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Single and multi-objective shape optimization of streamlined bridge decks

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Abstract

Civil engineers focus on developing an optimum design that is cost-effective without compromising the performance. Experiences from optimizing airplane wings in aerospace engineering have been extensively made for the last decades where the aim is to maximize the lift-to-drag ratios. In civil engineering, shape optimization of tall buildings and bridge cross-sections is still an open research field where the aim is to enhance the aerodynamic behavior of these structures. The main challenge, however, is to develop bridge decks that avoid excessive deformations and ensure a sufficient structural reliability. Within this framework, the paper outlines the single and multi-objective shape optimization for static aerodynamic forces of a streamlined box section. Computational fluid dynamic simulation based on vortex particle method provides the quantities of interest which are approximately treated by a Kriging surrogate for the optimization. Later, the performance of the optimized structure is checked against flutter instability.

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References

  • Abbas T (2016) Assessment of numerical prediction models for aeroelastic instabilities of bridges. PhD thesis, Bauhaus-Universität Weimar, Fakultät Bauingenieurwesen, Graduiertenkolleg 1462 Germany

  • Abbas T, Kavrakov I, Morgenthal G (2017) Methods for flutter stability analysis of long-span bridges: a review. Proceedings of the institution of civil engineers: Bridge engineering, pp 1–40

  • Abbas T, Morgenthal G (2012) Model combinations for assessing the flutter stability of suspension bridges. In: The 19th international conference on the applications of computer science and mathematics in architecture and civil engineering (IKM 2012), Weimar, Germany

  • Abbas T, Morgenthal G (2016) Framework for sensitivity and uncertainty quantification in the flutter assessment of bridges. Probabilistic Engineering Mechanics 43:91–105

    Google Scholar 

  • Amin JA, Ahuja AK (2010) Aerodynamic modifications to the shape of the buildings: a review of the state-of-the-art. Asian Journal of Civil Engineering (Building and Housing) 11(4):433–450

    Google Scholar 

  • Badawy MF, Msekh MA, Hamdia KM, Steiner MK, Lahmer T, Rabczuk T (2017) Hybrid nonlinear surrogate models for fracture behavior of polymeric nanocomposites. Probabilistic Engineering Mechanics 50:64–75

    Google Scholar 

  • Bernardini E, Spence SMJ, Wei D, Kareem A (2015) Aerodynamic shape optimization of civil structures: a CFD-enabled Kriging-based approach. J Wind Eng Ind Aerodyn 144:154–164

    Google Scholar 

  • Bruno L, Mancini G (2002) Importance of deck details in bridge aerodynamics. Struct Eng Int 12(4):289–294

    Google Scholar 

  • Chatterjee S, Hadi AS (2015) Regression analysis by example. Wiley, New York

    MATH  Google Scholar 

  • Díaz J., Montoya MC, Hernández S (2016) Efficient methodologies for reliability-based design optimization of composite panels. Adv Eng Softw 93:9–21

    Google Scholar 

  • Diwakar A, Srinath DN, Mittal S (2010) Aerodynamic shape optimization of airfoils in unsteady flow. Comput Model Eng Sci 69(1):61–89

    Google Scholar 

  • Eberhart R, Kennedy J (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, vol 4. Citeseer, pp 1942–1948

  • Eichfelder G (2009) An adaptive scalarization method in multiobjective optimization. SIAM J Optim 19 (4):1694–1718

    MathSciNet  MATH  Google Scholar 

  • Forrester AIJ, Sóbester A, Keane AJ (2008) Engineering design via surrogate modelling: a practical guide. Wiley, New York

    Google Scholar 

  • Gano SE, Renaud JE, Martin JD, Simpson TW (2006) Update strategies for Kriging models used in variable fidelity optimization. Struct Multidiscip Optim 32(4):287–298

    Google Scholar 

  • Gimsing NJ, Christos TG (1983) Cable supported bridges, vol 314. Wiley Online Library, Hoboken

    Google Scholar 

  • Holmes JD (2015) Wind loading of structures. CRC Press, Boca Raton

    Google Scholar 

  • Huyse L, Lewis RM (2001) Aerodynamic shape optimization of two-dimensional airfoils under uncertain conditions. In: International conference; 8th, Structural safety and reliability; ICOSSAR ’01; 2001; Newport Beach, Canada

