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The extraordinary properties of graphene render it ideal for diverse contemporary and future applications. Aiming at the investigation of certain aspects commonly overlooked in pertinent works, the authors study wave-propagation phenomena supported by graphene layers within a stochastic framework, i.e. when uncertainty in various factors affects the graphene’s surface conductivity. Given that the consideration of an increasing number of graphene sheets may increase the stochastic dimensionality of the corresponding problem, efficient surrogates with reasonable computational cost need to be developed.

The authors exploit the potential of generalized Polynomial Chaos (PC) expansions and develop low-cost surrogates that enable the efficient extraction of the necessary statistical properties displayed by stochastic graphene-related quantities of interest (QoI). A key step is the incorporation of an initial variance estimation, which unveils the significance of each input parameter and facilitates the selection of the most appropriate basis functions, by favoring anisotropic formulae. In addition, the impact of controlling the allowable input interactions in the expansion terms is investigated, aiming at further PC-basis elimination.

The proposed stochastic methodology is assessed via comparisons with reference Monte-Carlo results, and the developed reduced basis models are shown to be sufficiently reliable, being at the same time computationally cheaper than standard PC expansions. In this context, different graphene configurations with varying numbers of random inputs are modeled, and interesting conclusions are drawn regarding their stochastic responses.

The statistical properties of surface-plasmon polaritons and other QoIs are predicted reliably in diverse graphene configurations, when the surface conductivity displays non-trivial uncertainty levels. The suggested PC methodology features simple implementation and low complexity, yet its performance is not compromised, compared to other standard approaches, and it is shown to be capable of delivering valid results.

This paper aims to introduce a non-invasive and convenient method to detect a life-threatening disease called aortic dissection. A Bayesian inference based on enhanced multi-sensors impedance cardiography (ICG) method has been applied to classify signals from healthy and sick patients.

A 3D numerical model consisting of simplified organ geometries is used to simulate the electrical impedance changes in the ICG-relevant domain of the human torso. The Bayesian probability theory is used for detecting an aortic dissection, which provides information about the probabilities for both cases, a dissected and a healthy aorta. Thus, the reliability and the uncertainty of the disease identification are found by this method and may indicate further diagnostic clarification.

The Bayesian classification shows that the enhanced multi-sensors ICG is more reliable in detecting aortic dissection than conventional ICG. Bayesian probability theory allows a rigorous quantification of all uncertainties to draw reliable conclusions for the medical treatment of aortic dissection.

This paper presents a non-invasive and reliable method based on a numerical simulation that could be beneficial for the medical management of aortic dissection patients. With this method, clinicians would be able to monitor the patient’s status and make better decisions in the treatment procedure of each patient.

The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

The fabrication of electromagnetic (EM) components may induce randomness in several design parameters. In such cases, an uncertainty assessment is of high importance, as simulating the performance of those devices via deterministic approaches may lead to a misinterpretation of the extracted outcomes. This paper aims to present a novel heuristic for the sparse representation of the polynomial chaos (PC) expansion of the output of interest, aiming at calculating the involved coefficients with a small computational cost.

This paper presents a novel heuristic that aims to develop a sparse PC technique based on anisotropic index sets. Specifically, this study’s approach generates those indices by using the mean elementary effect of each input. Accurate outcomes are extracted in low computational times, by constructing design of experiments (DoE) which satisfy the D-optimality criterion.

The method proposed in this study is tested on three test problems; the first one involves a transmission line that exhibits several random dielectrics, while the second and the third cases examine the effects of various random design parameters to the transmission coefficient of microwave filters. Comparisons with the Monte Carlo technique and other PC approaches prove that accurate outcomes are obtained in a smaller computational cost, thus the efficiency of the PC scheme is enhanced.

This paper introduces a new sparse PC technique based on anisotropic indices. The proposed method manages to accurately extract the expansion coefficients by locating D-optimal DoE.

Stochastic uncertainties in material parameters have a significant impact on the analysis of real-world electromagnetic compatibility (EMC) problems. Conventional approaches via the Monte-Carlo scheme attempt to provide viable solutions, yet at the expense of prohibitively elongated simulations and system overhead, due to the large amount of statistical implementations. The purpose of this paper is to introduce a 3-D stochastic finite-difference time-domain (S-FDTD) technique for the accurate modelling of generalised EMC applications with highly random media properties, while concurrently offering fast and economical single-run realisations.

The proposed method establishes the concept of covariant/contravariant metrics for robust tessellations of arbitrarily curved structures and derives the mean value and standard deviation of the generated fields in a single-run. Also, the critical case of geometrical and physical uncertainties is handled via an optimal parameterisation, which locally reforms the curvilinear grid. In order to pursue extra speed efficiency, code implementation is conducted through contemporary graphics processor units and parallel programming.

