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The multi-quadrics (MQ) function is a kind of radial basis function. And the MQ method has been successfully adopted as a type of meshless method in solving electromagnetic boundary value problems. However, the accuracy of MQ interpolation or solving equations is severely influenced by shape parameter. Thus the purpose of this paper is to propose a case-independent shape parameter selection strategy from the aspect of coefficient matrix condition number analysis.

The condition number of coefficient matrix is investigated. It is shown that the condition number is only a function of shape parameter and MQ node number, and is irrelevant to the interpolated function which means case-independent. The effective condition number which takes into account the interpolated function is introduced. Then, the relation between the relative root mean square error and condition number is analyzed. Three numerical experiments as transmission line, cable channel and grounding metal box model were carried out.

In the numerical experiments, there is an approximate linear relationship between the logarithm of the condition number and shape parameter, an approximate quadratic relationship with node number. And the optimal shape parameter is corresponding to the early stage of condition number oscillation.

This paper proposed a case-independent shape parameter selection strategy. For a finite precision computation, the upper limit of the condition number is predetermined. Therefore, the shape parameter can be chosen where condition number oscillates in early stage.

In this study, the authors aim to upgrade their previous developments of the local radial basis function collocation method (LRBFCM) for heat transfer, fluid flow, electromagnetic problems and linear thermoelasticity to dynamic-coupled thermoelasticity problems.

The authors solve a thermoelastic benchmark by considering a linear thermoelastic plate under thermal and pressure shock. Spatial discretization is performed by a local collocation with multi-quadrics augmented by monomials. The implicit Euler formula is used to perform the time stepping. The system of equations obtained from the formula is solved using a Newton–Raphson algorithm with GMRES to iteratively obtain the solution. The LRBFCM solution is compared with the reference finite-element method (FEM) solution and, in one case, with a solution obtained using the meshless local Petrov–Galerkin method.

The performance of the LRBFCM is found to be comparable to the FEM, with some differences near the tip of the shock front. The LRBFCM appears to converge to the mesh-converged solution more smoothly than the FEM. Also, the LRBFCM seems to perform better than the MLPG in the studied case.

The performance of the LRBFCM near the tip of the shock front appears to be suboptimal because it does not capture the shock front as well as the FEM. With the exception of a solution obtained using the meshless local Petrov–Galerkin method, there is no other high-quality reference solution for the considered problem in the literature yet. In most cases, therefore, the authors are able to compare only two mesh-converged solutions obtained by the authors using two different discretization methods. The shock-capturing capabilities of the method should be studied in more detail.

For the first time, the LRBFCM has been applied to problems of coupled thermoelasticity.

The 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.

Through 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.

The 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.

The 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.

The performance measure approach (PMA) is widely adopted for reliability analysis and reliability-based design optimization because of its robustness and efficiency compared to reliability index approach. However, it has been reported that PMA involves repeat evaluations of probabilistic constraints therefore it is prohibitively expensive for many large-scale applications. In order to overcome these disadvantages, the purpose of this paper is to propose an efficient PMA-based reliability analysis technique using radial basis function (RBF).

The RBF is adopted to approximate the implicit limit state functions in combination with latin hypercube sampling (LHS) strategy. The advanced mean value method is applied to obtain the most probable point (MPP) with the prescribed target reliability and corresponding probabilistic performance measure to improve analysis accuracy. A sequential framework is proposed to relocate the sampling center to the obtained MPP and reconstruct RBF until a criteria is satisfied.

The method is shown to be better in the computation time to the PMA based on the actual model. The analysis results of probabilistic performance measure are accurately close to the reference solution. Five numerical examples are presented to demonstrate the effectiveness of the proposed method.

The main contribution of this paper is to propose a new reliability analysis technique using reconstructed RBF approximate model. The originalities of this paper may lie in: investigating the PMA using metamodel techniques, using RBF instead of the other types of metamodels to deal with the low efficiency problem.

Many engineering optimisation problems are difficult to describe mathematically and as such can not be easily optimised. Recently attention has focussed on developing methods to create approximations of the real object function using numerical model data instead. The approximated function can then be optimised using a suitable optimisation method. This paper describes the extraction of derivative information from a neuro‐fuzzy system. Subsequently, this permits the application of classic deterministic optimisation methods in order to identify the global minimum of any approximated objective function. For non‐differentiable functions this approach is of great benefit. Results from an analytical optimisation example, in which the objective function and the solution are known, and a two variable loudspeaker optimisation problem are discussed. In both cases, the neuro‐fuzzy system worked well to model the physical problem and the extracted derivative served to locate the minimum.

When dealing with problems entailing time consuming finite element solutions alternative methods are sought which can reduce the number of function calls whilst preserving solution accuracy. Two different strategies for practical electromagnetic design and optimisation are presented and compared. The main features and performance of each are described and evaluated on an analytical and a physical problem.

