Strategies in Decision Making in a Multiobjective Context: Integration of DOE, NBI, and CFD in the Optimization of a Centrifugal Fan

Resumo

Multiobjective optimization problems present significant challenges when attempting to balance conflicting variables simultaneously; furthermore, the creation of an adequate dataset can be a complex task. To address these challenges, an integrated approach is adopted, combining Design of Experiments (DOE) and Normal Boundary Intersection (NBI).
DOE is employed to plan experiments in a balanced and economical manner, allowing for valuable information to be obtained with fewer resources. Subsequently, NBI is used to optimize multiple objectives simultaneously, creating an equispaced Pareto surface that defines an efficient boundary.
To handle uncertainty in parameter estimates and analyze variable clustering, a confidence ellipse is constructed. This ellipse provides a visual representation of the uncertainty associated with estimates and assists in identifying patterns in the data.
Once the efficient boundary with numerous results is obtained, the challenge arises of choosing the best solution among those available. For this purpose, Mahalanobis Distance (MD) is utilized, which are weighted Euclidean distances, taking into account the covariance of variables. This technique aids the decision-maker in selecting the most suitable solution.
To demonstrate the effectiveness of integrating these techniques, a problem involving Computational Fluid Dynamics (CFD) is explored, encompassing an industrial centrifugal fan. In this scenario, conflicting variables include mass flow rate at the outlet and required torque, with four control variables: number of blades, blade inlet angle, blade outlet angle, and blade length.
After identifying the best possible fan based on the smallest MD, the product is computationally replicated under optimal conditions, and the result is verified.
This integrated approach combines techniques from DOE, CFD, and NBI that address all stages, from dataset creation to optimization and confirmation of results obtained, offering a comprehensive methodology for solving complex engineering problems.