Gaussian Radial Basis Function Research Articles

Benefit and risk evaluation of inland nuclear generation investment in Kazakhstan combined with an analytical MGT method

Purpose In the process of building the “Belt and Road” and “Bright Road” community of interests between China and Kazakhstan, this paper proposes the construction of an inland nuclear power plant in Kazakhstan. Considering the uncertainty of investment in nuclear power generation, the authors propose the MGT (Monte-Carlo and Gaussian Radial Basis with Tensor factorization) utility evaluation model to evaluate the risk of investment in nuclear power in Kazakhstan and provide a relevant reference for decision making on inland nuclear investment in Kazakhstan. Design/methodology/approach Based on real options portfolio combined with a weighted utility function, this study takes into account the uncertainties associated with nuclear power investments through a minimum variance Monte Carlo approach, proposes a noise-enhancing process combined with geometric Brownian motion in solving complex conditions, and incorporates a measure of investment flexibility and strategic value in the investment, and then uses a deep noise reduction encoder to learn the initial values for potential features of cost and investment effectiveness. A Gaussian radial basis function used to construct a weighted utility function for each uncertainty, generate a minimization of the objective function for the tensor decomposition, and then optimize the objective loss function for the tensor decomposition, find the corresponding weights, and perform noise reduction to generalize the nonlinear problem to evaluate the effectiveness of nuclear power investment. Finally, the two dimensions of cost and risk (estimation of investment value and measurement of investment risk) are applied and simulated through actual data in Kazakhstan. Findings The authors assess the core indicators of Kazakhstan's nuclear power plants throughout their construction and operating cycles, based on data relating to a cluster of nuclear power plants of 10 different technologies. The authors compared it with several popular methods for evaluating the benefits of nuclear power generation and conducted subsequent sensitivity analyses of key indicators. Experimental results on the dataset show that the MGT method outperforms the other four methods and that changes in nuclear investment returns are more sensitive to changes in costs while operating cash flows from nuclear power are certainly an effective way to drive investment reform in inland nuclear power generation in Kazakhstan at current levels of investment costs. Research limitations/implications Future research could consider exploring other excellent methods to improve the accuracy of the investment prediction further using sparseness and noise interference. Also consider collecting some expert advice and providing more appropriate specific suggestions, which will facilitate the application in practice. Practical implications The Novel Coronavirus epidemic has plunged the global economy into a deep recession, the tension between China and the US has made the energy cooperation road unusually tortuous, Kazakhstan in Central Asia has natural geographical and resource advantages, so China–Kazakhstan energy cooperation as a new era of opportunity, providing a strong guarantee for China's political and economic stability. The basic idea of building large-scale nuclear power plants in Balkhash and Aktau is put forward, considering the development strategy of building Kazakhstan into a regional international energy base. This work will be a good inspiration for the investment of nuclear generation. Originality/value This study solves the problem of increasing noise by combining Monte Carlo simulation with geometric Brownian motion under complex conditions, adds the measure of investment flexibility and strategic value, constructs the utility function of noise reduction weight based on Gaussian radial basis function and extends the nonlinear problem to the evaluation of nuclear power investment benefit.

Meshfree Galerkin Method for a Rotating Non-Uniform Rayleigh Beam with Refinement of Radial Basis Functions

The rotating Rayleigh beam problem is solved with meshfree method where the radial basis functions are explored. Numbers of basis functions have been used for meshfree methods which also include radial basis function. In this paper, the Gaussian radial basis function and multiquadrics radial basis functions are combined to get the new basis function which provides accuracy for higher natural frequencies. The radial basis functions satisfy the Kronecker delta property and it is easy to apply the essential boundary conditions. The Galerkin method is used for weak formulation. The matrices have been derived. The results are obtained for Gaussian radial basis function and new basis function. The results show more accurate values for fourth and fifth natural frequency with new basis function where only six nodes are used within the subdomain of trial and test function. The results are also obtained with conventional finite element method where forty, two node elements are considered. Also, the results are obtained for rotating Euler-Bernoulli beam to observe the difference in results with rotating Rayleigh beam.

