## 4 ANN Modeling Procedure  
The main objective of this study is to introduce a novel assisted-ANN modeling approach that can further improve the accuracy of the ANN predictions, and at the same time this approach enables the ANN to hold accurate even when relatively small datasets are used for training the network. The benefits and capabilities of this assisted-ANN modeling approach are demonstrated by applying it for developing an ANN model that can accurately predict the residual strength of panels with any lead and MSD cracks geometry for any panel configuration and geometry. In order to recognize the benefit of the assisted approach, two ANN modeling approaches are used and comparted in this investigation. Firstly, the traditional or typical approach is used. In this approach, independent parameters such as geometric quantities, panel configuration identifier and relevant material properties, are used as inputs to the ANN. Such input parameters maybe called direct parameters. Secondly, the proposed assisted-ANN approach is used. In this approach, in addition to the direct independent input parameters (geometry, material properties, etc. ), additional \"dependent\" parameters are used as inputs in order to assist the ANN to better capture the input/output relations and therefore improve the accuracy of the predicted outputs. These indirect dependent parameters, which may be called \"assistance parameters\", are obtained using the known analytical relations between the inputs and the output. It should be mentioned here that the traditional ANN modeling approach was previously used by [PERSON] et al. [27] on a slightly larger dataset than what is being used here and it was found to give reasonably high accuracy. The dataset used in [PERSON] et al. [27] had a total number of 147 data points where that included additional 34 datasets for two aluminum alloys (2524-T3 and 7075-T6) that are not considered here. In this study, only the Al 2024-T3 experimental data (113 data points) are considered since it includes the widest possible variety of different configurations. The same traditional ANN modeling approach used in [PERSON] et al. [27] is also being used in this investigation to serve as a benchmark for the accuracy level in order to evaluate the improvements attained by using the assisted approach. For both the traditional and assisted approaches, the ANN model is built using the supervised feed-forward scheme. The network consists of an input layer with several input nodes, an output layer with one output node (residual strength), and one intermediate hidden layer. The data points used in this investigation are separated into three general groups (given in Tables A1-A3) according to the panel configuration. For each of these three groups, the size percentages of datasets used for training, validation, and testing are set to be about 66%, 17% and 17%, respectively. Thus, the number of data points used for training/validation/testing for each of the different panel configuration groups are: 34/8/8 for the unstiffened panels, 24/6/6 for the stiffened panels and 17/5/5 for the lap-joint panels. This makes the total number of data points used for training (from all the different groups) to be 75 data points and the number of data points for the validation and testing to be 19 data points for each. The individual data points that are used in the training, validation and testing datasets should be chosen randomly such as to avoid any bias that might come from manually choosing the testing dataset. However, since the number of data points used in this investigation is relatively small, it is recommended to include some fixed manually selected data points in the training dataset to cover the upper and lower limits of each of the input parameters (e.g., ligament length, lead crack length, MSD crack length, etc.). This is done to avoid having some data points in the testing group that require the ANN to extrapolate out of the data ranges used for training.