Procedia Engineering 28 (2012) 419 – 423

1877-7058 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering doi:10.1016/j.proeng.2012.01.743

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Procedia

Engineering Procedia Engineering 00 (2011) 000–000

www.elsevier.com/locate/procedia

2012 International Conference on Modern Hydraulic Engineering

Optimized Program Design of Gravity Dam Section

GUAN Qi, a* College of civil Engineering&Architecture, China Three Gorges University, Yichang, 443002, China

Abstract

In this paper, a visual operation interface and a main program for computation are devoloped on the basis of constrained nonlinear complex optimization algorithm, Visual C programming language and parametric drawing techniques. They mainly help solve such problems as multi-state constraints and complexity of programs in optimal design of gravity dam section. The computing results show that the newly developed program is of high accuracy. While improving computation efficiency, it can also enhance human-computer interaction. © 2011 Published by Elsevier Ltd. Keywords: gravity dam; section optimization; complex algorithm; Visual C language; Visualization

1. Introduction

Domestic scholars have done a lot of researches into gravity dam section optimization. Some of them combined direct algorithm with VB Language [1]; some integrated mixed-language programming[2] (using the visual design of VB Language and the computing capacity of Fortan) with complex algorithm. There were certain weaknesses in such methods. The designs were too complex; the multi-state constraints were not considered, etc. First, the program design for direct search was simple, but it required too much time. Second, with the use of hybrid language and complex algorithm, time was saved, but the program design was still complex.

In order to solve these problems, this paper integrates C Language with complex algorithm and incorprates multi-state load combination into optimization model as constraints. Since C Language is generated by combining C++language and VB language, its grammatical structure is coherent, its computation capacity is great and grammatical rules are simple [3]. All of these make it suprior to the

* Corresponding author: GUAN Qi. Tel.: 15090958002. E-mail address: king584131421@163.com..

© 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering

420 GUAN Qi / Procedia Engineering 28 (2012) 419 – 4232 Author name / Procedia Engineering 00 (2011) 000–000

above mentioned two methods. Besides, the visual design is readily available in this way.

2. Model construction

(1) Design Constants Design constants should be set as required. Here are design constants involved in this paper: ①Dam height=H, depend on the water level and free board (based on the calculation modules of crest

elevation) ②The highest water level=Hu, based on flood regulating calculation; ③Basic parameters, with reference to relevant database (opterating through the input of module

parameters) (2) Design Variables The optimization calculation figure (in figure 1) is based on dam section in the section rendering

module. This paper includes three design variables, in a discrete variables can be expressed as:

1 2 3, , TX x x x (1)

Fig. 1.The picture of calculation of section optimum

(3) Geometric constraint conditions

1

2 1

2 3 2

00 0.2

0.6 0.8c c

x Hx x

H x H

(2)

(4) Stress constraints At the normal water level (basic portfolio), the dam toe stress should be less than the allowable

concrete compressive stress. 1 1[ ] - 0DamToe lg X (3)

At checking flood level (accidental combination), the dam toe stress should be less than the allowable concrete compressive stress.

2 2[ ] - 0DamToe lg X (4) The uplift stress within the limit in normal use, the stress on the dam heel should be lower than

allowable compressive stress of concrete. 3 - 0DamHeelg X (5)

421GUAN Qi / Procedia Engineering 28 (2012) 419 – 423 Author name / Procedia Engineering 00 (2011) 000–000 3

(5) Stability constraints At the normal water level (basic portfolio), the safety factor of sliding stability of dam foundation

should be less than that required;

' '

14 1

1

0f W c A

g x KP

(6)

At checking flood level (accidental combination), the safety factor of sliding stability of dam foundation should be less than that required;

' '

25 2

2

0f W c A

g x KP

(7)

(6) Objective function 1 2 1 3 20.5 0.5 cA X x x B H x H (8)

The objective function value should be the smallest.

minA X A X (9)

3. Process design

3.1. Process analysis

(1) First, form 2n (n represents the number of design variables) compound vertexes of feasibility based on initial composite points function. Then, figure out the objective function value of each composite point through sequence function and sort the values in order from the smallest to the largest. Finally, get the central point of the worst pont[4];

(2) Center feasibility function can return or not ( No, jump to (1) and start again. Yes, figure out whether it is the best point according to the law of convergence, and then output the result. Otherwise, jump to (3);

(3) Start reflecting, use the center feasibility function to determine the feasibility of the reflection point. If it is feasibile, replace the worst point with it. Finally, sort new composite points in order and turn to (1);

(4) If it is not feasible, define a reflection coefficient, and move the reflection point towards the central point, and jump to (3).