Experimental Lognormal Modeling of Harmonics Power of Switched-Mode Power Supplies

Switched-mode power supplies (SMPSs) are an important component in many electrical systems. As a highly non-linear device, an unavoidable side-effect of SMPS operation is its high harmonics power. One of the ways to model the harmonic power consumption profile is in terms of a random process. This paper addresses random process modeling with a corresponding probability density function (PDF), auto-covariance function (ACF) and spectral coherence. The consumed harmonics power was evaluated under different load conditions and is based on experimental results of current consumption from SMPSs. The analysis shows that harmonics power may be modeled by a lognormal distribution that is time-domain uncorrelated, and that has spectral-domain correlation modeled by a Gaussian radial basis function. Extensive discussion on the modeling results is also provided. Moreover, random simulation approach based on the modeling results was proposed.

Prediction of Probabilistic Transient Stability Using Support Vector Machine

Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for offline studies and thus, cannot be applied for online transient stability prediction, which is a major requirement in modern power systems. This motivated the requirement to apply an artificial intelligence-based approach. In this regard, supervised machine learning is beneficial for predicting transient stability status, in the presence of uncertainties. Therefore, this paper examines the application of a binary support vector machine-based supervised machine learning, for predicting the transient stability status of a power system, considering uncertainties of various factors, such as load, faulted line, fault type, fault location and fault clearing time. The support vector machine is trained using a Gaussian Radial Basis function kernel and its hyperparameters are optimized using Bayesian optimization. Results obtained for the IEEE 14-bus test system demonstrated that the proposed method offers a fast technique for probabilistic transient stability status prediction, with an excellent accuracy. DIgSILENT PowerFactory and MATLAB was utilized for transient stability time-domain simulations (for obtaining training data for support vector machine) and for applying support vector machine, respectively.

Support Vector Machine Kernel Model Calibration for Optimal Accuracy in Automatic Pineapple Slices Classification

Sorting pineapple can be automated with use of computer vision. The unique challenge with the pineapple slices is variability of the fruit slices color, ripeness and texture due to varying environmental parameters and fruit types. The most common types of pineapple fruit are smooth Caen and MD2. Currently the pineapple industries sort the slices manually using casual workers. Before commencement of a typical production shift, there is startup shift where machine are cleaned, prepared and calibrated for the production. Fruit slices are also sampled and processed to simulated actual production. A mock sorting is done to help guide the worker for the expected sorting for the five categories i.e: fancy ¾, fancy ½, choice, broken and reject. To achieve a fully automated sorting process there is a need to calibrate machine model and capture the day to day variability of fruit color, ripeness and texture. In this paper we propose to use an analytical method to calibrate the Support Vector Machine (SVM) with Gaussian radial basis function (RBF) for optimal sigma and box constraint (C). A compelling feature of the proposed algorithm is that it does not require an optimization search, making the selection process simpler and more computationally efficient. The proposed algorithm achieves the highest accuracy when used with the Gaussian multiclass SVM, as demonstrated by experimental results on three real-world datasets.

Investigating the cellular responses of osteosarcoma to cisplatin by confocal Raman microspectroscopy.

Confocal Raman Microspectroscopy (CRM) was employed to clarify the cellular response of cisplatin in osteosarcoma (OS) cells with different dosages and incubation times. The K7M2 mouse osteosarcoma cells were treated by cisplatin in 0μM (UT group), 20μM (20T group), and 40μM (40T group) doses for 24-h (24H group) and 48-h (48H group), respectively. Raman spectroscopy was utilized to analyze the drug induced variations of intracellular biochemical components in osteosarcoma cells. The spectral results shows that the main changes in its biochemical composition come from nucleic acids. By adopting three different kernel functions (linear, polynomial, and Gaussian radial basis function (RBF)), principal component analysis combined with support vector machine models (PCA-SVM) was built to address the spectral variations among all investigated groups. Meanwhile, multivariate curve resolution alternating least squares (MCR-ALS) was further utilized to discuss on the chemical interpretation on the acquired spectral results. Moreover, Raman spectral images, which is reconstructed by K-means cluster analysis (KCA) with point-scanned hyperspectral dataset, was applied to illustrate the drug induced compositional and morphological variations in each subcellular region. The achieved results not only prove the application potential of Raman based analytical technique in non-labeled intracellular studies, but also illustrate the detailed compositional and structural information of cisplatin induced OS cell responses from the perspective of multivariate analysis and imaging of Raman spectroscopy.

