Araujo et al 2019a - Revision history

Rimni: /* 6. Results */

2021-05-28T12:15:46Z

‎6. Results

Rimni at 12:11, 28 May 2021

2021-05-28T12:11:32Z

Rimni at 12:10, 28 May 2021

2021-05-28T12:10:58Z

Rimni: /* 4.3 Optdam */

2021-05-28T12:09:05Z

‎4.3 Optdam

Rimni at 12:06, 28 May 2021

2021-05-28T12:06:59Z

Rimni: /* 2. Stability analysis of concrete gravity dams */

2021-05-28T12:06:15Z

‎2. Stability analysis of concrete gravity dams

Rimni at 11:10, 19 March 2020

2020-03-19T11:10:42Z

Rimni at 07:56, 5 July 2019

2019-07-05T07:56:09Z

Leilsonjoaquim: Reference corrections

2019-07-05T02:38:51Z

Reference corrections

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Leilsonjoaquim: reference changes

2019-06-27T18:39:26Z

reference changes

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@@ Line 510: / Line 510: @@
 ==6. Results==
-The optimum design of the cross-section based on retaining-wall of Belo Monte HPP is given in Table 4. By comparing the solution obtained for the cross-section with the GA it's possible to note that the concrete volume can be significantly reduced.
+The optimum design of the cross-section based on retaining-wall of Belo Monte HPP is given in [[#tab-4|Table 4]]. By comparing the solution obtained for the cross-section with the GA it's possible to note that the concrete volume can be significantly reduced.
 <div class="center" style="font-size: 75%;">'''Table 4'''. Optimization results
 </div>
+<div id='tab-4'></div>
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-In order to limit the computational cost and to streamline the section optimization process, four stop criteria were defined for Optdam. They are presented in Table 1 along with the other program information. In order to make the program's functionality clearer, the stopping criteria are further analyzed here. The Optdam’s stopping criteria are stall generations, stall time, maximum number of generations and compile timeout.
+In order to limit the computational cost and to streamline the section optimization process, four stop criteria were defined for Optdam. They are presented in [[#tab-1|Table 1]] along with the other program information. In order to make the program's functionality clearer, the stopping criteria are further analyzed here. The Optdam’s stopping criteria are stall generations, stall time, maximum number of generations and compile timeout.
-Stall generations defines the number of generations in which there is no significant gain in the optimization of the objective function. Stall time defines the timeout in which there are generations without significant gain in optimization. Maximum number of generations specifies the maximum number of iterations the genetic algorithm performs and compile timeout defines the maximum time the program can take to find the optimal solution. Figure 8 shows the operation of the stop criteria in the example.
+Stall generations defines the number of generations in which there is no significant gain in the optimization of the objective function. Stall time defines the timeout in which there are generations without significant gain in optimization. Maximum number of generations specifies the maximum number of iterations the genetic algorithm performs and compile timeout defines the maximum time the program can take to find the optimal solution. [[#img-8|Figure 8]] shows the operation of the stop criteria in the example.
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-Due to the rapid convergence of GA, already in the first generations tends to obtain satisfactory results. This makes the number of fifty stall generations a high measure of reliability that global minimum has been achieved. Since stall generations is the decisive stopping criterion, it is noted that the stopping criteria validate each other. The graph in Figure 9 presents the best cross section area value of the objective function in each generation versus the generation number. The best values and mean values are highlighted for each iteration.
+Due to the rapid convergence of GA, already in the first generations tends to obtain satisfactory results. This makes the number of fifty stall generations a high measure of reliability that global minimum has been achieved. Since stall generations is the decisive stopping criterion, it is noted that the stopping criteria validate each other. The graph in [[#img-9|Figure 9]] presents the best cross section area value of the objective function in each generation versus the generation number. The best values and mean values are highlighted for each iteration.
+<div id='img-9'></div>
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@@ Line 589: / Line 589: @@
 It can be concluded that the methodology is robust for the problem at hand (reduction of area): As mentioned before, the best individuals in the first generations already feature low values of the cross section area.
-Figure 10 shows the optimized cross section within the actual section. The red area shows the savings of area obtained in the use of Optdam. The optimal shape shown in Figure 10 implies a 24.31% reduction in cross-section area, considering the shear resistance adopted.
+[[#img-10|Figure 10]] shows the optimized cross section within the actual section. The red area shows the savings of area obtained in the use of Optdam. The optimal shape shown in [[#img-10|Figure 10]] implies a 24.31% reduction in cross-section area, considering the shear resistance adopted.
+<div id='img-10'></div>
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@@ Line 429: / Line 429: @@
 Since the actual values of the hydrological parameters and other constraints are not known, for the example discussed here the dimensions for the lower boundary were hypothetically defined. In the other hand, the values of the upper border were defined by the values of the real section executed.
-[[#tab-3|Table 3]] 3 also shows the safety factors obtained for the initial cross section. Since they are higher than those recommended by the design criteria, the geometry can be optimized, finding safety factors close to the minimum required.
+[[#tab-3|Table 3]] also shows the safety factors obtained for the initial cross section. Since they are higher than those recommended by the design criteria, the geometry can be optimized, finding safety factors close to the minimum required.
 <div class="center" style="font-size: 75%;">'''Table 3'''. Dam information

