Novel gradient-enhanced Bayesian neural networks for uncertainty propagation
Abstract
Uncertainty propagation (UP) is crucial for assessing the impact of input uncertainty on structural responses, holding significant importance in engineering applications. However, achieving accurate and efficient UP remains challenging, especially for highly nonlinear structures. Bayesian neural networks (BNN) have gained attention for addressing UP issues, yet current BNN models only utilize input samples and corresponding structural responses for training. However, incorporating gradients of structural responses with respect to input samples provides valuable information. This study proposes a novel approach called gradient-enhanced Bayesian neural networks (GEBNN) to tackle UP tasks. In the GEBNN, a modified evidence lower bound (MELBO) loss is developed to consider both structural responses and gradient information simultaneously. This includes disparities between actual and predicted responses, as well as disparities between actual and predicted derivatives. Additionally, a gradient screening strategy based on the marginal probability density functions (PDFs) of input samples is established to identify significant derivative data for GEBNN training. Once the GEBNN is configured, it is utilized to replace the computationally intensive finite element model to efficiently provide UP results. Various applications, including nonlinear numerical examples, and mechanical, civil, and aeronautical structures, are presented to demonstrate the effectiveness of the GEBNN. The results show that the GEBNN significantly enhances the computational accuracy of the BNN in solving UP tasks.
Details
- Organisationseinheit(en)
-
Institut für Risiko und Zuverlässigkeit
- Externe Organisation(en)
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Xi'an Aircraft Industrial Corporation
The University of Liverpool
Tongji University
- Typ
- Artikel
- Journal
- Computer Methods in Applied Mechanics and Engineering
- Band
- 429
- Anzahl der Seiten
- 26
- ISSN
- 0045-7825
- Publikationsdatum
- 01.09.2024
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Allgemeine Physik und Astronomie, Angewandte Informatik
- Elektronische Version(en)
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https://doi.org/10.1016/j.cma.2024.117188 (Zugang:
Offen
)
