Neuro-regression-based modeling and stochastic optimization of ventilated brake disc for enhancing cooling performance

Abstract

Designing brake discs is a complex engineering challenge that involves the interplay of numerous variables. A systematic approach to these designs can be achieved through optimization. A critical aspect of this process is formulating the objective function of the engineering problem using modeling methods. Although recent advancements in artificial intelligence enable the construction of objective functions from existing data via machine learning algorithms, there remains a need for a comprehensive perspective to propose a feasible design. The present study introduces a novel methodology to overcome deficiencies in the design, modeling, and optimization of ventilated brake discs. This approach integrates multiple nonlinear neuro-regression analyses, leveraging artificial neural networks (ANNs), regression analysis, and stochastic optimization techniques to derive optimal designs that meet specified performance criteria. Unlike predefined conventional mathematical models such as polynomial, sigmoid, unit step, and hyperbolic tangent, the proposed methodology facilitates the generation of a diverse set of mathematical models. Furthermore, model evaluation is enhanced by incorporating both the coefficient of determination (R²) and the boundedness check criterion, ensuring a more comprehensive and robust assessment. To minimize the cooling time of a ventilated brake disc as a function of nine input variables, including both dimensional and material-related design parameters, 14 different types of multiple regression models – encompassing linear, quadratic, trigonometric, logarithmic, and their rational forms – were generated. Modified versions of four stochastic algorithms – Differential Evolution, Nelder-Mead, Simulated Annealing, and Random Search – were employed to achieve an optimal design that reduce the temperature of the brake disc from 400° to 100° in the minimum cooling time. The results indicated that the different algorithms converged on the same design, which corresponds to a cooling time of 271.43 s. This represents a 19% reduction compared to the value reported in the referenced study. Consequently, the findings demonstrate the feasibility of obtaining a viable design through an objective function systematically constructed with high predictive capability. The proposed methodology is anticipated to be highly effective in realistically defining complex engineering phenomena.