## 5 Conclusions  
In this study, an extensive ANN modelling activity was developed, with regards to the results of laboratory tests on HMA mixtures for road pavements. The experimental data set included 129 specimens, prepared with different aggregate and bitumen types. The main innovative feature of the research was the ANN model selection procedure, based on k-fold cross validation. In fact, to overcome the limitations of the standard approach of splitting the available data set into subsets with specific functions (i.e., for training and testing a model), a five-fold cross validation was used to compare the performance of 30 different network architectures and select the one that allows the best prediction accuracy of ITSM, MQ, and MS to be achieved, on the basis of four indicators. Five standard ANNs were also developed for each mechanical parameter of interest to demonstrate the wide variability of the models' predictive capacity that can be observed as a consequence of data sample variability. The main results can be summarized as follows:  
1. The standard approach has proved to be unreliable as the accuracy obtained for one test set can change considerably for a different test set. Hence, basic use of the MATLAB(r) ANN toolbox cannot ensure an identification of the ANN model that best fits the experimental data, especially in the case of relatively small data sets. 2. The five-fold cross validation allowed the predictive capacity of the mechanical parameters' models to be objectively estimated. In particular, the three-hidden layers ANN with eight neurons in each hidden layer and a positive linear transfer function was found to be the best performing model for predicting ITSM and MS. The development of a multiple hidden layers structure represents the second main innovative feature of the research. The MQ final model is a one-hidden layer network with a positive linear transfer function and 12 neurons. In summary, it was verified that the development of a multiple hidden layers structure could be useful, depending on the mechanical parameter investigated. 3. The use of the hyperbolic tangent transfer function, for multiple layer network architectures, has led to models that are characterized by overfitting problems. 4. It was verified that the positive linear transfer function is more effective with respect to the common hyperbolic tangent function; this is the third main innovative feature of the research, regarding the applications of ANNs in the pavement engineering field. 5. Analytical expressions of the proposed ANNs models, along with their associated weight values and normalization factors, were specified in detail to allow other researchers and engineers to compute a prediction of the parameters analyzed, modifying at their choice the composition of the mixture, within the range of variability of hot mix asphalt components considered in the study. 6. The good results achieved in the training and CV phases demonstrates that ANNs are an efficient data analysis system that is useful for the development of HMA's prediction models, as they were able to satisfactorily identify the complex intrinsic relation between the mixtures' properties and the analyzed mechanical parameters. 7. The ANNs models represent a typical \"black box\" method, which is not physically based; such a major drawback is compensated for by the possibility of obtaining satisfactory predictions of the mechanical parameters considered in a relatively easy way, within the ambit of materials and parameters considered. 8. The use of predictive models, elaborated by means of artificial neural networks, can be really useful during the design phase of hot mix asphalts because it is possible to obtain very quickly an accurate estimation of the analyzed mechanical parameters as a consequence of different input values regarding the mixture's composition, so avoiding any other experimental tests. 9.