scholarly journals Efficient Uncertainty Assessment in EM Problems via Dimensionality Reduction of Polynomial-Chaos Expansions

Technologies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 37
Author(s):  
Christos Salis ◽  
Nikolaos Kantartzis ◽  
Theodoros Zygiridis
Keyword(s):  
Dimensionality Reduction ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Uncertainty Assessment ◽  
Test Cases ◽  
Stochastic Inputs ◽  
Dimensionality Reduction Technique ◽  
Sensitivity Analysis Method ◽  
Polynomial Chaos Expansions ◽  
Involved Field

The uncertainties in various Electromagnetic (EM) problems may present a significant effect on the properties of the involved field components, and thus, they must be taken into consideration. However, there are cases when a number of stochastic inputs may feature a low influence on the variability of the outputs of interest. Having this in mind, a dimensionality reduction of the Polynomial Chaos (PC) technique is performed, by firstly applying a sensitivity analysis method to the stochastic inputs of multi-dimensional random problems. Therefore, the computational cost of the PC method is reduced, making it more efficient, as only a trivial accuracy loss is observed. We demonstrate numerical results about EM wave propagation in two test cases and a patch antenna problem. Comparisons with the Monte Carlo and the standard PC techniques prove that satisfying outcomes can be extracted with the proposed dimensionality-reduction technique.

An adaptive sparse polynomial-chaos technique based on anisotropic indices

2020 ◽  
Vol 39 (3) ◽  
pp. 691-707
Author(s):  
Christos Salis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros Zygiridis
Keyword(s):  
Polynomial Chaos ◽  
Computational Cost ◽  
Uncertainty Assessment ◽  
Design Parameters ◽  
Test Problems ◽  
Content Type ◽  
Sparse Polynomial ◽  
Index Sets ◽  
The Mean ◽  
Expansion Coefficients

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

scholarly journals Stability analysis of a clutch system with uncertain parameters using sparse polynomial chaos expansions

2019 ◽  
Vol 20 (1) ◽  
pp. 104
Author(s):  
Duc Thinh Kieu ◽  
Baptiste Bergeot ◽  
Marie-Laure Gobert ◽  
Sébastien Berger
Keyword(s):  
Stability Analysis ◽  
Polynomial Chaos ◽  
Deterministic Model ◽  
Computational Cost ◽  
Uncertain Parameters ◽  
Sparse Polynomial ◽  
Clutch System ◽  
Frictional Forces ◽  
The Stability ◽  
Polynomial Chaos Expansions

In vehicle transmission systems, frictional forces acting during the sliding phase of the clutch engagement may produce unwanted vibrations. The prediction of the stability of a clutch system remains however a laborious task, as the parameters which have the highest impact on the stability, such as the friction law or the damping, lead to significant dispersions and must be considered as uncertain in such studies. Non-intrusive generalized polynomial chaos (gPC) expansions have already been used in this context. However, the number of deterministic model evaluations (i.e. the computational cost) required to compute the PC coefficients becomes prohibitive for large numbers of uncertain parameters. The sparse polynomial chaos, recently developed by Blatman and Sudret, may overcome this issue. In this paper, the method has been applied to the stability analysis of a clutch system owning up to eight uncertain parameters. Comparisons with the reference Monte Carlo method and classic full PC expansions show that sparse PC expansions allow substantial computational cost reductions while ensuring a high accuracy of the results.

scholarly journals Surrogate models for unsteady aerodynamics using non-intrusive Polynomial Chaos Expansions

2020 ◽  
Author(s):  
Rad Haghi ◽  
Curran Crawford
Keyword(s):  
Wind Turbine ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Unsteady Aerodynamics ◽  
Turbulence Models ◽  
Accurate Estimation ◽  
Time Step ◽  
Extreme Loads ◽  
The Time Domain ◽  
Polynomial Chaos Expansions

Abstract. In common industrial practice based on IEC standards, wind turbine simulations are computed in the time domain for each mean wind speed bin using six unsteady wind seeds. Different software such as FAST, Balded or HAWC2 can be used to this purpose, to capture the unsteadiness and uncertainties of the wind in the simulations. The statistics of these simulations are extracted and used to calculate fatigue and extreme loads on the wind turbine components. Having only six seeds does not guarantee an accurate estimation of the overall statistics. One solution might be running more seeds; however, this will increase the computation cost. Moreover, to move beyond Blade Element Momentum based tools toward vortex/potential flow formulations, a reduction in the computational cost associated with the unsteady flow and uncertainty handling is required. This study illustrates the stationary character of the unsteady aerodynamic statistics based on the standard turbulence models. Afterward, we propose a non-intrusive Polynomial Chaos Expansion to build a surrogate model of the loads' statistics at each time step, to estimate the statistics more accurately and efficiently.

scholarly journals Sensitivity Analysis Based on Polynomial Chaos Expansions and Its Application in Ship Uncertainty-Based Design Optimization

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Xiao Wei ◽  
Haichao Chang ◽  
Baiwei Feng ◽  
Zuyuan Liu
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Polynomial Chaos ◽  
Early Stage ◽  
Computational Cost ◽  
Sensitivity Index ◽  
Uncertain Variables ◽  
Polynomial Coefficients ◽  
Sensitivity Indices ◽  
Polynomial Chaos Expansions

In order to truly reflect the ship performance under the influence of uncertainties, uncertainty-based design optimization (UDO) for ships that fully considers various uncertainties in the early stage of design has gradually received more and more attention. Meanwhile, it also brings high dimensionality problems, which may result in inefficient and impractical optimization. Sensitivity analysis (SA) is a feasible way to alleviate this problem, which can qualitatively or quantitatively evaluate the influence of the model input uncertainty on the model output, so that uninfluential uncertain variables can be determined for the descending dimension to achieve dimension reduction. In this paper, polynomial chaos expansions (PCE) with less computational cost are chosen to directly obtain Sobol' global sensitivity indices by its polynomial coefficients; that is, once the polynomial of the output variable is established, the analysis of the sensitivity index is only the postprocessing of polynomial coefficients. Besides, in order to further reduce the computational cost, for solving the polynomial coefficients of PCE, according to the properties of orthogonal polynomials, an improved probabilistic collocation method (IPCM) based on the linear independence principle is proposed to reduce sample points. Finally, the proposed method is applied to UDO of a bulk carrier preliminary design to ensure the robustness and reliability of the ship.

scholarly journals Efficient Bayesian calibration of aerodynamic wind turbine models using surrogate modeling

2021 ◽  
Author(s):  
Benjamin Sanderse ◽  
Vinit V. Dighe ◽  
Koen Boorsma ◽  
Gerard Schepers
Keyword(s):  
New Mexico ◽  
Wind Turbine ◽  
Polynomial Chaos ◽  
Global Sensitivity Analysis ◽  
Measurement Data ◽  
Model Parameters ◽  
Test Cases ◽  
Parameter Calibration ◽  
Bayesian Calibration ◽  
Polynomial Chaos Expansions

Abstract. This paper presents an efficient strategy for the Bayesian calibration of parameters of aerodynamic wind turbine models. The strategy relies on constructing a surrogate model (based on adaptive polynomial chaos expansions), which is used to perform both parameter selection using global sensitivity analysis and parameter calibration with Bayesian inference. The effectiveness of this approach is shown in two test cases: calibration of airfoil polars based on the measurements from the DanAero MW experiments, and calibration of five yaw model parameters based on measurements on the New MEXICO turbine in yawed conditions. In both cases, the calibrated models yield results much closer to the measurement data, and in addition they are equipped with an estimate of the uncertainty in the predictions.

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