Investigation of complex modulus of asphalt mastic by artificial neural networks

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 1, August 014, pp Investigation of complex modulus of asphalt mastic by artificial neural networks Kezhen Yan* & Lingyun You College of Civil Engineering, Hunan University, Changsha 41008, China Received 5 June 013; accepted 5 February 014 This study investigates the complex modulus of asphalt mastic by using artificial neural networks (ANNs). The complex modulus of asphalt mastic samples are determined by using dynamic shear rheometer (DSR). Seven filler-asphalt ratios (F/A) are considered in this study: 0.0, 0.4, 0.6, 0.9, 1., 1.5, 1.8 by the weight of asphalt binder. In ANN model, the asphalt mastic temperature, frequency and F/A are the parameters for the input layer where as the complex modulus is the parameter for the output layer. The variants of the algorithm, such as the Levenberg-Marquardt (LM), scaled conjugate gradient (SCG) and Pola-Ribiere conjugate gradient (CGP) algorithms are used in this study. A tangent sigmoid transfer function is used for both hidden layer and the output layer. The statistical indicators, such as the root-mean squared error (RMSE), the coefficient of multiple determination (R ) and the coefficient of variation (COV) are utilized to compare the predicted and measured values for model validation. Results indicate that the LM algorithm appears to be the most optimal topology. It is also demonstrated that neural networks is an excellent method that can reduce the time consumed and can be used as an important tool in evaluating complex modulus of asphalt mastic. Keywords: Asphalt mastic, Dynamic shear rheometer, Complex shear modulus, ANN Asphalt mastics are defined as a mixture of filler with asphalt binder. The filler refer to the fraction of mineral aggregate passing the No. 00 sieve. The amount of filler material is specified as a percentage of the weight of the mix, and becomes part of the mixture design. The bitumen-mineral filler mastic has long been known to influence the overall performance of asphalt pavements. Efforts have been directed towards relating the mastic behavior to pavement performance with regard to rutting, fatigue and low temperature cracking. Generally, the effect of the filler is based on a volumetric filler effect or an interactive role between the filler and the bitumen due to the fineness and the surface characteristics of the filler. The importance role of the bitumen-mineral filler mastic in asphalt mixtures has been studied extensively 1-9. However, the role of fillers in paving mixtures is extremely complex and has not been fully explained. To characterize the mechanical influence of fillers on the asphalt mastic it is necessary to start with an assessment of their viscoelastic material properties such as stiffness and/or complex modulus, since asphalt mastics are viscoelastic materials over a broad range of temperatures. The viscoelastic behavior of asphalt mastic is very complex, varying from purely *Corresponding author ( yankz004@163.com) viscous to elastic, depending on loading time and temperature 10. A considerable increase in complex modulus at high temperature (low frequency) is obtained by addition of the filler in the asphalt, and further increasing the filler content results in increased complex modulus 11. Besides the increased stiffness at high temperatures, fillers also cause a decreased complex modulus (G*) in bitumen at low service temperatures (high frequency). In order to evaluate the efficiency of additives the filler, the dynamic (oscillatory) mechanical analysis has been investigated. These oscillatory tests are undertaken using dynamic shear rheometer (DSR). The principal viscoelastic parameter obtained from the DSR is complex modulus which is strongly affected by the frequency, temperature, additive type and additive content. The test requires very accurate measurements and takes long times. In order to eliminate these drawbacks, this paper represents an artificial neural network (ANN) approach which will provide an estimation of the complex modulus of asphalt mastics. Artificial neural network is an artificial intelligence technique that does not require mathematical relationships between variables. It is a powerful modeling tool for problems where the rules that govern the results are either not defined properly or too complex 1,13. A number of applications of ANN in asphalt materials and structures have been

