Basis Function Approach Research Articles

Minimum spouting velocity of fine particles in fountain confined conical spouted beds using machine learning and least square fitting approaches

AbstractThe present study concerns the development of new models to estimate the minimum spouting velocity (Ums) in various configurations of fountain‐confined conical spouted beds (FC‐CSBs) with fine particles. Existing literature correlations were found to be inaccurate for FC‐CSBs. Therefore, smart modelling techniques were employed to design more accurate predictive tools. The radial basis function (RBF) approach provided the best predictions for systems without draft tubes as well as those with open‐sided draft tubes. Additionally, the Gaussian process regression (GPR) approach yielded the best predictions for systems with nonporous draft tubes. The mean absolute percentage error (MAPE) values for the testing phase were 5.80%, 5.67%, and 5.59%, respectively. These models consider how bed shape and particle properties affect Ums. The sensitivity analysis was conducted to determine the factors with more importance in controlling Ums. Finally, simpler correlations were derived for Ums prediction in different FC‐CSB configurations, with accuracy around 12% error.

Predicting responses to climate change using a joint species, spatially dependent physiologically guided abundance model.

Predicting the effects of warming temperatures on the abundance and distribution of organisms under future climate scenarios often requires extrapolating species-environment correlations to climatic conditions not currently experienced by a species, which can result in unrealistic predictions. For poikilotherms, incorporating species' thermal physiology to inform extrapolations under novel thermal conditions can result in more realistic predictions. Furthermore, models that incorporate species and spatial dependencies may improve predictions by capturing correlations present in ecological data that are not accounted for by predictor variables. Here, we present a joint species, spatially dependent physiologically guided abundance (jsPGA) model for predicting multispecies responses to climate warming. The jsPGA model uses a basis function approach to capture both species and spatial dependencies. We apply the jsPGA model to predict the response of eight fish species to projected climate warming in thousands of lakes in Minnesota, USA. By the end of the century, the cold-adapted species was predicted to have high probabilities of extirpation across its current range-with 10% of lakes currently inhabited by this species having an extirpation probability >0.90. The remaining species had varying levels of predicted changes in abundance, reflecting differences in their thermal physiology. Though the model did not identify many strong species dependencies, the variation in estimated spatial dependence across species suggested that accounting for both dependencies was important for predicting the abundance of these fishes. The jsPGA model provides a new tool for predicting changes in the abundance, distribution, and extirpation probability of poikilotherms under novel thermal conditions.

A reduced order model formulation for left atrium flow: an atrial fibrillation case

A data-driven reduced order model (ROM) based on a proper orthogonal decomposition-radial basis function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of atrial fibrillation (AF). The full order model (FOM) is represented by incompressible Navier–Stokes equations, discretized with a finite volume (FV) approach. Both the Newtonian and the Casson’s constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up.

Influences of radial basis function approach on flexural analysis of laminated plate embedded on elastic medium foundation subjected to transverse load used in industries

Influences of radial basis function approach on flexural analysis of laminated plate embedded on elastic medium foundation subjected to transverse load used in industries

Enhancing Student Performance Prediction Using a Combined SVM-Radial Basis Function Approach

This research aims to improve student performance predictions using a combined SVM (Support Vector Machine) and radial basis function (RBF) approach. The developed model utilizes a combination of the strengths of SVM in handling class separation and the ability of RBF to capture complex patterns in data. Student assessment data, including math, reading, and writing scores, is used as a feature to predict student performance on tests. Preprocessing steps, including feature normalization and label encoding, are applied to prepare the data for model training. Next, the SVM model with the RBF kernel is initialized and optimized using GridSearchCV to find the best parameters. Model evaluation was carried out using the R2 metric to evaluate how well the model predicts student performance. Experimental results show that the combined SVM-RBF approach can improve student performance predictions with fairly accurate prediction results of 88%. The practical implication of this research is the development of a more accurate model for predicting student performance, which can be used as a tool to improve educational interventions and decision-making in educational institutions.

Fourier-Hankel-Abel Nyquist-limited tomography: A spherical harmonic basis function approach to tomographic velocity-map image reconstruction.

