A mechanics-informed neural network method for structural modal identification: application to closely spaced modes

This paper investigates the mechanics-informed neural network (MINN) method for identifying closely spaced modes. The main contribution of this study lies in clearly illustrating the principle that the MINN method can discern closely spaced modes and validating the method's effectiveness in identifying closely spaced modes. Large structures typically have closely spaced modes, which pose significant challenges for traditional modal parameter identification methods. This study investigates the ability of MINN method for extracting closely spaced modes. The unique aspect of the MINN method lies in utilizing the characteristic that single source point ratios correspond to mode shapes. Besides, embedding of sparsity and independence in the neural network can increase effective redundancy, which is beneficial for accurate identification of model parameters. The time-domain vibration data and time-frequency (TF) domain single-source points (SSPs) are set as inputs to the network. The process then employs sparsity-constrained neural networks and cross-correlation minimization constrained neural networks to cluster SSPs, combined with modal response independence to solve for modal responses and mode shape results. Then, frequencies and damping ratios are calculated using the modal responses. A numerical simulation and an actual large-span spatial structure are employed to illustrate the efficacy of the MINN method. The method achieved a frequency resolution of 0.0148 Hz in the numerical simulation and successfully identified closely spaced modes with a frequency interval above 0.0761 Hz in the real-world structure. Traditional methods can only achieve identification of closely spaced modes with a frequency interval above 0.0508 Hz in the numerical simulation and closely spaced modes with a frequency interval above 0.1622 Hz in the real-world structure. The MINN method outperforms traditional methods by reducing frequency intervals for closely spaced modes from 0.0508 Hz to 0.0148 Hz (a 0.036 Hz improvement) in the numerical simulation and enhancing Modal Assurance Criterion (MAC) value precision by 3.61% in the real-world structure.