The design of electrical machines includes the computation of several requirements and, in general, the improvement of one requirement implies in a degradation of another one: this is a typical multi‐objective scenario. The paper focuses on the multi‐optimization analysis of a special switched reluctance motor.

Two design requirements were analyzed: the average torque and the ripple torque. The electromagnetic field computation was performed by the finite element method and the torque was computed by the Coulomb's Virtual Work for several positions. This allows us to calculate the average torque and the ripple torque. Three different methods were used to obtain the Pareto set: a min‐max approach, the non‐dominated sorting genetic algorithm (NSGA) and the strength Pareto evolutionary algorithm (SPEA). In order to save the computation time, the objective functions (the average torque and the ripple torque) were replaced with surrogate functions. Kriging models were used as surrogate functions.

The evolutionary methods (NSGA and SPEA) have a similar performance. The min‐max has not the same performance. It could have the same performance only if some unconstrained optimization problems are solved before the multi‐objective optimization. The maximum relative deviation between the approximated function (Kriging model) and the same value calculated by the finite element method was equal to 0.8 percent for the average torque and 1.2 percent for the ripple torque. The ripple torque, considered as the difference between the maximum and the minimum values in the 0‐90° region, has reduced while its frequency has doubled. This last characteristic provides a better mechanical stability for the driven load because its inertia softens the ripple effects at the double the frequency. The optimized prototype presents higher torques in the region θ<0° and this allows the electronic drive to switch in a broader range rendering the motor operation more flexible.

The use of surrogate functions save the computation time with high accuracy. This is very important on the design of electrical machines, a typical multi‐objective scenario. Evolutionary methods seem to be well suited to solve this class of problem.

The purpose of this paper is to present a constructive algorithm to design multilayer perceptron neural networks used as approximation models of electromagnetic devices.

The proposed procedure allows automatic determination of both the number of neurons and the synaptic weights of networks with a single hidden layer. The approximation model is used in design optimization problems. The inputs of the neural network correspond to the design parameters whereas the output corresponds to the objective function of the optimization problem. The neural model is then inverted in order to determine which input is associated to a prefixed output.

The performance of the algorithm has been tested on analytical function and on the TEAM workshop problem 25.

As the reliability of the optimum solution is strongly affected by the accuracy of the neural approximation model, the approximation error is kept as low as possible, especially in the maximum/minimum points.

Sensor arrays and pattern recognition-based electronic nose (E-nose) is a typical detection and recognition instrument for indoor air quality (IAQ). The E-nose is able to monitor several pollutants in the air by mimicking the human olfactory system. Formaldehyde concentration prediction is one of the major functionalities of the E-nose, and three typical machine learning (ML) algorithms are most frequently used, including back propagation (BP) neural network, radial basis function (RBF) neural network and support vector regression (SVR).

This paper comparatively evaluates and analyzes those three ML algorithms under controllable environment, which is built on a marketable sensor arrays E-nose platform. Variable temperature (T), relative humidity (RH) and pollutant concentrations (C) conditions were measured during experiments to support the investigation.

Regression models have been built using the above-mentioned three typical algorithms, and in-depth analysis demonstrates that the model of the BP neural network results in a better prediction performance than others.

Finally, the empirical results prove that ML algorithms, combined with low-cost sensors, can make high-precision contaminant concentration detection indoor.

The purpose of the present work is to develop the combination of the radial point interpolation method (RPIM) with a bi-directional evolutionary structural optimization (BESO) algorithm and extend it to the analysis of benchmark examples and automotive industry applications.

A BESO algorithm capable of detecting variations in the stress level of the structure, and thus respond to those changes by reinforcing the solid material, is developed. A meshless method, the RPIM, is used to iteratively obtain the stress field. The obtained optimal topologies are then recreated and numerically analyzed to validate its proficiency.

The proposed algorithm is capable to achieve accurate benchmark material distributions. Implementation of the BESO algorithm combined with the RPIM allows developing innovative lightweight automotive structures with increased performance.

Computational cost of the topology optimization analysis is constrained by the nodal density discretizing the problem domain. Topology optimization solutions are usually complex, whereby they must be fabricated by additive manufacturing techniques and experimentally validated.

In automotive industry, fuel consumption, carbon emissions and vehicle performance is influenced by structure weight. Therefore, implementation of accurate topology optimization algorithms to design lightweight (cost-efficient) components will be an asset in industry.

Meshless methods applications in topology optimization are not as widespread as the finite element method (FEM). Therefore, this work enhances the state-of-the-art of meshless methods and demonstrates the suitability of the RPIM to solve topology optimization problems. Innovative lightweight automotive structures are developed using the proposed methodology.