A new method for the fully generalized reconstruction of three-dimensional (3D) photoproduct distributions from velocity-map imaging (VMI) projection data is presented. This approach, dubbed Fourier-Hankel-Abel Nyquist-limited TOMography (FHANTOM), builds on recent previous work in tomographic image reconstruction [C. Sparling and D. Townsend, J. Chem. Phys. 157, 114201 (2022)] and takes advantage of the fact that the distributions produced in typical VMI experiments can be simply described as a sum over a small number of spherical harmonic functions. Knowing the solution is constrained in this way dramatically simplifies the reconstruction process and leads to a considerable reduction in the number of projections required for robust tomographic analysis. Our new method significantly extends basis set expansion approaches previously developed for the reconstruction of photoproduct distributions possessing an axis of cylindrical symmetry. FHANTOM, however, can be applied generally to any distribution-cylindrically symmetric or otherwise-that can be suitably described by an expansion in spherical harmonics. Using both simulated and real experimental data, this new approach is tested and benchmarked against other tomographic reconstruction strategies. In particular, the reconstruction of photoelectron angular distributions recorded in a strong-field ionization regime-marked by their extensive expansion in terms of spherical harmonics-serves as a key test of the FHANTOM methodology. With the increasing use of exotic optical polarization geometries in photoionization experiments, it is anticipated that FHANTOM and related reconstruction techniques will provide an easily accessible and relatively low-cost alternative to more advanced 3D-VMI spectrometers.

A data-adaptive network design for the regional gravity field modelling using spherical radial basis functions

A high-precision regional gravity field model is significant in various geodesy applications. In the field of modelling regional gravity fields, the spherical radial basis functions (SRBFs) approach has recently gained widespread attention, while the modelling precision is primarily influenced by the base function network. In this study, we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm, and the performance of the algorithm is verified by the observed gravity data in the Auvergne area. Furthermore, the turning point method is used to optimize the bandwidth of the basis function spectrum, which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously. Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model. Compared to the existing methods, the number of SRBFs used for modelling has been reduced by 15.8%, and the time cost to determine the centre positions of SRBFs has been saved by 12.5%. Hence, the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.

Comparison of two different integration methods for the (1+1)-dimensional Schrödinger-Poisson equation

We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schrödinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schrödinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling, e.g., non-relativistic gravity. For reasons of complexity, we treat a one-dimensional version of the problem whose numerical integration is still challenging because of the extreme long-range forces (being constant in the asymptotic limit). Both of our methods, a Strang splitting scheme and a basis function approach using B-splines, are compared in numerical convergence and effectivity. Overall, our Strang-splitting evolution compares favourably with the B-spline method. In particular, by using an adaptive time-stepper rather large one-dimensional boxes can be treated. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing, for instance, dark matter formation over cosmologically relevant scales.

Adaptive Basis Function Method for the Detection of an Undersurface Magnetic Anomaly Target

The orthogonal basis functions (OBFs) method is a prevailing choice for the detection of undersurface magnetic anomaly targets. However, it requires the detecting platform or target to move uniformly along a straight path. To circumvent the restrictions, a new adaptive basis functions (ABFs) approach is proposed in this article. It permits the detection platform to search for a possible target at different speeds along any course. The ABFs are constructed using the real-time data of the onboard triaxial fluxgate, GPS module, and attitude gyro. Based on the pseudo-energy of an apparent target signal, the constant false alarm rate (CFAR) method is employed to judge whether a target is present. Moreover, by defining the pixel as a relative possibility for a target at a geographic location, a magnetic anomaly target imaging scheme is introduced by displaying the pixels onto the searching area. On-site experimental data are utilized to demonstrate the proposed approach. Compared with the traditional OBFs method, the present ABFs approach can substantially improve the detection possibility and reduce false alarms.

Solving two-dimensional adjoint QCD with a basis-function approach

We apply a method (“eLCQ”) to find the asymptotic spectrum of a Hamiltonian from its symmetries to two-dimensional adjoint QCD. Streamlining the approach, we construct a complete set of asymptotic eigenfunctions in all parton sectors and use it in a basis-function approach to find the spectrum of the full theory. We are able to reproduce previous results including the degeneracy of fermionic and bosonic masses at the supersymmetric point, and to understand the properties of the lowest states in the massless theory. The approach taken here is continuous at fixed parton number, and therefore complementary to standard formulations, e.g. discretized light-cone quantization (DLCQ). Despite its limitation to rather small parton numbers, it can be used to test and validate conclusions of other frameworks in an independent way. Published by the American Physical Society 2024

Bayesian Spatial Models for Projecting Corn Yields

Climate change is predicted to impact corn yields. Previous studies analyzing these impacts differ in data and modeling approaches and, consequently, corn yield projections. We analyze the impacts of climate change on corn yields using two statistical models with different approaches for dealing with county-level effects. The first model, which is novel to modeling corn yields, uses a computationally efficient spatial basis function approach. We use a Bayesian framework to incorporate both parametric and climate model structural uncertainty. We find that the statistical models have similar predictive abilities, but the spatial basis function model is faster and hence potentially a useful tool for crop yield projections. We also explore how different gridded temperature datasets affect the statistical model fit and performance. Compared to the dataset with only weather station data, we find that the dataset composed of satellite and weather station data results in a model with a magnified relationship between temperature and corn yields. For all statistical models, we observe a relationship between temperature and corn yields that is broadly similar to previous studies. We use downscaled and bias-corrected CMIP5 climate model projections to obtain detrended corn yield projections for 2020–2049 and 2069–2098. In both periods, we project a decrease in the mean corn yield production, reinforcing the findings of other studies. However, the magnitude of the decrease and the associated uncertainties we obtain differ from previous studies.

