Free Vibration Analysis of Centrally Elliptically Perforated Functionally Graded Plates and Modeling Using Enhanced Grey Wolf Algorithm-Multi-Task Regression Neural Networks

Abstract Background In this study, the relationship between the arrangement of centrally located elliptical holes on Functional Graded Plates (FGPs) and their free vibration behavior was analyzed using the finite element method, while the performance of the hybrid GWMTR algorithm for multivariate regression problems was also evaluated. In the vibration analysis, the effects of material index, hole size, arrangement angle, boundary conditions, and plate aspect ratio on the natural frequencies were investigated. Methods In the field of regression analysis, a Multi-Task Regression Neural Network (MTRN) architecture optimized using the Grey Wolf Optimizer (GWO) was configured with hyperparameters determined via Particle Swarm Optimization (PSO). Results It has been observed that FGP with circular holes produce higher frequencies compared to those with elliptical holes, and that the arrangement angle and plate ratio significantly affect the frequencies. This configuration provided superior accuracy (Coefficient of Determination, R 2 ) and lower Root Mean Square Error (RMSE) for all outputs compared to the classical artificial neural network (ANN) architecture. Specifically, Root Mean Square Error (RMSE) values decreased by over 35% for outputs 1, 3, and 7, thereby significantly reducing the model’s error tolerance. Conclusion The findings indicate that the GWMTR algorithm is more effective for multi-output regression problems and offers reliable and accurate modeling capabilities for complex engineering problems.