Spline Interpolation Research Articles

Research on Target Allocation for Hard-Kill Swarm Anti-Unmanned Aerial Vehicle Swarm Systems

In response to the saturated attacks by low, slow, and small UAV swarms, there is currently a lack of effective countermeasures. Counter-UAV swarm technology is an important issue that urgently requires breakthroughs. This paper conducts research on a mid–short-range hard-kill counter-swarm scenario where fewer swarms confront multiple swarms and stronger swarms confront weaker swarms. The requirement is for counter-swarm UAVs to quickly penetrate the swarm at mid–short range and collide with as many incoming UAVs as possible to destroy them. To address the sparse solution space problem, an improved genetic algorithm that integrates multiple strategies is adopted to calculate the spatial density distribution of the incoming swarm. A baseline is identified through gradient descent that maximizes the density integral in a straight-line direction. Based on this baseline, the solution space for single strikes on the swarm is filtered. During the solution process, an elite strategy is introduced to prevent the overall degradation of the population performance. Additionally, the feasibility of the flight trajectory needs to be assessed. A piecewise cubic spline interpolation method is used to optimize the flight trajectory, minimizing the maximum curvature. Ultimately, multiple counter-swarm UAV targets within the swarm and their corresponding trajectories are obtained.

Cutting-edge techniques in 3D modeling and animation: Leveraging mathematical models and advanced software tools

Abstract. This paper explores the advancements in computer animation technology, focusing on 3D modeling and animation. It delves into the core aspects of character design, environment modeling, and animation rigging, emphasizing the mathematical models and algorithms that enhance realism and efficiency. Key techniques discussed include Bezier curves and spline interpolation for anatomy and proportions, Perlin noise and fractal algorithms for texturing, and Inverse Kinematics (IK) and Forward Kinematics (FK) for rigging. Additionally, the paper examines procedural generation and fluid dynamics simulations for environment modeling and the integration of motion capture data. The use of software tools like Blender, Autodesk Maya, and Houdini is highlighted. This study aims to provide a comprehensive understanding of the current state of 3D animation technology and its future directions.

Characteristics of Machine Learning-based Univariate Time Series Imputation Method

Handling missing values in univariate time series analysis poses a challenge, potentially leading to inaccurate conclusions, especially with frequently occurring consecutive missing values. Machine Learning-based Univariate Time Series Imputation (MLBUI) methods, utilizing Random Forest Regression (RFR) and Support Vector Regression (SVR), aim to address this challenge. Considering factors such as time series patterns, missing data patterns, and volume, this study explores the performance of MLBUI in simulated Autoregressive Integrated Moving Average (ARIMA) datasets. Various missing data scenarios (6%, 10%, and 14%) and model scenarios (Autoregressive (AR) models: AR(1) and AR(2); Moving Average (MA) models: MA(1) and MA(2); Autoregressive Moving Average (ARMA) models: ARMA(1,1) and ARMA(2,2); and Autoregressive Integrated Moving Average (ARIMA) models: ARIMA(1,1,1) and ARIMA(1,2,1)) with different standard deviations (0.5, 1, and 2) were examined. Five comparative methods were also used in this research, including Kalman StructTS, Kalman Auto-ARIMA, Spline Interpolation, Stine Interpolation, and Moving Average. The research findings indicate that MLBUI performs exceptionally well in imputing successive missing values. The results of this study indicate that the performance of MLBUI in imputing consecutive missing values, based on MAPE, yielded values of less than 10% across all scenarios used.

Horizontal walls effect on the subsonic flow around airfoil by the image method

The aim of this work consists in developing a new numerical method and a calculation program making it possible to determine the effect of one and two horizontal walls on the distribution of the pressure ratio, and the aerodynamics coefficients of a subsonic flow around airfoils. The model is considered for the perfect gas. The calculation is presented by adding the effect of one and two walls on the discretization of the airfoils boundary to obtain a closed surface. The method is called by the image method. So for the case of the existence of one wall, we will see a single image of the main airfoil, and in the case of two walls, we will have an infinity of images. The equation system is obtained by considering the effect of all images using alternating digital series, whose convergence is ensured numerically. We therefore obtain a large system of equations, the resolution of which is done by the Khaletski method to obtain the velocities and pressure. The application is made for some practical interest’s airfoils. Since the airfoils boundary is given by tabulated values, the cubic spline interpolation is used to obtain an analytical equation of the upper and the lower surfaces. The comparison is made with the case of open air flow by extending the distance between the walls and the airfoil chord towards infinity.

