How do different distributions of random input have an effect on output results in a simulated physical model?

Document Type : Original Scientific Paper

Authors

Department of Physics‎, ‎Yazd University‎, ‎Yazd‎, ‎Iran

Abstract

Statistical methods are practical and unavoidable in analysis of physical and engineering results‎. ‎Study of anufacturing errors and uncertainties in construction of radio frequency structures is one of cases which statistical quantities is used‎. ‎In this paper‎, ‎we quantify uncertainty in the cutoff frequency of a waveguide using the chaos polynomial expansion method‎. ‎Different distributions for uncertainty in the waveguide width are considered‎. ‎We then investigate the effect of the distributions on the waveguide cutoff frequency‎. ‎Using statistical quantities‎, ‎we determine the amount of acceptable error during the construction of the waveguide such that it does not affect the wavequide performance.

Keywords


Adelmann, A. (2015). On uncertainty quantification in particle accelerators modelling. arXiv:1509.08130.
Acharjee, S. and Zabaras, N. (2006). Uncertainty propagation in finite deformations-A spectral stochastic Lagrangian approach. Computer Methods in Applied Mechanics and Engineering, 195(19-22):2289–2312.
Ameta, G., Lipman, R., Moylan, S. and Witherell, P. (2015). Investigating the role of geometric dimensioning and tolerancing in additive manufacturing. Journal of Mechanical Design, 137(11):111706.
Barany, I. and Vu, V. (2007). Central limit theorems for Gaussian polytopes. The Annals of Probability, 55(4):1593–1621.
Carrillo, J.A. and Zanella, M. (2019). Monte Carlo gPC methods for diffusive kinetic flocking models with uncertainties. Vietnam Journal of Mathematics, 47(4):931–954.
DeGennaro, A.M., Rowley, C.W. and Martinelli, L. (2015). Uncertainty quantification for airfoil icing using polynomial chaos expansions. Journal of Aircraft, 52(5):1404–1411.
Ghanem, R.G. and Spanos, P.D. (1991). Stochastic finite element method: Response statistics. Stochastic Finite Elements: A Spectral Approach, 101–119.
Hadj Kacem, M., El Hami, A., Dammak, K., Trabelsi, H., Walha, L. and Haddar, M. (2022). Consideration of multi-variable uncertainty using the GPC method for the dynamic study of a two-stage gearbox of a wind turbine. Mechanics of Advanced Materials and Structures. doi: 10.1080/15376494.2022.2138650.
Le Maitre, O.P. and Knio, O.M. (2007). A stochastic particle-mesh scheme for uncertainty propagation in vortical flows. Journal of Computational Physics, 226(1):645–671.
Mesogitis, T.S., Skordos, A.A. and Long, A.C. (2014). Uncertainty in the manufacturing of fibrous thermosetting composites: A review. Composites Part A: Applied Science and Manufacturing, 57:67–75.
Mostajeran, M., Tulu, E.T. and van Rienen, U. (2021). Uncertainty in the isosceles multipactor threshold of triangularly grooved surfaces based on polynomial chaos. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 993:165001.
Poette, G. (2019). A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation. Journal of Computational Physics, 385:135–162.
Poette, G. (2022). Numerical analysis of the Monte-Carlo noise for the resolution of the deterministic and uncertain linear Boltzmann equation (comparison of non-intrusive gPC and MC-gPC). Journal of Computational and Theoretical Transport, 51(1-3):1–53.
Pollock, M.J., MacGregor, J.F. and Hamielec, A.E. (1979). A statistical evaluation of methods of chromatogram interpretation-gpc. Journal of Liquid Chromatography, 2(7):895–917.
Pozar, D.M. (2011). Microwave Engineering. John Wiley & Sons.
Schmidt, C., Flisgen, T., Heller, J. and van Rienen, U. (2014). Comparison of techniques for uncertainty quantification of superconducting radio frequency cavities. International Conference on Electromagnetics in Advanced Applications (ICEAA), 117–120.
Schmidt, C., Grant, P., Lowery, M. and van Rienen, U. (2012). Influence of uncertainties in the material properties of brain tissue on the probabilistic volume of tissue activated. IEEE Transactions on Biomedical Engineering, 60(5):1378–1387.
Stoer, J. (2006). Springer Series in Computational Mathematics. Springer Press.
Wan, X. and Karniadakis, G.E. (2006). Stochastic heat transfer enhancement in a grooved channel. Journal of Fluid Mechanics, 565:255–278.
Xiu, D. (2009). Fast numerical methods for stochastic computations: a review. Communications in Computational Physics, 5(2-4):242–272.