Optimized artificial neural networks to predict the impact response of functionally graded composite materials

Accurately predicting the Depth of Penetration (DOP) is essential for understanding the impact behavior of Functionally Graded Composite Materials (FGCMs) under high-velocity conditions. However, the nonlinear dynamic behavior governing FGCMs, coupled with the high cost and time-consuming nature of experimental tests, make precise DOP estimation a challenging task. This study proposes an efficient predictive framework that combines finite element (FE) simulations with artificial neural networks (ANNs) to overcome the constraints of conventional numerical and experimental approaches. This work focuses on applying the Whale Optimization Algorithm (WOA) and the Arithmetic Optimization Algorithm (AOA) as independent optimization strategies to improve the control parameters during the initiation phase, avoid convergence to local optima, and accelerate the learning process. Finite Element (FE) simulations were used to generate input-output datasets, which were used to train three ANN models: conventional back-propagation (BP), WOA-ANN, and AOA-ANN. The optimized ANNs accurately captured the nonlinear mapping between impact velocity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>i</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) and DOP. Results confirm that WOA-ANN model outperformed both AOA-ANN and BP models, achieving lower mean square error (MSE) and higher correlation coefficients. Moreover, the optimized ANNs provide reliable predictions with a limited number of FE simulations, considerably reducing computational effort while maintaining accuracy.