Interpolation Of Parameters Research Articles

A Novel Interpolation Method for Soil Parameters Combining RBF Neural Network and IDW in the Pearl River Delta

Soil fertility is a critical factor in agricultural production, directly impacting crop growth, yield, and quality. To achieve precise agricultural management, accurate spatial interpolation of soil parameters is essential. This study developed a new interpolation prediction framework that combines Radial Basis Function (RBF) neural networks with Inverse Distance Weighting (IDW), termed the IDW-RBFNN. This framework initially uses the IDW method to apply preliminary weights based on distance to the data points, which are then used as input for the RBF neural network to form a training dataset. Subsequently, the RBF neural network further trains on these data to refine the interpolation results, achieving more precise spatial data interpolation. We compared the interpolation prediction accuracy of the IDW-RBFNN framework with ordinary Kriging (OK) and RBF methods under three different parameter settings. Ultimately, the IDW-RBFNN demonstrated lower error rates in terms of RMSE and MRE compared to direct RBF interpolation methods when adjusting settings based on different power values, even with a fixed number of data samples. As the sample size decreases, the interpolation accuracy of OK and RBF methods is significantly affected, while the error of IDW-RBFNN remains relatively low. Considering both interpolation accuracy and resource limitations, we recommend using the IDW-RBFNN method (p = 2) with at least 60 samples as the minimum sampling density to ensure high interpolation accuracy under resource constraints. Our method overcomes limitations of existing approaches that use fixed steady-state distance decay parameters, providing an effective tool for soil fertility monitoring in delta regions.

Effect of Interpolation Artifacts on Perceived Stability of Nearby Sources in a Navigable Reverberant Virtual Environment

Convolution with spatial Room Impulse Responses can achieve realistic auralizations. When combined with interpolation between spatially distributed RIRs, this technique can be used to create navigable virtual environments. This study explores the impact of various interpolation parameters on the perceived auditory stability of a nearby static sound source with listener movements in a reverberant environment. The auditory scene was rendered via third-order Ambisonic RIR convolution combined with magnitude-least-squares binaural decoding using nonindividualized head-related transfer functions. First, the estimated direction of arrival as a function of the listener’s position within a 2D grid of RIRs under various configurations is examined as an objective metric. The perceived stability of the auditory source is then assessed through a perceptual experiment. Participants freely explored a virtual scene reproduced over headphones and a tracked head-mounted display. They were asked to rate the stability of a nonvisual source under various conditions of RIR grid density, interpolation panning method, and reverberation time. Results indicate no need to use an RIR grid size finer than 1m to optimize source stability when using a three-nearest-neighbor interpolation scheme.

A real-time dual NURBS interpolator with optimised control of flexible acceleration and deceleration for five-axis CNC machining

The limited computing capacity makes it difficult to plan a suitable feedrate profile in real-time for high speed and high accuracy machining of five-axis parametric toolpaths. In this paper, a real-time interpolation algorithm with optimised control of flexible acceleration and deceleration (acc-dec) for the dual NURBS toolpath is proposed. The toolpath is marked as subsegments with similar geometric properties by introducing the five-axis curvature. Machine kinematic and toolpath geometry constraints are considered in the kinematic parameter constraint model. Initial feedrate profiles are solved in a dynamic 3D window which preserves the motion performance of machine tools to a great extent. Convolution is used to smooth the initial feedrate profile to achieve a higher order continuity over the global range. Feedrate fluctuations caused by imprecise parameter interpolation are eliminated through modifying each interpolation periods. Resampling adjusts the position of interpolation points and unify the interpolation periods. All operations mentioned are in series and real-time is strictly guaranteed. Effectiveness of the developed algorithm is validated in simulations and also experimentally on a Self-developed-NC controlled 5-axis machine tool.