Gaussian RBF Centered Kernel Alignment (CKA) in the Large-Bandwidth Limit.

Centered kernel alignment (CKA), also known as centered kernel-target alignment, is useful as a similarity measure between kernels and as a kernel-based similarity measure between feature representations. We prove that CKA based on a Gaussian RBF kernel converges to linear CKA in the large-bandwidth limit. The result relies on mean-centering of the feature maps and on a Hilbert-Schmidt Independence Criterion (HSIC) identity. We show that convergence onset is sensitive to the geometry of the feature representations, and that a notion of representation eccentricity, ρ, constrains the bandwidth range for which Gaussian CKA can differ noticeably from linear CKA. Our experimental results suggest that Gaussian bandwidths less than ρ should be selected in order to enable nonlinear modeling.

Binary Tomography Reconstruction with Limited-Data by a Convex Level-Set燤ethod

This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions. In this technique, we derive generic evolution equations for shape reconstruction in terms of the underlying level-set parameters. We show that using the appropriate basis function to parameterize the level-set function results in an optimization problem with a small number of parameters, which overcomes many of the problems associated with the traditional level-set approach. More concretely, in this paper, we use Gaussian functions as a basis function placed at sparse grid points to represent the parametric level-set function and provide more flexibility in the binary representation of the reconstructed image. In addition, we suggest a convex optimization method that can overcome the problem of the local minimum of the cost function by successfully recovering the coefficients of the basis function. Finally, we illustrate the performance of the proposed method using synthetic images and real X-ray CT projection data. We show that the proposed reconstruction method compares favorably to various state-of-the-art reconstruction techniques for limited-data tomography, and it is also relatively stable in the presence of modest amounts of noise. Furthermore, the shape representation using a compact Gaussian radial basis function works well.

Developing a leap-frog meshless methods with radial basis functions for modeling of electromagnetic concentrator

<abstract><p>The main goal of this paper is to develop a fast and effective meshless method by using radial basis function (RBF) for the time domain model equations of electromagnetic wave concentration device. This is mainly because the complex model equations involve different partial differential equations in different subdomains, which makes the meshless method very attractive and also very challenging. In order to simulate the propagation of electromagnetic waves in the electromagnetic concentrator, perfect matching layer technology was used to reduce an unbounded domain problem into a bounded domain problem. Borrowing the idea of the leap-frog finite-difference time-domain scheme, I develop the leap-frog RBF meshless method to solve the coupled complex modeling equations. The numerical results obtained by using a multiquadric RBF and Gaussian RBF demonstrate that our RBF method is very effective.</p></abstract>

Feature Extraction and Classification of MRI Using Hybrid RBF Kernel and SVM

An enhanced classification system for classification of MR images using association of kernels with support vector machine is developed and presented in this paper along with the design and development of content-based image retrieval (CBIR) system. Content of image retrieval is the process of finding relevant image from large collection of image database using visual queries. Medical images have led to growth in large image collection. Oriented Rician Noise Reduction Anisotropic Diffusion filter is used for image denoising. A modified hybrid Otsu algorithm termed is used for image segmentation. The texture features are extracted using GLCM method. Genetic algorithm with Joint entropy is adopted for feature selection. The classification is done by support vector machine along with various kernels and the performance is validated. A classification accuracy of 98.83% is obtained using SVM with GRBF kernel. Various features have been extracted and these features are used to classify MR images into five different categories. Performance of the MC-SVM classifier is compared with different kernel functions. From the analysis and performance measures like classification accuracy, it is inferred that the brain and spinal cord MRI classification is best done using MC- SVM with Gaussian RBF kernel function than linear and polynomial kernel functions. The proposed system can provide best classification performance with high accuracy and low error rate.

