Sequential Radial Basis Function Using Support Vector Machine for Expensive Design Optimization

Satellite constellation system design is a challenging and complicated multidisciplinary design optimization (MDO) problem involving a number of computation-intensive multidisciplinary analysis models. In this paper, the MDO problem of a constellation system consisting of small observation satellites is investigated to simultaneously achieve the preliminary design of constellation configuration and the satellite subsystems. The constellation is established based on Walker-? configuration considering the coverage performance. Coupled with the constellation configuration, several disciplines including payload, power, thermal control, and structure are taken into account for satellite subsystems design subject to various constraints (i.e., ground resolution, power usage, natural frequencies, etc.). Considering the mixed-integer and time-consuming behavior of satellite constellation system MDO problem, a novel sequential radial basis function (RBF) method using the support vector machine (SVM) for discrete-continuous mixed variables notated as SRBF-SVM-DC is proposed. In this method, a discrete-continuous variable sampling method is utilized to handle the discrete variables, i.e., the number of orbit planes and number of satellites, in the satellite constellation system MDO problem. RBF surrogates are constructed and gradually refined to represent the time-consuming simulations during optimization, which can efficiently lead the search to the optimum. Finally, the proposed SRBF-SVM-DC utilized to solve the satellite constellation system MDO problem is compared with a conventional integer coding based genetic algorithm (ICGA). The results show that SRBF-SVM-DC significantly decreases the system mass by about 28.63% subject to all the constraints, which greatly reduces the cost of the satellite constellation system. Moreover, the computational budget of SRBF-SVM-DC is saved by over 85% compared with ICGA, which demonstrates the effectiveness and practicality of the proposed surrogate assisted optimization approach for satellite constellation system design.

Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval

In the framework of nondestructive eddy-current testing, an inversion method is proposed. It relies on a metamodel-based optimization method: a fast optimization by means of a particle swarm algorithm is performed wherein the exact forward computations are replaced by an appropriate metamodel. The latter is obtained by radial basis function interpolation over a database previously generated by sequential design. Both synthetically generated and laboratory-controlled experimental data are used to illustrate its performances. Comparisons to inversions by support vector machines, now common for defect characterization, are carried out. The proposed method appears to be an useful tool for decision analysis, highlighting the likeliest results.

Supervised learning approaches are widely used for driving style classification; however, they often require a large amount of labeled training data, which is usually scarce in a real-world setting. Moreover, it is time-consuming to manually label huge amounts of driving data due to uncertainties of driver behavior and variances among the data analysts. To address this problem, a semisupervised approach, a semisupervised support vector machine (S3VM), is employed to classify drivers into aggressive and normal styles based on a few labeled data points. First, a few data clusters are selected and manually labeled using a $ k$ -means clustering method. Then, a specific differentiable surrogate of a loss function is developed, which makes it feasible to use standard optimization tools to solve the nonconvex optimization problem. One of the most popular quasi-Newton algorithms is then used to assign the optimal label to all of the training data. Finally, we compare the S3VM method with a support vector machine method for classifying driving styles from different amounts of labeled data. Experiments show that the S3VM method can improve the classification accuracy by about 10% and reduce the labeling effort by using only a few labeled data clusters among huge amounts of unlabeled data.

The data interpolation is an essential part of Bidimensional Empirical Mode Decomposition (BEMD) of an image. In the decomposition process, local maxima and minima of the image are extracted at each iteration and then interpolated to form the upper and lower envelopes, respectively. Because of the properties of radial basis function (RBF) interpolators, they are good candidates for use in BEMD. However, only one or two of the RBF interpolators have been utilized for BEMD so far. This paper employs many RBF interpolators for BEMD, compares their performances, and finds out the useful ones for BEMD especially in the image filtering application. We propose to apply the BEMD approach with the adequate interpolation function in the image denoising domain. After that, we combine the BEMD with the DWT to improve the BEMD denoising method. The analysis is done using real images. Simulations are made to focus mainly on the effect of interpolation methods by providing less or negligible control on the other parameters of the BEMD process. The study is believed to work as a guideline in the area of BEMD based real image in the filtering application.

