Parametric Dynamic Simulation and Bayesian Design Optimization of a Front-Loading Washing Machine

This paper presents the dynamic modeling and design optimization of a fully parametrized front-loading washing machine. A thorough mathematical analysis is performed to capture the effect of nine design variables (including rotation speed, spring stiffness, weight balancer mass density, damping coefficient, spring and damper angles) on vibrational characteristics of the washing machine. The parametric simulation reveals a complex relationship between the vibrational dynamics and design variables, entailing a computationally efficient optimization approach. A Bayesian Optimization (BO) framework is developed, in which a Gaussian process model and Genetic Algorithm (GA) are utilized along with carefully selected acquisition functions to enable adaptive sampling and search for optimal design values. The objective function is to minimize the maximum amplitude of the tub displacement inside the washing machine body. Two case studies are performed to consider a different number of design variables and choices of various infill methods. Results show that the fully parametrized front-loading washing machine model is applicable for parametric simulation and design optimization. The proposed BO is able to successfully find a set of design variable values corresponding to the lowest maximum displacement for vibration reduction. A comparison analysis is also carried out to exhibit the difference in optimization convergence and computational cost caused by the choice of acquisition functions. It is shown that the fully parametrized washing machine model yields a lower maximum displacement than the model with fewer design variables. Of the two acquisition functions studied for optimization, the Expected Improvement function converges more rapidly than the Lower Bound criterion.