A rapid method for composition tracking in hydrogen-blended pipeline using Fourier neural operator

Blending hydrogen into natural gas for transportation is a crucial approach for achieving the widespread utilization of hydrogen. Tracking the concentration of the hydrogen within the pipeline is important for monitoring gas quality and managing pipeline operations. This study develops a rapid computational model to predict the hydrogen and natural gas concentrations within the pipeline during transportation based on the Fourier Neural Operator (FNO), an operator neural network capable of learning the differential operator in the partial differential equation. In the proposed model, the numerical method is employed to generate datasets, with the spline interpolation used to enhance data smoothness. The initial and boundary conditions are taken as the inputs to accommodate varying transportation scenarios. Comparison results indicate that the proposed model can notably reduce the time needed to predict the hydrogen and natural gas concentrations while maintaining prediction accuracy. The accuracy of the proposed model is validated by comparing its calculated results with the analytical solution and the concentrations of hydrogen and natural gas within the pipeline under two transportation scenarios, with relative errors of 0.49%, 0.31%, and 0.45%, respectively. Notably, the trained model demonstrates strong grid invariance, a type of model generalization. Trained on data generated from a coarse grid of 101 × 41 spatial-temporal resolution, the proposed model can accurately predict results on a fine grid of 401 × 81 spatial-temporal resolution with a relative error of only 0.38%. Regarding the prediction efficiency, the proposed model achieves an average 17.7-fold speedup compared to the numerical method. The positive results indicate that the proposed model can serve as a rapid and accurate solver for the composition transport equation.

Dynamic Path Planning for Spacecraft Rendezvous and Approach Based on Hybrid Honey Badger Algorithm

In order to solve the 3D path planning of the close-range guidance phase of spacecraft in space rendezvous and approaching, and improve its optimization performance in dynamic environments, a 3D dynamic path planning method based on hybrid honey badger algorithm and cubic spline interpolation is proposed. Firstly, a hybrid honey badger algorithm is presented for dynamic path planning: the chaotic reverse learning is used to initialize the population, so as to improve the global search ability; the transfer operators are introduced in the mode transition stage to balance exploration and exploitation capabilities; the sine and cosine operators are integrated during the stage of location update to improve the quality of the optimal solution; an adaptive disturbance coefficient is introduced into the mining mode to accelerate the convergence. Secondly, the cubic spline interpolation algorithm is combined to optimize the path curve and reduce the turning angle of the curve. Finally, the comparative simulation experiments verify that the proposed method can plan a smooth path without collision. The planned path length is relatively shortest, the path turning angle and the algorithm running time are relatively smallest.

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.

Comparison of Inverse Distance Weighted and Thin Plate Spline Interpolation Methods in Projecting the Strength of the West Sumatra Earthquake

The Indonesian archipelago is situated in a highly active geological zone, making it prone to frequent earthquakes. West Sumatra, located on the west coast of central Sumatra, comprises lowland coastal areas and volcanic plateaus formed by the Barisan Mountains, covering a land area of 42,297.30 km² (2.17% of Indonesia's territory). This research aims to determine which interpolation method—Inverse Distance Weighted (IDW) and Thin Plate Spline (TPS)—provides more accurate predictions of earthquake strength in West Sumatra. The dataset consists of 229 earthquake events, divided into 90% for training (206 points) and 10% for testing (23 points). The training data was further subdivided into 80% training data 2 (164 points) and 20% validation data (42 points). The interpolation processes using the IDW and TPS methods were repeated 100 times, with the training 2 and validation data randomly shuffled in each iteration. Visualization of the interpolation results indicated that the earthquake magnitudes ranged from 2.0 to 4.5. Although the Mean Absolute Percentage Error (MAPE) values for the TPS method on the test and validation datasets were 16.42 and 14.29, respectively—slightly lower than the MAPE values for the IDW method—the t-test results showed no statistically significant difference between the two methods. Statistically, there is no significant difference between IDW and TPS in terms of predictive accuracy. However, researchers prefer the IDW method due to its computational efficiency and simplicity. Therefore, IDW is considered the most suitable method for analyzing earthquake strength in the West Sumatra region

VNS-BA*: An Improved Bidirectional A* Path Planning Algorithm Based on Variable Neighborhood Search.

