David Anton, M.Sc.
Institut für rechnergestützte Modellierung im Bauingenieurwesen
Pockelsstraße 3
38106 Braunschweig
Research project:
Identification of material parameters using data-driven modeling methods
For the condition assessment of existing infrastructure buildings, the current material parameters are of great interest, as they reflect the resistance of the material to external impacts. Thus, these material parameters and, in particular, their decrease over the service life of the infrastructure building provide an indication of damage and material degradation. To the extent that the displacement field data are available and the boundary conditions are known, the material parameters can be identified by solving the momentum equation inversely by numerical methods. In the next step, the identified material parameters can, for example, be fed back into a finite element simulation to calculate the current resistance of the infrastructure for the given geometry and loading conditions. These conditions can drastically change during infrastructure service life, as evidenced, for example, by the increasing traffic volume of bridges.
While numerical methods such as the finite element method have proven successful for the forward solution of partial differential equations, these methods often reach their limits for inverse problems. However, it was recently shown that there is a method in the growing field of scientific machine learning, known as Physics-Informed Neural Networks (PINNs) [1], that is particularly suitable for solving partial differential equations inversely. Using the displacement field data and prior knowledge about the hidden physics formulated as partial differential equation, material parameters can be identified using PINNs. One possibility for measuring the displacement field is digital image correlation (DIC).
A challenge of the proposed approach is that the material parameters are stochastic in nature. Reasons are, among others, material inhomogeneities (model error) and noisy sensor data (measurement error). Because of the significance for real applications, the current research project also aims to quantify the effect of the aforementioned uncertainties on the predicted material parameters.
Additional Literature:
[1] M. Raissi, P. Perdikaris, and G. E. Karniadakis. “Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations”. In: Journal of Computational Physics 378 (2019), pp. 686-707.
Conference contribution with publication in conference proceedings:
D. Anton, H. Wessels. Identification of Material Parameters from Full-Field Displacement Data Using Physics-Informed Neural Networks. Proceedings of the 8th International Symposium on Reliability Engineering and Risk Management (ISRERM). Hannover, Germany. September 4-7, 2022. Available on https://rpsonline.com.sg/proceedings/isrerm2022/pdf/GS-07-026.pdf.
Conference contribution without publication in conference proceedings:
D. Anton, H. Wessels. Identification of Material Parameters from Full-Field Displacement Data Using Physics-Informed Neural Networks. 9th GACM. Essen, Germany. September 21-23, 2022.