  • Imai H, Yun CB, Maruyama O, Shinozuka M (1989) Fundamentals of system identification in structural dynamics. Probabilistic Engineering Mechanics 4(4):162–173

    Google Scholar 

  • Joseph VR, Hung Y, Sudjianto A (2008) Blind Kriging: a new method for developing metamodels. J Mech Des 130(3):031102

    Google Scholar 

  • Kanevski M, Maignan M (2004) Analysis and modelling of spatial environmental data, vol 6501. EPFL Press, Lausanne

    MATH  Google Scholar 

  • Kareem A, Bobby S, Spence SMJ, Bernardini E (2014) Optimizing the form of tall buildings to urban environments. In: CTBUH 2014 international conference

  • Kareem A, Spence SMJ, Bernardini E, Bobby S, Wei D (2013) Wind engineering using computational fluid dynamics to optimize tall building design. Council on Tall Buildings and Urban Habitat Journal (3):38–43

  • Kavrakov I, Morgenthal G (2017) A comparative assessment of aerodynamic models for buffeting and flutter of long-span bridges. Engineering 3(6):823–838

    Google Scholar 

  • Kavrakov I, Morgenthal G (2018) Aeroelastic analyses of bridges using a pseudo-3d vortex method and velocity-based synthetic turbulence generation. Eng Struct 176:825–839

    Google Scholar 

  • Kavrakov I, Morgenthal G (2018) A synergistic study of a CFD and semi-analytical models for aeroelastic analysis of bridges in turbulent wind conditions. J Fluids Struct 82:59–85

    Google Scholar 

  • Kim IY, De Weck O (2004) Adaptive weighted sum method for multiobjective optimization. In: 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, p 4322

  • Kulkarni R, Muthumani K (2016) Shape effects on wind induced response of tall buildings using CFD. Int J Innov Res Sci Eng Technol, 5(3)

  • Kusano I, Baldomir A., Jurado JA, Hernández S (2014) Reliability based design optimization of long-span bridges considering flutter. J Wind Eng Ind Aerodyn 135:149–162

    Google Scholar 

  • Kusano I, Baldomir A, Jurado JA, Hernández S (2015) Probabilistic optimization of the main cable and bridge deck of long-span suspension bridges under flutter constraint. J Wind Eng Ind Aerodyn 146:59–70

    Google Scholar 

  • Kusano I, Baldomir A, Jurado JA, Hernández S (2018) The importance of correlation among flutter derivatives for the reliability based optimum design of suspension bridges. Eng Struct 173:416–428

    Google Scholar 

  • Larose GL, Livesey FM (1997) Performance of streamlined bridge decks in relation to the aerodynamics of a flat plate. J Wind Eng Ind Aerodyn 69:851–860

    Google Scholar 

  • Larsen A (2008) Aerodynamic stability and vortex shedding excitation of suspension bridges. In: Proceedings, 4th international conference on advances in structural engineering and mechanics (ASEM08), Jeju, Korea

  • Larsen A (2017) Aerodynamics of large bridges: Proceedings of the first international symposium on aerodynamics of large bridges, Copenhagen, Denmark, 19-21 February 1992. Routledge

  • Lin Y (2004) An efficient robust concept exploration method and sequential exploratory experimental design. PhD thesis, Atlanta, Georgia Institute of Technology, Unites States

  • Lin Y, Cheng CM, Wu JC, Lan TL, Wu KT (2005) Effects of deck shape and oncoming turbulence on bridge aerodynamics. Tamkang Journal of Science and Engineering 8(1):43–56

    Google Scholar 

  • Lohade S, Kulkarni S (2016) Shape effects of wind induced response on tall buildings using CFD. Int J Eng Appl Sci, 3(6)

  • Madetoja E, Ruotsalainen H, Monkkonen VM, Hamalainen J, Deb K (2008) Visualizing multi-dimensional Pareto-optimal fronts with a 3D virtual reality system. In: The international multiconference on computer science and information technology. IEEE, pp 907–913

  • Marler RT, Arora JS (2010) The weighted sum method for multi-objective optimization: new insights. Struct Multidiscip Optim 41(6):853–862