The A* algorithm is an effective method for path planning; however, it has certain drawbacks, such as a high number of turns, low planning efficiency, and redundant searches. To address these issues, this paper proposes an improved bidirectional A* global path planning algorithm based on a variable neighborhood search strategy, named VNS-BA*. The new algorithm first employs an 8-11-13 neighborhood search method for node expansion. Then, the bidirectional search strategy is optimized by using the current nodes of the opposite path and the global target point, enabling the two paths to meet in the middle of the map. Finally, redundant turns are removed from the path, and cubic spline interpolation is applied to achieve local smoothing at the turns. The effectiveness of the improved algorithm was validated on different maps and compared with A* and its three derived improved versions. The simulation results indicate that VNS-BA* shows significant improvements in terms of the number of path turns, turn angles, and planning efficiency.

Implied volatility modeling and forecasting: evidence from China

PurposeTesting several approaches for implied volatility modeling and forecasting.Design/methodology/approachComparative empirical study with four traded options.FindingsNon-parametric higher-order spline is better than parametric stochastic volatility inspired (SVI) in China.Research limitations/implicationsOur results imply that even though popular on Wall Street, SVI seems not to be utilized by traders and market-makers in China.Practical implicationsTraders may consider higher-order spline as a better method for implied volatility modeling and forecasting.Originality/valuePropose to model and forecast implied volatility via the fifth-order spline interpolation as a first; initiates studies of the empirical performance of SVI and the fifth-order spline models in implied volatility modeling and forecasting.

A Study on the Impact and Mechanisms of Digital Economy Development on the Formation of New Productive Forces

This study investigates the impact of digital economy development on the formation of new productive forces in Guangdong Province. Utilizing key indicators such as GDP, education, and technology data, the research employs data cleaning and spline interpolation for preprocessing. Hypotheses P1 through P4 were proposed based on literature and regional policies. An evaluation system for new productive forces was established using the entropy weight method. Empirical analysis via STATA software confirmed a significant positive effect of the digital economy on new productive forces, supporting hypothesis P1. Mechanisms including technological breakthroughs, human capital, and industrial transformation were validated, confirming hypotheses P2, P3, and P4. The study highlights the spatial agglomeration effect between digital economy and new productive forces, suggesting mutual enhancement and significant spillover effects across regions.

Solving UAV 3D Path Planning Based on the Improved Lemur Optimizer Algorithm

This paper proposes an Improved Lemur Optimization algorithm (ILO), which combines the advantages of the Spider Monkey Optimization algorithm, Simulated Annealing algorithm, and Lemur Optimization algorithm. Through the use of an adaptive nonlinear decrement model, adaptive learning factors, and updated jump rates, the algorithm enhances its global exploration and local exploitation capabilities. A Gaussian function model is used to simulate the mountain environment, and a mathematical model for UAV flight is established based on constraints and objective functions. The fitness function is employed to determine the minimum cost for avoiding obstacles in a designated airspace, and cubic spline interpolation is used to smooth the flight path. The Improved Lemur Optimization algorithm was tested using the CEC2017 benchmark set, assessing its search capability, convergence speed, and accuracy. The simulation results show that ILO generates high-quality, smooth paths with fewer iterations, overcoming the issues of premature convergence and insufficient local search ability in traditional genetic algorithms. It adapts to complex terrain, providing an efficient and reliable solution.

Disentangling the impact of motion artifact correction algorithms on functional near-infrared spectroscopy-based brain network analysis.

