Pareto optimal robust design combining isogeometric analysis and sparse polynomial chaos: brake squeal case study

Abstract

Shape optimization is an increasingly prevalent tool for designing and manufacturing mechanical systems with gradient-free nonlinear performance metrics. Uncertainty quantification is an essential part of the process as optimality can be called into question in the presence of unavoidable discrepancies between numerical designs and manufactured parts. This paper combines isogeometric analysis (IGA) and polynomial chaos expansions (PCE) towards shape optimization of a disc brake for noise minimization under uncertainties. The proposed approach sets robustness to manufacturing uncertainties as an optimization objective in order to directly obtain robust optimal solutions. IGA is chosen over other shape design alternatives for its absence of meshing approximations, which makes it potentially more suitable in the presence of uncertainties. PCE is used to quantify robustness through the variance of the output, in an attempt to alleviate the computational burden of uncertainty quantification. The studied application is a simplified disc brake system whose shape is modified to minimize undesirable squeal noise, which is quantified through complex eigenvalue analysis. The noise prediction model, PCE model, and a genetic algorithm are then combined for the purpose of searching for robust optimal solutions. Results show the capability to converge to a Pareto front of robust noise-minimizing disc brake shapes and overall high computational efficiency compared to Monte Carlo simulation for output variance estimation. Furthermore, our findings confirm the superiority of sparse PCE methods over the classical ordinary least squares PCE method for output variance quantification.