Engineering design optimization problems often rely on iterative numerical procedures to identify high-quality system configurations, particularly when uncertainty, coupled subsystems, or nonlinear constraints are present. Reliability-Based Co-Design (RBCD) represents one important class of such problems, where both physical and control design variables must be optimized while satisfying reliability requirements. Traditional approaches, including the First-Order Reliability Method (FORM) and the Hasofer-Lind–Rackwitz-Fiessler (HLRF) algorithm, are mathematically rigorous but frequently incur high computational cost, especially in high-dimensional or strongly nonlinear settings. To address this challenge, this paper proposes a machine learning-based framework for the direct approximation of optimized system designs through Taylor-series-based problem transcription. Objective and constraint functions are represented using structured Taylor-series polynomial forms. By randomly sampling polynomial coefficients, a large set of synthetic optimization problems is generated and solved offline using numerical optimization. The resulting dataset is used to train supervised learning models that learn the mapping from encoded problem definitions to their corresponding optimized design solutions. A two-stage learning framework consisting of feasibility classification and regression-based optimal solution prediction is developed. Results demonstrate strong predictive performance across nonlinear optimization problems. An engineering case study based on NACA 4412 spar-location optimization is also presented to evaluate the applicability of the proposed approach.

Keywords

Machine Learning, Design Optimization, Taylor Series Expansion, Gaussian Process Regression, Reliability-Based Design.