1932

Abstract

Physical interactions between a fluid and structure, potentially manifested as self-sustained or divergent oscillations, can be sensitive to many parameters whose values are uncertain. Of interest here are aircraft aeroelastic interactions, which must be accounted for in aircraft certification and design. Deterministic prediction of these aeroelastic behaviors can be difficult owing to physical and computational complexity. New challenges are introduced when physical parameters and elements of the modeling process are uncertain. By viewing aeroelasticity through a nondeterministic prism, where key quantities are assumed stochastic, one may gain insights into how to reduce system uncertainty, increase system robustness, and maintain aeroelastic safety. This article reviews uncertainty quantification in aeroelasticity using traditional analytical techniques not reliant on computational fluid dynamics; compares and contrasts this work with emerging methods based on computational fluid dynamics, which target richer physics; and reviews the state of the art in aeroelastic optimization under uncertainty. Barriers to continued progress, for example, the so-called curse of dimensionality, are discussed.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-122414-034441
2017-01-03
2025-04-19
Loading full text...

Full text loading...

/deliver/fulltext/fluid/49/1/annurev-fluid-122414-034441.html?itemId=/content/journals/10.1146/annurev-fluid-122414-034441&mimeType=html&fmt=ahah

Literature Cited

  1. Allen M, Camberos J. 2009. Comparison of uncertainty propagation/response surface techniques for two aeroelastic systems Presented at AIAA Struct. Struct. Dyn. Mater. Conf., 50th, Palm Springs, CA, AIAA Pap. 2009-2269 [Google Scholar]
  2. Allen M, Maute K. 2004. Reliability-based design optimization of aeroelastic structures. Struct. Multidiscip. Optim. 27:228–42 [Google Scholar]
  3. Allen M, Maute K. 2005. Reliability-based shape optimization of structures undergoing fluid–structure interaction phenomena. Comput. Methods Appl. Mech. Eng. 194:3472–95 [Google Scholar]
  4. Attar PJ, Dowell EH. 2006. Stochastic analysis of a nonlinear aeroelastic model using the response surface method. J. Aircr. 43:1044–52 [Google Scholar]
  5. Badcock KJ, Timme S, Marques S, Khodaparast H, Prandina M. et al. 2011. Transonic aeroelastic simulation for instability searches and uncertainty analysis. Prog. Aerosp. Sci. 47:392–423 [Google Scholar]
  6. Bansal P, Pitt D. 2013. Stochastic variations in aerodynamic influence coefficients (AICs) on flutter prediction of a generic wing Presented at AIAA Struct. Struct. Dyn. Mater. Conf. , 54th. Boston, MA: AIAA Pap. 2013–1841 [Google Scholar]
  7. Barth T. 2013. Non-intrusive uncertainty propagation with error bounds for conservation laws containing discontinuities. See Bijl et al. 2013 1–57
  8. Basudhar A, Missoum S. 2013. Reliability assessment using probabilistic support vector machines. Int. J. Reliab. Saf. 7:156–73 [Google Scholar]
  9. Bendiksen OO. 2006. Non-Hopfian transonic flutter Presented at ASME 2006 Pressure Vessels Piping/ICPVT-11 Conf., PVP2006-ICPVT-11-93960 [Google Scholar]
  10. Bendiksen OO. 2009. High-altitude limit cycle flutter of transonic wings. J. Aircr. 46:123–36 [Google Scholar]
  11. Beran PS, Khot NS, Eastep FE, Snyder RD, Zweber JV. 2004a. Numerical analysis of store-induced limit-cycle oscillation. J. Aircr. 41:1315–26 [Google Scholar]
