An Inhomogeneous Model for Laser Welding of Industrial Interest

Munafó, Caterina; Palumbo, Annunziata; Versaci, Mario

doi:10.3390/math11153357

Cited by 8 publications

(6 citation statements)

References 38 publications

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“…After the Neumann boundary condition, given in Equation ( 1) is applied to Equation ( 16), the electric potential is computed by using quasi-minimal residual method. It is noteworthy that in FEM, another approach called Galerkin which is the weighted residuals method can be used (Jin, 2014;Munafò et al, 2023).…”

Section: Finite Element Methods Using Partial Integration Approach (P...mentioning

confidence: 99%

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling

Dayarian,

Khadem

2024

Front. Syst. Neurosci.

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This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

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Section: Finite Element Methods Using Partial Integration Approach (P...mentioning

confidence: 99%

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling

Dayarian,

Khadem

2024

Front. Syst. Neurosci.

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“…where λ is a positive regularization parameter and, as usual, I is the identity matrix. Thus, for the cost function (37), we need to add the addend λw T w obtaining:…”

Section: Bls For Optimizing the Fuzzy Outputmentioning

confidence: 99%

“…There is no lack of theoretical studies of physical-mathematical modeling of MGs with certainly interesting results, but almost all are based on the resolution of systems of differential equations [32,33]. However, it is worth noting that the systems of differential equations that describe the dynamic behaviors of PV and WT powers have different operating times and therefore suffer from synchronization problems [34][35][36][37]. A possible solution would require the adaptive insertion of delay times into each of the equations, resulting in the challenge of obtaining numerical solutions within a reasonable time.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Approach for Managing Renewable Energy Flows for DC-Microgrid with Composite PV-WT Generators and Energy Storage System

Versaci,

La Foresta

2024

Energies

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Recently, the implementation of software/hardware systems based on advanced artificial intelligence techniques for continuous monitoring of the electrical parameters of intelligent networks aimed at managing and controlling energy consumption has been of great interest. The contribution of this paper, starting from a recently studied DC-MG, fits into this context by proposing an intuitionistic fuzzy Takagi–Sugeno approach optimized for the energy management of isolated direct current microgrid systems consisting of a photovoltaic and a wind source. Furthermore, a lead-acid battery guarantees the stability of the DC bus while a hydrogen cell ensures the reliability of the system by avoiding blackout conditions and increasing interaction with the loads. The fuzzy rule bank, initially built using the expert’s knowledge, is optimized with the aforementioned procedure, maximizing external energy and minimizing consumption. The complete scheme, modeled using MatLab/Simulink, highlighted performance comparable to fuzzy Takagi–Sugeno systems optimized using a hybrid approach based on particle swarm optimization (to structure the antecedents of the rules) and minimum batch squares (to optimize the output).

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“…A constantan wire heated by the release of Joule heat is considered a heat source. The data were obtained by numerically solving the heat conduction equation [20,50]…”

Section: Synthetic Datamentioning

confidence: 99%

Methods of Partial Differential Equation Discovery: Application to Experimental Data on Heat Transfer Problem

Andreeva,

Bykov,

Gataulin

et al. 2023

Processes

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The paper presents two effective methods for discovering process models in the form of partial differential equations based on an evolutionary algorithm and an algorithm for the best subset selection. The methods are designed to work with sparse and noisy data and implement various numerical differentiation techniques, including piecewise local approximation using multidimensional polynomial functions, neural network approximation, and an additional algorithm for selecting differentiation steps. To verify the algorithms, the experiment is carried out on pulsed heating of a viscous liquid (glycerol) by a submerged horizontal cylindrical heat source. Temperature measurements are taken only at six points, which makes the data very sparse. The noise level ranges from 0.2 to 1% of the observed maximum temperature. The algorithms can successfully restore the structure of the heat transfer equation in cylindrical coordinates and determine the thermal diffusivity coefficient with an error of 2.5–20%, depending on the algorithm type and heating mode. Additional synthetic setups are employed to analyze the dependence of accuracy on the noise level. Results also demonstrate the algorithms’ ability to identify underlying processes such as convective motion.

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An Inhomogeneous Model for Laser Welding of Industrial Interest

Cited by 8 publications

References 38 publications

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling

Fuzzy Approach for Managing Renewable Energy Flows for DC-Microgrid with Composite PV-WT Generators and Energy Storage System

Methods of Partial Differential Equation Discovery: Application to Experimental Data on Heat Transfer Problem

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