Function Interpolation Method Research Articles

Towards improved description of plastic anisotropy in sheet metals under biaxial loading: A novel generalization of Hill48 yield criterion

Lightweight design and development of automobiles are strongly dependent on lightweight high-strength sheet metals. An accurate prediction of anisotropy and yield surface evolution of these materials under different sampling directions of biaxial tension (BT) is a necessary condition for the numerical analyses of stamping forming. In this work, the Hill48 model considering the principal stress direction is generalized to describe the anisotropic evolution and the yield loci on the normal and diagonal planes. The material parameters of the generalized M-Hill48 model (GM-Hill48) have analytical form and can be calibrated by the yield stresses and r-values expressed by the continuous equivalent plastic strain (EPS). A quadratic function interpolation method based on the near-plane strain (NPS) stress is established to control the yield locus under different plane stress states. In addition, a method for predicting the yield loci in arbitrary sampling directions under BT is proposed by tensor coordinate transformation. Different from the traditional model which can only determine material parameters by using equi-biaxial tension (EBT) or NPS stress along the rolling direction (RD) and transverse direction (TD), the yield stresses of BT in different sampling directions can be incorporated into the generalized model. The predictive capability of the GM-Hill48 model is verified by capturing the continuous evolution of yield stresses and strain for DP590 and AA6016-T4 materials. The convexity condition of the established modified model is given and discussed. Finally, the advantages of new model are further expounded in terms of the prediction accuracy and identified parameters compared with the advanced yield models.

Multi‐material topology optimization considering arbitrary strength and yield criteria constraints with single‐variable interpolation

AbstractMaterial heterogeneity gives composite constructions unique mechanical and physical qualities. Combining multiple materials takes full use of these features in stress‐constrained topology optimization. Traditional research in this field often assumes a consistent yield criterion for all possible materials but adapts their stiffness and strengths accordingly. To cope with this challenge, an innovative single‐variable interpolation approach is proposed to enable the simultaneous inclusion of distinct yield criteria and material strengths. A stress‐constrained topology optimization formulation is presented based on this yield function interpolation method, which can independently support various materials with different elastic characteristics, material strengths, and yield criteria. Then, the large‐scale problem of local stress constraints can be effectively solved by the Augmented Lagrangian (AL) method. Several two‐dimensional (2D) and three‐dimensional (3D) design scenarios are investigated to reduce the overall mass of the structure while considering stress constraints. The optimal composite designs exhibit several crucial benefits resulting from material heterogeneity, including the enlargement of the design possibilities, the dispersion of stress, and the utilization of asymmetry in tension‐compression strength.

A Comparison of Arterial Input Function Interpolation Methods for Patlak Plot Analysis of 68Ga-PSMA-11 PET Prostate Cancer Studies.

Positron emission tomography (PET) imaging enables quantitative assessment of tissue physiology. Dynamic pharmacokinetic analysis of PET images requires accurate estimation of the radiotracer plasma input function to derive meaningful parameter estimates, and small discrepancies in parameter estimation can mimic subtle physiologic tissue variation. This study evaluates the impact of input function interpolation method on the accuracy of Patlak kinetic parameter estimation through simulations modeling the pharmacokinetic properties of [68Ga]-PSMA-11. This study evaluated both trained and untrained methods. Although the mean kinetic parameter accuracy was similar across all interpolation models, the trained node weighting interpolation model estimated accurate kinetic parameters with reduced overall variability relative to standard linear interpolation. Trained node weighting interpolation reduced kinetic parameter estimation variance by a magnitude approximating the underlying physiologic differences between normal and diseased prostatic tissue. Overall, this analysis suggests that trained node weighting improves the reliability of Patlak kinetic parameter estimation for [68Ga]-PSMA-11 PET.

Accurately identifying the defects of bubbles and foreign objects under the protective films of electric vehicle batteries by using 3D point clouds

Abstract For the defects of bubbles and foreign objects under the protective film of electric vehicle batteries, it is difficult to accurately identify them over traditional 2D optical images. In this paper, we first propose a supervoxel-based region growing algorithm for pre-segmentation of point clouds. Secondly, we utilize radial basis function interpolation and threshold segmentation methods to accurately segment defect point clouds from the entire point cloud. Finally, we develop a feature descriptor and combine it with support vector machine to classify bubbles and foreign objects under the film. This paper achieves the identification of bubbles and foreign objects under the film through two steps: point cloud segmentation and point cloud classification. Experimental results demonstrate that the proposed point cloud segmentation method exhibits high robustness to noise and the intrinsic curvature of the workpiece. Additionally, in the classification scenario presented in this paper, the proposed feature descriptor outperforms classical feature descriptors. Compared to image-based deep learning methods, the defect recognition algorithm proposed in this paper has clear principles and superior performance, with precision and recall of 95.63% and 96.95%, and an intersection over union metric of 0.926.

