Detection of breathing cracks using physics-constrained hybrid network

During the operational lifespan of mechanical structures, the occurrence of “breathing” cracks in structural components due to long-term dynamic loading poses a significant risk of catastrophic failure to the overall mechanical system. In this research, we propose an innovative approach for detecting breathing cracks by leveraging the physics-constrained hybrid network (PCHN). The fundamental concept is embedding the implicit governing equations into the network training process. This integration constrains the solution space and results in a closed-form dynamical model, which reveals the index for breathing crack detection. Firstly, the state-constrained parallel networks (SCPNs) capable of making full-state predictions with partial labels are constructed by introducing state dependency constraints to the outputs of three parallel networks. Subsequently, a portable sparse regression layer (SRL) is built to recover the governing formulation, wherein the function library is constructed with the full-state predictions of the SCPNs. Finally, the SCPNs and SRL are synthesized to constitute the PCHN framework, providing both full-state predictions and the dynamical model of the breathing beam. An alternate optimization (AO) method is developed to optimize the two components sequentially. The effectiveness, robustness, and applicability of the proposed method are demonstrated through comprehensive numerical simulations, finite element simulations, and experimental studies. Our results indicate that the proposed PCHN method accurately identifies the dynamical model of the breathing beam and evaluates the degree of damage even when only partial noisy state observations are available. Notably, the robustness and sensitivity of the proposed approach make it a promising tool for practical damage detection applications. The code of PCHN is available on https://github.com/latexalpha/PCHN.