Adaptive neural sliding mode control with prescribed performance of robotic manipulators subject to backlash hysteresis

Robust and precise control of robot systems are still challenging problems due to the existence of uncertainties and backlash hysteresis. To deal with the problems, an adaptive neural sliding mode control with prescribed performance is proposed for robotic manipulators. A finite-time nonsingular terminal sliding mode control combined with a new prescribed performance function (PPF) is developed to guarantee the transient and steady-state performance of the closed-loop system. Based on the sliding mode variable, an adaptive law is presented to effectively estimate the bound of system uncertainties where the prior knowledge of uncertainties is not needed. To approximate nonlinear function and unknown dynamics, the Gaussian radial basis function neural networks(RBFNNs) is introduced to compensate the lumped nonlinearities. All signals of the closed-loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov analysis. Finally, comparative simulations are conducted to illustrate superiority and reliability of the proposed control strategy.

Solution of time‐fractional stochastic nonlinear sine‐Gordon equation via finite difference and meshfree techniques

In this article, we introduce a numerical procedure to solve time‐fractional stochastic sine‐Gordon equation. The suggested technique is based on finite difference method and radial basis functions interpolation. By using this algorithm, first time‐fractional stochastic nonlinear sine‐Gordon equation is converted to elliptic stochastic differential equations. Then, the meshfree method based on radial basis functions (RBFs) is used to approximate the obtained equation. In fact, the finite difference method is used to approximate the unknown function in the time direction and generalized Gaussian RBF is applied to estimate the obtained equation in the space direction. The most important advantage of this method is that the noise terms are simulated directly at the collocation points at each time step. By employing this method, the equation decreased to a nonlinear system of algebraic equations which can be solved simply. The obtained results of solving three examples confirm the validity and capability of the proposed solution.

An empirical assessment of different kernel functions on the performance of support vector machines

Artificial intelligence (AI) and machine learning (ML) have influenced every part of our day-to-day activities in this era of technological advancement, making a living more comfortable on the earth. Among the several AI and ML algorithms, the support vector machine (SVM) has become one of the most generally used algorithms for data mining, prediction and other (AI and ML) activities in several domains. The SVM’s performance is significantly centred on the kernel function (KF); nonetheless, there is no universal accepted ground for selecting an optimal KF for a specific domain. In this paper, we investigate empirically different KFs on the SVM performance in various fields. We illustrated the performance of the SVM based on different KF through extensive experimental results. Our empirical results show that no single KF is always suitable for achieving high accuracy and generalisation in all domains. However, the gaussian radial basis function (RBF) kernel is often the default choice. Also, if the KF parameters of the RBF and exponential RBF are optimised, they outperform the linear and sigmoid KF based SVM method in terms of accuracy. Besides, the linear KF is more suitable for the linearly separable dataset.

Multi-Floor Indoor Localization Based on RBF Network With Initialization, Calibration, and Update

Received Signal Strength Indicator (RSSI) fingerprinting is known as the most concerned method for indoor localization as its high accuracy and low cost. Numerous RSSI based methods have shown their attractive performances, but the major drawback is the high dependency on the database. In this paper, we propose a multi-floor indoor localization method which includes floor detection and location estimation based on the radial basis function (RBF) network. To ensure the localization accuracy and stability, the network is constructed according to the probabilistic algorithm. Choosing Gaussian radial basis functions with appropriate widths, the network parameters can be initialized appropriately regardless of deficiency of RSSI data. By further conducting the supervised learning of RBF network, the network parameters will be effectively calibrated and updated, so as to achieve a better localization performance. In addition, a radio map quality evaluation criterion is proposed to conduct a comprehensive analysis and interpretation for the localization approach. Finally, experimental results of a publicly accessible dataset which includes multi-floors buildings verify that the performance of the proposed RBF network is superior to other commonly used methods.

