Shape design of arch dams under load uncertainties with robust optimization

Abstract

Due to an increased need in hydro-electricity, water storage, and flood protection, it is assumed that a series of new dams will be build throughout the world. The focus of this paper is on the non-probabilistic-based design of new arch-type dams by applying means of robust design optimization (RDO). This type of optimization takes into account uncertainties in the loads and in the material properties of the structure. As classical procedures of probabilistic-based optimization under uncertainties, such as RDO and reliability-based design optimization (RBDO), are in general computationally expensive and rely on estimates of the system’s response variance, we will not follow a full-probabilistic approach but work with predefined confidence levels. This leads to a bi-level optimization program where the volume of the dam is optimized under the worst combination of the uncertain parameters. As a result, robust and reliable designs are obtained and the result is independent from any assumptions on stochastic properties of the random variables in the model. The optimization of an arch-type dam is realized here by a robust optimization method under load uncertainty, where hydraulic and thermal loads are considered. The load uncertainty is modeled as an ellipsoidal expression. Comparing with any traditional deterministic optimization method, which only concerns the minimum objective value and offers a solution candidate close to limit-states, the RDO method provides a robust solution against uncertainty. To reduce the computational cost, a ranking strategy and an approximation model are further involved to do a preliminary screening. By this means, the robust design can generate an improved arch dam structure that ensures both safety and serviceability during its lifetime.

Keywords

arch dam / shape optimization / robust optimization / load uncertainty / approximation model

References

[1] Li S, Ding L, Zhao L, Zhou W. Optimization design of arch dam shape with modified complex method. Advances in Engineering Software, 2009, 40(9): 804–808

[2] Seyedpoor S M, Salajegheh J. Adaptive neuro-fuzzy inference system for high speed computing in optimal shape design of arch dams subjected to earthquake loading. Mechanics Based Design of Structures and Machines, 2009, 37(1): 31–59

[3] Zhu B, Rao B, Jia J, Li Y. Shape optimization of arch dam for static and dynamic loads. Journal of Structural Engineering, 1992, 118(11): 2996–3015

[4] Youn B D, Choi K K. A new response surface methodology for reliability-based design optimization. Computers & Structures, 2004, 82(2–3): 241–256

[5] Karadeniz H, Toğan, V, Vrouwenvelder T. An integrated reliability-based design optimization of offshore towers. Reliability Engineering & System Safety, 2009, 94(10): 1510–1516

[6] Sherali H D, Ganesan V. An inverse reliability-based approach for designing under uncertainty with application to robust piston design. Journal of Global Optimization, 2006, 37(1): 47–62

[7] Tan F, Lahmer T. Shape optimization based design of arch-type dams under uncertainties. Engineering Optimization, 2017, 50(9): 1470–1482

[8] Lee K H, Park G J. Robust optimization considering tolerances of design variables. Computers & Structures, 2001, 79(1): 77–86

[9] Lee K H, Eom I S, Park G J, Lee W I. Robust Design for un- constrained optimization problems using the Taguchi method. AIAA Journal, 1996, 34(5): 1059–1063

[10] Sandgren E, Cameron T M. Robust design optimization of structures through consideration of variation. Computers & Structures, 2002, 80(20–21): 1605–1613

[11] Ben-Tal A, Ghaoui L E I, Nemirovski A. Robust Optimization, Princeton and Oxford, MA: Princeton University Press, 2009

[12] Ben-Tal A, Nemirovski A. Robust optimization methodology and applications. Mathematical Programming, 2002, 92(3): 453–480

[13] Sundaresan S, Ishii K, Houser D R. A robust optimization procedure with variations on design variables and constraints. Engineering Optimization, 1995, 24(2): 101–117

[14] Guo X, Bai W, Zhang W, Gao X. Confidence structural robust design and optimization under stiffness and load uncertainties. Computer Methods in Applied Mechanics and Engineering, 2009, 198(41–44): 3378–3399

[15] Sun G, Li G, Gong Z, Cui X, Yang X, Li Q. Multiobjective robust optimization method for drawbead design in sheet metal forming. Materials & Design, 2010, 31(4): 1917–1929

[16] Kanno Y, Takewaki I. Sequential semidefinite program for maximum robustness design of structures under load uncertainty. Journal of Optimization Theory and Applications, 2006, 130(2): 265–287

[17] Schmit L A, Farshi B. Some approximation concepts for structural synthesis. AIAA Journal, 1974, 12(5): 692–699

[18] Zhu B, Gao J, Chen Z, Li Y. Design and Research for Concrete Arch Dams. Beijing: China WaterPower Press, 2002

[19] Jin R, Du X, Chen W. The use of metamodeling techniques for optimization under uncertainty. Structural and Multidisciplinary Optimization, 2003, 25(2): 99–116

[20] Fenton G A, Griffiths D V. Risk Assessment in Geotechnical En-gineering. Hoboken: John Wiley and Sons, 2008

[21] Rasmussen C E, Williams C K I. Gaussian Processes for Machine Learning. London: MIT Press, 2006

[22] Marelli S, Lataniotis C, Sudret B. UQLab User manual- Kriging(Gaussian Process model), Report UqLab Chair of Risk, Safty and Uncertainty Quantification, ETH Zurich, 2015, 9–105

[23] Marelli S, Sudret B. UQLab: A framework for uncertainty quan-tification in Matlab. In: Proceedings of 2nd International Conf-erence on Vulnerability, Risk Analysis and Management (ICVRAM2014). Liverpool: 2014, 2554–2563

[24] Boyd S, Vandenberghe L. Convex Optimization. Cambridge: Cambridge University Press, 2004

Acknowledgment

The corresponding author, Fengjie Tan, kindly likes to thank for the support of the Chinese Scholarship Council (No. 201406260202), and to Bauhaus University for providing a good working environment.

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