Extension of the GISSMO fracture model for thin-walled structures under combined tensile and bending loads

Ductile fracture prediction for thin-walled structures requires computationally efficient simulation tools able to approximately represent the key effects that occur on the sub-thickness scale. Unfortunately, classical shell elements, typically used to model deformation and failure of thin components, are inherently in a state of plane stress and therefore unable to capture the through-thickness stress distribution. This is consequential considering recent studies that demonstrated the differences between fracture in bending vs. in-plane tension. A laterally constrained thin metal plate under in-plane tension is likely to fracture under significantly lower plastic strain than the same plate under bending (with fracture initiating on the tensile side), even though both these conditions are examples of plane strain tension. Under in-plane tension fracture is preceded by a through-thickness neck, and therefore higher stress triaxiality than in the case of plane strain bending, where necking is absent. To account for these differences, we propose an extension of the GISSMO model, which relies on a simple fracture criterion based on stress-dependent fracture strain defined by the user (i.e. fracture locus). The fracture strain is typically determined experimentally using a combination of in-plane tensile tests under varying degree of lateral constraint and shear tests. The proposed extension involves defining a separate fracture locus for bending, also determined experimentally using bending tests. Fracture occurs when the equivalent plastic strain reaches its critical level represented by interpolation between the two bounding cases, i.e. bending and in-plane tension, with a bending index Ω used as an interpolation parameter.

Optimized Design of Direct Digital Frequency Synthesizer Based on Hermite Interpolation

To address the issue of suboptimal spectral purity in Direct Digital Frequency Synthesis (DDFS) within resource-constrained environments, this paper proposes an optimized DDFS technique based on cubic Hermite interpolation. Initially, a DDFS hardware architecture is implemented on a Field-Programmable Gate Array (FPGA); subsequently, essential interpolation parameters are extracted by combining the derivative relations of sine and cosine functions with a dual-port Read-Only Memory (ROM) structure using the cubic Hermite interpolation method to reconstruct high-fidelity target waveforms. This approach effectively mitigates spurious issues caused by amplitude quantization during the DDFS digitalization process while reducing data node storage units. Moreover, this paper introduces single-quadrant ROM compression technology to further diminish the required storage space. Experimental results indicate that, compared to traditional DDFS methods, the optimization scheme proposed in this work achieves a ROM resource compression ratio of 1792:1 and a 14-bit output Spurious-Free Dynamic Range (SFDR) of −88.134 dBc, effectively enhancing amplitude quantization precision and significantly lowering spurious levels. This significantly improves amplitude quantization precision and reduces spurious levels. The proposed scheme demonstrates notable advantages in both spectral performance and resource utilization efficiency, making it highly suitable for resource-constrained embedded systems and high-performance applications such as radar and communication systems.

Estimating vehicle sideslip angle through kinematic and dynamic contributions: Theory and experimental results

Vehicle lateral stability plays an important role within vehicle passenger safety. The study of lateral stability is typically related to investigating the dynamics of relevant vehicle states: among these, the vehicle sideslip angle ([Formula: see text]) emerges as a prominent candidate. Sideslip angle measurement is expensive and impractical, hence estimation techniques are often used, typically based on Kalman filters or neural networks, both with their issues. This work presents an alternative estimation method based on the idea of splitting sideslip angle into kinematic and dynamic contributions, and by observing that the kinematic contribution is straightforward to estimate. Therefore, efforts are devoted into estimating dynamic sideslip angle, which is herein obtained through a parametric interpolation harnessing lateral acceleration. Only data available from traditional vehicle onboard sensors are used in the process. Experimental results are presented along several manoeuvres on a full-scale vehicle, with the estimator running online within a dSPACE unit, ultimately supporting the efficacy and real-time feasibility of the proposed approach.

Modeling two-dimensional ice shape based on fractal interpolation

The ice accretion data obtained from ice wind tunnel tests reveal a multiscale structure and rough surface. In the follow-up aerodynamic evaluation of icing airfoils, simplified two-dimensional ice shapes are generally used as substitutes, but this simplification changes the aerodynamic effects of the original ice shape. Therefore, finding a simple and effective two-dimensional ice shape simulation method is urgent. Due to the self-similarity characteristics of ice shape surfaces, fractal interpolation is proposed for ice shape simulation. First, the geometric characteristics of the ice shapes are analyzed to determine interpolation points, and an iterative function system is constructed for interpolation simulation. Considering the influence of various characteristics of ice shapes on aerodynamics, interpolation parameters are limited to simulating more realistic ice shapes. High-order numerical simulation methods were utilized to numerically simulate and analyze the aerodynamic characteristics of icing airfoil while also verifying the feasibility of fractal interpolation for simulating ice shapes. The analysis revealed that this method could effectively simulate ice profiles of various feature scales with minimal ice shape data. These simulated shapes closely resemble real ice formations and maintain the original aerodynamic characteristics of the icing airfoil. This method can be used to improve the computational accuracy of ice accretion codes and provide improvement strategies for complex ice shape prediction; thus, this method has great application prospects in engineering.