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Martinez CM, Cao D (2018) Horizon-enabled energy management for electrified vehicles. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Marzban S, Lahmer T (2016) Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects. Journal of Statistical Theory and Practice 10(4):589–611

    MathSciNet  MATH  Google Scholar 

  • Montoya MC, Hernández S, Kusano I, Nieto F, Jurado JA (2016) The role of surrogate models in combined aeroelastic and structural optimization of cable-stayed bridges with single box deck. High Performance and Optimum Design of Structures and Materials II 166:1

    Google Scholar 

  • Montoya MC, Hernández S, Nieto F (2018) Shape optimization of streamlined decks of cable-stayed bridges considering aeroelastic and structural constraints. J Wind Eng Ind Aerodyn 177:429–455

    Google Scholar 

  • Morgenthal G (2002) Aerodynamic analysis of structures using high-resolution vortex particle methods. PhD thesis, University of Cambridge

  • Morgenthal G (2005) Advances in numerical bridge aerodynamics and recent applications. Struct Eng Int 15 (2):95–95

    Google Scholar 

  • Morgenthal G, Asia MC (2006) Numerical analysis of bridge aerodynamics. Struct Concr 7(1):35

    Google Scholar 

  • Morgenthal G, Corriols AS, Bendig B (2014) A GPU-accelerated pseudo-3D vortex method for aerodynamic analysis. J Wind Eng Ind Aerodyn 125:69–80

    Google Scholar 

  • Morgenthal G, Walther JH (2007) An immersed interface method for the vortex-in-cell algorithm. Computers & Structures 85(11-14):712–726

    MATH  Google Scholar 

  • Most T, Will J (2008) Metamodel of optimal prognosis: An automatic approach for variable reduction and optimal metamodel selection. In: Weimarer Optimierungs und Stochastiktage, Weimar, Germany, vol 5, pp 20–21

  • Most T, Will J (2010) Recent advances in meta-model of optimal prognosis. In: Weimarer Optimierungs und Stochastiktage, Weimar, Germany, vol 7, pp 21–22

  • Most T, Will J (2011) Sensitivity analysis using the metamodel of optimal prognosis. In: Weimarer Optimierungs und Stochastiktage, Weimar, Germany, vol 8, pp 24–40

  • Oliveira M, Pinheiro D, Macedo M, Bastos-Filho C, Menezes R (2017) Better exploration-exploitation pace, better swarm: examining the social interactions. In: 2017 IEEE Latin American conference on computational intelligence (LA-CCI). IEEE, pp 1–6

  • Parisi S, Blank A, Viernickel T, Peters J (2016) Local-utopia policy selection for multi-objective reinforcement learning. In: 2016 IEEE symposium series on computational intelligence (SSCI). IEEE, pp 1–7

  • Parsopoulos KE, Vrahatis MN (2002) Particle swarm optimization method for constrained optimization problems. Intelligent Technologies–Theory and Application: New Trends in Intelligent Technologies 76(1):214–220

    MATH  Google Scholar 

  • Poon SSY (2009) Optimization of span-to-depth ratios in high-strength concrete girder bridges. PhD thesis, University of Toronto, Canada

  • Poulsen NK, Damsgaard A, Reinhold TA (1992) Determination of flutter derivatives for the Great Belt Bridge. J Wind Eng Ind Aerodyn 41(1-3):153–164

    Google Scholar 

  • Rini DP, Shamsuddin SM, Yuhaniz SS (2011) Particle swarm optimization: technique, system and challenges. Int J Comput Appl 14(1):19–26

    Google Scholar 

  • Sadrehaghighi I, Smith RE, Tiwari SN (1995) Grid sensitivity and aerodynamic optimization of generic airfoils. J Aircr 32(6):1234–1239

    Google Scholar 

  • Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, New York

    MATH  Google Scholar 

  • Scanlan RH (1978) Methods of calculation of the wind-induced responses of suspended-span bridges. In: Bridge Engineering Conference, 1st, 1978, St Louis, Missouri, United States, vol 2, pp 108–111

  • Scanlan RH, Tomo J (1971) Air foil and bridge deck flutter derivatives. Journal of Soil Mechanics & Foundations Division 97:1717–1737

