Presenting an Appropriate Neural Network for Optimal Mix Design of Roller Compacted Concrete Dams

In general, one of the main targets to achieve the optimal mix design of concrete dams is to reduce the amount of cement, heat of hydration, increasing the size of aggregate (coarse) and reduced the permeability. Thus, one of the methods which is used in construction of concrete and soil dams as a suitable replacement is construction of dams in roller compacted concrete method. Spending fewer budgets, using road building machinery, short time of construction and continuation of construction all are the specifications of this construction method, which have caused priority of these two methods and finally this method has been known as a suitable replacement for constructing dams in different parts of the world. On the other hand, expansion of the materials used in this type of concrete, complexity of its mix design, effect of different parameters on its mix design and also finding relations between different parameters of its mix design have necessitated the presentation of a model for roller compacted concretemix design. Artificial neural networks are one of the modeling methods which have shown very high power for adjustment to engineering problems. A kind of these networks, called Multi -Layer Perceptron (MLP) neural networks, was used as the main core of modeling in this study along with error-back propagation training algorithm, which is mostly applied in modeling mapping behaviors.


INTRODUCTION
By discovering this fact that human brain performs calculations using a method completely different from common digital computers, studies have started on artificial neural networks which are usually called neural networks.Brain is in fact a very complex and nonlinear computer with a parallel structure.Due to its ability in organizing fundamental elements, i.e., neurons, brain is able to perform many calculations (such as pattern recognition, perception, etc.) with a speed much higher than the fastest modern digital computers (Demuth and Beale, 1998).Genetic algorithm which is based on Darwin's Evolution Theory was first introduced by Holland in 1975 and later (Goldberg, 1989) presented a complete and accurate introduction for this method (Yeh, 1998).
Artificial neural networks are one of the applications of artificial intelligence which is widely used in modeling a large number of engineering and scientific problems.Numerous studies have been conducted on predicting compressive strength of concrete using neural networks (Sarıdemir et al., 2009).
Roller compacted concrete is one of the relatively new methods for constructing dams in Iran.Prediction and modeling of mix design and strength of this concrete have the same or even more complexity than other types of concrete.On the other hand, inclusion of all kinds of pozzolans, new additives in concrete mix design and effect of different concrete methods on this concrete have doubled mix and compaction and also complexity of its mix design (Yeh, 1998).Modeling roller compacted concrete by traditional and regression methods is not able to make appropriate prediction considering the existing complexities of this issue because resistance behavior of concrete is affected by nonlinear conditions and also by the smallest components available in the mix and the interaction between these components (Sarıdemir et al., 2009).Characteristics of neural networks with error-back propagation training algorithm have made use of this nonlinear modeling method very attractive and suitable for predicting strengths of all kinds of concretes (Gao et al., 2006).Therefore, this technique was applied as the main basis of modeling in this research.

RESEARCH METHODOLOGY
Neural networks applied for modeling: Multi -Layer Perceptron (MLP) neural networks with error-back propagation algorithm are one of the most commonly applied tools which have shown an extraordinary ability in all kinds of nonlinear and linear modeling (Papadakis and Tsimas, 2002).In this research, MLP neural networks with a hidden layer, which acted according to Fig. 1, were used because this structure was able to simulate all kinds of different functions and mappings with a suitable number of processor (neural cells) in the hidden layer (Gao et al., 2006).Figure 1 demonstrates structure of the applied network for modeling, which consisted of three input, hidden and output layers forming xp1, xp2, …, xpN as N element inputs and Whi and Wjh as adjustable weights of the network.
These networks act based on processing elements called neural cells Fig. 1.Input layer cells of input vector elements transfer each one of the patterns to the hidden layer without any processing and cells of the hidden layer and output layer process information on their input values based on Fig. 2. Function f is recognized as the stimulation function in this figure and can be linear, hyperbolic tangent or sigmoid function (Sarıdemir et al., 2009).
In these neural networks, two procedures are performed.Functional procedure includes application of patterns and input examples to the network and determination of cellular outputs of each layer and transferring the output of each layer to the next one.Error-back propagation procedure starts with comparing result of output layer with target value of each pattern and determining error of this comparison (Relation 1); then, this error is transferred from end layers to the previous ones based on different training algorithms while adjusting weights and biases such that error of the network reaches its lowest level (Sarıdemir et al., 2009).

