A robust-weighted hybrid nonlinear regression for reliability based topology optimization with multi-source uncertainties

Abstract

The computational burden in topology optimization (TO) under probabilistic constraints is a major challenge for both topology optimization and reliability analysis methods. The machine learning method can be applied for controlling the computational burden of inverse TO method for approximating the optimal volume fraction (Vf) which is related to max/min a probabilistic constraint. In this current work a hybrid nonlinear modelling training method is proposed by using the exponential nonlinear function and improved harmony search optimization for approximating the optimal Vf applied in reliability-based TO (RBTO) problems. For improving the accuracy predictions of nonlinear model a weighted training scheme is proposed given based on absolute bi-linear loss function applied as robust learning format. The applied weights given from near optimal constraints computed by Vf and loss function is determined based on two absolute function with different slop as 1 and 0.1. The proposed learning approach for nonlinear function is compared with the results of TO-based bisection under multi-source uncertainties for both accuracy and computational burden through four engineering problems. Results indicated that the proposed robust-weighted hybrid learning method computed by hybrid nonlinear regression and harmony search optimization is strongly improved the computational burden for evaluating the optimal Vf in TO and RBTO problems compared to TO and RBTO using bisection while it is more accurate as the nonlinear regression.