## 4 ANN Modeling Procedure
### Assisted-ANN Modeling Approach  
The purpose of the assisted approach proposed in this paper is to assist the ANN learning process; and therefore, improve the accuracy of the output predictions. This is done by including additional \"dependent\" input parameters that are obtained from the known analytical input/output relations. A schematic illustration of the structure of the implemented ANN model for the assisted-ANN approach is shown in Figure 2b. As in the traditional approach, the input layer includes geometry and material related inputs as well as the panel configuration identifier. In addition to these direct independent inputs, one or more assistance parameter input(s) is/are included. The assistance parameters being used here are mainly geometric corrections for the crack-tip SIF. In general, the choice of the assistance parameters for any type of problem depends on the specific knowledge of the existing relations between the inputs and outputs. For the MSD problem being considered here, from the previous investigations, it can be seen that the linkup model, though not accurate, can capture the general trend of the experimental data to some extent. Since the linkup model is basically based on SIFs (the SIF is used to calculate the plastic zone size, Equation (3), it becomes reasonable to assume that the SIF's geometric correction factors can assist the ANN in the learning/prediction process. In order to demonstrate the effect of this assisted approach, four different levels of assistance are used. In each of the four levels, assistance parameter(s) that provide progressively higher level of assistance are used. Table 1 lists the different input assistance parameters that are used at each of the four levels. The details of the four assistance levels are as follows:  
* _First assistance level_: here, the panel configuration SIF correction factor (\(\beta_{\text{P-config}}\)) is used as an assistance parameter. This correction factor corrects the SIF of the lead crack for all effects related to the panel configuration, where the unstiffened panel configuration (seen in Figure 1) is taken as a reference configuration. Therefore, the value of \(\beta_{\text{P-config}}\) for the unstiffened panels (listed in Table 1) is unity (\(\beta_{\text{P-config}}=1\)) since this is the reference configuration. For the stiffened panels, the panel configuration correction factor is basically the stiffeners' effect correction factor (\(\beta_{\text{P-config}}=\beta_{\text{sft}}\)), and its value for each of the different cracks/stiffeners configurations is given in Table 2. This stiffeners' effect correction factor accounts not only for the presence of the stiffeners and their arrangement, but it also accounts for their cross-sectional area and spacing, the fasteners stiffness and spacing, and the crack location and length. Finally, for the lap-joint panels, the panel configuration correction factor is the lap-joint effect correction factor (\(\beta_{\text{P-config}}=\beta_{\text{LJ}}\)), and its value for each of the different cracks configurations is given in Table 3. This factor mainly accounts for the fasteners arrangement, stiffness and spacing, and for the point loads induced by the fasteners along the crack plane. * _Second assistance level_: here, instead of using the panel configuration SIF correction factor (\(\beta_{\text{P-config}}\)), the overall lead crack SIF correction factor (\(\beta_{a}\)) is used. The \(\beta_{a}\) includes both the finite width correction and the cracks interaction correction (as seen in Equation (5)), and it also includes the panel configuration correction factor (\(\beta_{\text{sft}}\) or \(\beta_{\text{LJ}}\)). The values of \(\beta_{a}\) for all the 113 data points are given in Tables 1-3. * _Third assistance level_: here, instead of using one assistance parameter as in the previous assistance levels, two assistance parameters are used simultaneously.