A Modified High-Selective Frequency Selective Surface Designed by Multilevel Green’s Function Interpolation Method

A compact high-selective band-pass frequency selective surface (FSS) with the unit cell less than λ/7 is presented. For the simulation of the structure, the multilevel Green’s function interpolation method (MLGFIM) using Floquet theory is adopted to accelerate the calculation of the complex unit cell. The radial basis function (RBF)-QR method is used in the interpolation, which makes the shape parameter in the RBF function not required to be retested for different periodicity. In this design, with an aperture coupling structure between the top and bottom layers patterned by triangular patches and meander lines, the FSS has two transmission zeros (TZs) on both sides of the pass-band and achieves a steep roll-off rate of 192 dB/GHz. Consequently, the FSS has high selectivity and out-of-band suppression, besides profiting from the low profile and symmetric geometry, this FSS exhibits good angular and polarization stabilities. The prototype of the proposed FSS is fabricated and good performance is obtained.

High Wideband Digital Oscilloscope Design

In most test applications, acquisition and analysis involving simultaneous processing of analog and digital signals. However, the bandwidth of most mainstream digital oscilloscopes is limited to 100 MHz, which is unable to meet the testing needs of high-frequency signals in complex electronic systems [1], and therefore, high-bandwidth digital oscilloscopes have emerged. Based on this background, this paper designs a digital oscilloscope hardware platform with high bandwidth by integrating FPGA and ARM technologies, aiming to meet the rigorous testing requirements of modern electronic systems. The FPGA module is based on the xc7s75fgga676 chip, which is mainly responsible for ADC control, data processing and frequency measurement functions. AM5708 is selected as the ARM module to realize the trigger, time base, amplitude and automatic setting functions of the oscilloscope. In order to ensure the accuracy and fidelity of waveform changes, the Sinc function interpolation method is used. This design further improves the acquisition bandwidth and processing speed on the basis of traditional MSO (Mixed Signal Oscilloscope) oscilloscopes, which is of great significance for the acquisition and processing of high-speed signals.

3D spatial distribution of soil pollutants based on geo-shadowing anisotropic RBF-PCA

Research on soil contamination has become increasingly important, but there is limited information about where to sample for pollutants. Thus, the use of three-dimensional (3D) spatial interpolation techniques has been promoted in this area of study. However, the application of traditional interpolation methods is limited in geography, especially in the expression of anisotropy, and it is not associated with geographical properties. To address this issue, we used a test site (a factory in Nanjing) to develop a new research method based on the geographical shading radial basis function (RBF) interpolation method, which considers 3D anisotropy and geographical attribute expression. Drilling and uniform sampling were used to sample the contaminated area at this test site. This approach included two steps: i) An ellipsoid with anisotropic properties was constructed. Thus, the first step was to determine the shape of the ellipsoid using principal component analysis (PCA) to determine the main orientations and construct a rotational and stretched matrix. The second step was determining the ellipsoid size by computing the range using the variogram method for orientations. ii) During field measurement, the geospatial direction influences soil attribute values, so a shadowing calculation method was derived for quadratic weight determination. Then, the weight of the attribute value of known points can be assigned to meet the field conditions. Lastly, the model was evaluated using the root mean square error (RMSE). For the 2D space, the RMSE values of Kriging, RBF, and the proposed method are 6.09, 7.12, and 5.02, respectively. The R2 values of Kriging, RBF, and the proposed method are 0.871, 0.832, and 0.946, respectively. For the 3D space, the RMSE values of Kriging, RBF, and the proposed method are 2.65, 2.23, and 2.58, respectively. The R2 values of Kriging, RBF, and the proposed method are 0.934, 0.912, and 0.953, respectively. The resulting fitted model was relatively smooth and met experimental needs. Thus, we believe that the interpolation method can be applied as a new method to predict the distribution of soil pollutants.

