# Detection and Monitoring of Bottom-Up Cracks in Road Pavement Using a Machine-Learning Approach
## 4 Results and Discussions  
### Multilayer Perceptron  
The results of the classification procedure based on the MLP classifiers are presented in Table 1, where, for each data set size (D, first column), the following pieces of information were reported: (a) best data set partition (number of samples used in training versus testing processing); (b) number of nodes (nodes in each hidden layer); (c) number of epochs (number of times that the learning algorithm will work through the entire training dataset); (d) batch size (the training dataset is divided into more batches); and (e) model accuracy.  
Figure 3 is an example of both graphical and numerical (confusion matrices) results that it is possible to obtain through the ML algorithms used in this study. In more detail, Figure 3a shows the trends of the training and testing losses during the epochs (e.g., 15) in which the algorithm (e.g., the MLP) works. Figure 3b shows the confusion matrix derived from (top) the training phase of the MLP algorithm, and (bottom) the testing phase. In more detail, a perfect training and a perfect testing (i.e. a perfect classification) were obtained when A) the losses tended to be zero when the epochs tended to be infinite and B) the non-zero elements of both the matrices mentioned above had all the non-zero elements in the main diagonal.  
The results reported in Table 1 and Figure 4 point out how many signals were required to properly classify the SHS of a road pavement using the MLP. The results in Table 1 were derived in order to (i) minimize the use of signals for the training process, (ii) use few epochs that are a crucial factor when a real time monitoring is needed, (iii) have an overall reduction of the training loss (see Figure 3) of at least 65% (i.e., the difference between the highest, starting value and the lowest, final value), (iv) use a constant batch size of 16 samples, and (v) consider satisfying a model accuracy of at least 80%. Note that model accuracy is derived from the confusion matrixes of the training and testing processes. For example, by considering the results reported in the last row of Table 1 (recalled in Figure 3), the accuracy of 91.8% was derived dividing the sum of main diagonal elements of the confusion matrix of the testing phase (i.e., 644+635+638+653=2570; see Figure 3b bottom), with the training data set size (i.e., all the elements of the confusion matrix of the testing phase, which were 2800, and represented 70% of 4000).  
Figure 3: Examples of (**a**) convergence of the first network used, i.e., the multilayer perceptron (MLP), and (**b**) confusion matrixes that express the accuracy of the network (training loss reduction = 80%).  
Table 1 shows the best results obtained using the MLP. It is important to underline that, the MLP allows obtaining good results for the data sets with size greater than 800. It was not possible to reach the convergence of the model, which was measured considering a reduction of the training loss values (defined above) of 65% as lower limit. In addition, based on results, it can be stated that if the data set size increased (from 1600 to 4000), it is possible to (i) use a lower percentage of signals in the training phase (i.e., from 60% to 30%; see Table 1, column \"Dataset partition\", rows 4 th - 6 th), (ii) speed-up the model by halving the epochs from 30 to 15 (see Table 1, column \"# of epochs\"), and (iii) obtain a better model accuracy (from 84.4% to 91.8% (see Table 1, last column)).