  12. Beran PS, Lucia D, Pettit CL. 2004b. Reduced-order modelling of limit-cycle oscillation for aeroelastic systems. J. Fluids Struct. 19:575–90 [Google Scholar]
  13. Beran PS, Pettit CL. 2004. A direct method for quantifying limit-cycle oscillation response characteristics in the presence of uncertainties Presented at AIAA Struct. Struct. Dyn. Mater. Conf. , 45th. Palm Springs, CA: AIAA Pap. 2004–1695 [Google Scholar]
  14. Beran PS, Pettit CL, Millman DR. 2006. Uncertainty quantification of limit-cycle oscillations. J. Comput. Phys. 217:217–47 [Google Scholar]
  15. Beran PS, Stanford B. 2013. Uncertainty quantification in aeroelasticity. See Bijl et al. 2013 59–103
  16. Bhatia M, Beran P. 2014. Higher-order transonic flutter solutions Presented at AIAA Struct. Struct. Dyn. Mater. Conf. , 55th. National Harbor, MD: AIAA Pap. 2014–0336 [Google Scholar]
  17. Bhatia M, Beran P. 2015. h-Adaptive stabilized finite-element solver for calculation of generalized aerodynamic forces. AIAA J. 53:554–72 [Google Scholar]
  18. Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM. 2008. Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J. 46:2459–68 [Google Scholar]
  19. Bijl H, Lucor D, Mishra S, Schwab C. 2013. Uncertainty Quantification in Computational Fluid Dynamics Lect. Notes Comput. Sci. Eng. 92. New York: Springer [Google Scholar]
  20. Bisplinghoff RL, Ashley H, Halfman RL. 1955. Aeroelasticity New York: Addison-Wesley [Google Scholar]
  21. Blatman G, Sudret B. 2010. An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probab. Eng. Mech. 25:1831–97 [Google Scholar]
  22. Bryson DE, Rumpfkeil MP. 2016. Variable-fidelity surrogate modeling of lambda wing transonic aerodynamic performance Presented at AIAA Aerosp. Sci. Meet. , 54th. San Diego, CA: AIAA Pap. 2016–0294 [Google Scholar]
  23. Bunton RW, Denegri CM. 2000. Limit cycle oscillation characteristics of fighter aircraft. J. Aircr. 37:916–18 [Google Scholar]
  24. Caracoglia L. 2013. An Euler–Monte Carlo algorithm assessing moment Lyapunov exponents for stochastic bridge flutter predictions. Comput. Struct. 122:65–77 [Google Scholar]
  25. Castravete SC, Ibrahim RA. 2008. Effect of stiffness uncertainties on the flutter of a cantilever wing. AIAA J. 46:925–35 [Google Scholar]
  26. Chen P, Sarhaddi D, Liu D. 1998. Limit-cycle oscillation studies of a fighter with external stores Presented at AIAA Struct. Struct. Dyn. Mater. Conf. , 39th. Long Beach, CA: AIAA Pap. 1998–1727 [Google Scholar]
  27. Constantine PG, Dow E, Wang Q. 2014. Active subspace methods in theory and practice: applications to Kriging surfaces. SIAM J. Sci. Comput. 36:A1500–24 [Google Scholar]
  28. Cunningham A. 1998. The role of non-linear aerodynamics in fluid-structure interaction Presented at AIAA Fluid Dyn. Conf , 29th. Albuquerque, NM: AIAA Pap. 1998–2423 [Google Scholar]
  29. Dai Y, Yang C. 2014. Methods and advances in the study of aeroelasticity with uncertainties. Chin. J. Aeronaut. 27:461–74 [Google Scholar]
  30. Denegri CM, Dubben JA, Kernazhitskiy SL. 2013. Underwing missile aerodynamic effects on flight-measured limit-cycle oscillations. J. Aircr. 50:1637–45 [Google Scholar]
  31. Devathi H, Hu Z, Mahadevan S. 2016. Modeling epistemic uncertainty in the representation of spatial and temporal variability in reliability analysis Presented at AIAA Non-Deterministic Approaches Conf. , 18th. San Diego, CA: AIAA Pap. 2016–1677 [Google Scholar]