Functional near-infrared spectroscopy (fNIRS) has been widely used to assess brain functional networks due to its superior ecological validity. Generally, fNIRS signals are sensitive to motion artifacts (MA), which can be removed by various MA correction algorithms. Yet, fNIRS signals may also undergo varying degrees of distortion due to MA correction, leading to notable alternation in functional connectivity (FC) analysis results. We aimed to investigate the effect of different MA correction algorithms on the performance of brain FC and topology analyses. We evaluated various MA correction algorithms on simulated and experimental datasets, including principal component analysis, spline interpolation, correlation-based signal improvement, Kalman filtering, wavelet filtering, and temporal derivative distribution repair (TDDR). The mean FC of each pre-defined network, receiver operating characteristic (ROC), and graph theory metrics were investigated to assess the performance of different algorithms. Although most algorithms did not differ significantly from each other, the TDDR and wavelet filtering turned out to be the most effective methods for FC and topological analysis, as evidenced by their superior denoising ability, the best ROC, and an enhanced ability to recover the original FC pattern. The findings of our study elucidate the varying impact of MA correction algorithms on brain FC analysis, which could serve as a reference for choosing the most appropriate method for future FC research. As guidance, we recommend using TDDR or wavelet filtering to minimize the impact of MA correction in brain network analysis.

A fractional-order improved FitzHugh-Nagumo neuron model

Abstract In this paper, we propose a fractional-order improved FitzHugh-Nagumo (FHN) neuron model in terms of a generalised Caputo fractional derivative. Following the existence of a unique solution for the proposed model, we derive the numerical solution using a recently proposed L1 predictor-corrector method. The given method is based on the L1-type discretization algorithm and the spline interpolation scheme. We perform the error and stability analyses for the given method. We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns, chaotic patterns, and quasi-periodic patterns. The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics, which are inherent to many biological systems.

A Two-Stage Facial Kinematic Control Strategy for Humanoid Robots Based on Keyframe Detection and Keypoint Cubic Spline Interpolation

A plentiful number of facial expressions is the basis of natural human–robot interaction for high-fidelity humanoid robots. The facial expression imitation of humanoid robots involves the transmission of human facial expression data to servos situated within the robot’s head. These data drive the servos to manipulate the skin, thereby enabling the robot to exhibit various facial expressions. However, since the mechanical transmission rate cannot keep up with the data processing rate, humanoid robots often suffer from jitters in the imitation. We conducted a thorough analysis of the transmitted facial expression sequence data and discovered that they are extremely redundant. Therefore, we designed a two-stage strategy for humanoid robots based on facial keyframe detection and facial keypoint detection to achieve more natural and smooth expression imitation. We first built a facial keyframe detection model based on ResNet-50, combined with optical flow estimation, which can identify key expression frames in the sequence. Then, a facial keypoint detection model is used on the keyframes to obtain the facial keypoint coordinates. Based on the coordinates, the cubic spline interpolation method is used to obtain the motion trajectory parameters of the servos, thus realizing the robust control of the humanoid robot’s facial expression. Experiments show that, unlike before where the robot’s imitation would stutter at frame rates above 25 fps, our strategy allows the robot to maintain good facial expression imitation similarity (cosine similarity of 0.7226), even at higher frame rates.

The effect of low-temperature starting on the thermal safety of lithium-ion batteries

With the widespread application of lithium-ion batteries (LIBs) in the field of energy equipment, their probability of starting or operating in low-temperature environments is also increasing. However, there is currently a lack of research on the changes in thermal safety of batteries after use in corresponding environments. In this work, the thermal safety performance, degradation mechanisms and evaluation method of LIBs at low-temperature start-up conditions are studied. The results show that starting at low temperature leads to the decrease of cell capacity. Electrochemical characterization and cell disassembly analysis indicate that the loss of active lithium ions is mainly caused by the evolution of lithium and the growth of solid electrolyte interface films. In addition, the low-temperature startup results in the decrease of thermal runaway (TR) onset temperature and the advance of TR time. In order to quantitatively evaluate the safety state of the LIBs, an evaluation model based on Informer algorithm is established. The model extracts the discharge capacity, discharge energy and dV/dQ as aging characteristic parameters, and extracts TR temperature as thermal safety characteristic parameters. The data set is processed by cubic spline interpolation. After training and verification, the accuracy of the model reaches 80 %.