Optical image provides a unique spectral and textural opportunity to acquire data free of charge in cloud-free weather conditions. However, textural information from recent Sentinel-2A data has not been sufficiently recognized. Several researches have shown that texture features are essential for extracting crop information. This study presents a new scheme that integrates spectral bands and textural features for mapping maize fields and other land cover types (i.e., build-up, trees, others, and water) and evaluates the effectiveness of random forest (RF) and support vector machine (SVM) classifiers with different kernel functions based on Sentinel 2A (S-2A) data. The textural features were derived from multiple bands of S-2A image using a grey-level co-occurrence matrix (GLCM) algorithm. To normalize the analysis of these features, Random Forest feature selection was employed. The outcomes show that S-2A images are appropriate for mapping maize fields and other land covers when the image is accessible during the growing season. The SVM classifier with a radial basis function (RBF) kernel is superior to a polynomial (P), linear (L), and sigmoid (S) kernel functions, and the RF classifiers. For the SVM_RBF, the highest overall accuracy was obtained from the integration of spectral bands and textural features at scenario 2 SVM_RBF (87.40%), followed by the combination of spectral and textural features at scenario 2 SVM_P kernel (86.56%). However, scenario 5 SVM_P kernel (85.54%), scenario 4 SVM_P kernel function (85.30%), the spectral features alone, and the SVM_P kernel function, have the highest O/A (83.90%) than that of the SVM_RBF (83.66%). The inclusion of textural features contributed significantly in mapping the smallholder’s maize field in the study area. This demonstrated the value of S-2A in agricultural research.

Preserving details while restoring images highly corrupted by impulsive salt and pepper noise remains a challenging problem. The authors proposed an algorithm based on radial basis functions (RBFs) interpolation which estimates the intensities of corrupted pixels by their neighbours. In this algorithm, intensity values of noisy pixels in the corrupted image are first estimated using RBFs. Next, the image is smoothed. The proposed algorithm can effectively remove the highly dense, impulsive salt and pepper noise. Experimental results show the superiority of the proposed algorithm both in noise suppression and details preservation in comparison to the recent similar methods. Extensive simulations show better results measured by peak signal-to-noise ratio and structural similarity index, especially when the image is corrupted by very highly dense impulse noise.

The design optimization of acoustic metamaterials represents a critical challenge in modern noise control applications. Global sensitivity analysis (GSA) has emerged as a powerful tool for quantifying the correlation between metamaterials' design variables and corresponding sound quality metrics (loudness, sharpness, and speech intelligibility index). However, GSA's high computational intensity limits the practical application of design optimization, especially for sound quality metrics which vary with sound stimulus. This study introduces a computational framework using radial basis function (RBF) interpolation to accelerate the GSA of acoustic metamaterials, with a periodic arrangement of micro-perforated panels (MPPs) serving as an exemplary case study. The methodology employs RBF interpolation to create a surrogate model of metamaterial acoustic response, demonstrating the potential for computational cost reduction while maintaining accuracy. It is validated across three acoustic scenarios that represent common challenges in noise control: stationary signals (broad/narrowband noise), environmental sounds (mechanical noise, traffic), and dynamic signals (speech, music). The study systematically compares sensitivity indices derived from direct numerical simulation and interpolated predictions, assessing the RBF's impact on GSA accuracy. [The European Commission is gratefully acknowledged for supporting the Marie Sklodowska Curie program through the Horizon Europe DN METAVISION project (GA 101072415)]

A 2‐D divergence‐free interpolator is presented which is demonstrated to give more realistic values between sparse velocity data than interpolating velocity components independently. The interpolator enforces physical dependence between the velocity components by ensuring mass is conserved. Tests using data for a synthetic eddy show that independent interpolation of components can give unrealistic velocities between widely spaced data. However, divergence‐free interpolation can reproduce the eddy almost as well with sparse data as with dense data. In the synthetic tests the divergence‐free radial basis function (RBF) interpolator performed as well as, or better than, optimal interpolation. A significant advantage of the “greedy fit” RBF interpolator implemented here is the small number of coefficients required to describe the interpolating surface. For large data sets this gives the interpolator a significant computational advantage over techniques, like Optimal Interpolation, which require one coefficient per data point. The RBF's economy of parameters and imposing physics with the divergence‐free constraint makes RBF interpolation of sparse data much more resistant to following the noise. The 2‐D divergence‐free interpolator can be used to interpolate geostrophic velocities or the horizontal transport of high‐frequency flows such as tidal currents. Tests with data from the local dynamics experiment moorings and from moving vessel acoustic Doppler current profiler measurements of tidal flow show the divergence‐free interpolator is better able to reproduce data left out of the interpolation than interpolating velocity components independently.

