URBaM: A Novel Surrogate Modelling Method to Determine Design Scaling Rules for Product Families

The use of regression-based surrogate models to determine design scaling rules for mechanical product families has proven to be a powerful approach for dimensioning complex geometries. However, there is a broad range of surrogate models in the literature, and each model can be configured in multiple ways. The optimal model election is highly conditioned by the case study nature (e.g., non-linearity level), and consequently, it is mandatory to evaluate different surrogate models. This process can be cumbersome and time consuming, but the election of an inaccurate model may lead to several design–analysis iterations that increase the product cost and development time. Therefore, in this paper, a novel surrogate modelling technique to determine representative design scaling rules for product families—named Univariate Regression-Based Multivariate (URBaM)—is presented. The proposed method seeks to minimize design–analysis iterations while suppressing the process involved in evaluating different surrogate models, independent of the non-linearity level nature of the design problem. The URBaM model is evaluated through six oil and gas valve family design case studies, addressing critical mechanical component design problems across different non-linearity levels (two low, two medium, and two high). The results obtained with the URBaM model in these six cases are compared against 14 configurations of eight widely used techniques in the literature. The obtained results demonstrate that the URBaM model is capable of accurately adapting to different non-linearity levels with a single configuration and presents high stability regarding MAPE, NRMSE, and RMAE metrics from case to case. Consequently, the potential of the URBaM surrogate modelling technique to assist the design process of scalable mechanical product families is proven.