Challenges

This study explores trajectory planning and cutting force control for spinal surgical robots, focusing on managing cutting deformation and vibration during vertebral plate cutting—a critical challenge in robotic spinal surgery. Through theoretical analysis, simulation, and experimental validation, the research addresses the complexities of cutting force dynamics and the associated deformations. A dynamic equation for vertebral plate cutting is established, providing a theoretical foundation for trajectory planning. A new trajectory planning method using B-spline curves and an interpolation point constraint formula is introduced, enabling precise robot trajectory control. Additionally, an adaptive fuzzy PID control strategy with force feedback is proposed to dynamically adjust the feed rate, effectively suppressing cutting deformation and vibration in real time. Simulations and experiments validate the effectiveness of these methods in reducing force fluctuations and enhancing control stability. The findings offer valuable guidance for improving the performance and safety of spinal surgery robots, optimizing their trajectories, incorporating dynamic sensing, and enhancing safety controls. Future research should focus on refining control strategies for more complex surgical scenarios and validating their applicability under conditions closer to actual surgical environments. This work provides theoretical and practical insights into advancing robotic spinal surgery, contributing to better surgical outcomes and patient safety.

Accurate simulations of moving flexible objects with an improved immersed boundary-lattice Boltzmann method

Accurately capturing boundaries is crucial for simulating fluid–structure interaction (FSI) problems involving flexible objects undergoing large deformations. This paper presents a coupling of the immersed boundary-lattice Boltzmann method with a node-based partly smoothed point interpolation method (NPS-PIM) to enhance the accuracy of simulating moving flexible bodies in FSI problems. The proposed method integrates a multiple relaxation time scheme and employs a force correction technique to address boundary capturing inaccuracies. The effect of virtual fluid is accounted for through a Lagrangian point approximation, ensuring precise FSI force calculations for unsteady solid motions. NPS-PIM is utilized as the solid solver, constructing a moderately softened model stiffness by combining the finite element method (FEM) with the node-based smoothed PIM (NS-PIM). Simulations of flow fields near flexible objects with large deformations demonstrate that the proposed approach reduces numerical errors, improves computational efficiency compared to traditional FSI models using FEM and NS-PIM, and accurately captures the behavior of moving flexible bodies and detailed flow fields.

Seafloor Topographic Data Processing in Near-Seafloor Acoustic Field Simulation

Near-seafloor acoustic field characteristics are essential prior knowledge for near-seafloor underwater acoustic engineering. Scholte waves are a crucial component of the near-seafloor acoustic fields. These fields, when considering Scholte waves, are susceptible to seafloor relief. However, open-source bathymetric datasets generally lack sufficient precision. Therefore, acoustic field simulations using open-source data can contain significant errors or even introduce erroneous propagation characteristics. The spectral element method (SEM) is an example of exploring the influence of an inadequate spatial-sampling rate and sea-depth precision on acoustic field simulations. In this article, appropriate methods for topographic processing are presented. The results indicate that the terrain can be corrected using cubic spline interpolation in cases of an inadequate spatial-sampling rate. Where there is insufficient sea-depth precision, this study proposes a terrain processing method. The first step involves sequentially determining the interpolation points for the rising and falling edge, depressions, bulges, and horizontal segments. Then, it adopts cubic spline interpolation. The SEM examples effectively verify this effect. Given the limited research on terrain correction in acoustic field simulations, this study introduces a low-complexity method that can effectively support exploring acoustic fields affected by seafloor terrain.

Nonlinear analysis of three-dimensional hyperelastic problems using radial point interpolation method

Hyperelastic materials are primarily common in real life as well as in industry applications, and studying this kind of material is still an active research area. Naturally, the characteristic of hyperelastic material will be expressed when it undergoes large deformation, so the geometrical nonlinear effect should be considered. To analyze the behavior of hyperelastic material, the Neo-Hookean model is imposed in this study because of its simplicity. The model shows the nonlinear behavior when the deformation becomes large due to the nonlinear displacement-strain relation. This constitutive relation also gives a good correlation with experimental data. This study performs a meshless method, namely the radial point interpolation method (RPIM), to analyze the nonlinear behavior of Neo-Hookean hyperelastic material under a finite deformation state in three-dimensional space. The standard Newton-Raphson technique is applied to obtain the nonlinear solutions. Unlike mesh-based approaches, the meshless method shows its advantages in large deformation problems due to its mesh independence. In this paper, the numerical results of three-dimensional problems that undergo large deformation will be calculated and validated with solutions derived from previous studies. By investigating the obtained results, the superior ability of RPIM in hyperelastic problems can be proved.