Interpolation of local potential parameters in allocating village fund formulation as an effort to development of local-based tourism

Interpolation of local potential parameters in allocating village fund formulation as an effort to development of local-based tourism

Breaking the baryon-dark matter degeneracy in a model-independent way through the Sunyaev-Zeldovich effect

Context. In cosmological fits, it is common to fix the baryon density ωb via the cosmic microwave background. We here constrain ωb by means of a model-independent interpolation of the acoustic parameter from correlated baryonic acoustic oscillations. Aims. The proposed technique is used to alleviate the degeneracy between baryonic and dark matter abundances. Methods. We propose a model-independent Bézier parametric interpolation and applied it to intermediate-redshift data. We first interpolated the observational Hubble data to extract cosmic bounds over the (reduced) Hubble constant h0 and interpolated the angular diameter distances, D(z), of the galaxy clusters, inferred from the Sunyaev-Zeldovich effect, to constrain the spatial curvature, Ωk. Through the Hubble points and D(z) determined in this way, we interpolated uncorrelated data of baryonic acoustic oscillations bounding the baryon ωb and total matter ωm densities, reinforcing the constraints on h0 and Ωk with the same technique. Finally, to remove the matter sector degeneracy, we obtained ωb by interpolating the acoustic parameter from correlated baryonic acoustic oscillations. Results. Monte Carlo Markov chain simulations agree at 1σ confidence level with the flat ΛCDM model and are roughly suitable at 1σ with its nonflat extension, while the Hubble constant appears in tension up to the 2σ confidence levels. Conclusions. Our method excludes very small extensions of the standard cosmological model, and on the Hubble tension side, seems to match local constraints slightly.

Enhancing Damage Detection in 2D Concrete Plates: A Comprehensive Study on Interpolation Methods and Parameters

In an era marked by increasing demands for stability and durability in construction, the importance of damage detection in concrete structures cannot be overstated. As these structures underpin the safety and longevity of vital assets, this paper embarks on a comprehensive exploration of methodologies to enhance precision and reliability in 2D concrete plate damage detection. By focusing on the interpolation of damage index values and leveraging the insights gained from energy loss analysis and the characterization of the time of arrival of signals, we address the pressing need for improved non-destructive damage detection techniques. Our study encompasses a range of simulation attempts, each involving various interpolation parameters, and systematically evaluates their performance. The culmination of this research identifies the most effective combination of techniques and parameters, leading to the best results in damage detection. This multidimensional investigation promises to provide valuable contributions to the field of structural health monitoring, benefiting both researchers and practitioners engaged in the evaluation of concrete structures.

EVALUATION OF DIFFERENT INTERPOLATION METHODS VIA ArcGIS, APPLIED TO SATELLITE DATA OF SEA SURFACE TEMPERATURE SST, CASE OF THE ALBORAN SEA

In various fields such as Oceanography, interpolation methods are pivotal in generating continuous surface data from discrete point data. This research endeavors to conduct a comprehensive comparison and evaluation of deterministic interpolation techniques, including Radial Basis Function (RBF), Inverse Distance Weighting (IDW), and geostatistical methods like Kriging Universal (KU) and Kriging Ordinary (KO), in the context of mapping sea surface temperature (SST) within the Alboran Sea. Among these methods, the KO interpolation method emerges as particularly promising, boasting a Root Mean Square Error (RMSE) of 0.035 and an impressive coefficient of determination (R²) approaching unity (0.999). Furthermore, the cross-validation results reveal that the KO method not only provides the most accurate estimates but exhibits minimal bias, as evidenced by a mean error close to zero. These findings not only contribute to the field of SST mapping but also have broader implications for the interpolation of other climate parameters.