  32. Dowell EH. 2015. A Modern Course in Aeroelasticity New York: Springer, 5th rev. ed.. [Google Scholar]
  33. Dowell EH, Edwards J, Strganac T. 2003. Nonlinear aeroelasticity. J. Aircr. 40:857–74 [Google Scholar]
  34. Dowell EH, Hall KC. 2001. Modeling of fluid-structure interaction. Annu. Rev. Fluid Mech. 33:445–90 [Google Scholar]
  35. Dwight RP, Witteveen JA, Bijl H. 2013. Adaptive uncertainty quantification for computational fluid dynamics. See Bijl et al. 2013 151–91
  36. Eldred M. 2009. Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design Presented at AIAA Struct. Struct. Dyn. Mater. Conf , 50th. Palm Springs, CA: AIAA Pap. 2009–2274 [Google Scholar]
  37. Eldred M, Burkardt J. 2009. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification Presented at AIAA Aerosp. Sci. Meet. , 47th. Orlando, FL: AIAA Pap. 2009–976 [Google Scholar]
  38. Farhat C, Geuzaine P, Brown G. 2003. Application of a three-field nonlinear fluid–structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Comput. Fluids 32:3–29 [Google Scholar]
  39. Friedmann PP, Hodges DH. 2003. Rotary wing aeroelasticity: a historical perspective. J. Aircr. 40:1019–46 [Google Scholar]
  40. Georgiou G, Manan A, Cooper J. 2012. Modeling composite wing aeroelastic behavior with uncertain damage severity and material properties. Mech. Syst. Signal. Proc. 32:32–43 [Google Scholar]
  41. Ghanem RG, Spanos PD. 1991. Stochastic Finite Elements: A Spectral Approach New York: Springer-Verlag [Google Scholar]
  42. Ghommem M, Hajj MR, Nayfeh AH. 2010. Uncertainty analysis near bifurcation of an aeroelastic system. J. Sound. Vib. 329:3335–47 [Google Scholar]
  43. Gordnier R, Melville R. 1999. Physical mechanisms for limit-cycle oscillations of a cropped delta wing Presented at Fluid Dyn. Conf. , 30th. Norfolk, VA: AIAA Pap. 1999–3796 [Google Scholar]
  44. Gordnier R, Visbal M. 2004. Computation of the aeroelastic response of a flexible delta wing at high angles of attack. J. Fluids Struct. 19:785–800 [Google Scholar]
  45. Hammersley J, Handscomb D. 1964. Monte Carlo Methods London: Methuen & Co. [Google Scholar]
  46. Hassig HJ. 1971. An approximate true damping solution of the flutter equation by determinant iteration. J. Aircr. 8:885–89 [Google Scholar]
  47. Hayes R, Marques SP. 2015. Prediction of limit cycle oscillations under uncertainty using a harmonic balance method. Comput. Struct. 148:1–13 [Google Scholar]
  48. Hayes R, Marques SP, Yao W. 2014. Analysis of transonic limit cycle oscillations under uncertainty Presented at R. Aeronaut. Soc. Aircr. Struct. Des. Conf. , 4th. Belfast [Google Scholar]
  49. Hosder S, Walters R, Balch M. 2008. Efficient uncertainty quantification applied to the aeroelastic analysis of a transonic wing Presented at AIAA Aerosp. Sci. Meet. Exhib. , 46th. Reno, NV: AIAA Pap. 2008–729 [Google Scholar]
  50. Khodaparast HH. 2010. Stochastic finite element model updating and its application in aeroelasticity PhD Thesis Univ. Liverpool [Google Scholar]
  51. Khodaparast HH, Mottershead JE, Badcock KJ. 2010. Propagation of structural uncertainty to linear aeroelastic stability. Comput. Struct. 88:223–36 [Google Scholar]
  52. Komerath NM, Schwartz RJ, Kim JM. 1992. Flow over a twin-tailed aircraft at angle of attack. II. Temporal characteristics. J. Aircr. 29:553–58 [Google Scholar]
  53. Kunz DL. 2005. Analysis of proprotor whirl flutter: review and update. J. Aircr. 42:172–78 [Google Scholar]
