PSI - Issue 57

Mohammad F. Tamimi et al. / Procedia Structural Integrity 57 (2024) 121–132 Mohammad F. Tamimi & Mohamed Soliman/ Structural Integrity Procedia 00 (2023) 000 – 000 6

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incorporating the distinct properties of the weld material. This assumption was taken as the weld region is small in comparison to the overall geometry of the stiffened panel that mainly consists of base metal (i.e., steel material).

Fig. 3. A view of the developed finite element model of Specimen 3 showing the loading and boundary conditions, as well as mesh configuration around the crack tip. 5.1. Application of ANNs to Quantify the Crack Driving Parameter To calculate the fatigue service life of stiffened panels, the FE model is required to compute the crack driving parameter ( J -integral) for each load cycle as the crack propagates. However, each stiffened panel in this context might undergo millions of cycles, making direct use of FE analysis for each cycle infeasible. Due to the significant computational demands of continuously executing FE models, feedforward ANNs employing the LMA were chosen to approximate the FE model, allowing for the computation of the crack driving parameter based on specific input parameters. To date, LMA is one of the most widely used algorithms for training machine learning models (Ly et al., 2021; Kunaver et al., 2022; Žic and Pereverzyev, 2023). LMA offers a practical balance be tween the speed of the Gauss-Newton method and the stability of the Gradient Descent, making it particularly suitable for our specific application. This algorithm minimizes the total mean square error between the actual output of the multi-layer network and the desired output (Khan et al., 2013). A wide range of variations in input parameters is used in the ANN training dataset, including various stiffener characteristics and main panel thicknesses as well as stress levels. For example, it includes panel thicknesses from 6 mm to 30 mm, stiffener heights between 50 mm and 450 mm, and stress levels ranging from 0 to 100 MPa. The training dataset also covers a wide range of spacing between stiffeners. It's worth noting that only a single, center positioned, through-thickness initial crack was introduced in the panels at the mid-section, and its propagation across the width of the panel. Table 1 shows the input parameters and the range covered in the training process. A schematic representation of the general layout of multilayer feedforward ANN, emphasizing the selected input parameters, is shown in Figure 4. The Sobol sequence experimental sampling design technique (Sobol & Levitan, 1999) is used to generate the set of input parameter combinations for the training dataset, resulting in a total of 45,000 samples. The selection of 45,000 samples was made through an in-depth convergence analysis, to achieve a prediction error of less than 5%. Figure 5(a) highlights the relationship between the error percentage and the number of samples in the trained dataset. As shown, as the number of samples increased, a noticeable reduction in the prediction error was observed, stabilizing around the 45,000 samples. This optimal number ensured the targeted accuracy level, striking a balance between precision and computational demands. These samples are divided into 75% for training the ANN, 15% for validation, and the remaining 10% for testing (Jaimes et al., 2005).