Learning Solutions for Electromagnetic Problems Using RBF Network-Based FE-LSSVM

Approximation methods such as response surface method and artificial neural network (ANN) method are widely used to alleviate the computation costs in structural reliability analysis. However most of the ANN methods proposed in the literature suffer various drawbacks such as poor choice of parameter setting, poor generalization and local minimum. In this study, a support vector machine-based radial basis function (RBF) network method is proposed, in which the improved RBF model is used to approximate the limit state function and then is connected to a reliability method to estimate failure probability. Since the learning algorithm of RBF network is replaced by the support vector algorithm, the advantage of the latter, such as good generalization ability and global optimization are propagated to the former, thus the inherent drawback of RBF network can be defeated. Numerical examples are given to demonstrate the applicability of the improved RBF network method in structural reliability analysis, as well as to illustrate the validity and effectiveness of the proposed method.

A mixed method for Dirichlet problems with radial basis functions

The present work aims to study the development and application of Radial Basis Function (RBF) networks for predicting auger energy consumption based on input energy. The study utilized RBF networks and explored the input energy with treatments 2 (Soil moisture content), 2 (Rotary speeds), 2 (Hole depths) and 4 (Replication) based on field operations. As indicated by the results, energy input differed between the treatments but was not significant. The highest input value in transaction soil moisture content was 14.75 %, rotary speeds of 235 rpm, and hole depths of 40 cm. In comparison, the lower input energy at transaction soil moisture content was 7.9%, rotary speeds of 235 rpm, and hole depths of 20 cm. Input energy in treatment (14.75 %, 235 rpm, and 40 cm) and treatment (7.9 %,235 rpm, and 20 cm) were 100.204 and 57.135 MJ. ha-1, respectively. The highest input energy shares were recorded for diesel fuel at all treatments. Furthermore, the RBF network with one hidden layer had good convergence. The output results showed 10 and five hidden neurons in a hidden layer with high accuracy for treatment (14.75 %, 235 rpm, and 40 cm) and treatment (7.9%, 235 rpm, and 20 cm). In the treatment (14.75 %, 235 rpm, and 40 cm), the MSE for the training and testing sets was 0.0001 % and 0.01 % for data points with Ordinary RBF (ORBF type). The performance of the 3-10-1 architecture was better than other architectures. Finally, this research concluded that the RBF network method can forecast the input energy and energy expenditures related to the types of treatments.

To improve the efficiency and quality of solving expensive engineering design optimization problems, recently metamodel-based design and optimization technologies have been widely employed. In this paper, a novel adaptive metamodel-based optimization method called sequential radial basis function using support vector machine is proposed to solve the practical engineering optimization problems involving computationally expensive objective and constraints. The proposed metamodel-based optimization method uses the radial basis function metamodel to approximate the expensive simulations in the interesting sampling region, which is a subregion of the design space. To identify the interesting sampling region, a novel feature space fuzzy -means clustering method is proposed to obtain the cluster center of superior cheap points classified by support vector machine. The procedure of sequential radial basis function using support vector machine is presented first, and the interesting sampling region and feature space fuzzy -means clustering methods are discussed in detail. Several numerical benchmark problems are used to compare the proposed method with other well-known metamodel-based design and optimization methods including efficient global optimization, multiple surrogate efficient global optimization methodology, mode-pursuing sampling, constraint importance mode pursuing sampling, and constrained optimization by radial basis function interpolation. The comparison results show that the proposed method generally outperforms the competitive methods in terms of efficiency, convergence, and robustness. Finally, sequential radial basis function using support vector machine is applied in an Earth observation satellite multidisciplinary design optimization problem. The results illustrate that compared with genetic algorithm and sequential quadratic programming, the proposed method can find a better solution with fewer function evaluations, which demonstrates the practicality and effectiveness of the proposed method in solving real-world engineering design optimization problems.

An automatically adaptive element free method is presented to analyze the seismic response of liquefiable soils. The method is based on the element free Galerkin method (EFGM) and the fission procedure that is part of h-refinement, indicated by error estimation. In the proposed method, a posteriori error estimate procedure that depends on the energy norm of stress and the T-Belytschko (TB) stress recovery scheme is incorporated. The effective cyclic elasto-plastic constitutive model is used to describe the nonlinear behavior of the saturated soil. The governing equations are established by u-p formulation. The proposed method can effectively avoid the volumetric locking due to large deformation that usually occurs in numerical computations using the finite element method (FEM). The efficiency of the proposed method is demonstrated by evaluating the seismic response of an embankment and comparing it to results obtained through FEM. It is shown that the proposed method provides an accurate seismic analysis of saturated soil that includes the effects of liquefaction

This paper describes a Lagrange multiplier technique for implementing Dirichlet boundary conditions in finite element methods for the compressible Euler and Navier-Stokes equations. Equivalent to the classic calculus of variations treatment of boundary conditions for scalar equations, this Lagrange multiplier technique provides a unified formulation for systems to locally combine Dirichlet conditions and partial differential equations at both the continuous and discrete levels. The analysis identifies natural boundary conditions associated with the specified Dirichlet conditions in the continuous case. In the discrete finite element case, the Lagrange multiplier technique identifies components of the Navier-Stokes equations evaluated near the boundary that should be retained in combination with the Dirichlet boundary conditions. Specific examples are provided for implementation of inviscid and viscous wall boundary conditions and inflow/outflow boundary conditions. Motivated by the possibility of obtaining continuous adjoint fields, the Lagrange multiplier technique is also applied to continuous and discrete adjoint analysis. Adjoints have been successfully applied to design, functional correction and adaptive grid error estimates. However, most applications of discrete adjoints used in conjunction with strongly imposed Dirichlet boundary conditions have been plagued by a discontinuous adjoint field near boundaries. We postulate that these discontinuous boundary adjoints are actually the adjoints of the Lagrange multipliers. By carefully formulating both the primal problem and the cost functional, discrete adjoint fields that are continuous near boundaries are demonstrated. The key appears to be retention of the Lagrange multipliers in the primal problem and formulation of the adjoint cost functional as a function of the discretely conservative boundary flux. In the present analysis, this conservative boundary flux is a function of both the boundary solution and the Lagrange multipliers associated with that boundary.