Multilayer perceptron neural network activated by adaptive Gaussian radial basis function and its application to predict lid-driven cavity flow

Multilayer perceptron neural network activated by adaptive Gaussian radial basis function and its application to predict lid-driven cavity flow

Application of Gaussian Radial Basis Functions for Fast Spatial Imaging of Ground Penetration Radar Data Obtained on an Irregular Grid

Spatial imaging of ground penetrating radar (GPR) measurement data is a difficult computational problem that is time consuming and requires substantial memory resources. The complexity of the problem increases when the measurements are performed on an irregular grid. Such grid irregularities are typical for handheld or flying GPR systems. In this paper, a fast and efficient method of GPR data imaging based on radial basis functions is described. A compactly supported modified Gaussian radial basis function (RBF) and a hierarchical approximation method were used for computation. The approximation was performed in multiple layers with decreasing approximation radius, where in successive layers, increasingly finer details of the imaging were exposed. The proposed method provides high flexibility and accuracy of approximation with a computational cost of N·log (N) for model building and N·M for function evaluation, where N is the number of measurement points and M is the number of approximation centres. The method also allows for the control smoothing of measurement noise. The computation of one high-quality imaging using 5000 measurement points utilises about 5 s on an Intel Core i5-7200U CPU 2.5 GHz, 8 GB RAM computer. Such short time enables real-time image processing during field measurements.

Multiple Kernel Learning with Maximum Inundation Extent from MODIS Imagery for Spatial Prediction of Flood Susceptibility

Identifying flood prone areas is essential for basin management. In this paper, a spatial prediction technology of flood susceptibility based on multiple kernel learning (MKL) is proposed. We establish the flood susceptibility model by using EasyMKL, nonlinear MKL (NLMKL), Representative MKL(RMKL), Generalized MKL(GMKL), support vector machine(SVM) with linear kernel and SVM with Gaussian radial base function(RBF) kernel, The spatial prediction of flood susceptibility in Sanhuajian basin of the Yellow River is carried out. We use MODIS remote sensing images to obtain historical flood inundation sites in the study area. Then, ten flood conditioning factors are used as inputs to the flood susceptibility model. The model performance is evaluated in terms of accuracy (ACC), balanced F Score (F1 score), and areas under the curve (AUC). According to the results, MKL significantly outperforms the SVM adopting single kernel, and NLMKL(ACC=0.833,F1=0.841,AUC=0.889) demonstrates the best comprehensive performance. The flood susceptibility map generated by MODIS remote sensing images and MKL, therefore, can provide effective help for researchers and decision makers in flood management.

On a high-order Gaussian radial basis function generated Hermite finite difference method and its application

On a high-order Gaussian radial basis function generated Hermite finite difference method and its application

Optimal learning with anisotropic Gaussian SVMs

This paper investigates the nonparametric regression problem using SVMs with anisotropic Gaussian RBF kernels. Under the assumption that the target functions are resided in certain anisotropic Besov spaces, we establish the almost optimal learning rates, more precisely, optimal up to some logarithmic factor, presented by the effective smoothness. By taking the effective smoothness into consideration, our almost optimal learning rates are faster than those obtained with the underlying RKHSs being certain anisotropic Sobolev spaces. Moreover, if the target function depends only on fewer dimensions, faster learning rates can be further achieved.

Edge Directed Radial Basis Function based Interpolation Towards PCA based PAN-sharpening

ABSTRACT In this research, we proposed a new PAN-sharpening algorithm by using edge-directed Gaussian Radial Basis Function (RBF) and Principal Component Analysis (PCA). Up-scaling is a procedure to upgrade the spectral data of a Low Resolution (LR) Multi Spectral (MS) imagery. Non-linear up-scaling methods generate fewer artefacts in the interpolated image as they are edge-adaptive in nature. Adaptive interpolation techniques consider different features of an image during up-scaling. These techniques are proven efficient compared with non-adaptive methods. However, they may generate distorted output in fine-textured areas and can have lower luminance information. We consider the Laplacian of Gaussian (LoG) or Marr-Hildreth edge detection operator to preserve missing structure and luminance information. It generates smooth edges by minimizing artefacts in the interpolated image. We have considered multi-source and multi-sensor datasets obtained from LISS-IV, CATROSAT-I, and Quickbird to perform all experiments. We have carried out a broad quantitative and subjective assessment and comparison of the proposed algorithm with the standard and cutting-edge methods.