  54. Kurdi M, Lindsley N, Beran P. 2007. Uncertainty quantification of the Goland+wing's flutter boundary Presented at AIAA Atmos. Flight Mech. Conf. Hilton Head, SC: AIAA Pap. 2007–6309 [Google Scholar]
  55. Lamorte N, Friedmann PP, Glaz B, Culler AJ, Crowell AR, McNamara JJ. 2014. Uncertainty propagation in hypersonic aerothermoelastic analysis. J. Aircr. 51:192–203 [Google Scholar]
  56. Le Maître OP, Knio OM, Najm HN, Ghanem RG. 2001. A stochastic projection method for fluid flow: I. Basic formulation. J. Comput. Phys. 173:481–511 [Google Scholar]
  57. Liaw D, Yang HT. 1991. Reliability of uncertain laminated shells due to buckling and supersonic flutter. AIAA J. 29:1698–708 [Google Scholar]
  58. Lindsley NJ, Beran PS, Pettit CL. 2006a. Integration of model reduction and probabilistic techniques with deterministic multi-physics models Presented at AIAA Aerosp. Sci. Meet. Exhib. , 44th. Reno, NV: AIAA Pap. 2006–192 [Google Scholar]
  59. Lindsley NJ, Pettit CL, Beran PS. 2006b. Nonlinear plate aeroelastic response with uncertain stiffness and boundary conditions. Struct. Infrastruct. Eng. 2:201–20 [Google Scholar]
  60. Livne E. 2003. Future of airplane aeroelasticity. J. Aircr. 40:1066–92 [Google Scholar]
  61. Lucia DJ, Beran PS, Silva WA. 2004. Reduced-order modeling: new approaches for computational physics. Prog. Aerosp. Sci. 40:51–117 [Google Scholar]
  62. Manan A, Cooper J. 2009. Design of composite wings including uncertainties: a probabilistic approach. J. Aircr. 46:601–7 [Google Scholar]
  63. Mani K, Mavriplis DJ. 2008. Unsteady discrete adjoint formulation for two-dimensional flow problems with deforming meshes. AIAA J. 46:1351–64 [Google Scholar]
  64. Mantegazza P, Bindolino G. 1987. Aeroelastic derivatives as a sensitivity analysis of nonlinear equations. AIAA J. 25:1145–46 [Google Scholar]
  65. Marques S, Badcock KJ, Khodaparast HH, Mottershead JE. 2010. Transonic aeroelastic stability predictions under the influence of structural variability. J. Aircr. 47:1229–39 [Google Scholar]
  66. Melchers RE. 1987. Structural Reliability Chichester, UK: Horwood [Google Scholar]
  67. Millman DR. 2004. Quantifying initial condition and parametric uncertainties in a nonlinear aeroelastic system with an efficient stochastic algorithm PhD Thesis Air Force Inst. Technol., Wright-Patterson Air Force Base OH: [Google Scholar]
  68. Millman DR, King PI, Beran PS. 2005. Airfoil pitch-and-plunge bifurcation behavior with Fourier chaos expansions. J. Aircr. 42:376–84 [Google Scholar]
  69. Millman DR, King PI, Maple RC, Beran PS, Chilton LK. 2006a. Estimating the probability of failure of a nonlinear aeroelastic system. J. Aircr. 43:504–16 [Google Scholar]
  70. Millman DR, King PI, Maple RC, Beran PS, Chilton LK. 2006b. Uncertainty quantification with a B-spline stochastic projection. AIAA J. 44:1845–53 [Google Scholar]
  71. Missoum S, Dribusch C, Beran P. 2010. Reliability-based design optimization of nonlinear aeroelasticity problems. J. Aircr. 47:992–98 [Google Scholar]
  72. Morton SA, Beran PS. 1999. Hopf-bifurcation analysis of airfoil flutter at transonic speeds. J. Aircr. 36:421–29 [Google Scholar]
  73. Murugan S, Harusampath D, Ganguli R. 2008. Material uncertainty propagation in helicopter nonlinear aeroelastic response and vibration analysis. AIAA J. 46:2332–44 [Google Scholar]
  74. Najm HN. 2009. Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. Annu. Rev. Fluid Mech. 41:35–52 [Google Scholar]