Radial basis function based mesh deformation applied to simulation of flow around flapping wings

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

Background: Implicit surface is a kind of surface modeling tool, which is widely used in point cloud reconstruction, deformation and fusion due to its advantages of good smoothness and Boolean operation. The most typical method is the surface reconstruction with Radial Basis Functions (RBF) under normal constraints. RBF has become one of the main methods of point cloud fitting because it has a strong mathematical foundation, an advantage of computation simplicity, and the ability of processing nonuniform points. Objective: Techniques and patents of implicit surface reconstruction interpolation with RBF are surveyed. Theory, algorithm, and application are discussed to provide a comprehensive summary for implicit surface reconstruction in RBF and Hermite Radial Basis Functions (HRBF) interpolation. Methods: RBF implicit surface reconstruction interpolation can be divided into RBF interpolation under the constraints of points and HRBF interpolation under the constraints of points and corresponding normals. Results: A total of 125 articles were reviewed, in which more than 30% were related to RBF in the last decade. The continuity properties and application fields of the popular global supported radial basis functions and compactly supported radial basis functions are analyzed. Different methods of RBF and HRBF implicit surface reconstruction are evaluated, and the challenges of these methods are discussed. Conclusion: In future work, implicit surface reconstruction via RBF and HRBF should be further studied in fitting accuracy, computation speed, and other fundamental problems. In addition, it is a more challenging but valuable research direction to construct a new RBF with both compact support and improved fitting accuracy.

Beras Miskin (Raskin) Program is a program of social protection, as supporters of other programs such as nutrition improvement, healthy increase, education and productivity improvement of Poor Households. According to Badan Pusat Statistika, there were 14 criteria to determine a household is classified as poor households. Based on these criteria it will be classified of recipient households and non-recipient households of Beras Miskin (Raskin) Program by Support Vector Machine (SVM) method using LibSVM. The concept of classification by SVM is search for the best hyperplane which serves as a separator of two classes of data in the input space. Kernel function is used to convert the data into a higher dimensional space to allow a separation. LibSVM is a package program created by Chih-Chung Chang and Chih-Jen Lin from Department of Computer Science at National Taiwan University. The method used by LibSVM to obtain global solution of duality lagrange problem is decomposition method. To determine the best parameters of kernel function, used k-vold cross validation method and grid search algorithm. In this classification by SVM method using LibSVM, obtain the best accuracy value as 83,1933%, which is the kernel function Radial Basis Function (RBF). Keywords : Beras Miskin (Raskin) Program, Classification, Support Vector Machine (SVM), LibSVM, Kernel Function

Evaluation of meshless radial basis collocation method (RBCM) for heterogeneous conduction and simulation of temperature inside the biological tissues

With the effective control of the new crown epidemic, how to develop China's financial industry in the post-epidemic era still lacks a suitable regional index system. Taking Beijing, where the financial economy occupies an important position, as an example, this paper selects 12 typical relevant indicators from the four dimensions of structure, scale, vitality and efficiency, and constructs a model based on Radial Basis Function (RBF) and Support Vector Machine (SVM). The threelevel Bagging integrated learning area financial development index system. First, the coefficient of variation method (CVM) is used to determine the weight of each index to measure the level of financial development, and then based on RBF and SVM, the Bagging integrated learning prediction is performed, and the financial development index is obtained. The results show that the RBF-SVM integrated model is more fitting than the single RBF or SVM. The financial development index of Beijing has generally shown positive growth in the past 20 years, and the financial industry has a good development trend. In this paper, we establish a financial development index system to judge regional financial development differences and predict the development trend of the financial industry, thus providing suggestions for the healthy development of my country's financial industry.