Arch dam point cloud segmentation based on deep feature learning and normal vector data optimization

Separating the dam body, spillway, and other structures from the point cloud in the dam area is an important step in dam deformation monitoring. Manual segmentation is time consuming and inaccurate. This study proposes a point cloud segmentation neural network model based on normal vector optimization suitable for dam environment: (1) This model utilizes the voxel uniform sampling method of equal length cubes to solve the problem of uneven point cloud density caused by wide range and long-distance measurement during point cloud measurement in dam areas. (2) Designed block input and combined output modules in the model, achieving efficient input of large volume point cloud and eliminating the impact of interpolation points offset during seq2seq model decoding process. (3) In response to the diverse characteristics of point cloud normal vectors presented by vegetation, rock mass, and complex dam structures in the dam area, this paper proposes an adaptive radius plane fitting vector estimation method based on eigenvalue method to improve the accuracy of segmentation. The experiment on the prototype arch dam shows that the proposed normal estimation method improves the classification accuracy of PointNet + + from 96.26 to 98.27%. Compared with the other three normal estimation methods (2-jets, Hough CNN, iterative PCA), the overall accuracy is improved by 0.82%, 1.22%, and 0.22%, and the joint average intersection is improved by 0.0293, 0.0325, and 0.0104. The prototype arch dam experiment shows that our proposed method has a segmentation accuracy of 98.27%. Compared with 2-jets, Hough CNN, and iterative PCA, the overall accuracy has been improved by 0.82%, 1.22%, and 0.22%. This study provides a high-precision segmentation scheme for applications such as deformation detection of dam components based on point clouds.

Research on a coal seam modeling construction method based on improved kriging interpolation

To address the issues of large anomalous triangulations, invalid interpolations, and uneven boundary interpolations in kriging interpolation, we propose research on a coal seam modeling construction method based on improved kriging interpolation. The work methodology assumes that by introducing kriging interpolation and analyzing its problems, we improve the interpolation method via a local interpolation algorithm for large anomalous triangulations, an optimization algorithm for locally redundant interpolation points, and a nonuniform boundary adaptive local interpolation algorithm. These improvements allow the interpolation method to better reflect the variability and realistic nature of coal seams. The research results indicate that applying this method to the construction of the Dananhu No. 2 open-pit mine coal seam model has improved the issue of coal seam transition stiffness, such as abnormal large-area triangulation in areas with significant elevation differences. This approach appropriately reduces the memory space usage without altering the coal seam morphology (which saves approximately 27,000 KB of memory, equivalent to the space occupied by 4 out of 21 coal seams). It has also prevented inaccuracies in boundary line positioning and transitions caused by too low a density of points on the coal seam reserve boundary line, resulting in smoother model transitions at the boundaries that better align with the actual coal seam change trends, the error rate in coal quality estimation decreased by 62.69%. This study provides data support for mining planning and reduces costs. This method can be extended to the construction of all mine models.

Meshfree method for bending and free vibration analysis of laminated plates using the Reissner’s mixed variational theorem

Free vibration and bending behavior of laminated plates are investigated using a combination of Reissner’s mixed variational theorem and the meshless radial point interpolation method. By introducing Reissner’s mixed variational theorem, a refined transverse shear stress field is derived based on three-dimensional (3D) elasticity equations. The efficiency and accuracy of this model are demonstrated through numerical examples. It is found that accurate prediction of shear stresses significantly improves the prediction of natural frequency for composite laminated plates. The difference between shear stresses derived from 3D equilibrium equations and that from constitutive equations is significant.

Enhanced meshfree method with nodal integration for analysis of functionally graded material sandwich curved shells

This paper presents a nodal integration technique, the sub-domain stabilized conforming integration (SSCI), for the meshfree radial point interpolation method (RPIM) applied to the static and modal analysis of functionally graded material (FGM) sandwich curved shells. FGM sandwich shells with different kinds of core and face sheets are considered in this work while the interested curved shell is formulated by the first-order shear deformation theory. The numerical integration technique to compute the stiffness and mass matrices in the equilibrium equation is the SSCI, which is a stabilized nodal integration with strain smoothing to preserve the accuracy and stability of the numerical results. The RPIM shape functions are utilized in this study for interpolating both the field variables and the geometry of the curved shell due to their ability to satisfy the Kronecker delta property, a rare advantage among meshfree methods. The static and modal analysis of different geometry curved shells with various sandwich FGMs are conducted. Through several numerical examples, the accuracy and efficiency of the SSCI technique in the meshfree RPIM are demonstrated and discussed.