  75. Nav. Air Syst. Command. 1993. Airplane strength and rigidity, vibration, flutter, and divergence. Mil. Specif. MIL-A-8870C, Nav. Air Syst. Command, Dep. Navy [Google Scholar]
  76. Nikbay M, Acar P. 2015. Multidisciplinary uncertainty quantification in aeroelastic analyses of semi-span supersonic transport wing Presented at AIAA Multidiscip. Anal. Optim. Conf. , 16th. AIAA Pap. 2015–3441 [Google Scholar]
  77. Nikbay M, Kuru MN. 2013. Reliability based multidisciplinary optimization of aeroelastic systems with structural and aerodynamic uncertainties. J. Aircr. 50:708–15 [Google Scholar]
  78. Oberkampf WL, Roy CJ. 2010. Verification and Validation in Scientific Computing Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  79. Padulo M, Campobasso MS, Guenov MD. 2011. Novel uncertainty propagation method for robust aerodynamic design. AIAA J. 49:530–43 [Google Scholar]
  80. Paiva RM, Crawford C, Suleman A. 2014. Robust and reliability-based design optimization framework for wing design. AIAA J. 52:711–24 [Google Scholar]
  81. Pettit CL. 2004. Uncertainty quantification in aeroelasticity: recent results and research challenges. J. Aircr. 41:1217–29 [Google Scholar]
  82. Pettit CL, Beran PS. 2004. Polynomial chaos expansion applied to airfoil limit cycle oscillations Presented at AIAA Struct. Struct. Dyn. Mater. Conf. , 45th. Palm Springs, CA: AIAA Pap. 2004–1691 [Google Scholar]
  83. Pettit CL, Grandhi RV. 2003. Optimization of a wing structure for gust response and aileron effectiveness. J. Aircr. 40:1185–91 [Google Scholar]
  84. Rackwitz R. 2001. Reliability analysis—a review and some perspectives. Struct. Saf. 23:365–95 [Google Scholar]
  85. Rallabhandi S, West T, Nielsen E. 2015. Uncertainty analysis and robust design of low-boom concepts using atmospheric adjoints Presented at AIAA Appl. Aerodyn. Conf. , 33rd. Dallas, TX: AIAA Pap. 2015–2582 [Google Scholar]
  86. Reed B. 1981. Flutter at a Glance NASA Tech. Film Serial L-1274, NASA Washington, DC: [Google Scholar]
  87. Riley ME. 2011. Quantification of model-form, predictive, and parametric uncertainties in simulation-based design PhD Thesis Wright State Univ. Dayton, OH: [Google Scholar]
  88. Riley ME, Grandhi RV, Kolonay R. 2011. Quantification of modeling uncertainty in aeroelastic analyses. J. Aircr. 48:866–73 [Google Scholar]
  89. Roache PJ. 1997. Quantification of uncertainty in computational fluid dynamics. Annu. Rev. Fluid Mech. 29:123–60 [Google Scholar]
  90. Roderick O, Anitescu M, Fischer P. 2010. Polynomial regression approaches using derivative information for uncertainty quantification. Nucl. Sci. Eng. 164:122–39 [Google Scholar]
  91. Sarkar S, Witteveen JAS, Loeven A, Bijl H. 2009. Effect of uncertainty on the bifurcation behavior of pitching airfoil stall flutter. J. Fluids Struct. 25:304–20 [Google Scholar]
  92. Scarth C, Cooper JE, Weaver PM, Silva GHC. 2014. Uncertainty quantification of aeroelastic stability of composite plate wings using lamination parameters. Compos. Struct. 116:84–93 [Google Scholar]
  93. Scarth C, Sartor P, Cooper J, Weaver P, Silva G. 2015. Robust aeroelastic design of a composite wing-box Presented at AIAA Non-Deterministic Approaches Conf. , 17th. Kissimmee, FL: AIAA Pap. 2015–0918 [Google Scholar]
  94. Stanford B, Beran P. 2012. Computational strategies for reliability-based structural optimization of aeroelastic limit cycle oscillations. Struct. Multidiscip. Optim. 45:83–99 [Google Scholar]