Modeling Strategies Based on Multiple Neural Network Systems Applied for a Monopolar and Bipolar Electrocoagulation

The objective of this research was to evaluate the efficiency of an electrocoagulation system using iron and aluminum electrodes, arranged in both monopolar and bipolar arrangements, for the removal of acid red 18 dye. Experimental and modeling approaches were employed to investigate the system’s performance. The effects of operating parameters: including initial pH (3–9), current density (0.4–5.6 mA cm−2), charge passed (2.16–21.6 C cm−2), and initial dye concentration (50–300 mg l−1) were studied. The results demonstrated that an increase in electric current intensity and passed charge enhanced the removal of COD and dye. However, to minimize energy consumption, these parameters were optimized for different dye concentrations. The monopolar arrangement exhibited favorable performance for the both electrodes, primarily due to reduced ohmic drop effect, although the iron electrode generated sludge with better settling characteristics. The monopolar iron electrode consumed the least energy (38.3 kWh kg−1 COD). Experimental evaluation was conducted to assess the influence of key electrolysis process parameters on dye and COD removal. Additionally, neural network models, employing radial basis function and multilayer perceptron approaches, were utilized to predict system outputs based on initial characteristics (COD and dye) and operation conditions. The neural network models provided accurate predictions, offering practical insights for experimental applications.

Basis Function Approaches for Numerical Solutions of Nonlinear Partial Differential Equations

Basis Function Approaches for Numerical Solutions of Nonlinear Partial Differential Equations

Comparing data driven soft independent class analogy (DD-SIMCA) and one class partial least square (OC-PLS) to authenticate sacha inchi (Plukenetia volubilis L.) oil using portable NIR spectrometer

Sacha Inchi (SI) oil is valuable due to high content of omega-3 and omega-6, which are important in human diet, thus being susceptible to adulteration. In this work, a low-cost and portable Near Infrared (NIR) spectrometer was used to authenticate pure sacha inchi oil from adulterated one with cheaper oils. Principal component analysis (PCA) was applied as screening technique and showed a good class separation between pure SI oil and blends, with significant impact of unsaturated fatty acids present in SI oil. Data Driven Soft Independent Class Analogy (DD-SIMCA) provided better results when compared to One Class Partial Least Square (OC-PLS) for data analysis. DD-SIMCA was implemented in rigorous approach, and it reached Sensitivity (SEN) = 89.8 % and Specificity (SPE) = 93 % using α = 0.05 and 4 PCs, while ordinary OC-PLS required 10 LVs to reach SEN = 87.8 % and SPE = 84.3 %, performing better than Gaussian radial basis function (GRBF-OCPLS) and partial robust M-regression (PRM) approaches. Results indicate that low-cost NIR spectrometer coupled to one-class classifiers could be used to authenticate pure SI oil.

Study on the Optimal Design of a Shark-like Shape AUV Based on the CFD Method

In previous AUV designs, the thrusters were often placed outside the vehicle, resulting in their performance being significantly influenced by the shape of the vehicle. Additionally, this placement also leads to the generation of strong radiated noise that propagates in all directions, making noise reduction challenging. Taking inspiration from the shape of sharks, this paper proposes a slender, shark-inspired AUV. The model features a continuous passageway in the middle where a pump-jet thruster is installed to provide propulsion. The walls of the passageway are then covered with sound-absorbing materials to reduce radiated noise. To address the problem of low design efficiency caused by multiple design parameters, a multi-objective optimization method is proposed to optimize the shape of the AUV. The performance targets of speed, displacement, and energy consumption are determined as objective functions, and a multi-island genetic algorithm is used as the optimization algorithm to build the multi-objective optimization process. An automated optimization platform was then developed which integrates parametric modeling, mesh partitioning, the CFD calculation, and the optimized design. To enhance the efficiency of optimization, a surrogate model was developed to approximate the CFD calculation. Using the optimal Latin hypercube method, experimental factors were designed, and a surrogate model was constructed based on the radial basis function approach. Following optimization, the resistance was reduced by 9.1%, while the displacement volume was increased by 10.7% and energy consumption was decreased by 6.3%. By analyzing the velocity and entropy production distribution of the AUV, the effectiveness of the optimization method was verified.