2 446 INDIAN J ENG. MATER. SCI., AUGUST 014 proposed by several researchers Artificial neural network has learning, self-organizing, and auto-improving capabilities allowing it to capture complex interactions among variables without any previous knowledge of the nature of these interactions 18. A properly trained ANN also has the ability to recall full patterns from incomplete or noisy data 19. Due to such exceptional capabilities, ANN has been used in a wide range of engineering applications. Experimental Procedure Typical petroleum asphalt Foushan AH-70 is being used in heavy traffic. In order to characterize the properties of the base bitumen, conventional test methods such as penetration test, softening point test, and ductility test were performed. The properties of base bitumen are given in Table 1. The limestone filler was obtained from a local source. The fillers were conditioned in an oven at 105 C for 4 h to ensure moisture-free particle surfaces. The asphalt was preheated for h at 150 C in order to liquefy it for mixing. Asphalt was transferred to the mixing container maintained at 150 C. Keep the mixer at a constant stirring speed to ensure the gap in asphalt mixture as small as possible during mixing process. Filler was slowly added while stirring was maintained at 500 rpm for Properties Table 1 Properties of the base asphalt Unit Results Specification limits Penetration (100g,5s,5 C) 0.1 mm Penetration index Softening point C Ductility (5cm/min,5 C) cm 6.9 approximately 10 min. The asphalt mastics were prepared according to the filler-asphalt ratios (F/A): 0.0, 0.4, 0.6, 0.9, 1., 1.5, 1.8. At present the most commonly used method of fundamental rheological testing of bitumen is by means of dynamic mechanical methods using oscillatory-type testing, generally conducted within the region of linear viscoelastic (LVE) response. These oscillatory tests are undertaken using dynamic shear rheometer (DSR) 0. The principal viscoelastic parameters obtained from the DSR are the magnitude of the complex shear modulus (G*) and the phase angle (δ). By measuring the complex shear modulus of the asphalt material, the total complex shear modulus values as well as its elastic and viscous components are determined. The phase angle is the time lag between the applied shear stress and the resulting shear strain. The DSR test machine is shown in Fig. 1. The tests were performed under controlled-stress loading conditions using frequency sweeps between 1 rad/s and 100 rad/s and at temperatures between 10 C and 80 C. The tests were carried out with 8 mm diameter, mm gap parallel plate testing geometry between 10 C and 30 C, and with 5 mm diameter, 1 mm gap geometry between 30 C and 80 C. The stress amplitude for all the tests were confined within the linear viscoelastic response of the bitumen. Artificial Neural Networks Artificial neural network is examples of the way that the biological neural system works. It can exhibit a surprising number of human brain's characteristics, e.g., learning from experience and generalizing from previous examples to new problems. Therefore, an Fig. 1 DSR test machine

3 YAN & YOU: INVESTIGATION OF COMPLEX MODULUS OF ASPHALT MASTIC BY ANN 447 ANN can be a powerful tool for engineering applications 1. A schematic diagram for an artificial neuron architecture is shown in Fig.. A typical structure of ANN consists of a number of processing elements or neurons that is usually arranged in layers: an input layer, an output layer, and one or more hidden layers. The input from each processing element in the previous layer is multiplied by an adjustable connection weight (w in ). Weight values help the neural network to express knowledge. At each neuron, the weighted input signals are summed and a threshold value bias (b k ) is added. The combined input (y k ) is then passed through a nonlinear transfer function { f( ) } to produce the output of processing element. The adjustable connection weights and biases are obtained by learning or training process, which is nonlinear optimization of an error function. This is equivalent to the parameter estimation phase unconventional statistical models. There are different learning algorithms available for training neural network models. A popular algorithm is the back-propagation (BP) algorithm, which has different variants. Back-propagation training algorithms gradient descent and gradient descent with momentum are often too slow for practical problems because they require small learning rates for stable learning. In addition, success in the algorithms depends of the user-dependent parameters learning rate and momentum constant. Some faster algorithms such as Levenberg Marquardt use standard numerical optimization-techniques. These algorithms eliminate some of the disadvantages mentioned above. An ANN with back-propagation algorithm learns by changing the weights, these changes are stored as knowledge. Application of the Artificial Neural Network There are many types