Interpolation Basis Research Articles

The Resampling Methods Direct Sequence Spread Spectrum Signal’s Demodulator Implementation

Relevance. The direct spread spectrum signals are widely used in navigation and communication systems recently. These signals prevail in modern satellite navigation systems and are used in various communication systems with code division multiplexing in particularly. In this regard, the tasks of building direct spread spectrum signals’ demodulators have the key importance. Mach importance in the construction of demodulators is the problem chip rate variability.The purpose of the study is to propose a demodulator structure focused on solving this problem.Methods. The research is based on computer modeling methods.Decision. The paper proposes an approach to the construction of the direct spread spectrum signal’s demodulators based on modern methods of digital signal processing. It is shown that the main advantage of the proposed approach is the possibility of rebuilding the variable chip rate demodulators. Based on the results obtained, a scheme for the direct spread spectrum signals demodulator using resampling methods is proposed. Resampling, in turn, is implemented on the basis of polynomial interpolation using Lagrange polynomials. The structure of the resampler is proposed, similar to the structure of an interpolating filter with a finite impulse response. The presented simulation results show the effectiveness of the proposed approach.Novelty. It seems that the currently common methods of implementing direct spread spectrum signal in terms of delay synchronization do not sufficiently meet modern requirements. The implementation of delay synchronization schemes based on resampling is practically not discussed in well-known works. At the same time, modern methods and devices of digital signal processing make it possible to ensure an effective hardware implementation of the scheme in question. In this context, the approach proposed in the paper to the construction of demodulators seems to be very relevant.Significance. The results of the work can be used in the construction with direct spread spectrum signals’ demodulators for a wide range of communication and navigation systems. The synchronous sampling structure proposed in this paper is very promising, especially for variable chip rate demodulators.

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.

A Finite Operator Learning Technique for Mapping the Elastic Properties of Microstructures to Their Mechanical Deformations

ABSTRACTTo obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics‐informed neural networks and concept of neural operators. We propose directly utilizing the available discretized weak form in finite element packages to construct the loss functions algebraically, thereby demonstrating the ability to find solutions even in the presence of sharp discontinuities. Our focus is on micromechanics as an example, where knowledge of deformation and stress fields for a given heterogeneous microstructure is crucial for further design applications. The primary parameter under investigation is the Young's modulus distribution within the heterogeneous solid system. Our investigations reveal that physics‐based training yields higher accuracy compared with purely data‐driven approaches for unseen microstructures. Additionally, we offer two methods to directly improve the process of obtaining high‐resolution solutions, avoiding the need to use basic interpolation techniques. The first one is based on an autoencoder approach to enhance the efficiency for calculation on high resolution grid points. Next, Fourier‐based parametrization is utilized to address complex 2D and 3D problems in micromechanics. The latter idea aims to represent complex microstructures efficiently using Fourier coefficients. The proposed approach draws from finite element and deep energy methods but generalizes and enhances them by learning parametric solutions without relying on external data. Compared with other operator learning frameworks, it leverages finite element domain decomposition in several ways: (1) it uses shape functions to construct derivatives instead of automatic differentiation; (2) it automatically includes node and element connectivity, making the solver flexible for approximating sharp jumps in the solution fields; and (3) it can handle arbitrary complex shapes and directly enforce boundary conditions. We provided some initial comparisons with other well‐known operator learning algorithms, further emphasize the advantages of the newly proposed method.

MAESSTRO: Masked Autoencoders for Sea Surface Temperature Reconstruction under Occlusion

Abstract. This study investigates the use of a masked autoencoder (MAE) to address the challenge of filling gaps in high-resolution (1 km) sea surface temperature (SST) fields caused by cloud cover, which often result in gaps in the SST data and/or blurry imagery in blended SST products. Our study demonstrates that MAE, a deep learning model, can efficiently learn the anisotropic nature of small-scale ocean fronts from numerical simulations and reconstruct the artificially masked SST images. The MAE model is trained and evaluated on synthetic SST fields and tested on real satellite SST data from the Visible Infrared Imaging Radiometer Suite (VIIRS) sensor on the Suomi NPP satellite. We demonstrate that the MAE model trained on numerical simulations can provide a computationally efficient alternative for filling gaps in satellite SST. MAE can reconstruct randomly occluded images with a root mean square error (RMSE) of under 0.2 °C for masking ratios of up to 80 %. A trained MAE model in inference mode is exceptionally efficient, requiring 3 orders of magnitude (approximately 5000×) less time compared to the conventional approaches of cubic radial basis interpolation and Kriging tested on a single CPU. The ability to reconstruct high-resolution SST fields under cloud cover has important implications for understanding and predicting global and regional climates and detecting small-scale SST fronts that play a crucial role in the exchange of heat, carbon, and nutrients between the ocean surface and deeper layers. Our findings highlight the potential of deep learning models such as MAE to improve the accuracy and resolution of SST data at kilometer scales. This presents a promising avenue for future research in the field of small-scale ocean remote sensing analyses.

