Using Radial Basis Function Artificial Neural Network for Predicting Asphalt Content of Asphalt Paving Mixture

The determination of the asphalt content of asphalt paving mixtures is a fundamentally important test for many authorities and researchers in highways field . This study seek to examined the application and use of radial basis function artificial neural network with Gaussian activation function by MATLAB software for predicting the asphalt content of the hot mix asphalt paving mixtures using their properties of Marshall test. The architecture of the study developed network consist of five input nodes representing five properties of Marshall test, with six hidden nods, while the output consist of one output node representing the asphalt content percent. The study results have show that the radial basis function network can be applied as a recommended and appropriate computational tool to accurately and quickly determine the asphalt content of asphalt mixtures as alternative to using traditional techniques.


Introduction
Asphalt binders are an essential component of asphalt concrete, they are the cement that holds the aggregate together.Binder content is one of the most important characteristics of asphalt concrete.Use of the proper amount of binder is essential to good performance in hot mix asphalt (HAM) paving mixtures.HMA is a mixture of asphalt cement and aggregate.Too little binder will result in a dry stiff mix that is difficult to place and compact and will be prone to fatigue cracking and other durability problems.Too much binder will be uneconomical, since asphalt binder is, by far, the most expensive component of the mixture and will make the mixture prone to rutting and shoving [Transportation Research Board, 2011].The Marshall method is the first systematic and widely used method of HMA mix design in Iraq.The Marshall properties of the mixtures to be determined should be good indicators of performance of the mixtures in service, so that these properties can be used to determine the acceptability of the mixtures and to select the optimum mix design to be used [Tia,2005].Artificial Neural Networks (ANN) have been successfully used for tasks involving pattern recognition, function approximation, optimization, forecasting, data retrieval, and automatic control, to name just a few [Haykin, 1999].In recent years many researchers have applied the use of ANN in an effort to improve evaluation and prediction of corrective measures [Thomas, 2001].The Radial Basis Function (RBF) neural network is a kind of feedforward neural network with the input layer, hidden layer and output layer, which has the global approximation [Li, 2012].RBF networks provide an excellent solution to many pattern recognition and classification problems [Yaol and Han, 2012]; also these networks have been successfully applied for nonlinear function approximation and data classification in wide range areas [Pekcan, Tutumluer, and Thompson, 2008].

Problem and objective of Research
In recent years there has been a growing interest in using performance testing and performance prediction models in HMA mixture design and acceptance.Laboratory investigation is the primary tool used by pavement engineers and researchers to understand mixture behavior and resolve the real world pavement problems [Taha, (2011].Traditionally, asphalt content has been measured in the laboratory by extraction from the paving mixture with hazardous solvents.A new method for prediction of asphalt content of a given HMA mixture should be made to dispense with the need for these harmful solvents.The prediction of asphalt content of a given HMA mixture is based on several variables and properties of the mixture according to the design method and specifications.In Marshall design method, the correlation of the asphalt content percent with each of the Marshall properties of HMA mixtures { Marshall stability, Marshall flow, percent of air voids, percent of voids in the mineral aggregate (VMA), and density} is non-linear.ANNs are useful tools in place of conventional physical models for analyzing complex relationships involving multiple variables, and for correlating nonlinear relationships between the inputs and outputs variables .These attributes make the study problem a suitable for analysis based on ANN.The main objective of this research is to explore the possibility of application and using of RBF neural network as a predictive tool for asphalt content percent in HMA mixture using software of MATLAB and its neural network toolbox according to the properties of Marshall test.The study seek to develop an architecture for RBF neural network that can discover a pattern in the relationship among the Marshall properties and it can then predict the percent of the asphalt content of a given HMA paving mixture.

Pavement Applications of ANNs
Over the past few years, ANN models have been successfully used in many civil engineering applications [Waszczyszyn, 2011].The results indicated that these models are more effective than the traditional models and can easily be implemented in a spreadsheet, thus making it easy to apply [Zhang and Zhang, 2004].ANNs are particularly amenable to modeling the complex behavior of these applications and have generally demonstrated superior predictive performance when compared with traditional methods.These models have been widely applied to various relevant civil engineering areas such as structural engineering [Nazarko, and Ziemia ski, 2011], geotechnical engineering [Jaksa, Maier, and Shahin, 2008].Recently, there has been an increased interest in ANNs for use in many fields of pavement engineering applications as well as other fields of transportation engineering [Taha, (2011].