    Google Scholar 

  • Shimada K, Ishihara T (2002) Application of a modified k–ε model to the prediction of aerodynamic characteristics of rectangular cross-section cylinders. J Fluids Struct 16(4):465–485

    Google Scholar 

  • Simiu E, Scanlan RH (1996) Wind effects on structures: fundamentals and applications to design. Wiley, New York

    Google Scholar 

  • Snyman JA, Wilke DN (2018) Practical mathematical optimization: basic optimization theory and gradient-based algorithms, vol 133. Springer, Berlin

    MATH  Google Scholar 

  • Sobol IM (1993) Sensitivity estimates for nonlinear mathematical models. Mathematical Modelling and Computational Experiments 1(4):407–414

    MathSciNet  MATH  Google Scholar 

  • Stanimirovic IP, Zlatanovic MLj, Petkovic MD (2011) On the linear weighted sum method for multi-objective optimization. Facta Acta Universitatis, 26(4)

  • Theodorsen T (1949) General theory of aerodynamic instability and the mechanism of flutter. Report 496, NACA

  • Tolstrup C (1992) The fixed link across the Great Belt. In: Aerodynamics of large bridges: Proceedings of the first international symposium on aerodynamics of large bridges, Copenhagen, Denmark

  • Viana FAC, Haftka RT, Steffen V (2009) Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct Multidiscip Optim 39(4):439–457

    Google Scholar 

  • Wang GG, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–380

    Google Scholar 

  • Wang Q, Liao H, Li M, Ma C (2011) Influence of aerodynamic configuration of a streamline box girder on bridge flutter and vortex-induced vibration. J Mod Transp 19(4):261–267

    Google Scholar 

  • Wang Q, Liao HL, Li MS, Xian R (2009) Wind tunnel study on aerodynamic optimization of suspension bridge deck based on flutter stability. In: Seventh Asia-Pacific conference on wind engineering

  • Wang Z, Dragomirescu E (2016) Flutter derivatives identification and aerodynamic performance of an optimized multibox bridge deck. Advances in Civil Engineering 2016:1–13

    Google Scholar 

  • Wardlaw RL (2012) The improvement of aerodynamic performance. In: Aerodynamics of large bridges. Routledge, pp 59–70

  • Xu YL (2013) Wind effects on cable-supported bridges. Wiley, New York

    Google Scholar 

  • Yamada H, Miyata T, Ichikawa H (1992) Measurement of aerodynamic coefficients by system identification methods. J Wind Eng Ind Aerodyn 42(1-3):1255–1263

    Google Scholar 

  • Yang XS, Karamanoglu M (2013) Swarm intelligence and bio-inspired computation: an overview. In: Swarm intelligence and bio-inspired computation. Elsevier, pp 3–23

  • Zhang XY, Trame MN, Lesko LJ, Schmidt S (2015) Sobol sensitivity analysis: a tool to guide the development and evaluation of systems pharmacology models. CPT: Pharmacometrics & Systems Pharmacology 4 (2):69–79

    Google Scholar 

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Acknowledgments

The authors gratefully acknowledge this support.

Funding

The work was supported by the German Research Foundation (DFG) through the Research Training Group 1462 in Weimar and through the DFG Project 329120866 “Optimierung winderregter Tragstrukturen unter Berücksichtigung stochastischer Einwirkungen und verschiedenartiger Grenzzustände.”

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Authors and Affiliations

  1. Research Training Group 1462, Bauhaus-Universität Weimar, 99423, Weimar, Germany

    Zouhour Jaouadi

  2. Chair of Modelling and Simulation of Structures, Bauhaus-Universität Weimar, 99423, Weimar, Germany

    Tajammal Abbas & Guido Morgenthal

  3. Institute of Structural Mechanics, Bauhaus-Universität Weimar, 99423, Weimar, Germany

    Tom Lahmer

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  1. Zouhour Jaouadi
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  2. Tajammal Abbas
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Correspondence to Zouhour Jaouadi.

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Jaouadi, Z., Abbas, T., Morgenthal, G. et al. Single and multi-objective shape optimization of streamlined bridge decks. Struct Multidisc Optim 61, 1495–1514 (2020). https://doi.org/10.1007/s00158-019-02431-3

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