Maize Phenotypic Parameters Based on the Constrained Region Point Cloud Phenotyping Algorithm as a Developed Method

As one of the world’s most crucial food crops, maize plays a pivotal role in ensuring food security and driving economic growth. The diversification of maize variety breeding is significantly enhancing the cumulative benefits in these areas. Precise measurement of phenotypic data is pivotal for the selection and breeding of maize varieties in cultivation and production. However, in outdoor environments, conventional phenotyping methods, including point cloud processing techniques based on region growing algorithms and clustering segmentation, encounter significant challenges due to the low density and frequent loss of point cloud data. These issues substantially compromise measurement accuracy and computational efficiency. Consequently, this paper introduces a Constrained Region Point Cloud Phenotyping (CRPCP) algorithm that proficiently detects the phenotypic traits of multiple maize plants in sparse outdoor point cloud data. The CRPCP algorithm consists primarily of three core components: (1) a constrained region growth algorithm for effective segmentation of maize stem point clouds in complex backgrounds; (2) a radial basis interpolation technique to bridge gaps in point cloud data caused by environmental factors; and (3) a multi-level parallel decomposition strategy leveraging scene blocking and plant instances to enable high-throughput real-time computation. The results demonstrate that the CRPCP algorithm achieves a segmentation accuracy of 96.2%. When assessing maize plant height, the algorithm demonstrated a strong correlation with manual measurements, evidenced by a coefficient of determination R2 of 0.9534, a root mean square error (RMSE) of 0.4835 cm, and a mean absolute error (MAE) of 0.383 cm. In evaluating the diameter at breast height (DBH) of the plants, the algorithm yielded an R2 of 0.9407, an RMSE of 0.0368 cm, and an MAE of 0.031 cm. Compared to the PointNet point cloud segmentation method, the CRPCP algorithm reduced segmentation time by more than 44.7%. The CRPCP algorithm proposed in this paper enables efficient segmentation and precise phenotypic measurement of low-density maize multi-plant point cloud data in outdoor environments. This algorithm offers an automated, high-precision, and highly efficient solution for large-scale field phenotypic analysis, with broad applicability in precision breeding, agronomic management, and yield prediction.

Density estimation for time-dependent PDE with random input by a Legendre-based multi-element probabilistic collocation method

This paper proposed a Legendre-based multi-element probabilistic collocation method for time-dependent stochastic differential equations, used for density estimation of unknown functions. This method involves discretizing the stochastic space, and on each element, constructing Lagrange interpolation basis functions based on Legendre–Gauss–Lobatto collocation/quadrature nodes. The proposed method is applied to approximate one-dimensional/two-dimensional smooth/non-smooth functions and is tested for accuracy in approximating random function values, density estimations, and mathematical expectations. This method is applied to stochastic nonlinear Schrödinger equations and coupled stochastic nonlinear Schrödinger equations, and all numerical results are compared with Monte Carlo simulation.

GANSharp: High-definition image reconstruction using generative adversarial networks

In the realm of digital imaging, enhancing low-resolution images to high-definition quality is a pivotal challenge, particularly crucial for applications in medical imaging, security, and remote sensing. Traditional methods, primarily relying on basic interpolation techniques, often result in images that lack detail and fidelity. GANSharp introduces an innovative GAN-based framework that substantially improves the generator network, incorporating adversarial and perceptual loss functions for enhanced image reconstruction. The core issue addressed is the loss of critical information during down-sampling processes. To counteract this, we proposed a GAN-based method leveraging deep learning algorithms, trained using sets of both low- and high-resolution images. Our approach, which focuses on expanding the generator network’s size and depth and integrating adversarial and perceptual loss, was thoroughly evaluated on various benchmark datasets. The experimental results showed remarkable outcomes. On the Set5 dataset, our method achieved a PSNR of 34.18 dB and a SSIM of 0.956. Comparatively, on the Set14 dataset, it yielded a PSNR of 31.16 dB and an SSIM of 0.920, and on the B100 dataset, it achieved a PSNR of 30.51 dB and an SSIM of 0.912. These results were superior or comparable to those of existing advanced algorithms, demonstrating the proposed method’s potential in generating high-quality, high-resolution images. Our research underscores the potency of GANs in image super-resolution, making it a promising tool for applications spanning medical diagnostics, security systems, and remote sensing. Future exploration could extend to the utilization of alternative loss functions and novel training techniques, aiming to further refine the efficacy of GAN-based image restoration algorithms.