@@ Line 354: / Line 354: @@
 ==5. Example: Idealized cross-section of the Belo Monte HPP==
-The Belo Monte Hydropower Plant has a retaining wall between the main intake and the earth/rockfill dam, which is usually designed following the same criteria as a concrete gravity dam. In order to present the applicability of the Optdam programa in a practical situation, an optimization study using Optdam program is applied on cross-section of the retaining wall. The initial design of Belo Monte cross-section is shown in Figure 7.
+The Belo Monte Hydropower Plant has a retaining wall between the main intake and the earth/rockfill dam, which is usually designed following the same criteria as a concrete gravity dam. In order to present the applicability of the Optdam programa in a practical situation, an optimization study using Optdam program is applied on cross-section of the retaining wall. The initial design of Belo Monte cross-section is shown in [[#img-7|Figure 7]].
+<div id='img-7'></div>
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@@ Line 364: / Line 364: @@
-The material properties for the calculation were taken from commonly used values for dams built in the Belo Monte region. They are included in Table 2.
+The material properties for the calculation were taken from commonly used values for dams built in the Belo Monte region. They are included in [[#tab-2|Table 2]].
 <div class="center" style="font-size: 75%;">'''Table 2'''. Materials properties
 </div>
+<div id='tab-2'></div>
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 |-
@@ Line 423: / Line 423: @@
-The analyzed section presents the geometric parameters shown in Table 3 which also includes other important parameters for optimizing the section, such as hydrostatic loads and the search space defined from the minimum dimensions defined by the project specifications (such as free-board).
+The analyzed section presents the geometric parameters shown in [[#tab-3|Table 3]] which also includes other important parameters for optimizing the section, such as hydrostatic loads and the search space defined from the minimum dimensions defined by the project specifications (such as free-board).
 In this way, the lower boundary of the section is defined by the hydrological parameters, topographic conditions, terrain and other specific constraints that change. Hence, the upper boundary is defined by the designer, based on experience. In case little information is available, wide ranges can be adopted, since the program is able to search for the optimal.
@@ Line 429: / Line 429: @@
 Since the actual values of the hydrological parameters and other constraints are not known, for the example discussed here the dimensions for the lower boundary were hypothetically defined. In the other hand, the values of the upper border were defined by the values of the real section executed.
-Table 3 also shows the safety factors obtained for the initial cross section. Since they are higher than those recommended by the design criteria, the geometry can be optimized, finding safety factors close to the minimum required.
+[[#tab-3|Table 3]] 3 also shows the safety factors obtained for the initial cross section. Since they are higher than those recommended by the design criteria, the geometry can be optimized, finding safety factors close to the minimum required.
 <div class="center" style="font-size: 75%;">'''Table 3'''. Dam information
 </div>
+<div id='tab-3'></div>
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 |-

