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- Title
Nonlinear response modelling of material systems using constrained Gaussian processes.
- Authors
Herath, Sumudu; Chakraborty, Souvik
- Abstract
This article investigates the suitability of constrained Gaussian process regression in predicting nonlinear mechanical responses of material systems with notably reduced uncertainties. This study reinforces the conventional Gaussian processes with mechanics‐informed prior knowledge observed in various kinematic responses. Stiffening and softening responses of material systems mostly demonstrate at least one of the boundedness, monotonicity and convexity conditions with respect to some kinematic variables. These relationships or impositions in turn are encoded into a constrained Gaussian process for prediction, uncertainty quantification and extrapolation. Using numerous examples and comparative studies, this article evidently proves that the use of constrained Gaussian processes is data‐efficient, highly accurate, yields low uncertainties, recovers model overfitting and extrapolates very well compared to unconstrained or conventional Gaussian processes. Moreover, the usability of the proposed numerical method across various engineering modelling domains such as multiscale homogenisation, experimentation, structural optimisation, material constitutive modelling and structural idealisation is demonstrated.
- Subjects
GAUSSIAN processes; STRUCTURAL optimization; KRIGING; ENGINEERING models; MULTISCALE modeling; STRUCTURAL models
- Publication
International Journal for Numerical Methods in Engineering, 2024, Vol 125, Issue 14, p1
- ISSN
0029-5981
- Publication type
Article
- DOI
10.1002/nme.7486