Optimization design for the installation position of hold bracket in railway bogie system by uniform design method

ABSTRACT The sensor hold bracket design is an essential element for running safety in the railway vehicle bogie braking system. The installation position of the hold bracket in the bogie system affects the brake sensing performance. This paper aims to determine the optimal installation position of the hold bracket. Three installation angles and one geometry dimension of a holding bracket are selected for the control factors. The uniform design of the experiment method creates a set of experiments. The surrogate models from input and output data are obtained and compared by applying Kriging interpolation and radial basis functions. The final optimal design models of the holding bracket for two surrogate models are determined using the genetic algorithm. The results show that the optimized parameters could substantially improve the installation angle error of the pressure switch from 4° to 0.04°, which aligns with expectations. Finally, to confirm the effect of the control parameters and their reliability and validity, the impact of the pressure switch is expected when the optimal hold bracket model is installed in the railway vehicle bogie system. As a result, the optimal design procedure can improve and reduce the risk of sensor failure during train operation.

Geotechnical interpolation methodology for determining intermediate values of soil properties

The article considers the application of geotechnical interpolation using ArcGIS software to determine the intermediate geotechnical properties of soils at a construction site in a residential complex in Astana, Esil district. The study is based on data from 8 boreholes drilled to a depth of 26 meters, and the purpose of the work is to use the kriging interpolation method to determine intermediate soil properties. The raw data include the results of analyzing the physical and mechanical properties of the soils from the boreholes, which served as a basis for interpolation and mapping. The results of the study are presented in the form of maps showing the intermediate mechanical properties of the soil at depths of 5, 10 and 15 m. The maps allow obtaining more accurate intermediate values. The proposed methodology not only facilitates the work of designers, but also provides data for realistic scenarios of soil strength and deformation characteristics, which significantly influences the selection of optimal types and sizes of foundations.

An Adapted NURBS Interpolator with a Switched Optimized Method of Feed-Rate Scheduling

With the increasing demand for processing precision in the manufacturing industry, feed-rate scheduling is a crucial component in achieving the processing quality of complex surfaces. A smooth feed-rate profile not only guarantees machining quality but also improves machining efficiency. Although the typical offline feed-rate scheduling method possesses good processing efficiency, it may not provide an optimal solution due to the NP-hard problem caused by the feed-rate scheduling of continuous curve segments, which easily results in excess kinetic limitations and feed-rate fluctuations in a real-time interpolation. Instead, the FIR (Finite Impulse Response) method is widely used to realize interpolation in real-time processing. However, the FIR method will filter out a large number of high-frequency signals, leading to a low-processing efficiency. Further, greater acceleration or deceleration is required to ensure the interpolation passes through the segment end at a predefined feed rate and the deceleration in the feed rate profile appears earlier, which allows the interpolation to easily exceed the kinetic limitation. At present, a simple offline or online method cannot realize the global optimization of the feed-rate profile and guarantee the machining efficiency. Moreover, the current feed-rate scheduling that considers both offline and online methods does not consider the situation that the call of offline data and online prediction data will lead to a decrease in the real-time performance of the CNC system. Further, real-time feed-rate scheduling data tend to dominate the whole interpolation process, thus reducing the effect of the offline feed-rate scheduling data. Hence, based on the tool path with C3 continuity (Cubic Continuously Differentiable), this paper first presents a basic interpolation unit relevant to the S-type interpolation feed-rate profile. Then, an offline local smooth strategy is proposed to smooth the feed-rate profile and reduce the exceeding of kinetic limitations and feed-rate fluctuations caused by frequent acceleration and deceleration. Further, a global online smoothing strategy based on the data generated by offline pre-interpolation is presented. What is more, FIR login and logout conditions are proposed to further smooth the feed-rate profile and improve the real-time performance and machining efficiency. The case study validates that the proposed method performs better in kinetic results compared with the typical offline and FIR methods in both the simulation experiment and actual machining experiments. Especially, in actual processing experiments, the proposed method obtains a 28% reduction in contour errors. Further, the proposed method compared with the FIR method obtains a 15% increase in machining efficiency but only a 4% decrease compared with the typical offline method.

