Effect of Crushed Aggregates Percentage on Marshal Stability of Asphalt Concrete, Using Artificial Neural Networks

In this research the variation of Marshal stability with percentage of crushed aggregates is simulated using Artificial Neural Networks (ANNs) with Levenberg-Marquardt Back Propagation (LMBP) training algorithm. To develop the model, the percentage of crushed aggregates, percentage passing through sieves 50, 20, 4, 8, 30 and 1/2 inch and percentage of asphalt content considered as network inputs and Marshal stability as network output so the number of input layer neurons is eight and the output layer neuron is one. The tangent sigmoid transfer function is selected for hidden layer neurons and linear transfer function for output layer. The inputs and outputs are normalized between -1 and 1, to improve the performance of the networks. At the first stage, the maximum generalization ability of each network with specified number of neurons (3, 5, 8, and 10) in hidden layer is determined. Comparing these maximum values reveals that the network with 8 neurons in the hidden layer has the maximum generalization ability. At the second stage, the variation of Marshal stability with percentage of crushed aggregates is simulated by applying sensitivity analysis on the network with maximum generalization ability. MATLAB 7 has been used as main software in this research. In order to collect the required data needed to design networks and evaluate the generalization ability of them, a database of 110 Asphalt concrete specimens are selected before compaction from the road surface. The specimens include Binder and Topeka with 0-19 mm gradation. The Binder Type is asphalt cement with the penetration grade 60/70. Having done the Marshal stability, extraction, percentage of crushed aggregate tests, the Marshal stability, the asphalt content, the gradation curve, the percent of crushed aggregates are derived. The optimum number of hidden layer neurons is determined based on 85 data for training and 25 data to assess the generalization ability of the networks. The training of the network with 3 neurons in the hidden layer is depicted in Fig. 1. In this figure the dashed line indicates the simulation error for new data versus the training cycles and the solid line indicates the training error or performance (MSE) versus the training cycles (epochs). Based on Fig. 1, the maximum generalization ability of the network happens in the initial training cycles so the training rate of the networks must be minimized and training parameters of the networks, mu-inc, mu-dec are selected close to 1.0 to reduce the training rate. In order to assess the variation of generalization ability of the network, a curve representing R versus MSE is expressed for each network with a specified number of neurons (3, 5, 8 and 10) in hidden layer, e.g. that which is shown in the Fig. 2. Comparing the maximum relative coefficients shows that the maximum generalization ability is achieved for T8P4 network with 8 neurons in hidden layer (R=0.768), so the optimum value for the neurons is selected to be 8. Based on the investigations made in this paper, increasing the number of hidden layer neurons more than 8 has negligible effect on generalization ability also, due to the sensitivity of network generalization ability to training error, in spite of reducing the training rate, the determination of maximum generalization ability requires designing and training of various networks.