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Surrogate based optimization of helicopter rotor blades for vibration reduction in forward flight

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Abstract

The effectiveness of surrogate modeling of helicopter vibrations, and the use of the surrogates for minimization of helicopter rotor vibrations are studied. The accuracies of kriging, radial basis function interpolation, and polynomial regression surrogates are compared. In addition, the surrogates are used to generate an objective function which is employed in an optimization study. The design variables consist of the cross-sectional dimensions of the structural member of the blade and non-structural masses. The optimized blade is compared with a baseline rotor blade which resembles an MBB BO-105 blade. Results indicate that: (a) kriging surrogates best approximate vibratory hub loads over the entire design space and (b) the surrogates can be used effectively in helicopter rotor vibration reduction studies.

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References

  • Alexandrov N, Dennis Jr JE, Lewis RM, Torczon V (1998) A trust region framework for managing the use of approximate models in optimization. Struct Optim 15(1):16–23

    Article  Google Scholar 

  • Booker AJ, Dennis Jr JE, Frank PD, Serafini DB, Torczon V, Trosset MW (1999) A rigorous framework for optimization of expensive functions by surrogates. Struct Optim 17:1–13

    Google Scholar 

  • Celi R (1999) Recent applications of design optimization to rotorcraft - a survey. J Aircraft 36(1):176–189

    Google Scholar 

  • Celi R, Friedmann PP (1990) Structural optimization with aeroelastic constraints of rotor blades with straight and swept tips. AIAA J 28(5):928–936

    Google Scholar 

  • Chen VCP, Tsui K, Barton RB, Meckesheimer M (2006) A review on design, modeling, and applications of computer experiments. IIE Trans 38:273–291

    Article  Google Scholar 

  • Depailler G, Friedmann PP (2002) Reductions of vibrations due to dynamic stall in helicopters using an actively controlled flap. In: Proceedings of the 43rd AIAA/ASME/ASCE/ AHS/ACS Structures, Structural Dynamics and Materials Conference, Denver, CO, AIAA Paper No. 2002-1431

  • Forsberg J, Nilsson L (2005) On polynomial response surfaces and kriging for use in structural optimization of crashworthiness. Struct Multidisc Optim 29(3):232–243

    Article  Google Scholar 

  • Friedmann PP (1991) Helicopter vibration reduction using structural optimization with aeroelastic/multidisciplinary constraints - a survey. J Aircr 28(1):8–21

    Google Scholar 

  • Friedmann PP, Millott T (1995) Vibration reduction in rotorcraft using active control: a comparison of various approaches. J Guidance, Control, Dyn 18(4):664–673

    Google Scholar 

  • Friedmann PP, Shanthakumaran P (1984) Optimum design of rotor blades for vibration reduction in forward flight. J Am Helicopter Soc 29(4):70–80

    Google Scholar 

  • Ganguli R (2002) Optimal design of a low vibration helicopter rotor using response surface approximation. J Sound Vib 258(2):327–344

    Article  Google Scholar 

  • Ganguli R (2004) Survey of recent developments in rotorcraft design optimization. J Aircr 41(3):493–510

    MathSciNet  Google Scholar 

  • Glaz B, Friedmann PP, Liu L (2006) Surrogate based optimization of helicopter rotor blades for vibration reduction in forward flight. In: 47th AIAA/ASME/ASCHE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Newport, RI, pp 1–21, AIAA Paper 2006-1821

  • Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodeling techniques under multiple modeling criteria. Struct Multidisc Optim. 23:1–13

    Article  Google Scholar 

  • Jin R, Chen W, Sudjianto A (2005) An efficient algorithm for constructing optimal design of computer experiments. J Stat Plan Inference 134(1):268–287

    Article  MATH  MathSciNet  Google Scholar 

  • Johnson W (1988a) CAMRAD/JA - A Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, Vol I. Theory Manual. Johnson Aeronautics, Palo Alto, CA

    Google Scholar 

  • Johnson W (1988b) CAMRAD/JA - A Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, Vol II. Users’ Manual. Johnson Aeronautics, Palo Alto, CA

    Google Scholar 

  • Jones DR (2001) The direct global optimization algorithm. Encyclopedia Optim 1:431–440

    Article  Google Scholar 

  • Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Global Optim 13:455–492

    Article  MATH  MathSciNet  Google Scholar 

  • Koch PN, Evans JP, Powell D (2002) Interdigitation for effective design space exploration using iSIGHT. Struct Multidisc Optim 23(2):111–126

    Article  Google Scholar 

  • Lim JW, Chopra I (1989) Aeroelastic optimization of a helicopter rotor. J Am Helicopter Soc 34(1):55–62

    Article  Google Scholar 

  • Lim JW, Chopra I (1991) Aeroelastic optimization of a helicopter rotor using an efficient sensitivity analysis. J Aircr 28(1): 29–37

    Google Scholar 

  • Liu L (2005) BVI induced vibration and noise alleviation by active and passive approaches. PhD thesis, University of Michigan, Aerospace Engineering

  • Liu L, Friedmann PP, Patt D (2005) Simultaneous vibration and noise reduction in rotorcraft - practical implementation issues. In: Proceedings of the 46th AIAA/ASME/ASCE/ AHS/ACS Structures, Structural Dynamics and Materials Conference, Austin, TX, AIAA Paper 2005-2245

  • Lophaven SN, Nielsen HB, Søndergaard J (2002) A Matlab Kriging Toolbox, Version 2.0. Informatics and Mathematical Modeling, DTU, Technical Report IMM-TR-2002-12

  • Martin J, Simpson T (2005) Use of kriging models to approximate deterministic computer models. AIAA J 43(4):853–863