3.2. Important functions

(1) The Formation of the Initial Composite Point The initial composite point can be generated artificially or randomly through computer [5]. The latter

is adopted in this paper. Although the process is most time-consuming, it is crucial in complex algorithm. It is a great difficulty in the program design, because it affects the accuracy of the optimization result.

In this paper, the initial section size, a composite point, is obtained from the system. The other 2n-1 composite points (n represents the number of design variables) are formed through the progam. The concrete processes are as follows:

Private void CalInitalPoints generate 2n-1 random numbers through Random(); for(For 2n-1 cycle ) Form 2n-1 initial composite points according to this formula: Xi=X(top)+Qi(X(bottom)-X(top))

422 GUAN Qi / Procedia Engineering 28 (2012) 419 – 4234 Author name / Procedia Engineering 00 (2011) 000–000

for(2n-1 cycle) If(XFalseorTrue())//Complex shape point feasible Figure out the central point of the constrained composite points and then jump to the loop of the initial

composite point; (2) Sorting Composite Points By sorting composite points, the worst point can be identified on the basis of objective function. There

are various means, such as bubble sort, shell sort, etc. Each has its own advantages. The bubble sort is faster than the shell sort provided that sequencing targets are few. In this paper, bubble sort is adopted. It is simple and thus needs no further explanation

(3) Composite Points Feasibility Function and Central Point Function By complex algorithm, the central point of composite points and its feasibility are gained through

repeated caculation. Therefore, the program design can be simplified by defining these two fuctions. ①Composite point feasibility function private bool XfalseorTrue Calculating the constraint conditions value； return true; return flase; ②Center point function Center point calculation formula

1

1 q

c jj

X Xq

(10)

4. Optimization results

The preliminary variable of the section size of a gravity dam is represented by X(X=[44.0, 8.8, 56.6]). The initial cross-section covers an area of 2589.8m2. The optimization computation of sections optimization goes on with the input of such data as the basic parameters, hydrological parameters, and section size parameters. Seen from the results, through optimization, the area of the section is cut from 2589.82m2 to 2186.55 m2,the width of the dam bottom is reduced from 70.4m to 59.0m. It brings a great slash in the amount of concrete. Thus, the cost can also be cut. Under such load combnations, the factor of safety and the stress on the dam toe and heel meet the requirements.

Input the variables of parametres before and after optimization into the Section Size Window, and the results can be directly seen in the sectional drawing(in figure 2) (part of the screen-capture). The left is the sectional drawing before optimization, the right, after optimization.

Fig. 2. The picture of optimum before and last

423GUAN Qi / Procedia Engineering 28 (2012) 419 – 423 Author name / Procedia Engineering 00 (2011) 000–000 5

5. Conclusion

On the basis of the previous achievement, this paper comes out with a new program design for gravity dam section optimization. Here are my conclusions: ①The program design is optimized through the combination of complex optimization algorithm, and Visual C programming language. It improves the speed and accuracy in computing; ②In the process of optimization,consideration is given to basic portfolio and accidental combination. This improves the accuracy of computation results further; ③As an integral part of gravity dam aided design system, this paper makes visual representation possible in sectional drawing.

References

[1] XU Yunqian; LV Aizhong, Section Optimization Design of Solid Gravity Dam Based on Visual Basic[J], Water Resources and Power, 2011, 29(9), P79-81.

[2] SUN Xushu; CHAI Junrui; SUN Xinzhuang, et al. Application of Mixed-language Programming in Optimal Design of Cross Section of Gravity Dam[J], Water Resources and Power, 2009, 27(2), P94-97.

[3] ZHANG Li; HAN Qirui, The characteristics of C# program language and its potential new functions, [J], Electronics Instrumentation Customer, 2005, 12(5), P82-84.

[4] Qian Ling-xi; Zhong Wanxie; Cheng Gengdong; Sui Yunkang, Sequential Quadratic Programming Approach Engineering Structural Optimization[J], Acta Mechanica Solida Sinica, 1983, 12(4), P369-478.

[5] SUI Yunkang; LI Shanpo, Brief Review on Modeling Method in Structural Optimization[J], Advances in Mechanics, 2008, 38(2), P190-200.