Enhancing OpenEP: atrial conduction velocity and conduction velocity heterogeneity quantification through EP Workbench

Abstract Background Alterations in atrial conduction velocity have been implicated in the pathogenesis of atrial arrhythmias, with conduction velocity thought to be slower and more heterogeneous in areas promoting atrial fibrillation. However, clinical studies of conduction velocity are challenging since there are no available platforms that provide researchers and clinicians with the ability to quantify conduction velocity and analyse conduction heterogeneity from electroanatomic mapping data. Purpose In this paper we sought to address these limitations by enhancing the OpenEP Python library by (1) automating calculations using previously-published conduction velocity estimation algorithms; (2) providing an interactive graphical representing of conduction velocity and conduction heterogeneity and (3) implementing a histogram analysis tool to quantify conduction velocity and enable the identification of slow conduction regions. Method Two well-known and previously published methods for calculating cardiac conduction velocity, Triangulation and polynomial surface fitting, were implemented. Conduction velocity estimation was improved further by excluding regions with wave collisions and focal discharges. These regions were identified using the divergence of conduction velocity vector fields, with positive divergence representing focal sources and negative divergence representing areas of collision. Finally, calculated conduction velocities using electrogram data were interpolated over the surface mesh via Radial Basis Function (RBF) interpolation method. All algorithms were implemented in the OpenEP Python library (openep-py), with visualisation tools provided in the complementary graphical interface, EP Workbench. Results An extensible "Analysis" feature was created in openep-py, to provide conduction velocity and divergence calculations which are fully customisable through the graphical interface based on user preferences. The EP Workbench desktop application displays resulting cardiac surface maps to depict calculated conduction velocity and divergence fields, together with conventional activation and voltage maps (Figure 1). The histogram analysis tool can be used to identify regions of slow conduction velocity from electroanatomic mapping data. Using a threshold of <0.3m/s, two slow conducting channels are visualised on the posterior wall of a test case (Figure 2). The tool is not specific to conduction velocity and may also be used to quantify other data types in EP Workbench. Finally, computed conduction velocity and divergence values and surface maps are stored in the standard OpenEP data structure, allowing further analysis following data export. Conclusion We have extended OpenEP to provide a comprehensive set of tools for conduction velocity calculation and analysis which will facilitate investigation of the structural and functional basis of conduction velocity alterations in disease states.

A new contact and road model for multi-body dynamic simulation of wheeled vehicles on soft-soil terrain

AbstractIn this paper, a new high-performance and memory-efficient contact and road model is developed. Specifically, the road is modeled as a rectangular structured grid of deformable springs in the vertical direction, thus enabling fast execution. The new road model stands out due to its ability to handle large road scenarios by allocating computer memory dynamically for each spring, resulting in efficient memory utilization. Furthermore, each spring represents a small road patch that entails various information, such as the soil elevation, the soil properties, and the soil compaction, allowing for complicated simulations incorporating spatially varying soil properties and phenomena related to the multi-pass effect. In addition, using the new contact model, complex terrain geometries are handled in a computationally efficient way by approximating locally the irregular road profile with a suitable equivalent plane. For this, two different strategies are proposed, namely the radial basis function (RBF) interpolation method and the 3D enveloping contact model. Finally, the proposed techniques are implemented in Altair MotionSolve, a comprehensive multi-body simulation software for complex mechanical systems. In particular, a single-wheel test bed is initially examined followed by a four-wheeled rover model and the next-generation NATO reference mobility model (NG-NRMM). In all cases, the proposed model is validated by using available experimental data. Lastly, a case involving both wheeled and tracked vehicles is also examined by using a shared road model.

A comparative study of different radial basis function interpolation algorithms in the reconstruction and path planning of γ radiation fields

Accurate reconstruction of radiation field and path planning are very important for the safety of operators in the process of dismantling nuclear facilities. Based on radial basis function (RBF) interpolation algorithm, this paper discussed the application of inverse multiquadric radial basis Function (IMRBF) interpolation method to the reconstruction of gamma radiation field, and proved the feasibility of reconstructing a radiation field with multiple γ sources. The average relative errors of IMRBF interpolation results were 4.28% and 8.76%, respectively, for the experimental scenarios with single and double gamma sources. After comparing the consistency between the simulated scene and the experimental scene, IMRBF method and Cubic Spline method were respectively used to reconstruct the gamma radiation field by Geant4 simulation data. The results showed that the interpolation accuracy of IMRBF method was superior to that of Cubic Spline method. Further, more RBF interpolation algorithms were used to reconstruct the multi-γ source radiation field, and then the Probabilistic Roadmap (PRM) algorithm was used to optimize the human walking path in the radiation field reconstructed by different interpolation methods. The optimal paths in radiation fields generated by multiple interpolation methods were compared. The results herein contribute to a comprehensive understanding of RBF interpolation methods in reconstructing γ radiation fields and their application in optimizing paths in radiation environments. The insights may provide valuable information for decision-making in radiation protection during the decommissioning of nuclear facilities.