of ANN architectures in the literature. However, multi-layer feed-forward neural network is the most widely used for prediction. The multi-layer feed-forward neural network consists of three layers at least, an input layer, an output layer and one hidden layer at least. The input and output layers represent the input and output variables of the model and the hidden layers hold the network s ability to learn the non-linear relationships between the input and output 3. The objective of the network training using the back-propagation algorithm is to minimize the network output error through determination and updating of the connection weights and biases. The feed-forward neural network in this paper, shown in Fig. 3, was trained with the experimental data. The output of the network, the stiffness value G*, was calculated as 4 : ( )] (1) n m * G = ft B0 + Wk ft BHK + Wik Pi k = 1 i= 1 where B 0 is the bias at the output layer; W k is the weight of the connection between neuron k of the hidden layer and the single output layer neuron; B HK is the bias at neuron k of the hidden layer; W ik is the weight of the connection between input variable i and neuron k of the hidden layer; P i is the input ith parameter; and f T is the transfer function, defined as 1 f ( x) =, a > 0 1+ exp( ax) () In Eq. (1), the number of input variables (m) is 3; the input variables defined previously are P 1 = the temperature of the asphalt mastic (T), P = frequency (ω), and P 3 = filler-asphalt ratios (F/A). Inputs and outputs were normalized in the [0, 1]range. The output layer is the complex modulus of bitumen (G*). The back propagation learning algorithm has been performed in a feed forward, hidden layer neural network. The variants of the algorithm used in the study are the scaled conjugate gradient (SCG), Pola-Ribiere conjugate gradient (CGP), and Levenberg Marquardt (LM) algorithms. Several Fig. Artificial neuron model Fig. 3 Schematic diagram of artificial neural network

4 448 INDIAN J ENG. MATER. SCI., AUGUST 014 numbers of neurons were applied in the hidden layer to define the output accurately. Model validation is the utilization of the test data in trained network to see the prediction capability by comparing the output and target pairs. The statistical parameters such as the root-mean-squared error (RMSE), the absolute fraction of variance (R ) and the coefficient of variation as a percentage (COV) are used to compare predicted and measured (target) values for model validation. The RMSE, R, and COV can be defined as: 1 RMSE = t o R n ( i i) (3) n i = 1 ( t o ) i i = 1 i ( oi ) i (4) * RMS COV = 100 (5) O mean where t is the target value, o is the output value, n is the pattern. Results and Discussion Dynamic mechanical analysis test results The DSR complex modulus values at 10 rad/s obtained for the asphalt mastics at different temperatures were plotted with the F/A ratio as shown in Fig. 4. In this figure it is clear that G* value of asphalt mastic increases nonlinearly with the increase in the F/A ratio. The variation on complex modulus versus temperature and filler content at 10 rad/s is shown in Fig. 5. It can be seen that the complex modulus decreases significantly with the increase in temperature. The complex modulus of the asphalt mastic is greater than the complex modulus of base bitumen. Besides, for the same level of temperature, the complex modulus increases with the increase in filler content. The values of complex modulus of the base and asphalt mastic (F/A=0.6) with frequency and temperature are presented in Fig. 6. As shown in Fig. 6, as the frequency increases, the complex modulus increases as well. This is due to the rheological behavior of the bitumen since bitumen under shorter loading time exhibits elastic behavior. Besides, the temperature has a significant affect on the value of complex modulus, for the same frequency level, the increase in temperature decreases the complex modulus. ANN model results In order to obtain better performance, different models were performed by using the software MATLAB environment by using the neural network toolbox. These models were built up using a dataset including 01 patterns. In the training step, 160 of these patterns (80% of total) were used. The remaining patterns, randomly selected from a number of 41, were used for testing. In the training, an increased numbers of neurons in a single (from to 6) and double hidden-layer (the second hidden layer Fig. 5 G*value versus temperature at different F/A ratio Fig. 4 G*value versus F/A ratio at different temperature Fig. 6 Variation on complex modulus versus frequency

