## 1 Introduction
The maximum stress level a cracked structure can withstand before it fractures is referred to as residual strength. For a panel having a lead (large) crack along with MSD cracks, residual strength usually refers to the stress level at which the ligaments between the lead crack and adjacent MSD cracks, on both sides, collapse. Several analytical and computational methodologies can theoretically be used to estimate the residual strength of panels with MSD, and the accuracy of these methodologies varies substantially [29; 30; 31; 32; 33; 34]. The use of data-driven approaches, such as ANN, for predicting residual strength of panels with MSD cracks is very rare in literature. As a matter of fact, testing panels with MSD cracks is not a quick and easy experimental task, and it is usually a time-and-cost-intensive process in both preparation and testing. In general, the panels need to be relatively large in order to resemble the actual case of aircraft structures realistically. For this reason, it is not possible to find large experimental datasets for panels with MSD in the literature. [PERSON] et al. [25; 26] used ANN for predicting the corrosion rate and residual strength of unstiffened aluminum panels with corrosion thinning and MSD. Comparison of the ANN residual strength predictions with the experimental results showed that the mean absolute error to be about 12%. Such an error level is considered to be relatively high, even when compared to some of the other relatively simple engineering models reported in the literature [29; 30; 31; 32; 33; 34]. The reason behind this relatively high ANN prediction error can partly be attributed to the small size of the dataset used for training the network (only about 40 data points). The authors of this study, [PERSON] et al. [27], have recently used ANN modeling for residual strength prediction of panels with MSD. A dataset comprising 147 different configurations was assembled form many literature sources where 97 data points were used for training, 25 data points for validation and 25 data points for testing. The dataset included data for three different aluminum alloys (2024-T3, 2524-T3 and 7075-T6), four different test panel configurations (unstiffened, stiffened, stiffened with broken middle stiffener, and lap-joints), and many different panel and cracks geometries. Through the careful selection of the ANN inputs and the use of a comprehensive optimization procedure, a single ANN model was developed where this model was able to give reasonably accurate residual strength predictions for all the different materials and panel configurations. Comparison of the ANN model predictions with the experimental results (of the testing dataset) showed that the mean absolute error is less than 4%, which puts the ANN model at the same accuracy level with the best semi-analytical and computational models available in the literature. Situations where only small experimental datasets are available may be encountered in many fields because generating large datasets is time-and-cost prohibitive [14; 27; 35; 36]. Therefore, different methods have been developed and implemented in ANN modeling to cope with the small dataset conditions. Examples of these methods include using simulated data [37], using virtual data [38], using multiple runs for models development and surrogate data analysis for model validation [39], using duplicated experimental runs [9], using stacked auto-encoder pre-training [14], using analytical models with errors revised by intelligent algorithms [35], using optimization aided generalized regression approach [36], and simultaneously considering data samples with their posterior probabilities [40]. [PERSON] et al. [37] used datasets obtained from finite element simulations to develop an ANN model for diagnosing and predicting cracks in aircraft fuselage panels.