The curvilinear S-FDTD algorithm is proven very precise and stable, compared to existing multiple-realisation approaches, in the analysis of statistically-varying problems. Moreover, its generalised formulation allows the effective treatment of realistic structures with arbitrarily curved geometries, unlike staircase schemes. Finally, the GPU-based enhancements accomplish notably accelerated simulations that may exceed the level of 120 times. Conclusively, the featured technique can successfully attain highly accurate results with very limited system requirements.

Development of a generalised curvilinear S-FDTD methodology, based on a covariant/contravariant algorithm. Incorporation of the important geometric/physical uncertainties through a locally adaptive curved mesh. Speed advancement via modern GPU and CUDA programming which leads to reliable estimations, even for abrupt statistical media parameter fluctuations.

Classically the magnetic material models are considered with a deterministic approach. Nevertheless, when submitted to the fabrication process, the magnetic core properties are negatively impacted and may be subject to variability during the process. This variability can be of such importance that the performances of the final device (electrical machine) will also present a noticeable variability. The aim of this research is to develop a stochastic model of the magnetic behaviour law of slinky stators used in claw pole generators. The proposed methodology is general and can be applied to other physical properties of electrical devices.

The approach is based on a methodology that uses experimental data and a statistical description of the magnetic properties. To that end, a set of samples issued from the same chain of assembly is considered. The hysteresis model is then developed by accounting for the parameter correlation structure.

It is found that the magnetic hysteresis properties of the studied samples can be modelled by means of statistical tools applied to the parameters of the hysteresis model. The dependency of the parameters can also be accounted for a more accurate modelling.

The paper proposes a statistical approach and a methodology that are applied to the hysteresis modelling accounting for the variability of the magnetic properties. The developed model can be further used in a numerical tool to represent the impact on the performances of electrical devices that are subject to the fabrication process variability.

This paper aims to propose the use of isogeometric analysis (IGA) for the simulation of electrical machines to represent their geometries exactly and obtain numerical solutions of high accuracy and regularity.

IGA makes use of non-uniform rational b-splines to parametrise the domain and approximate the solution spaces. Dealing with the different stator and rotor topologies, the computational domain is split into two non-overlapping parts on which Maxwell’s equations are solved independently and are interconnected by a classical Schwarz domain decomposition scheme. The results are compared with the conventional polynomial finite element method (FEM).

The new methodology is reliable and efficient. The obtained solutions of the fields are in good agreement with the ones obtained by the FEM approach. IGA offers a better accuracy than FEM.

The application of IGA combined with domain decomposition to the model of an electric machine is a new and original contribution.

Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations.

Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed.

The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation.

The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

Manufacturing processes, such as laminations, may introduce uncertainties in the magnetic properties of materials used in electrical machines. This issue, together with magnetization errors, can cause serious deterioration in the performance of the machines. Hence, stochastic material models are required for the study of the influences of the material uncertainties. The purpose of this paper is to present a methodology to study the impact of magnetization pattern uncertainties in permanent magnet electric machines.

The impacts of material uncertainties on the performances of an interior permanent magnet (IPM) machine were analyzed using two different robustness metrics (worst-case analysis and statistical study). In addition, two different robust design formulations were applied to robust multi-objective machine design problems.

The computational analyses show that material uncertainties may result in deviations of the machine performances and cause nominal solutions to become non-robust.

In this paper, the authors present stochastic models for the quantification of uncertainties in both ferromagnetic and permanent magnet materials. A robust multi-objective evolutionary algorithm is demonstrated and successfully applied to the robust design optimization of an IPM machine considering manufacturing errors and operational condition changes.

Random media uncertainties exhibit a significant impact on the properties of electromagnetic fields that usually deterministic models tend to neglect. As a result, these models fail to quantify the variation in the calculated electromagnetic fields, leading to inaccurate outcomes. This paper aims to introduce an unconditionally stable finite-difference time-domain (FDTD) method for assessing two-dimensional random media uncertainties in one simulation.

The proposed technique is an extension of the stochastic FDTD (S-FDTD) scheme, which approximates the variance of a given field component using the Delta method. Specifically in this paper, the Delta method is applied to the locally one-dimensional (LOD) FDTD scheme (hence named S-LOD-FDTD), to achieve unconditional stability. The validity of this algorithm is tested by solving two-dimensional random media problems and comparing the results with other methods, such as the Monte-Carlo (MC) and the S-FDTD techniques.

This paper provides numerical results that prove the unconditional stability of the S-LOD-FDTD technique. Also, the comparison with the MC and the S-FDTD methods shows that reliable outcomes can be extracted even with larger time steps, thus making this technique more efficient than the other two aforementioned schemes.

The S-LOD-FDTD method requires the proper quantification of various correlation coefficients between the calculated fields and the electrical parameters, to achieve reliable results. This cannot be known beforehand and the only known way to calculate them is to run a fraction of MC simulations.

This paper introduces a new unconditional stable technique for measuring material uncertainties in one realization.