An optimized method for AUV trajectory model in benthonic hydrothermal area based on improved slime mold algorithm

The optimization of the desired autonomous underwater vehicle (AUV) trajectory modeling and AUV trajectory tracking control in the benthonic hydrothermal area were studied. In the conventional trajectory tracking model construction methods, the time points were roughly combined with the position points of the planned path, making it difficult to produce a smooth trajectory. Although the spline interpolation method was an ideal option for smooth curves, a great number of points were needed for a complex desired trajectory mode. In response to the demanding requirements of AUV trajectory tracking control in the benthonic hydrothermal area, an under-actuated test platform was first established, and the cubic spline interpolation was adopted to process the preset path points for a smooth desired trajectory. An improved slime mold algorithm (SMA) was put forward to optimize the interpolating points used in the trajectory modeling. The Levy flight technology and the compactness technique to speed up the search process and increase the search accuracy. The simulation experiments were conducted in comparison with the artificial fish swarm algorithm (AFSA), the particle swarm optimization (PSO), and the compact cuckoo search (CCS). The results showed that the improved SMA shortened the search process, effectively avoided the local extreme values, and generated a high-precision desired trajectory model in a shorter time. The pool test also verified the feasibility and effectiveness of the proposed method. The method proposed in this study can satisfy the modeling of benthonic hydrothermal trajectory with a fewer number of nodes, faster search progress and search accuracy.

A fourth-order compact finite volume method on unstructured grids for simulation of two-dimensional incompressible flow

This paper introduces a novel and efficient compact reconstruction procedure for high-order finite volume methods applied to unstructured grids. In this procedure, we establish a set of constitutive relations that ensure the continuity of the reconstruction polynomial and its normal derivatives between adjacent elements at control points. The paper delves into the details of the fourth-order compact reconstruction method specifically designed for two-dimensional triangular grids. This method can be considered an extension of the one-dimensional compact scheme and cubic spline interpolation methods to two-dimensional triangular unstructured grids. In the cubic polynomial reconstruction, a two-dimensional cubic polynomial is reconstructed using the cell averages of elements in the standard stencil and the function values at control points. The determination of function values at control points is achieved by adhering to the constraint of normal derivative continuity. This reconstruction is solved using a relaxation iteration method and has been verified to be solvable for triangular grids. Compared to other fourth-order implicit compact polynomial reconstructions, our method requires solving a smaller number of unknowns, which means less computational cost in reconstruction. By applying this method to solve the Poisson equation, the linear convection equation, and incompressible flow benchmarks, it demonstrates that the proposed method exhibits the expected high-order accuracy and performs well in incompressible flow problems.

Multispectral two-dimensional temperature field reconstruction using particle swarm optimization and the Broyden–Fletcher–Goldfarb–Shanno algorithm with multiple extreme value optimization

The flame temperature is a crucial parameter in combustion, indicating heat generation and transfer. However, determining the correct temperature becomes challenging when flame emissivity is unknown. This article presents a multispectral 2D temperature field reconstruction method using particle swarm optimization and the Broyden–Fletcher–Goldfarb–Shanno algorithm, combined with multivariate extreme-value optimization. This method establishes an objective function based on the correlation between the true temperature and spectral data. The objective function was minimized by adjusting the emissivity, enabling the reconstruction of 2D temperature and emissivity images without assuming an emissivity model. Calibration with a multispectral camera yielded the spectral response coefficients, and three-time spline interpolation was used to verify the calibration data. The reconstructed 2D temperature field showed a mean absolute error (MAE) of 4.61 and structural similarity (SSIM) of 0.995. The reconstructed emissivity image had an MAE range of 0.04 to 0.053 and an SSIM range of 0.897 to 0.915. The system, tested on a butane flame, showed a temperature range of 1001 K to 1356 K, with an average temperature of 1194 K and emissivity values ranging from 0.3166 to 0.8621. The results align with the expected combustion process and radiation characteristics distribution of the butane flame.

Hidden data recovery using reservoir computing: Adaptive network model and experimental brain signals.

The problem of hidden data recovery is crucial in various scientific and technological fields, particularly in neurophysiology, where experimental data can often be incomplete or corrupted. We investigate the application of reservoir computing (RC) to recover hidden data from both model Kuramoto network system and real neurophysiological signals (EEG). Using an adaptive network of Kuramoto phase oscillators, we generated and analyzed macroscopic signals to understand the efficiency of RC in hidden signal recovery compared to linear regression (LR). Our findings indicate that RC significantly outperforms LR, especially in scenarios with reduced signal information. Furthermore, when applied to real EEG data, RC achieved more accurate signal reconstruction than traditional spline interpolation methods. These results underscore RC's potential for enhancing data recovery in neurophysiological studies, offering a robust solution to improve data integrity and reliability, which is essential for accurate scientific analysis and interpretation.