## 2 Materials and Methods
### Artificial Neural Networks (ANN)  
The nature of some ANNs, such as the multilayer perceptron, as universal approximators (Figure 2) [53], and their robustness against outliers, give them the ability to model all kinds of relations between variables with a high degree of reliability, especially when obtaining an accurate result is more important than knowing the relationships between the variables involved in the process [54]. The ANN model chosen was the multilayer perceptron. This network type has demonstrated its ability to model various properties of wood-based products, particularly in boards [12; 13; 14; 55; 56], but also in solid wood [57] and other products [58; 16; 59]. The network input variables were the temperature of particles and resin, mat moisture content, resin percentage, percentage of additives, mat speed, and press temperature. The output variable was internal bond. The type of network chosen to develop the internal structure was the multilayer perceptron, as described by the authors elsewhere [12; 13; 60]. As there is no precise rule to define the internal structure of a network, it was determined in each case by trial and error. To avoid the problem of overfitting, the initial dataset was randomly divided into three subsets (training, validation, and testing) at percentages of 60, 20, and 20% of the total dataset, with the condition of there being no significant differences between the subsets for a confidence level of 95%. In this way, the representativeness of the datasets in respect to the total dataset was verified. The training subset was used for the learning of the model, while the validation subset was used to monitor and prevent over-fitting during training. The test subset was used to independently assess the reliability of the model. Training was controlled by the early-stopping technique. This stops the process when a 10% variation occurs in the validation set in two consecutive cycles, either in the mean squared error (mse) or in the correlation coefficient. Before the network was designed, a principal component analysis was conducted on the input vector to detect any correlation between the input variables and improve the network output [61]. The selection criterion for the variables was that they had to contribute more than 2% to sample variability [61; 62]. All data were normalised (Equation (5)) before they were used to develop the networks, to improve network performance [61]. \[X^{\prime}=\frac{X-X_{m}}{s} \tag{5}\]  
where \(X^{\prime}\) is the value after vector \(X\) has been normalised, \(X_{m}\) is the mean of vector \(X\), and \(S\) is the standard deviation of vector \(X\). In all the networks, the transfer function used was the hyperbolic tangent sigmoid (Equation (6)), to enhance network performance [61]. \[f(x)=\frac{2}{1+e^{(-2x)}}-1 \tag{6}\]  
Figure 2: Example of a typical artificial neural network structure with eight input variables and two hidden layers. where f(x) is the output value of the neuron and x is the input value of the neuron. All the networks were developed so that they would be mathematically defined [63]; i.e., the training set had more data than the number of internal connections in the network. The acceptance criterion for the networks was defined as the absence of significant differences between the real data and the simulators for the testing set, following the 2014 version of standard EN 326-2 [64]. For greater assurance in the modelling output, the criterion applied was a correlation coefficient (R) greater than 0.70 between the real data and the simulated data, following the requirements of the 2000 version of standard EN 326-2 [65] to accept test results obtained using non-standard test methods. To calculate the confidence intervals, 250 different ANN were initially developed, varying the number of hidden layers and the number of neurons in each layer. Twenty of these ANN were selected as having the highest number of correlation coefficients in the testing set (Figure 3) and complied with the criterion of standards EN 326-2 [64; 65].