Construction of a new class of quadrilateral spline elements based on the scaled boundary coordinates

The scaled boundary finite element method (SBFEM) is a semi-analytical numerical approach based on the scaled boundary coordinates. Recently, the method which uses interpolations in both the circumferential and radial directions has also been developed based on the scaled boundary representation. However, the stress fields are always discontinuous within the S-elements by both the original SBFEM and the latter method. In this paper, a new class of quadrilateral elements with interior smoothness is constructed by extending the B-net method based on the area coordinates into the S-net method based on the scaled boundary coordinates. In the S-net method, the Bernstein bases are separately applied to discretize both circumferential and radial directions in each sub-triangle of an S-element (or quadrilateral element), and the smoothness conditions between adjacent triangles can be simply represented in the form of linear equations. Then, by using the S-net method, we obtain a new class of quadrilateral elements with interior smoothness and high-order completeness. The shape functions or interpolation bases can be obtained explicitly and determined by the same interpolation nodes of the S-element as the original SBFEM. Some numerical tests also show that the proposed elements can obtain good results.

Reduced-order prediction of unsteady spatial-temporal aerodynamics in a turbine cascade

A low-cost prediction method that effectively captures the detailed dynamics of unsteady motions is necessary for turbomachinery design. This paper applies two data-driven methods for unsteady cascade flow of a T106 low-pressure turbine with periodic incoming wakes under unknown conditions and unknown instants, respectively. For the prediction under unknown conditions, the dominant coherent structures of the unsteady flows are obtained using sparsity-promoting dynamic mode decomposition. An arbitrary case's sparse promoting modes serve as a basis for prediction and polynomial interpolation is employed to predict the characteristic parameters, including the amplitude and frequency. Based on the predicted characteristic parameters and sparse promoting modes, the flow fields within a range of Reynolds numbers can be reconstructed. The results show that the large-scale flow structure at different Reynolds numbers can be predicted with reasonable error. The detailed flow structure of cascade flow fields also agrees well with simulation results, demonstrating the method's excellent applicability. For the prediction under unknown instants, the dominant coherent structures of the unsteady flows are obtained using proper order decomposition. The extreme gradient boosting method is utilized to construct a surrogate model and predict the time coefficients at unknown times. Based on the dominating modes and predicted time coefficients, the flow fields within a range of unknown instants can be reconstructed. The cascade flow fields can be recovered with a relative error of less than 3 %. The vortex structures and blade surface pressure agree well with simulation results. The present work provides a promising approach for turbomachinery design and investigating underlying mechanisms with low data requirements.

Application of Trigonometric Polynomial Fitting Method in Simulating the Spatial Distribution of PM2.5 Concentration in South-Central China

Near-surface PM2.5 estimates remain a global scientific research challenge due to their effect on human fitness and atmospheric environmental quality. However, practical near-surface PM2.5 estimates are impeded by the incomplete monitoring data. In this study, we propose the trigonometric polynomial fitting (TPF) method to estimate near-surface PM2.5 concentrations in south-central China during 2015. We employ 10-fold cross-validation (CV) to assess the reliability of TPF in estimating practical PM2.5 values. When compared to alternative methods such as the orthogonal polynomial fitting (OBF) method based on Chebyshev basis functions, Kriging interpolation, and radial basis function (RBF) interpolation, our results show that utilizing TPF31, with a maximum order of 3 in the x direction and a maximum order of 1 in the y direction, leads to superior efficiency through error minimization. TPF31 reduces MAE and RMSE by 1.93%, 24%, 6.96% and 3.6%, 23.07%, 10.43%, respectively, compared to the other three methods. In addition, the TPF31 method effectively reconstructs the spatial distribution of PM2.5 concentrations in the unevenly distributed observation stations of Inner Mongolia and the marginal regions of the study area. The reconstructed spatial distribution is remarkably smooth. Despite the non-uniform distribution of observation stations and the presence of missing data, the TPF31 method demonstrates exceptional effectiveness in accurately capturing the inherent physical attributes of spatial distribution. The theoretical and experimental results emphasize that the TPF method holds significant potential for accurately reconstructing the spatial distribution of PM2.5 in China.

Vibration control of interconnected composite beams: Dynamical analysis and experimental validations

This paper presents a comprehensive theoretical investigation and experimental validation of vibration and nonlinear vibration control in interconnected composite beams with fixed ends operating within a thermal environment. The study employs the Rayleigh-Ritz method, utilizing a series of orthogonal polynomials as interpolation basis functions to derive the vibration mode functions of the composite structure under thermal conditions. Furthermore, the motion control equation for the system is derived based on Lagrange's equation. These equations of motion are then simplified using the Galerkin method, leading to ordinary differential equations. The response of the system is subsequently computed using the harmonic balance method and validated through the Runge-Kutta method. Finally, experimental results confirm that the NiTiNOL-steel wire rope effectively controls the vibration of interconnected composite beams in a thermal environment and is consistent with the theoretical results.