Research on the hydroelastic response of ice floes and wave scattering field

Abstract The marginal ice zone (MIZ) is the area between sea ice and open water, the structure of which is mainly determined by wave and ice interactions. Thus mastering the characteristics of MIZ is of great significance to the Arctic routes opening and the natural resources development. In this paper, the hydroelastic response of ice floes in waves is studied, a three-dimensional numerical wave tank is established based on the computational fluid dynamics (CFD) technology. The finite volume method (FVM) and finite element method (FEM) are respectively utilized for discrete fluid domain and ice domain. A mapping interface at the junction of the fluid and ice floes domains is created to perform data mapping by the shape function interpolation method and the least square method. This work presents a series of numerical simulations to study the fluid-solid interaction (FSI) of waves and ice floes. Under the given incident wave parameters, the vertical bending deformation of ice floes with different shapes under the excitation of waves, the effect of ice floes' deformation on the wave field are studied, and the effect of wave overwash on the transmitted wave field is emphasized. Results show that the shape of the ice floes significantly affects its elastic deformation and scattered wave field, and the wave overwash phenomenon attenuates the scattering wave.

A Stable and Efficient Interpolation Method for Two-dimensional Periodic Green's Functions

A Stable and Efficient Interpolation Method for Two-dimensional Periodic Green's Functions

Study on the regional ASF prediction method based on the ordinary kriging interpolation

The eLoran system functions as a robust backup to the Global Navigation Satellite System (GNSS), providing substantial signal power, robust anti-jamming capabilities, and an easily maintainable ground system. Nonetheless, the propagation time delay of the system, primarily driven by the Additional Secondary Phase Factor (ASF), significantly influences the positioning accuracy. Compensating for ASF can effectively enhance the positioning performance. Traditional propagation delay theories frequently yield substantial discrepancies between the predicted and measured values in regions characterized by extended propagation distances and varying topographic features. To address this issue, we conducted ASF measurements within a selected test area using a limited number of measurement points. We employed the ordinary Kriging interpolation method to predict ASF values across the entire test area, and used cross-validation to validate our predictions. The results confirmed the accuracy and effectiveness of the Kriging interpolation algorithm in predicting ASF values within specific regions. The cross-validation demonstrated that the errors remained within acceptable ranges. Furthermore, we applied Ordinary Kriging, Inverse Distance Weighting, and Radial Basis Function Interpolation methods to evaluate the positioning accuracy of the test area before and after ASF correction. Compared to other methods, using the Ordinary Kriging interpolation algorithm for predicting ASF values resulted in a corrected positioning accuracy of up to 68.8 m at various test locations. This approach effectively resolves the challenge of low accuracy in theoretical calculations in complex environments. By utilizing ordinary Kriging interpolation, we required measurements of only a few ASF values within a specific region to create an ASF correction map, addressing the challenges related to inaccurate theoretical calculations in complex pathways and avoiding time-consuming and labor-intensive large-scale measurements. The results of this study offer valuable theoretical support for improving the accuracy of land-based navigation systems.

Real-space tight-binding model for twisted bilayer graphene based on mapped Wannier functions

Twisted multi-layer heterostructures have been considered a platform for studying highly correlated many-particle systems, hosting the emerging phenomena of correlation physics. Electronic structure calculations of such materials which mainly focused on Twisted Bilayer Graphene (TBG) in the framework of the independent-electron approximation, despite the complexity, accurately match the experimental results around the Fermi level. Here, we present a convenient real space π-bands tight-binding model to calculate the band structure of TBG based on the Wannier interlayer hopping parameters obtained from non-twisted bilayer graphene. Our approach is based on mapping hopping parameters onto the real space TBG interlayer couplings, using Radial Basis Function (RBF) interpolation method. This accurate mapping, naturally, transfers all the symmetries and orbital shape features of the bilayer graphene lattice to the TBG lattice and preserves coupling orientation dependencies in addition to distance dependencies. The importance of this fact is explained by showing the effect of the threefold rotation symmetry of AB′ interlayer coupling on the flat band of the TBG band structure. In addition, due to real space study, the model gives us a comprehensive and intuitive view of the role of each interlayer orbital coupling in the TBG band structure and the structural variation relative to twisting.