Research on NURBS Curve Interpolation Algorithm Based on Mline-Gear

Aiming at the problem of speed fluctuation caused by the large error between the ideal interpolation step and the actual interpolation step in the traditional non-uniform rational B-spline ( NURBS ) curve interpolation, a NURBS curve interpolation algorithm based on Mline-Gear is proposed. The differential and derivative definitions are derived to transform the Mline and Gear formulas respectively, and the prediction and correction formulas of the interpolation parameters are obtained. Then, it is judged whether the interpolation parameter values obtained by the correction formula meet the speed fluctuation rate requirements, and the interpolation can be continued. Otherwise, the Steffensen descent formula is used to iteratively correct the interpolation parameter values. In order to ensure the calculation accuracy and avoid solving high-order derivatives, the fourth-order Runge-Kutta method is used to solve the initial two interpolation parameters. Finally, the algorithm is simulated. The simulation results show that the algorithm reduces the feed speed fluctuation rate while ensuring a small number of iterations.

Improving the Near-Surface Wind and Turbulence at the Edge of the Orographic Drag Gray Zone by Tuning the Roughness Length

Abstract In this paper, we present the implementation and evaluate the impact of the new roughness length configuration in the ALARO canonical model configuration of the ALADIN system at the edge of the orographic gravity wave drag gray zone. As an essential input for turbulence parameterization, the roughness length affects the near-surface turbulent fluxes and the screen-level interpolation of meteorological parameters. We utilize GMTED2010 and ECOCLIMAP-II databases to derive orographic and vegetation components of the effective roughness length and introduce tuning parameters enabling us to optimize predicted near-surface turbulent momentum fluxes and 10-m wind speed. Based on sensitivity tests, we (i) prove the necessity of tuning the roughness length fields, (ii) considerably reduce the RMSE of near-surface turbulent momentum fluxes (6%–7%) and 10-m wind speed for different groups of stations (3%–10%), and (iii) identify the tree height as the most influential input parameter in our computational domain. The RMSE decomposition indicates that the improvement of 10-m wind speed mostly comes from a decrease in the random error and bias of the mean. The variability is slightly underestimated, thus reducing the model accuracy for wind speeds above the 95th percentile but at an acceptable level. We explain that roughness length tuning also compensates for the missing roughness sublayer correction in our system. Finally, we show that, although the impact of the orographic gravity wave drag scheme at a horizontal mesh size of 1.8 km is generally small, it is still beneficial for capturing some finer features observed in atmospheric soundings. Significance Statement Aiming to improve the 10-m wind speed forecast without sacrificing the accuracy of turbulent momentum fluxes in the kilometric resolution numerical weather prediction model, we derived new roughness length fields from high-resolution physiography databases. Therein, we proved the importance of tuning the input orography and vegetation fields and, depending on the time of day and year, reduced the root-mean-square error of 10-m wind speed by 3%–10%. Further, we demonstrated that orographic gravity wave drag parameterization is still needed to predict finer details seen in wind profiles from atmospheric soundings. Finally, we discussed the related simplifications in our model and their implications and proposed steps toward a more consistent and complete treatment of the near-surface turbulence.

Data-driven nonlinear parametric model order reduction framework using deep hierarchical variational autoencoder

A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, a least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing nonlinear MOR for the parametric interpolation of a nonlinear dynamic system with a significant number of degrees of freedom. LSH-VAE differs from existing networks in two major respects: a deep hierarchical structure and a hybrid weighted, probabilistic loss function. The enhancements result in significantly improved accuracy and stability compared with conventional nonlinear MOR methods, autoencoders, and variational autoencoders. In LSH-VAE, the parametric MOR framework is based on the spherically linear interpolation of the latent manifold. The present framework is validated and evaluated on three nonlinear and multiphysics dynamic systems. First, the present framework is evaluated on the fluid–structure interaction benchmark problem to assess its efficiency and accuracy. Then, a highly nonlinear aeroelastic phenomenon, limit cycle oscillation, is analyzed. Finally, the framework is applied to three-dimensional fluid flow to demonstrate its capability to efficiently analyze a significantly large number of degrees of freedom. The superior performance of LSH-VAE is emphasized by comparing its results against those of widely used nonlinear MOR methods, a convolutional autoencoder, and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-VAE. The proposed framework exhibits significantly enhanced accuracy compared with that of conventional methods, while the computational efficiency continues to remain significantly higher.