A computationally efficient Element Edge point numerical integration scheme in the meshless method framework for solving fracture problems

The fracture problem is modeled using the Radial Point Interpolation Meshless Method (RPIM) to solve for displacements. Further, the stresses and Stress Intensity Factor (SIF) are calculated using obtained displacements. An effective numerical integral quadrature called the Element Edge point(EE) scheme is used as an alternative to conventional Gauss Quadrature to improve computational efficiency. A comparative study based on two numerical integration schemes, the Element Edge point scheme and Gauss Quadrature, is conducted on four benchmark problems of thick, cracked plates owing to plane strain conditions. The study reveals that the proposed Element Edge point (EE) scheme is computationally efficient and works well in the meshless method framework.

Deformation monitoring for fixed-wing UAS through Inverse Mesh-free Method

This study proposes the Inverse Local Radial Point Interpolation Method (iLRPIM) for reconstructing the deformation of irregular plate structures. The proposed methodology eliminates the drawbacks of the existing inverse finite-element method (iFEM), where the Jacobian matrix results in reduced computational accuracy for irregular plate-shape sensing. To this end, this paper released from the element and used the Mesh-Free method to describe the calculated strains. Subsequently, the system equation was formulated by minimizing the error between the measured and calculated strains. The deformation parameters were then computed by solving this system equation. Additionally, compared to iFEM, iLRPIM allows for easier adjustment of the interpolation function, making it more suitable for real-world engineering applications. The effectiveness of iLRPIM has been validated through simulations and practical experiments using four typical models. In simulations of the UAS wing box equivalent model, peak errors were below 0.8 mm for a deformation range of 25 mm. In practical scenarios, peak errors were below 3.1 mm for a deformation range of 85 mm. These results underscore the system’s capability to accurately sense the shapes of irregular plate structures using iLRPIM.

Extending the Natural Neighbour Radial Point Interpolation Meshless Method to the Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core

This work investigates the mechanical behaviour of sandwich beams with cellular cores using a multiscale approach combined with a meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The analysis is divided into two steps, aiming to analyse the efficiency of NNRPIM formulation when combined with homogenisation techniques for a multiscale computational framework of large-scale sandwich beam problems. In the first step, the cellular core material undergoes a controlled modification process in which circular holes are introduced into bulk polyurethane foam (PUF) to create materials with varying volume fractions. Subsequently, a homogenisation technique is combined with NNRPIM to determine the homogenised mechanical properties of these PUF materials with different porosities. In this step, NNRPIM solutions are compared with high-order FEM simulations. While the results demonstrate that RPIM can approximate high-order FEM solutions, it is observed that the computational cost increases significantly when aiming for comparable smoothness in the approximations. The second step applies the homogenised mechanical properties obtained in the first step to analyse large-scale sandwich beam problems with both homogeneous and functionally graded cores. The results reveal the capability of NNRPIM to closely replicate the solutions obtained from FEM analyses. Furthermore, an analysis of stress distributions along the beam thickness highlights a tendency for some NNRPIM formulations to yield slightly lower stress values near the domain boundaries. However, convergence towards agreement among different formulations is observed with mesh refinement. The findings of this study show that NNRPIM can be used as an alternative numerical method to FEM for analysing sandwich structures.

A Meshless Radial Point Interpolation Method for Solving Fractional Navier–Stokes Equations

This paper aims to develop a meshless radial point interpolation (RPI) method for obtaining the numerical solution of fractional Navier–Stokes equations. The proposed RPI method discretizes differential equations into highly nonlinear algebraic equations, which are subsequently solved using a fixed-point method. Furthermore, a comprehensive analysis regarding the effects of spatial and temporal discretization, polynomial order, and fractional order is conducted. These factors’ impacts on the accuracy and efficiency of the solutions are discussed in detail. It can be shown that the meshless RPI method works quite well for solving some benchmark problems accurately.