Relation (1):
Error functions and network performance: The number of cells in output S 0 = The number of pattern Different parameters of neural network in resistance modeling: BP networks with a hidden layer and linear stimulation function in the output layer were used as the basis of modeling.Hyperbolic tangent stimulation function (Tanh) was used in the hidden layer.In addition, MATLAB software was used for the programming required for modeling.Model input parameters: Different parameters are effective on resistance of roller compacted consecrate such as the amount and type of cement and pozzolan, sand and gravel, fineness of cement particles, amount of water, sand module, maximum dimension of aggregate, aggregates' granulation and amount and type of additive.In addition to these cases, there are combined parameters which have been called indices effective on resistance (Delatte et al., 2003).Among the independent parameters effective on resistance of roller compacted concrete, the parameters and characteristics which were present in the collected information were selected so that they can be used under different conditions.These parameters included: Aggregate 25˷50, Aggregate 5˷25, Sand 0˷5, Sand 0˷3, Cement, Khash pozzolan, Water, additive such as Chrysoplast CER, Chryso Tard CHR, Conplast RP264M and Washing and don't washing materials.
Preparing and standardizing the data: In order to perform calculations, first, it is necessary to standardize raw data between 0 and 1 (Demuth and Beale, 1998).Therefore, input data were standardized considering rate of the maximum and minimum data.This action, which is called data normalization, is more applicable than other standardization methods.After taking the output from network, standardized outputs should be converted to real data to be compared with the observed values.Maximum and minimum limits of data are described in Table 1.

RESULTS
After analyzing the data with MATLAB software neural network, the outputs are presented as weight of  The relation according to whom MATLAB program was performed was as Relation (2): where, W 1,1 , W 2,1 and b 1 and b 2 are calculation coefficients by the software and A is initial values of the mix design.
For example, if 90 day compressive strength of a design with total cementitious materials is 120 kg/m 3 and is considered with mix ratios according to Table 10, the following is performed: First, values of each one of the materials are multiplied by the weights related to the second row of Table 11 for 90 day compressive strength (Table 6), which are W (1,1) s; then, the product is added to value of b 1 in second row of Table 7.
Afterwards, the answer is considered equal to x and placed in Relation (3): and the final answer equals: 100.3 .

CONCLUSION
Use of neural networks has changed modeling roller compacted resistance modeling and has included very suitable and accurate results.In the research which was conducted by Sorkon et al., very accurate results were presented on the prediction of compressive strength of concrete due to neural networks (Delatte et al., 2003).This model was made only once, predicted resistance instantaneously and accurately and could reduce costs of sampling the roller compacted mix design.Compressive strength of the cement mortars including different types of Pozzolan based on neural network without need for performing any laboratory studies has saved costs to a great extent in projects (Yeh, 1998).
By applying these models of resistance prediction and using minimization methods, one can achieve optimal mix designs from the structural and financial aspects considering many specifications of the mix design and without making laboratory samples.Application of these models is very useful for more study of parameters effective on roller compacted concrete.Use of more characteristics of aggregates (type of mineral, conditions of aggregates to prevent separation, etc.), type of the consumed cement and conditions of making samples (mixing time, mixing manner, time interval between completion of mix and concrete work, etc.) besides other input parameters make prediction of resistance more accurate.

Fig. 1 :
Fig. 1: Structure of neural networks with error-back propagation algorithm is multiplied by value of w (2, 1) in the second row of Table7and added to number b 2 .At the end, because the relations are normalized based on numbers, one should multiply the product by the maximum data, which equals 109.1

Table 1 :
Limits of data for mix design

Table 9 :
Result of w (2, 1), b1 and b2 and maximum data for compressive strength for 180 days