Uncertainty Analysis of a Near-Field Acoustic Levitation System

  • Fran Sérgio LobatoEmail author
  • Geisa Arruda Zuffi
  • Aldemir Ap. CavaliniJr.
  • Valder SteffenJr.
Part of the Studies in Computational Intelligence book series (SCI, volume 872)


Near-field acoustic levitation is a physical phenomenon that occurs when a planar object is placed in the proximity of a vibrating surface. Consequently, a thin layer of ambient gas, commonly referred to as squeeze film, is trapped in the clearance between a vibrating surface and an adjacent planar object performing its levitation. Mathematically, this phenomenon is described by using the Reynolds equation, which is derived from the Navier–Stokes momentum and continuity equations. The equation of motion that represents the dynamic behavior of the levitated object is also considered. However, the performance of the near-field acoustic levitation can be significantly affected by uncertainties on its geometrical parameters and operating conditions. Thus, the present contribution aims to evaluate the influence of uncertain parameters on the resulting levitation force. For this purpose, the differential evolution algorithm is associated with two strategies (inverse reliability analysis and effective mean concept). This multi-objective optimization problem considers the maximization of the levitation force associated with the maximization of both the reliability and robustness coefficients. Numerical simulations demonstrated the sensitivity of each uncertain parameter associated to the obtained levitation forces. As expected, it was verified that the levitation force decreases as the considered reliability and robustness coefficients increases.


Uncertainties Sensitivity Near-field acoustic levitation Multi-objective optimization Differential evolution 



The authors are thankful for the financial support provided to the present research effort by CNPq (574001/2008-5, 304546/2018-8, and 431337/2018-7), FAPEMIG (TEC-APQ-3076-09, TEC-APQ-02284-15, TEC-APQ-00464-16, and PPM-00187-18), and CAPES through the INCT-EIE.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Fran Sérgio Lobato
    • 1
    Email author
  • Geisa Arruda Zuffi
    • 2
  • Aldemir Ap. CavaliniJr.
    • 2
  • Valder SteffenJr.
    • 2
  1. 1.NUCOP, Laboratory of Modeling, Simulation, Control and Optimization of Processes, School of Chemical EngineeringFederal University of UberlândiaUberlândiaBrazil
  2. 2.LMEst, Laboratory of Mechanics and Structures, School of Mechanical EngineeringFederal University of UberlândiaUberlândiaBrazil

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