A Case Study on Vibration Analysis using DeepONet

Structural Health Monitoring (SHM) is a crucial element in maintenance management, playing a vital role in ensuring public safety and economic sustainability. The effectiveness of SHM relies on accurately identifying and analyzing the underlying dynamic behaviors. However, the complexity of structures, material properties, and environmental factors often introduces nonlinear characteristics into the collected dynamic responses from sensing instruments, posing a challenge in accurately identifying the underlying complex (nonlinear) dynamics. Machine learning has the potential to complement physics-based methods for SHM, offering higher accuracy and other benefits. However, many resulting systems lack interpretability and trustworthiness. In addressing these challenges, this paper proposes a novel approach for identifying and analyzing underlying complex dynamics in a broad range of mechanical and civil structures. The approach is based on the recently developed Deep Operator Network (DeepONet), employed for learning nonlinear operators. In this approach, DeepONet is initially utilized to capture the fundamental operators of the dynamic system. Subsequently, these operators are optimized and reassembled based on existing physical knowledge. This strategy yields results demonstrating not only a high level of accuracy in predicting dynamic responses but also an intuitive representation of complex modes within the dynamic system. It establishes a tangible connection between the outcomes of the system response and the underlying mechanics of vibration, facilitating a more intuitive analysis of the system's vibrational properties. To validate this approach, an Euler beam model is employed, and the experimental results convincingly affirm the effectiveness of the strategy.