Multivariable regression as a tool for design and performance optimization and prevision of a mechanical component

In mechanical component design, performance optimization often relies on iterative FEM analyses or topological optimization, both computationally demanding and sometimes producing geometries incompatible with conventional manufacturing. This study explores multivariable regression as an effective alternative for performance prediction and design optimization. A full factorial Design of Experiments (DOE) was performed on a parametrized 2D plate with a central slot, evaluating the influence of three geometric variables on maximum principal stress through 64 FEM simulations. Six polynomial regression models of increasing complexity were developed, and their accuracy assessed using the adjusted coefficient of determination and the standard error of estimate. Validation was carried out by comparing model predictions with FEM results on ten additional test cases, both within and outside the regression domain. The best-performing model achieved an average error of about 10% within the DOE range, demonstrating the method’s ability to reduce reliance on repetitive FEM simulations. The findings confirm that, when properly calibrated, multivariable regression provides a low-cost, computationally efficient design tool. It enables real-time prediction of component performance and supports the identification of manufacturable optimal geometries. The approach is particularly valuable in early design stages, where flexibility, speed, and interpretability are crucial.