Radial Basis Function Networks
The radial basis function (RBF) network comprises one of the most used network models.RBF networks can be used to solve a common set of problems [ Miller, 2011].The built-in commands provided by the package and the associated options are very similar.Problems where these networks are useful include; function approximation, classification, and modeling of dynamic systems and time series.The idea of RBF Networks derives from the theory of function approximation [Tsai, and Chuang, 2004].The structure of RBF networks typically have three layers: an input layer, a hidden layer with a non-linear RBF activation function and a linear output layer [Guoqiang, Zhongzhi, and Zongyi, 2010].The input can be modeled as a vector of real numbers (x R n ).The output of the network is then a scalar function of the input vector, : R n R [Qingjiang, 2012] , and is given by: Where N is the number of neurons (nodes) in the hidden layer, is the center vector for neuron i, and is the weight of neuron i in the linear output neuron.Functions that depend only on the distance from a center vector are radially symmetric about that vector, hence the name radial basis function.In the basic form all inputs are connected to each hidden n e u r o n [ D a c h a p a k e t a l ., 2 0 0 4 ] .T h e n o r m i s t y p i c a l l y t a k e n t o b e the Euclidean distance (although the Mahalanobis distance appears to perform better in general) and the radial basis function is commonly taken to be Gaussian: i.e. changing parameters of one neuron has only a small effect for input values that are far away from the center of that neuron.Given certain mild conditions on the shape of the activation function, RBF networks are universal approximators on a compact subset of R 2 .This means that an RBF network with enough hidden neurons can approximate any continuous function with arbitrary precision.The parameters a i , ci, and i are determined in a manner that optimizes the fit between and the data [Wen, Wang, and Wang, 2012].

Network Architecture
(ANN) is a network consisting of several nodes, known as neuron.The connection between these neurons carries weights, which defines the relationship between input and output data.One of the most important issues in the development of an ANN model is its architecture, i.e. the determination of the input and output variables, and number of neurons (nodes) in the hidden layer.The architecture of the ANN model has significant effect on the success of the developed model [Haykin, 1999].The number of neurons (nodes) in the middle (hidden) layers can be varied depending on the complexity of the problem and size of the input formation.The MATLAB Neural Network Toolbox is used to construct and train the networks.The implementation of this network is readily available in popular software MATLAB and its neural network toolbox.MATLAB is a high-performance language for technical computing, it integrates computation, visualization, and programming in an easy-touse environment, where problems and solutions are expressed in familiar mathematical rotation [Demuth, H, and Beale, 2003].The typical RBF network used in this study is sketch in Figure 1.The selected network for this study has one input layer with five input nodes, and one output layer with one output node .The input layer will have five nodes corresponding to the Marshall Properties of HMA mixtures: Marshall stability, Marshall flow, percent of air voids, percent of voids in the mineral aggregate, and density G mb .All these properties must meet the requirements of the General Specification for Roads and Bridges in Iraq for binder course [Republic of Iraq , Ministry of Housing and Construction, 2003].The hidden layer will have five nodes and the node threshold (bias node), six nodes in total.While the output layer will have one node corresponding to the predictive percent of asphalt content, as quality control parameter of HMA mixtures.

Mixture Design Method
Due to its simplicity, the Marshall method of HMA design is adopted for use in this study.This method involves selecting the aggregates and asphalt to be used, testing the asphalt mixtures at various different proportions of ingredients, and selecting the optimum mix design which give the best anticipated performance in service [Tia, 2005].The tests to be run on the Marshall specimens include: The study data are generated from 10 mixtures based on laboratory mix design using Marshall method for developing the plant job mix formula curried out in Highway Laboratory at University of Mosul.For each mixture, the correlation of the asphalt content percent with each of the Marshall properties of HMA mixtures is derived using the statistical analysis.Using curve fitting method and from the plots of the Marshall properties versus asphalt content percent, the equation which representing the best relationship between each of these properties and asphalt content is determined, corresponding to the statistical values of coefficient of determination (R 2 ), standard error of estimate (S.E.), and t-statistics.For example, Table (1) presents the best relationships between the Marshall properties and the asphalt content percent for study mixture No.3.Then, by using these equations, the generated data of each properties are calculated for different percents of asphalt content within the acceptance limits of the Iraqi specifications for the binder course.Sample of these calculations of generated data for study mixture No.3 is shown in Table (2).Finally, the available HMA data of 400 records are used in this study.These data are divided into two sets: 1. Training set: used to determine the network weights, where 300 records are used to develop the network.2. Testing set: used to verify the effectiveness of the stop criterion and to overcome network over-fitting , then to estimate the network performance.Remaining 100 records are used as input for testing the trained network.3.For validating the study network, new data of 30 records are used, these data are collected from Extraction experiments.Extraction experiments are conducted according to ASTM D2172 [American Society for Testing and Materials, 2004]by using the centrifuge extractor to determine the asphalt quantity for all of the HMA samples.

