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

Abstract

The use of surrogate models to determine scaling rules for product families has been proven to be a powerful tool for dimensioning complex shape geometries by replacing costly to evaluate problems with almost instantly to solve mathematical functions. However, there is a broad range of surrogate models in the literature and each model can be configured in multiple ways. In addition, the optimal selection of a surrogate model and its configuration is highly conditioned by the case study nature. Consequently, nowadays it is mandatory to evaluate different surrogate models and configurations to choose the most appropriate model for each case study, which can be cumbersome and time consuming. Moreover, unrepresentative scaling rules derived from an inadequate evaluation process may lead to several design iterations increasing 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 was developed with two main objectives. Firstly, to avoid the cumbersome and time-consuming evaluation process of different surrogate model types and configurations required nowadays. Secondly, to reduce close to zero the design-analysis iterations when scaling a new family member. For this purpose, the URBaM model was developed with the capability to adapt to different non-linearity levels with a single configuration. In the present work, the structure of the proposed technique is first delineated. Then, the model is evaluated in six engineering case studies of different non-linearity levels (2 low, 2 medium and 2 high) and compared against 14 configurations of 8 most representative techniques in the literature. The obtained results demonstrate that the URBaM model is capable to accurately adapt to different nonlinearity levels with a single configuration with average values of MAPE, NRMSE, and RMAE of 10.5%, 0.22, and 0.66 respectively. In addition, in the performed comparison, the URBaM model presented the highest stability in the accuracy 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.