A Novel Multi-Fidelity Support Vector Classification Method for Boundary Prediction in Engineering Applications

The accurate prediction of failure boundaries in engineering applications is essential for ensuring safety and reliability. Traditional methods often rely heavily on high-fidelity physical experiments or numerical simulations, which are prohibitively expensive and time-consuming. In response to this challenge, our research proposes an innovative multi-fidelity support vector classification approach that leverages an abundant supply of low-fidelity data alongside a limited amount of high-fidelity data. This combination significantly reduces modeling costs while maintaining or even enhancing predictive accuracy. The key points of the proposed method include the design of a reasonable kernel function to effectively describe the relationship between the input and output of multiple fidelities, and the determination of the optimal hyperparameters. In addition, in practical engineering problems, real data often exhibit data imbalance, leading to poor performance of the trained models. Our novel method addresses this limitation by integrating a strategy for managing the data imbalance. By effectively treating data imbalance, our approach significantly improves the classification and boundary prediction capabilities of the model. To validate our method, we applied it to three distinct engineering problems: predicting the failure boundary of a zero Poisson ratio structure, analyzing surge and choke boundaries in an axial flow compressor rotor, and tackling a 31-dimensional simulation failure boundary prediction problem within the computational fluid dynamics context of the same rotor. The results demonstrate that our multi-fidelity support vector classification method not only effectively predicts boundaries in these practical scenarios but also outperforms alternative methods, showing its potential as a powerful tool for engineers.