Monitoring of robot trajectory deviation based on multimodal fusion perception in WAAM process

During wire arc additive manufacturing (WAAM) process, the movement trajectory of robot directly determines cladding layer position, therefore, monitoring of robot trajectory is particularly important. This paper proposes an approach for monitoring robot trajectory deviation based on multimodal fusion perception. First, a visual sensing system is constructed using monochrome camera and infrared camera, which collected visual image of molten pool and measured the temperature of workpiece sidewall. Second, the weld pool contour is extracted based on deep learning, and the histogram of oriented gradient (HOG) algorithm on the basis of trilinear interpolation is adopted to extract temperature distribution characteristics of workpiece sidewall. Finally, a prediction model for robot trajectory deviation is developed using artificial neural network. The experimental results indicate that the proposed approach for monitoring robot trajectory deviation has high detection precision and strong generalization capability, it provides an effective means to ensure weldment quality in WAAM.

Fracture modeling of carbonate rocks via radial basis interpolation and discrete fracture network

Fracture modeling of carbonate rocks via radial basis interpolation and discrete fracture network

A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams

The free vibration and buckling behaviours of 2D-FG porous microbeams are explored in this paper utilizing the Quasi-3D beam deformation theory based on the modified couple stress theory and a Differential Quadrature Galerkin Method (DQGM) systematically, as a combination of the Differential Quadrature Method (DQM) and the semi-analytical Galerkin method, which has used to reduce computational cost for problems in dynamics. The governing equations are obtained using the Lagrange’s principle. The mass and stiffness matrices are calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The matrices are expressed in a similar form to that of the Differential Quadrature Method by introducing an interpolation basis on the element boundary of the Galerkin method. The sampling points are determined by the Gauss-Lobatto node method. The influence of the thickness-to-material length scale parameter (MLSP) on the nondimensional natural frequencies and nondimensional critical buckling loads of 2D-FG porous microbeams are investigated, along with the effects of the boundary condition, aspect ratio and gradient index. The results are validated with literature to establish the accuracy of the procedure described. This work will provide a numerical basis for the design of FG microstructures in the field of micromechanics. These results can be applied to the engineering design of porous FG microstructures.

Barycentric Interpolation Collocation Method for Solving Fractional Linear Fredholm-Volterra Integro-Differential Equation

In this article, barycentric interpolation collocation method (BICM) is presented to solve the fractional linear Fredholm-Volterra integro-differential equation (FVIDE). Firstly, the fractional order term of equation is transformed into the Riemann integral with Caputo definition, and this integral term is approximated by the Gauss quadrature formula. Secondly, the barycentric interpolation basis function is used to approximate the unknown function, and the matrix equation of BICM is obtained. Finally, several numerical examples are given to solve one-dimensional differential equation.

Efficient and accurate nonlinear model reduction via first-order empirical interpolation

We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs). In the presence of nonlinearity, the Galerkin reduced basis approximation remains computationally expensive due to the high complexity of evaluating the nonlinear terms, which depends on the dimension of the truth approximation. The empirical interpolation method (EIM) was proposed as a nonlinear model reduction technique to render the complexity of evaluating the nonlinear terms independent of the dimension of the truth approximation. We introduce a first-order empirical interpolation method (FOEIM) that makes use of the partial derivative information to construct an inexpensive and stable interpolation of the nonlinear terms. We propose two different FOEIM algorithms to generate interpolation points and basis functions. We apply the FOEIM to nonlinear elliptic PDEs and compare it to the Galerkin reduced basis approximation and the EIM. Numerical results are presented to demonstrate the performance of the three reduced basis approaches.

On one semi-analytical approximation of the normal derivative of the simple layer potential near the boundary of a two-dimensional domain

On the basis of piecewise quadratic interpolation, semi-analytical approximations of the normal derivative of the simple layer potential near and on the boundary of a two-dimensional domain are obtained. To calculate the integrals formed after the interpolation of the density function, exact integration over the variable $\rho=(r^{2}-d^{2})^{1/2} $ is used, where $d$ and $r$ are the distances from the observed point to the boundary of the domain and to the boundary point of integration, respectively. The study proves the stable convergence of such approximations with cubic velocity uniformly near the boundary of the class $C^{5}$, as well as on the boundary itself. It is also proved that, by analogy with the exact function, the approximations suffer a discontinuity at the boundary, the magnitude of which is proportional to the values of the interpolated density function, but they can be extended on the boundary to functions that are continuous either on a closed internal border domain or on a closed external one. Theoretical conclusions about uniform convergence are confirmed by the results of calculating the normal derivative near the boundary of a unit circle.