Artificial Intelligence Technology Boosts the Construction of English Intelligent Teaching Mode in Colleges and Universities

Abstract With the goal of improving the teaching effect of English in colleges and universities, this paper combines artificial intelligence technology with teaching and constructs an English-intelligent tutoring teaching model. By analyzing the main forms of artificial intelligence in the field of teaching, the advantages of intelligent teaching mode in college English teaching are explored from personalized teaching as well as teaching effect. Combining the RBF neural network to analyze the students’ learning data, the function approximation principle and interpolation method are used to improve the accuracy of the analysis of the students’ data. Using the form of network topology, the information transfer process in English intelligent teaching is explored. To improve the classification of students’ abilities and the prediction of their grades, judgment trees are added to the network. The English Intelligent Assisted Teaching model was applied to teaching to explore its feasibility and effectiveness. The results show that students’ satisfaction with personalized teaching is 0.85, and their satisfaction with personalized evaluation is 0.8. The students’ translation ability under the English Intelligent Assisted Teaching Model has improved more, from 75 to 90.

Reconstruction of incomplete flow fields based on unsupervised learning

The loss of flow field data is a common challenge in experimental techniques and data transmission processes. Traditional methods often rely on another complete or high-fidelity dataset to compensate for missing information regarding fluid characteristics. However, obtaining such complete data is not always feasible. In this study, we propose an unsupervised learning approach that efficiently, swiftly, and cost-effectively reconstructs the complete flow field by leveraging the inherent properties of the flow field itself, without the need for high-fidelity data integration. Our proposed methods primarily encompass three techniques: Fourier basis function interpolation, the Autoregressive Integrated Moving Average model (ARIMA), and AMF (ARIMA-Median Filter). The first two methods are founded on the temporal evolution characteristics of the flow field and reconstruct the missing fluid information by extrapolating from the available data. The AMF method, building upon the ARIMA reconstruction outcomes, employs a median filtering approach to eliminate noise and outliers introduced by the lack of spatial correlation. All three methods perform well, with the AMF method exhibiting superior performance, particularly in cases involving scatter missing data with higher absence rates. While ARIMA and AMF entail longer computational times, they offer stability and are less prone to overfitting during the reconstruction process, rendering them more suitable for reconstructing flow fields with varying degrees of missing data. The Fourier basis function interpolation method, with its shorter runtime, is better suited for swiftly reconstructing flow fields with lower rates of missing data. However, it is worth noting that improper parameter selection for this method can lead to overfitting. Additionally, the non-stationarity of the flow field has an impact on reconstruction accuracy, with regions exhibiting stronger non-stationarity resulting in more noticeable reconstruction errors. For the ARIMA method, which relies on temporal correlation for reconstruction, the missing structures have a relatively minor effect. However, in the case of flow fields with block missing data, the improvement in reconstruction accuracy when using median filtering compared to ARIMA is not substantial.

Polyharmonic splines interpolation on scattered data in 2D and 3D with applications

Data interpolation is a fundamental problem in many applied mathematics and scientific computing fields. This paper introduces a modified implicit local radial basis function interpolation method for scattered data using polyharmonic splines (PS) with a low degree of polynomial basis. This is an improvement to the original method proposed in 2015 by Yao et al.. In the original approach, only radial basis functions (RBFs) with shape parameters, such as multiquadrics (MQ), inverse multiquadrics (IMQ), Gaussian, and Matern RBF are used. The authors claimed that the conditionally positive definite RBFs such as polyharmonic splines r2nlnr and r2n+1 “failed to produce acceptable results”.In this paper, we verified that when polyharmonic splines together with a polynomial basis is used on the interpolation scheme, high-order accuracy and excellent conditioning of the global sparse systems are gained without selecting a shape parameter. The scheme predicts functions’ values at a set of discrete evaluation points, through a global sparse linear system. Compared to standard implementation, computational efficiency is achieved by using parallel computing. Applications of the proposed algorithms to 2D and 3D benchmark functions on uniformly distributed random points, the Halton quasi-points on regular or Stanford bunny shape domains, and an image interpolation problem confirmed the effectiveness of the method. We also compared the algorithms with other methods available in the literature to show the superiority of using PS augmented with a polynomial basis. High accuracy can be easily achieved by increasing the order of polyharmonic splines or the number of points in local domains, when small order of polynomials are used in the basis. MATLAB code for the 3D bunny example is shared on MATLAB Central File Exchange (Yao, 2023).

