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Bayesian Regression Based Approach for Beam Deflection Estimation

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Języki publikacji
EN
Abstrakty
EN
Deflection of a beam is the movement of the beam from its initial position to another position depending on the applied load. Beam deflection estimation gives an indication about the possible deformation of the beam. A parametric Bayesian linear based model is introduced to mimic the experimentally collected data to estimate the stochastic deflection of a simply supported beam. A Gaussian noise is assumed to understand the stochastic behavior of the beam deflection as well as a Gaussian prior. The model mapping function used in this work is known as radial basis function, which can be linear or nonlinear. Three basis functions are compared, namely are linear, Gaussian and modified Gaussian function proposed in this work. The modified Gaussian function is a simple function introduced in this work. The performance of the functions is analyzed for three central concentrated loads. The best model can describe the observed data is found to be the modified Gaussian model with regularization factor of 0.9 for three loading cases. The prediction based linear basis function is better than the use of the Gaussian basis function prediction according to error of estimation. The maximum RMS error obtained for modified Gaussian radial basis function corresponding to central load of 4kg is smaller than that of a theoretical based model for the same loading conditions.
Twórcy
  • Basra Engineering Technical College, Southern Technical University, Basra, Iraq
  • Basra Engineering Technical College, Southern Technical University, Basra, Iraq
  • Basra Engineering Technical College, Southern Technical University, Basra, Iraq
  • Basra Engineering Technical College, Southern Technical University, Basra, Iraq
Bibliografia
  • 1. Groth C, Porziani S, Biancolini ME. Radial basis functions vector fields interpolation for complex fluid structure interaction problems. Fluids. 2021; 6(9): 314.
  • 2. Geronzi L, Gasparotti E, Capellini K, Cella U, Groth C, Porziani S, et al. High fidelity fluid-structure interaction by radial basis functions mesh adaption of moving walls: A workflow applied to an aortic valve. Journal of Computational Science. 2021; 51: 101327.
  • 3. Belendez T, Neipp C, Belendez A. Numerical and Experimental Analysis of a Cantilever Beam: a Laboratory Project to Introduce Geometric Nonlinearity in Mechanics of Materials. Int. J. Eng. Ed. 2003; 19(6): 885-892.
  • 4. Zhang Q, Fu X, Ren L. Deflection estimation of beam structures based on the measured strain mode shape. Smart Materials and Structures. 2021; 30(10): 105003.
  • 5. Argyris C, Papadimitriou C, Panetsos P, Tsopelas P. Bayesian model-updating using features of modal data: Application to the Metsovo Bridge. Journal of Sensor and Actuator Networks. 2020; 9(2): 27.
  • 6. Wang F, Zheng K, Ahmad I, Ahmad H. Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena. Open Physics. 2021; 19(1): 69–76.
  • 7. Zeng J, Kim Y. Stiffness modification-based bayesian finite element model updating to solve coupling effect of structural parameters: Formulations. Applied Sciences. 2021; 11: 10615.
  • 8. Kundu A, Adhikari S, Friswell M. Stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty. International Journal for Numerical Methods in Engineering. 2014; 100: 183–221.
  • 9. Hon Y,Ling L, Liew K. Numerical analysis of parameters in a laminated beam model by radial basis functions. CMC. 2005; 2(1): 39-49.
  • 10. Beam deflection estimation by Monte Carlo simulation and Kalman filter based ultrasonic distance sensor. In: Proc. of 2nd International Scientific Conference of Al-Ayen University IOP Conf. Series: Materials Science and Engineering. 2020, 928, 022113.
  • 11. El-beltagy M, Galal O. Uncertainty Quantification of a 1-D Beam Deflection Due Stochastic Parameters. In: Numerical Analysis and Applied Mathematics (ICNAAM) conference, Greece, 2011, 2000-2003.
  • 12. Kraaij CS Model updating of a ‘clamped’-free beam system using FEMTOOLS. Technische Universiteit Eindhoven, 2007.
  • 13. Boulkaibet I, Marwala T, Mthembu L, Friswell M, Adhikari S. Sampling techniques in bayesian finite element model updating. In: Proc. of Conference of the Society for Experimental Mechanics. 2012, 75-83.
  • 14. Hack E, Lin X, Patterson E. A reference material for establishing uncertainties in full-field displacement measurements, Measurement Science and Technology. 2015; 26: 1-13.
  • 15. Soman R, Malinowski P, Majewska K. Kalman filter based neutral axis tracking in composites under varying temperature conditions. Mechanical Systems and Signal Processing. 2018; 110: 485-498.
  • 16. Barber D. In: Bayesian reasoning and Machine Learning. Cambridge: Cambridge University Press; 2018.
  • 17. Murphy KP. Machine learning: A probabilistic perspective. Cambridge, MA: MIT Press; 2021.
  • 18. Bishop CM. Pattern recognition and machine learning. New York: Springer; 2016.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-d9395aef-3dbe-4fb7-aa0a-38019e796c51
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