A Physics-Guided Data-Driven Feedforward Tracking Controller for Systems With Unmodeled Dynamics—Applied to 3D Printing

A hybrid (i.e., physics-guided data-driven) feedforward tracking controller is proposed for systems with unmodeled linear or nonlinear dynamics. The proposed controller is based on the filtered basis functions (FBF) approach, and hence called a hybrid FBF controller. It formulates the feedforward control input to a system as a linear combination of a set of basis functions whose coefficients are selected to minimize tracking errors. To predict the system response and thereby the tracking errors, the basis functions are filtered using a combination of two linear models. The first model is physics-based and remains unaltered during the execution of the controller, while the second is data-driven and is continuously updated during the execution of the controller. To ensure its practicality and safe learning, the proposed hybrid FBF controller is equipped with the abilities to handle delays in data acquisition and to detect impending instability due to its inherent data-driven feedback loop. The effectiveness of the hybrid FBF controller is demonstrated via application to vibration compensation of a 3D printer with unmodeled linear and nonlinear dynamics. Thanks to the proposed hybrid FBF controller, the tracking accuracy of the 3D printer and the print quality are both significantly improved in experiments involving high-speed printing, compared to standard FBF controller that does not incorporate a data-driven model. Furthermore, the ability of the hybrid FBF controller to detect, and hence to potentially avoid, impending instability is demonstrated offline using data collected online from experiments.

Task flexible and high performance ILC: Preliminary analysis of combining a basis function and frequency-domain approach

As the demand for faster and more precise control has exponentially increased, the quality of feedforward (FF) control has become increasingly important. In this sense, iterative learning control (ILC) enables significant performance enhancements by learning the FF signal from previously repeated tasks. This study aims to develop a new framework that potentially creates a breakthrough in the current trade-off between the high performance and task flexibility of ILC. By combining a high-performance but non-flexible frequency-domain ILC (F-ILC) and a task-flexible and good (but not great) performance basis function ILC (B-ILC), both a task-flexible and high-performance ILC (C-ILC) is achieved. The proposed C-ILC framework was validated through a second-order system simulation, showing a task flexibility as high as that of B-ILC and a higher tracking performance then that of the current F-ILC framework.

Application of the radial basis function in solving an operational risk management model: investigating the probability of bank survival with risk reserves

Operational risk is one of the influential risks identified by banking practitioners, and as the international banking supervisor, the Basel Committee on Banking Supervision has paid special attention to it. There are various methods for measuring and managing this type of banking risk (eg, the advanced measurement approach). Using the radial basis function approach, we compute the probability of bank survival using a partial Volterra integrodifferential equation. Given the importance of operational risk in financial institutions, especially banks, we examine a mathematical model of this risk and solve it using numerical methods. Also, by considering the impact of the bank’s probability of survival on the amount of risk reserves, we investigate the effect of fluctuation in risk reserves on the probability of survival of an organization. To complete the investigation, we calculated the amount of risk storage required to achieve the desired probability of survival.

A Framework for Optimal Sensor Placement to Support Structural Health Monitoring

Offshore or drydock inspection performed by trained surveyors is required within the integrity management of an in-service marine structure to ensure safety and fitness for purpose. However, these physical inspection activities can lead to a considerable increase in lifecycle cost and significant downtime, and they can impose hazards for the surveyors. To this end, the use of a structural health monitoring (SHM) system could be an effective resolution. One of the key performance indicators of an SHM system is its ability to predict the structural response of unmonitored locations by using monitored data, i.e., an inverse prediction problem. This is highly relevant in practical engineering, since monitoring can only be performed at limited and discrete locations, and it is likely that structurally critical areas are inaccessible for the installation of sensors. An accurate inverse prediction can be achieved, ideally, via a dense sensor network such that more data can be provided. However, this is usually economically unfeasible due to budget limits. Hence, to improve the monitoring performance of an SHM system, an optimal sensor placement should be developed. This paper introduces a framework for optimising the sensor placement scheme to support SHM. The framework is demonstrated with an illustrative example to optimise the sensor placement of a cantilever steel plate. The inverse prediction problem is addressed by using a radial basis function approach, and the optimisation is carried out by means of an evolutionary algorithm. The results obtained from the demonstration support the proposal.

Sub Coulomb barrier d+ 208Pb scattering in the time-dependent basis function approach

We employ the non-perturbative time-dependent basis function (tBF) approach to study the scattering of the deuteron on 208Pb below the Coulomb barrier. We obtain the bound and discretized scattering states of the projectile, which form the basis representation of the tBF approach, by diagonalizing a realistic Hamiltonian in a large harmonic oscillator basis. We find that the higher-order inelastic scattering effects are noticeable for sub barrier scatterings with the tBF method. We have successfully reproduced experimental sub Coulomb barrier elastic cross section ratios with the tBF approach by considering only the electric dipole (E1) component of the Coulomb interaction between the projectile and the target during scatterings. We find that the correction of the polarization potential to the Rutherford trajectory is dominant in reproducing the data at very low bombarding energies, whereas the role of internal transitions of the deuteron projectile induced by the E1 interaction during the scattering becomes increasingly significant at higher bombarding energies.