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.

In this research, two methods for crack detection in structures are presented and compared. The considered structure is a cantilever beam with rectangular cross section. In order to find cracks, firstly, a new technique based on wavelet analysis and finite element method (FEM) is applied. The advantage of this technique is that the crack detection process is more clear and comfortable than previous works. Then the process of crack detection is performed using FEM and combination of two types of artificial neural network (ANN) including radial basis function (RBF) and back-error propagation (BEP) neural networks. For crack identification in the proposed method, firstly, a RBF neural network is used to detect the number of cracks of structure. Then a BEP neural network is trained to detect the locations of cracks. Training of neural networks is performed using obtained data from FEM. Finally obtained results from two methods are compared with each other.

Radial basis function based finite element method: Formulation and applications

For the better management of available groundwater, it is essential to understand the flow behavior within the aquifer systems. The groundwater flow behavior in the complex aquifer system can be studied by solving the governing equations using either analytical or numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method (FEM) are generally used. The Meshless method is a recently developed alternative numerical approach for the solution of existing problem. A variety of Meshless methods like point interpolation method, smooth particle hydrodynamics, Galerkin methods, etc. are under the development for the solution of many solid mechanics and fluid mechanics problems. Meshless method eliminates many of the drawbacks of grid-based methods such as difficulties in meshing and re-meshing as in FDM and FEM which require huge efforts in pre-processing and with Meshless method it translates in the lesser computational time and costs. In this paper, Meshless Local Petrov-Galerkin (MLPG) method with strong form of collocation with exponential/Gaussian radial basis function is used for solving the groundwater flow problem. A computer model in MATLAB has been developed in 1D and 2D for the solution of confined aquifer problems. The developed 1D model is verified with available analytical solution for a hypothetical problem and found to be satisfactory. Further, the 2D model is applied to two case studies and results are compared with the FEM based solutions and found to be satisfactory. The present study shows that the MLPG based Meshless method is very effective in the simulation of groundwater flow problems.

Objective. The quantitative assessment of Parkinsonian tremor, e.g. (0, 1, 2, 3, 4) according to the Movement Disorder Society-Unified Parkinson’s Disease Rating Scale, is crucial for treating Parkinson’s disease. However, the tremor amplitude constantly fluctuates due to environmental and psychological effects on the patient. In clinical practice, clinicians assess the tremor severity for a short duration, whereas manual tremor labeling relies on the clinician’s physician experience. Therefore, automatic tremor quantification based on wearable inertial sensors and machine learning algorithms is affected by the manual labels of clinicians. In this study, an automatic modification method for the labels judged by clinicians is presented to improve Parkinsonian tremor quantitation. Approach. For the severe overlapping of dynamic feature range between different severities, an outlier modification algorithm (PCA-IQR) based on the combination of principal component analysis and interquartile range statistic rule is proposed to learn the blurred borders between different severity scores, thereby optimizing the labels. Afterward, according to the modified feature vectors, a support vector machine (SVM) with a radial basis function (RBF) kernel is proposed to classify the tremor severity. The classifier models of SVM with RBF kernel, k-nearest neighbors, and SVM with the linear kernel are compared. Main results. Experimental results show that the proposed method has high classification performance and excellent model generalization ability for tremor quantitation (accuracy: 97.93%, precision: 97.96%, sensitivity: 97.93%, F1-score: 97.94%). Significance. The proposed method may not only provide valuable assistance for clinicians to assess the tremor severity accurately, but also provides self-monitoring for patients at home and improve the assessment skills of clinicians.

Topology optimization for cross-section designs of electromagnetic waveguides targeting guiding characteristics

Magnetic anomaly detection (MAD) has been widely used for detecting the magnetic targets in many areas. In low signal-to-noise ratio (SNR) situations, the magnetic anomaly is usually buried in the magnetic noise, which leads to a decrease in the detection performance of traditional MAD methods. In order to improve the detection probability of MAD in low SNR, we propose an adaptive method of MAD using support vector machine (SVM). First, we design a detection model using SVM with radial basis function (RBF) kernel function. Meanwhile, we analyze the magnetic anomaly signal and determined the orthonormal basis function (OBF) energy and magnetic entropy as the features of the magnetic anomaly, which are as the input of the model. Then, the model is trained based on the data set with the magnetic signals. Finally, the trained model is applied to the raw magnetic signal to detect the anomaly. Compared to the traditional methods, the proposed method has a better performance and adaptive ability. The proposed method is validated by the real magnetic noise. The results show that the proposed method can reduce the case of false alarm and improve the detection performance in low SNR.

PurposeThe purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history.Design/methodology/approachThrough analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation.FindingsThe accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history.Originality/valueThe application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.

A new hybrid computational procedure utilizing the Element-free Galerkin method (EFGM) and the finite element method (FEM) for electromagnetic field computations is proposed. With the proposed method, only a part of the analyzed domain is modeled using the EFGM, while the rest of the analysis domain is discretized using the ordinary FEM. The connection between both subdomains is enabled using an intermediate analysis subdomain where new hybrid shape functions are defined utilizing both EFGM and FEM shape functions as bases. The accuracy of the obtained results by the proposed method is of the same order with those obtained by the ordinary FEM, but with less computation effort.