  95. Stanford B, Beran P. 2013a. Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization. J. Fluids Struct. 36:111–23 [Google Scholar]
  96. Stanford B, Beran P. 2013b. Minimum-mass panels under probabilistic aeroelastic flutter constraints. Finite Element Anal. Des. 70–71:15–26 [Google Scholar]
  97. Tang D, Dowell EH. 2010. Aeroelastic airfoil with free play at angle of attack with gust excitation. AIAA J. 48:427–42 [Google Scholar]
  98. Thomas J, Dowell E, Hall K, Denegri C. 2006. An investigation of the sensitivity of F-16 fighter flutter onset and limit cycle oscillations to uncertainties Presented at AIAA Struct. Struct. Dyn. Mater. Conf. , 47th. Newport, RI: AIAA Pap. 2006–1847 [Google Scholar]
  99. Timme S. 2010. Transonic aeroelastic instability searches using a hierarchy of aerodynamic models PhD Thesis Univ. Liverpool [Google Scholar]
  100. Timme S, Badcock KJ. 2009. Oscillatory behavior of transonic aeroelastic instability boundaries. AIAA J. 47:1590–92 [Google Scholar]
  101. Timme S, Badcock KJ. 2010. Searching for transonic aeroelastic instability using an aerodynamic model hierarchy Presented at AIAA/ASME/ASCE/AHS/ASC Struct. Struct. Dyn. Mater. Conf. , 51st. Orlando, FL: AIAA Pap. 2010–3048 [Google Scholar]
  102. Timme S, Marques S, Badcock K. 2010. Transonic aeroelastic stability analysis using a Kriging-based Schur complement formulation Presented at AIAA Atmos. Flight Mech. Conf. Toronto: AIAA Pap. 2010–8228 [Google Scholar]
  103. Verhoosel CV, Scholcz TP, Hulshoff SJ, Gutiérrez MA. 2009. Uncertainty and reliability analysis of fluid-structure stability boundaries. AIAA J. 47:91–104 [Google Scholar]
  104. Wang Q, Hu R, Blonigan P. 2014. Least squares shadowing sensitivity analysis of chaotic limit cycle oscillations. J. Comput. Phys. 267:210–24 [Google Scholar]
  105. Witteveen JA. 2009. Efficient and robust uncertainty quantification for computational fluid dynamics and fluid-structure interaction PhD Thesis Delft Univ. Technol. [Google Scholar]
  106. Xiu D, Karniadakis G. 2002. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24:619–44 [Google Scholar]
  107. Xiu D, Lucor D, Su CH, Karniadakis GM. 2002. Stochastic modeling of flow-structure interactions using generalized polynomial chaos. J. Fluids Eng. 124:51–59 [Google Scholar]
  108. Yao W, Chen X, Luo W, van Tooren M, Guo J. 2011. Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles. Prog. Aerosp. Sci. 47:450–79 [Google Scholar]
  109. Yates EC. 1988. Agard standard aeroelastic configurations for dynamic response I—wing 445.6 AGARD Rep. 265, NATO Brussels: [Google Scholar]
  110. Yi L, Zhichun Y. 2010. Uncertainty quantification in flutter analysis for an airfoil with preloaded freeplay. J. Aircr. 47:1454–57 [Google Scholar]
  111. Zang TA, Hemsch MJ, Hilburger MW, Kenny SP, Luckring JM. et al. 2002. Needs and opportunities for uncertainty-based multidisciplinary design methods for aerospace vehicles Tech. Rep. TM-2002-211462, NASA Langley Res. Cent. Hampton, VA: [Google Scholar]
  112. Zhang Z, Chen PC, Wang X, Mignolet MP. 2016. Nonlinear aerodynamics and nonlinear structures interaction for F-16 limit cycle oscillation prediction Presented at Dyn. Specialists Conf., 15th, AIAA Pap. 2016–1796 [Google Scholar]
/content/journals/10.1146/annurev-fluid-122414-034441
Loading
/content/journals/10.1146/annurev-fluid-122414-034441
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error