Results and Discussion
When researchers discuss a set of test results, the two most important characteristics of the data are the central tendency and variability [1].All real data sets exhibit variability, that is, the test results are not all exactly the same but vary within a certain range.The overall value of a data set is usually measured by calculating the mean value, often called the average.Variability in a set of numbers is usually measured by calculating the standard deviation.Table (3) shows the descriptive statistics for the study data.
The selected RBF network is trained for several epoch with respect to the mean squared error (MSE).The number of epochs against the MSE for the predicted values of the output parameter is shown in the Figure (2).The MSE decreased, training converged, as the number of epochs were increased as shown in this figure.With 1000 epochs and more , the MSE decreased slightly.Figure (3) describes the predicted values (outputs) versus the actual values (targets) of percent of asphalt content for both training and testing phases.The smaller spread of the result points would mean that predicted values of the output parameter are closer to the actual values and hence errors are small and vice-versa.These insignificant levels of MSE and high values of coefficient of determination (R 2 ) are a good indication to degree of the applicability and acceptability of the network performance.

Conclusions and Recommendations
ANNs are increasingly becoming an engineering tool for deriving datadriven predictive models.The developed ANN can easily be implemented in a spreadsheet module for practical applications.In this work, radial basis function neural network is treated as an analysis tool, just like statistical regression method.Study results indicate that radial basis function neural network predicts the asphalt content percent of the hot mix asphalt paving mixtures with reasonable accuracy.Also, this network has been shown to be a feasible predictive method that can reduce the time consumed and can provide environmental and health benefits, and cost saving when compared with traditional laboratory methods.This network can be used as an appropriated and effective tool for laboratories conducting quality control test and performing independent assurance, verification and acceptance testing because it is easy to understand, and can be easily implemented as a software simulation.Many researches and works should be applied the use of different types of ANN in an effort to improve evaluation and prediction of corrective measures in pavement engineering.Also, more efforts will be required to investigate various quality control processes of measure the acceptance of HMA paving mixtures.

The 6 th
Scientific Conference of the College of Computer Sciences & Mathematics ] 185 [ The Gaussian basis functions are local to the center vector in the sense that: ( xc i ) = 0 ……..…..… 3

Figure 1 :
Figure 1: Structure of Radial Basis Function Network

The 6 th
Scientific Conference of the College of Computer Sciences & Mathematics ] 189 [

Figure 2 :
Figure 2: Mean Squared Error for the Output Parameter at Different Numbers Epochs of the Study RBF Network.

INPUT LAYER HIDDEN LAYER OUTPUT LAYER Density Marshall Stability Marshall Flow Air Voids Voids in Mineral Aggrega te Asphalt Content The 6 th Scientific Conference of the College of Computer Sciences & Mathematics ] 187 [ 1
. Marshall test, which measures the Marshall stability and Marshall flow, in accordance with ASTM-D1559 [American Society for Testing and Materials, 2004] 2. Two different measures of densities in accordance with ASTM-D2726 [American Society for Testing and Materials,2004] are taken; bulk specific gravity(G mb ).These densities are used to calculate the volumetric parameters, air voids and voids in the mineral aggregate(V.M.A.).

Table 1 :
The Correlation Equations Between the Marshall Properties and the Asphalt Content Percent for Study HMA Mixture No.3.

Table 2 :
Sample of the Calculation Results of the Generated Data of Marshall Properties for Study HMA Mixture No.3.

Table 3 :
Descriptive Statistics for all Properties of the HMA Samples.