System identification via validation and adaptation (SIVA) for model identification of nonlinear vibrating structures

Estimating the governing equation parameter values is essential for integrating experimental data with scientific theory to understand, validate, and predict the dynamics of complex systems. In this work, we propose a new method for structural system identification (SI), uncertainty quantification, and validation directly from data. Inspired by generative modeling frameworks, a neural network maps random noise to physically meaningful parameters. These parameters are then used in the known equation of motion to obtain fake accelerations, which are compared to real training data via a mean square error loss. To simultaneously validate the learned parameters, we use independent validation datasets. The generated accelerations from these datasets are evaluated by a discriminator network, which determines whether the output is real or fake, and guides the parameter-generator network. The uncertainty in each parameter is quantified by fitting a Gaussian distribution to each parameter, then computing the 95% confidence bounds. Analytical and real experiments show the parameter estimation accuracy and model validation for different nonlinear structural systems.