NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systems [[arXiv]](https://arxiv.org/abs/2208.12771)

@inproceedings{li2022neuralsi,
  title={NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systems},
  author={Li, Xuyang and Bolandi, Hamed and Salem, Talal and Lajnef, Nizar and Boddeti, Vishnu Naresh},
  booktitle={European Conference on Computer Vision},
  pages={332--348},
  year={2022},
  organization={Springer}
}

Overview

In this work, we propose NeuralSI for nonlinear dynamic system identification that allows us to discover the unknown parameters of partial differential equations from measured sensing data.

We consider the class of non-linear structural problems with unknown spatially distributed parameters. The parameters correspond to geometric and material variations and energy dissipation mechanisms, which could be due to damping or other system imperfections that are not typically captured in designs. As an instance of this problem class, we consider forced vibration responses in beams with spatially varying parameters. The primary challenges in such problems arise from the spatially variable nature of the properties and the distributed energy dissipation. This is typical for built civil structures, where energy dissipation and other hard-to-model phenomena physically drive the dynamic response behavior. In addition, it is very common to have structural systems with unknown strength distributions, which can be driven by geometric non-linearities or indiscernible/hidden material weaknesses. Finally, a typical challenge in structural systems is the rarity of measured data, especially for extreme loading cases.

Parameter estimation

Upon estimating the unknown system parameters, we apply them to the differential model and efficiently prognosticate the time evolution of the structural response. It is observed that the modulus coefficient $P$ matches well with the sinusoidal ground truth since the modulus dominates the magnitude of the response.

The ground truth and predicted dynamic displacement response, along with the error are visualized at beam midspan. The maximum peak-peak value in the displacement error is only 0.3% of the ground truth. The peak error in temporal extrapolation does not increase much compared to the peak error in temporal interpolation.

Hyperparameter investigation

We tested the effect of the number of dense layers, training sample ratio, and minibatch size on the parameter identification and prediction of dynamic responses.

Comparison to a Physics-Informed Neural Networks (PINN) and DNN

At last, we investigate the performance of NeuralSI compared to PINN and DNN, under a limited training data regime across different input beam loading conditions. This replicates the expected challenges in monitoring real structures with limited sensors and sampling capabilities.

Due to a limited amount of data for training, the DNN fails to predict the response. Furthermore, both PINN and DNN fail to extrapolate the structural behavior temporally.

The trade-off among the three methods is evaluated.