Parametric Model Order Reduction by Box Clustering with Applications in Mechatronic Systems

Abstract

High temperatures and structural deformations can compromise the functionality and reliability of new components for mechatronic systems. Therefore, high-fidelity simulations (HFS) are employed during the design process, as they enable a detailed analysis of the thermal and structural behavior of the system. However, such simulations are both computationally expensive and tedious, particularly during iterative optimization procedures. Establishing a parametric reduced order model (pROM) can accelerate the design's optimization if the model can accurately predict the behavior over a wide range of material and geometric properties. However, many existing methods exhibit limitations when applied to wide design ranges. In this work, we introduce the parametric Box Reduction (pBR) method, a matrix interpolation technique that minimizes the non-physical influence of training points due to the large parameter ranges. For this purpose, we define a new interpolation function that computes a local weight for each design variable and integrates them into the global function. Furthermore, we develop an intuitive clustering technique to select the training points for the model, avoiding numerical artifacts from distant points. Additionally, these two strategies do not require normalizing the parameter space and handle every property equally. The effectiveness of the pBR method is validated through two physical applications: structural deformation of a cantilever Timoshenko beam and heat transfer of a power module of a power converter. The results demonstrate that the pBR approach can accurately capture the behavior of mechatronic components across large parameter ranges without sacrificing computational efficiency.