Accurate Interpolation of Library Timing Parameters Through Recurrent Convolutional Neural Network

Accurate Interpolation of Library Timing Parameters Through Recurrent Convolutional Neural Network

Grid-Based Channel Modeling Technique for Scenario-Specific Wireless Channel Emulator Based on Path Parameters Interpolation

Grid-Based Channel Modeling Technique for Scenario-Specific Wireless Channel Emulator Based on Path Parameters Interpolation

Parametric Interpolation Model Order Reduction on Grassmann Manifolds by Parallelization

Parametric Interpolation Model Order Reduction on Grassmann Manifolds by Parallelization

A High-Precision Planar NURBS Interpolation System Based on Segmentation Method for Industrial Robot

NURBS curve parameter interpolation is extensively employed in precision trajectory tasks for industrial robots due to its smoother performance compared to traditional linear or circular interpolation methods. The trajectory planning systems for industrial robots necessitate four essential functional modules: first, the spline curve discretization technique ensuring chord error compliance; second, the contour scanning technique for determining the maximum feasible feed rate for multi-constraint and multi-segment paths; third, the technique for achieving a smooth feed rate profile; and fourth, the continuous curve parameter interpolation technique. Therefore, this paper proposes a high-precision planar NURBS interpolation system for industrial robots. Firstly, a segmentation method for NURBS curves based on a closed-loop chord error constraint is proposed, which segments the original global NURBS curve into a collection of Bezier curves that strictly meet the chord error constraint. Secondly, a bidirectional scanning technique is presented to meet the joint space constraint, establishing an analytical mapping between the tool tip kinematic constraint and the joint kinematic constraint. Then, based on the traditional S-shaped feed rate profile, an adaptive algorithm with a displacement constraint is introduced, considering the real-time speed adjustment requirements of robots. Finally, a compensation interpolation strategy based on arc length parameterization is adopted to solve the accumulated error problem in parameter interpolation. The effectiveness of and potential for enhancing the quality of planar machining of the proposed planar NURBS interpolation system for industrial robots are validated through simulations and experiments. The results demonstrate the system’s applicability and accuracy, and its ability to improve planar machining quality.

Performance versus resilience in modern quark-gluon tagging

Discriminating quark-like from gluon-like jets is, in many ways, a key challenge for many LHC analyses. First, we use a known difference in PYTHIA and HERWIG simulations to show how decorrelated taggers would break down when the most distinctive feature is aligned with theory uncertainties. We propose conditional training on interpolated samples, combined with a controlled Bayesian network, as a more resilient framework. The interpolation parameter can be used to optimize the training evaluated on a calibration dataset, and to test the stability of this optimization. The interpolated training might also be useful to track generalization errors when training networks on simulations.

Accurate prediction of five-axis machining cycle times with deep neural networks using Bi-LSTM

This paper presents a novel machine learning (ML) based approach to predict machining cycle (part program running) times for complex 5-axis machining. Typical 5-axis machining toolpaths consist of short-segmented discrete linear cutter location lines (CL-lines) with simultaneously varying tool center point (TCP) and orientation vectors (ORI). As the 5-axis machine tool NC (numerical control) system tries to interpolate such part programs smoothly, the TCP motion decelerates and accelerates repeatedly causing the actual feedrate to fluctuate. The actual observed (resultant) feedrate can be approximately 30 % lower than the user commanded one. Furthermore, if the toolpath requires the 5-axis machine tool to travel closer to its singular point, or if the workpiece placement on the table is not optimal, actual feedrate is even lowered further. This paper presents two ML-based approaches to accurately predict 5-axis machining toolpaths. The first strategy uses a bidirectional long short-term memory (Bi-LSTM) network to model the machine tool behavior and generates a direct final cycle time estimation for any given part program. This approach only uses the toolpath geometry to predict the cycle time, and for training it only needs the “final” cycle times of similar part programs making it practical on today’s shop floors. The second strategy requires individual CL-line processing times for training. In return, it can provide highly accurate cycle time predictions. Both strategies can capture the interpolation dynamics of 5-axis machine tool NC systems accurately. Simulation studies and experimental validations are conducted on modern 5-axis machine tools with varying workpiece placements and interpolation parameters. Proposed approaches have shown to predict cycle times with 90–95 % accuracy on real-life complex 5-axis machining toolpaths.