Shape design of arch dams under load uncertainties with robust optimization

doi:10.1007/s11709-019-0522-x

Front. Struct. Civ. Eng.

2019, Vol. 13

Issue (4) : 852-862 https://doi.org/10.1007/s11709-019-0522-x

RESEARCH ARTICLE

Shape design of arch dams under load uncertainties with robust optimization

Fengjie TAN, Tom LAHMER(

)

Institute of Structural Mechanics, Bauhaus-Universität, Weimar D-99423, Germany

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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

Corresponding Author(s): Tom LAHMER

Just Accepted Date: 07 March 2019 Online First Date: 23 April 2019 Issue Date: 10 July 2019

Cite this article:

Fengjie TAN,Tom LAHMER. Shape design of arch dams under load uncertainties with robust optimization[J]. Front. Struct. Civ. Eng., 2019, 13(4): 852-862.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-019-0522-x
https://academic.hep.com.cn/fsce/EN/Y2019/V13/I4/852

Fig.1 Description of the shape of arch type dam. (a) The central vertical section of the arch dam (b) the horizontal curves of the arch type dam

Fig.2 Temperature distributions in winter time and summer time

Fig.3 Comparison of DO-based optimum design with an RO-based optimum design

Fig.4 The procedure of the optimization

Fig.5 Approximation with Kriging metamodel. (a) The approximation of tensile stress with Kriging Metamodel; (b) the approximation of dam volume with Kriging metamodel

Tab.1 Approximation model of tensile stress and dam volume

$0.5 ≤ α ≤ 0.9$	$0.3 ≤ β 1 ≤ 0.7$	$0.3 ≤ β 2 ≤ 0.7$
$3 ≤ t 1 ≤ 10$	$10 ≤ t 2 ≤ 30$	$15 ≤ t 1 ≤ 35$
$25 ≤ ϕ 1 ≤ 70$	$25 ≤ ϕ 2 ≤ 70$	$15 ≤ ϕ 3 ≤ 40$
$− 2 ≤ α 1 ≤ 2$	$− 2 ≤ α 2 ≤ 2$	$− 2 ≤ α 3 ≤ 2$

Tab.2 The upper and lower boundaries of shape design variables

Tab.3 Loads and material parameters of the dam model

Tab.4 Geometrical parameters of the dam model according to the DO

Tab.5 Geometrical parameters of the dam model according to the RO

Fig.6 Comparison of the geometries between DO optimal design and RO optimal designs

Fig.7 The sum displacement of optimal arch dam based on DO

Fig.8 The sum displacement of optimal arch dam based on RO

Tab.6 Comparison

Fig.9 Comparison of mechanical properties between the arch dams acquired with DO method and RO method. (a) Comparison of tensile stress; (b) comparison of von Mises stress; (c) comparison of displacement

Tab.7 Range of random samples

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