@@ Line 237: / Line 237: @@
 ===4.3 Optdam===
-Bearing in mind the importance of studying dams and application for evolutionary computing methods of optimization, the aim now is to comment on the Optdam program developed in Matlab. This program allows finding an optical dam’s cross section. The program was developed to cover general cross sections of dams in terms of geometry as showed in Figure 2.
+Bearing in mind the importance of studying dams and application for evolutionary computing methods of optimization, the aim now is to comment on the Optdam program developed in Matlab. This program allows finding an optical dam’s cross section. The program was developed to cover general cross sections of dams in terms of geometry as showed in [[#img-2|Figure 2]].
-−
-First, a set of solutions is initialized and denoted as the initial population. This initialization is recommended to randomly cover the whole solution space or to model and incorporate expert knowledge. The representation determines the initialization process. Initial population is shown in Figure 3 [16].
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 |-
@@ Line 251: / Line 251: @@
 After initial population, GA scores each member of the current population by computing its fitness value, scales the raw fitness scores to convert them into a more usable range of values, then selects members, called parents, based on their fitness.
-Some of the individuals in the current population that have lower fitness are chosen as elite [17]. These elite individuals are taken as parents for the next population. Hence, children are produced either by making random changes to a single parent, mutation, or by combining the vector entries of a pair of parents, crossover. Therefore, GA replaces the current population with the children to form the next generation [5] and [6]. The conception of the new generations is presented in Figure 4.
+Some of the individuals in the current population that have lower fitness are chosen as elite [17]. These elite individuals are taken as parents for the next population. Hence, children are produced either by making random changes to a single parent, mutation, or by combining the vector entries of a pair of parents, crossover. Therefore, GA replaces the current population with the children to form the next generation [5] and [6]. The conception of the new generations is presented in [[#img-4|Figure 4]].
+<div id='img-4'></div>
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 |-
@@ Line 269: / Line 269: @@
 :* Mutation rules apply random changes to individual parents to form children.
-The algorithm stops when one of the stopping criteria is met. Figure 5 shown the convergence process. The GA parameters of Optdam program are shown in Table 1. Figure 6 shows a flowchart illustrating the process.
+The algorithm stops when one of the stopping criteria is met. [[#img-5|Figure 5]] shown the convergence process. The GA parameters of Optdam program are shown in [[#tab-1|Table 1]]. [[#img-6|Figure 6]] shows a flowchart illustrating the process.
+<div id='img-5'></div>
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 |-
@@ Line 281: / Line 281: @@
 <div class="center" style="font-size: 75%;">'''Table 1'''. GA Information
 </div>
+<div id='tab-1'></div>
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 |-
@@ Line 344: / Line 344: @@
 |}
+<div id='img-6'></div>
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 |-

@@ Line 109: / Line 109: @@
 ==3. Geometrical model of concrete gravity dams and problem formulation==
-Based on the model of concrete gravity dam depicted in Figure 2, the cross-section of concrete gravity dam studied is defined by the four parameters given by Equation (5)
+Based on the model of concrete gravity dam depicted in [[#img-2|Figure 2]], the cross-section of concrete gravity dam studied is defined by the four parameters given by Equation (5)
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@@ Line 123: / Line 123: @@
 where <math>{b}_{c}</math> is a parameter required to define the dam crest. Also, the downstream slope is specified by the <math>{b}_{x}</math> and <math>{h}_{t}</math> design variables and h<sub>b </sub>is the dam’s height.
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@@ Line 192: / Line 193: @@
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 <math display="inline">\,</math>  <math display="inline">\,</math>  </div>
 ==4. The Optimization Algorithm (Optdam)==

@@ Line 39: / Line 39: @@
 ==2. Stability analysis of concrete gravity dams==
-Figure 1 shows the usual loads acting in a dam considering drainage. Water pressure is the  major external load acting on such a dam. The horizontal water pressure, exerted by the weight of the water stored on the upstream side on the dam can be estimated from rule of hydrostatic pressure distribution.
+[[#img-1|Figure 1]] shows the usual loads acting in a dam considering drainage. Water pressure is the  major external load acting on such a dam. The horizontal water pressure, exerted by the weight of the water stored on the upstream side on the dam can be estimated from rule of hydrostatic pressure distribution.
 In other to meet the safety requirements, the dam cross section is verified against floating, overturning and sliding.
@@ Line 85: / Line 85: @@
 <math>FSS</math>  is the safety factor against sliding which should also be greater than 1.0, <math>\mu</math>  the reduced coefficient of friction, <math>\sum V</math> the total vertical force acting on dam and <math>\sum H</math> the total horizontal force acting on dam.
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@@ Line 613: / Line 613: @@
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@@ Line 682: / Line 684: @@
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