Advanced Crack Detection in Bidirectional Gradient Material FGM Beams: A Neural Network Approach with Adam Optimization

This research presents a novel approach for accurately detecting crack depth and location in 2D Functionally Graded Materials beams. By employing natural frequencies as the primary indicator, we have developed a predictive model that integrates a discrete physical model with artificial neural networks (ANNs) optimized using the adaptive moment estimation (Adam) algorithm. Adam plays a crucial role in this process by efficiently updating the weights and biases of the ANN, which significantly enhances the training process. Additionally, a contour-based method was employed to detect the position and depth of cracks more effectively. Initially, a comprehensive numerical analysis of free vibration was conducted using the discrete model for beams with both Simply Supported and Clamped-Clamped boundary conditions. The results from this analysis served as valuable training data for the ANN model. The trained ANN was then utilized to predict the crack characteristics, with predictions closely aligning with those obtained from the numerical model and exhibiting minimal error margins. This research highlights the effectiveness of computational intelligence techniques, particularly ANNs, in solving complex structural analysis problems. The integration of Adam optimization significantly enhances the ANN training process by minimizing the error between the target outputs and the predicted outputs, resulting in a more accurate and efficient model, as confirmed by our convergence study. Sensitivity analysis of various hidden layer configurations further validates the robustness of the proposed method.