    Article  Google Scholar 

  • McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245

    Article  MATH  MathSciNet  Google Scholar 

  • Millott TA, Friedmann PP (1994) Vibration Reduction in Helicopter Rotors Using an Actively Controlled Partial Span Trailing Edge Flap Located on the Blade. NASA CR 4611

  • Murugan S, Ganguli R (2005) Aeroelastic stability enhancement and vibration supression in a composite helicopter rotor. J Aircr 42(4):1013–1024

    Google Scholar 

  • Myrtle TF (1998) Development of an improved aeroelastic model for the investigation of vibration reduction in helicopter rotors using trailing edge flaps. PhD thesis, University of California, Los Angeles, Mechanical and Aerospace Engineering

  • Myrtle TF, Friedmann PP (2001) Application of a new compressible time domain aerodynamic model to vibration reduction in helicopters using an actively controlled flap. J Am Helicopter Soc 46(1):32–43

    Google Scholar 

  • Palmer K, Realff M (2002a) Metamodeling approach to optimization of steady-state flowsheet simulations - model generation. Trans Inst Chem Eng 80(7):760–772

    Article  Google Scholar 

  • Palmer K, Realff M (2002b) Optimization and validation of steady-state flowsheet simulation metamodels. Trans Inst Chem Eng 80(7):773–782

    Article  Google Scholar 

  • Patt D, Liu L, Friedmann PP (2005) Rotorcraft vibration reduction and noise prediction using a unified aeroelastic response simulation. J Am Helicopter Soc 50(1):95–106

    Article  Google Scholar 

  • Patt D, Liu L, Friedmann PP (2006) Simultaneous vibration and noise reduction in rotorcraft using aeroelastic simulation. J Am Helicopter Soc 51(2):127–140

    Google Scholar 

  • Queipo NV, Haftka RT, Shy W, Goel T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerospace Sci 41:1–28

    Article  Google Scholar 

  • Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4): 409–435

    Article  MATH  MathSciNet  Google Scholar 

  • Sasena M (2002) Flexibility and efficiency enhancements for constrained global optimization with kriging approximations. PhD thesis, University of Michigan, Mechanical Engineering

  • Schmit LA, Miura H (1976) Concepts for Efficient Structural Synthesis. NASA CR-2552

  • Schonlau M (1997) Computer experiments and global optimization. PhD thesis, University of Waterloo, Statistics and Actuarial Science

  • Shultz LA, Panda B, Tarzanin FJ, Derham RC, Oh BK, Dadone L (1994) Interdisciplinary analysis for advanced rotors - approach, capabilities, and status. In: American Helicopter Society Aeromechanics Specialists Conference, PS 4-1-4-15

  • Simpson TW, Mauery TM, Korte JJ, Mistree F (2001a) Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA J 39(12):2233–2241

    Google Scholar 

  • Simpson TW, Peplinski D, Koch PN, Allen JK (2001b) Metamodels for computer-based engineering design: Survey and recommendations. Eng Comp 17:129–150

    Article  MATH  Google Scholar 

  • Simpson TW, Booker AJ, Ghosh D, Giunta AA, Koch PN, Yang R (2004) Approximation methods in multidisciplinary analysis and optimization: A panel discussion. Struct Multidisc Optim 27(5):302–313

    Article  Google Scholar 

  • Sóbester A, Leary SJ, Keane AJ (2004) A parallel updating scheme for approximating and optimizing high fidelity computer simulations. Struct Multidisc Optim 27:371–383

    Article  Google Scholar 

  • Stander N, Roux W, Giger M, Redhe M, Fedorova N, Haarhoff J (2004) A comparison of metamodeling techniques for crashworthiness optimization. In: 10th AIAA/ISSMO Multidisciplinary Analysis & Optimization Conference, Albany, New York, pp 1–11, AIAA Paper 2004-4489

  • de Terlizzi M, Friedmann PP (1998) Aeroelastic response of swept tip rotors including the effects of BVI. In: Proceedings of the 54th Annual Forum of the American Helicopter Society, Washington D.C., pp 644–663

  • de Terlizzi M, Friedmann PP (1999) Active control of BVI induced vibrations using a refined aerodynamic model and experimental correlation. In: Proceedings of the 55th Annual Forum of the American Helicopter Society, Montreal, Canada, pp 599–615

  • Won K, Ray T (2005) A framework for design optimization using surrogates. Eng Optim 37(7):685–703

    Article  MathSciNet  Google Scholar 

  • Wujek BA, Renaud JE (1998) Improved trust region model management for approximate optimization. In: Advances in Design Automation, Atlanta, Georgia, paper No. DETC98/ DAC-5616

  • Yuan KA, Friedmann PP (1995) Aeroelasticity and Structural Optimization of Composite Helicopter Rotor Blades with Swept Tips. NASA CR 4665

  • Yuan KA, Friedmann PP (1998) Structural optimization for vibratory loads reduction of composite helicopter rotor blades with advanced geometry tips. J Am Helicopter Soc 43(3):246–256

    Google Scholar 

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Authors and Affiliations

  1. Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI, 48109, USA

    Bryan Glaz, Peretz P. Friedmann & Li Liu

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  1. Bryan Glaz
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  2. Peretz P. Friedmann
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  3. Li Liu
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Correspondence to Bryan Glaz.

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Glaz, B., Friedmann, P.P. & Liu, L. Surrogate based optimization of helicopter rotor blades for vibration reduction in forward flight. Struct Multidisc Optim 35, 341–363 (2008). https://doi.org/10.1007/s00158-007-0137-z

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  • DOI: https://doi.org/10.1007/s00158-007-0137-z

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