Multi-fidelity physics-informed machine learning for probabilistic damage diagnosis

Machine learning (ML) models are gaining popularity in structural health monitoring (SHM) because of their ability to learn the complex relationship between damage and sensor data. However, the lack of sufficient experimental data for structures with different degrees of damage is a key problem in training ML models for SHM. This problem can be alleviated by using physics-based models to generate the required training data to build physics-informed ML (PIML) models for SHM. However, it takes significant computational effort to perform enough high-fidelity simulations of the diagnostic test. It is thus desirable to know whether the available computational resource budget should be expended on numerous low-fidelity physics simulations, or a small number of high-fidelity simulations, or their combination. In this paper, we investigate this aspect of generating adequate training data for PIML, by constructing multi-fidelity PIML models. We evaluate the performance of several PIML models, trained with different amounts of low-fidelity and high-fidelity data, in locating hidden cracks in concrete structures using a nonlinear dynamics-based diagnosis technique. We find that high-fidelity physics simulations that do not cover the (test and damage) parameter space do not improve the performance of diagnostic PIML models built using data from many low-fidelity physics simulations.