5 YAN & YOU: INVESTIGATION OF COMPLEX MODULUS OF ASPHALT MASTIC BY ANN 449 numbers of neurons from 1 to 5) for 6000 epochs were applied to define the output accurately. According to statistical performance evaluation, the summarized results are given in Tables and 3. As seen in Tables and 3, all the developed ANN models are very satisfactory and can be used for the prediction G* value of asphalt mastic with an acceptable Furthermore, the learning time was relatively slower than LM So the LM3-5-1 was determined as the best ANN model. The training performance of the ANN for LM3-5-1 architecture is shown in Fig. 7 where the variation of mean square error with training epochs is illustrated. The comparison of the real and ANN outputs for LM3-5-1 are shown in Fig. 8. Table A comparison of error values for studied single-hidden layer ANN topologies Algorithm train test R RMSE COV R RMSE COV LM LM LM LM LM CGP CGP CGP CGP CGP SCG SCG SCG SCG SCG Table 3 A comparison of error values for studied double-hidden layer ANN topologies Algorithm train test R RMSE COV R RMSE COV LM LM LM LM LM accuracy. The LM training algorithm with 5 neurons in a single-hidden layer was determined as the best ANN model in Table (LM3-5-1). In the training step of this topology, RMSE was determined as 1.37% when the values of COV and R obtained were and for the output of G*. These values were respectively 1.47%, and in the testing step. The LM (the first hidden layer with 5 neurons and second hidden layer with 4 neurons in a double-hidden layer of LM training algorithm) are determined as the best ANN model in Table 3. In the training step of this topology, RMSE was determined as 1.88% when the values of COV and R obtained were and for the output of G *. These values were respectively 1.55%,.850 and in the testing of G *. Different models with double hidden layers were also tested but none were as accurate as LM Fig. 7 The training performance of the ANN (LM3-5-1 topology)

6 450 INDIAN J ENG. MATER. SCI., AUGUST 014 This study also indicates the presented method has the potential for practical applications in more complicated problems. Fig. 8 The comparison of actual and ANN (LM3-5-1 topology) predicted G* Conclusions Based on the results of the study, the relationships between the complex modulus of asphalt mastic and temperature, frequency and filler content were investigated. From the experimental study, complex modulus of asphalt mastic increase with the increase in filler addition level and frequency, but decrease with the temperature increase. The back propagation neural networks for prediction of the complex modulus of asphalt mastics were investigated. Several ANN algorithms such as CGP, LM and SCG were used to model the G* of asphalt mastics. The trained algorithms then were tested and evaluated by means of statistical parameters such as COV, RMSE and R. These statistical values showed that LM algorithm appeared to be the most optimal topology. The LM algorithms in a single-hidden layer and in a double-hidden layer are compared, a single-hidden layer is better. It is also shown from the statistical evaluation that the neural network can effectively predict the complex modulus of asphalt mastics with high accuracy, and it can be an effective tool for asphalt mix designers to support their decision process and improve design efficiency. References 1 Shashidhar N & Romero P, Transport Res Rec, 1638 (1998) Shashidhar N, Needham S P, Chollar B H & Romero P, Proc Assoc Asphalt Paving Technol, 68 (1999) Shashidhar N & Shenoy A, Mech Mater, 34(10) (00) Buttlar W G, Bozkurt D, Al-Khateeb G & Waldhoff A S, Transport Res Rec, 1681 (1999) Chen J S & Peng C H, J Mater Civil Eng, 10(4) (1998) Kim Y R, Little D N & Song I, Transport Res Rec, 183 (003) Kim Y R & Little D N, J Mater Civil Eng, 16 (004) Abbas A, Masad E, Papagiannakis T & Shenoy A, Int J Pavement Eng, 6() (005) AI-Hadidy A & Tan Y Q, Construct Build Mater, 5(9) (011) Wang H N, Dang Z X, You Z P & Cao D W, Construct Build Mater, 35 (01) Chen J S, Kuo P H, Lin P S, Huang C C & Lin K Y, Mater Struct, 41 (008) Adeli H, Comput Aided Civil Infrastruct Eng, 16() (001) Flood I & Kartam N, J Comput Civil Eng, 8() (1994) Ozsahin T S & Oruc S, Construct Build Mater, (008) Specht L P, Khatchatourian O, Brito LAT & Ceratti J A P, Mater Res, 10(1) (007) Far S, Sadat M, Shane U B & Richard K Y, Transport Res Board Ann Meet, 09 (009) Golzar K, Jalali-Arani A & Nematollah M, Construct Build Mater, 37 (01) Demir F, Construct Build Mater, (7) (008) Rafiq M, Bugmann G, & Easterbrook D, Comput Struct, 79(17) (001) Kok B V, Yilmaz M, Sengoz B, Sengur A & Avci A, Expert Syst Appl, 37 (010) Ince R, Eng Fract Mech, 71(15) (004) Esen H, Inalli M, Sengur A & Esen M, Energy Build, 40(6) (008) Kalogirou S A, Appl Energy, 67 (000) Juang, C H & Chen, C J, Comput Aided Civil Infrastruct Eng, 14 (1999) 1-9.