A framework for simulating snow accumulation and ice accretion on high-speed trains

A simulation framework for three-dimensional particle trajectory tracking, snow accumulation and ice accretion modelling on solid bodies in high-speed air flow is presented. The framework, named HADICE, solves the aerodynamic flow field as Reynolds averaged Navier-Stokes (RANS), with optional hybrid RANS/LES capabilities for modelling complex turbulent flows. Particle trajectory tracking is performed in an Eulerian-Lagrangian approach and wall collision is modelled using a hard collision model with reflect condition and a momentum based trap condition. A novel accurate and robust iterative evaluation method for the local collection efficiency is proposed for arbitrary 3D geometry and flow. Ice accretion is modelled in a multi-step approach and iced geometry is updated through mesh deformation using a radial basis function (RBF) interpolation method. Snow accumulation and ice accretion predictions based on the framework are validated against climatic wind tunnel experimental measurements. A full 3D simulation is demonstrated for snow accumulation and ice accretion on a 1:8 scaled high-speed train model. Using the presented framework, snow accumulation and icing simulation for high-speed trains can be conducted in an accurate and efficient manner, which is of great importance for physical investigations and the design of anti-snow and ice protection systems.

Design of large-angle distortion-free and spot adjustable LED spot array projector based on microlens array and eyepiece

The spot array projector has long been a challenging and intriguing research focus in the fields of projection and lighting applications. In the current literature, there is a lack of a comprehensive and detailed presentation on the design and analysis method for a spot array generator based on the structure of imaging eyepiece and MLA. We present a novel design and optimization method for a large-angle, distortion-free and spot adjustable LED spot array projector that is composed of an eyepiece, two microlens arrays (MLAs), and a micro-LED array (MLEDA). The eyepiece system is optimized using imaging optical methods to project sub-beams to the target plane with a large angle. The sub-lens of condenser MLA is also optimized using imaging optical methods to refocus the collimating beam and match the numerical aperture (NA) with the eyepiece, and the sub-lens of the collimating MLA is acquired by using simulated annealing (SA) global illumination optics optimization method to achieve collimation and far-field homogenization. The predistortion MLEDA and the MLAs are proposed and implemented by the radial basis function (RBF) interpolation method, which correct the large-angle distortion introduced by the eyepiece. Both near-field and far-field applications can be realized by the proposed system. In the near-field applications, different spot geometries at the near-field target plane can be achieved. In the far-field applications, the power matching of the MLEDA is used to improve far-field uniformity of spot array. Moreover, the predefined-geometry arrangement spot array can be realized in both near and far fields. Two design examples with full field of view (FOV) projection of 80° and 100° are provided to validate the proposed method. Overall, the proposed system offers a promising solution for various applications requiring target identification or 3D calibration.

Net-HDMR Metamodeling Method for High-Dimensional Problems

Abstract Metamodel technology provides an efficient method to approximate complex engineering design problems. However, the approximation for high-dimensional problems usually requires a large number of samples for most traditional metamodeling methods, which leads to the difficulty of “curse of dimensionality.” To address the aforementioned issue, this paper presents the Net-high dimension model representation (HDMR) method based on the Cut-HDMR framework. Compared with traditional HDMR modeling, the Net-HDMR method incorporates two novel modeling approaches that improve the modeling efficiency of high-dimensional problems. The first approach enhances the modeling accuracy of HDMR by using the net function interpolation method to decompose the component functions into a series of one-dimensional net functions. The second approach adopts the CV-Voronoi sequence sampling method to effectively represent one-dimensional net functions with limited samples. Overall, the proposed method transforms complex high-dimensional problems into fitting finite one-dimensional splines, thereby increasing the modeling efficiency while ensuring approximate accuracy. Six numerical benchmark examples with different dimensions are examined to demonstrate the accuracy and efficiency of the proposed Net-HDMR. An engineering problem of thermal stress and deformation analysis for a jet engine turbine blade was introduced to verify the engineering feasibility of the proposed Net-HDMR.