Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning
In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yieldin...
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| Published in: | European journal of mechanics, A, Solids Vol. 87; p. 104225 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin
Elsevier Masson SAS
01.05.2021
Elsevier BV |
| Subjects: | |
| ISSN: | 0997-7538, 1873-7285 |
| Online Access: | Get full text |
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| Abstract | In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on generated collocation points inside the physical domain so that the total potential energy is minimized at all points. For the vibration and buckling analysis, the loss function is constructed based on Rayleigh’s principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending. The DAEM is implemented using Pytorch and the LBFGS optimizer. To further improve the computational efficiency and enhance the generality of this machine learning method, we employ transfer learning. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions.
•Deep autoencoder based energy method (DAEM) with tailored activation function.•Stable and accurate results without gradient vanishing/exploding problems.•Unsupervised DAEM applied to Kirchhoff plates. |
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| AbstractList | In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on generated collocation points inside the physical domain so that the total potential energy is minimized at all points. For the vibration and buckling analysis, the loss function is constructed based on Rayleigh's principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending. The DAEM is implemented using Pytorch and the LBFGS optimizer. To further improve the computational efficiency and enhance the generality of this machine learning method, we employ transfer learning. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions. In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on generated collocation points inside the physical domain so that the total potential energy is minimized at all points. For the vibration and buckling analysis, the loss function is constructed based on Rayleigh’s principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending. The DAEM is implemented using Pytorch and the LBFGS optimizer. To further improve the computational efficiency and enhance the generality of this machine learning method, we employ transfer learning. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions. •Deep autoencoder based energy method (DAEM) with tailored activation function.•Stable and accurate results without gradient vanishing/exploding problems.•Unsupervised DAEM applied to Kirchhoff plates. |
| ArticleNumber | 104225 |
| Author | Guo, Hongwei Zhuang, Xiaoying Alajlan, Naif Rabczuk, Timon Zhu, Hehua |
| Author_xml | – sequence: 1 givenname: Xiaoying surname: Zhuang fullname: Zhuang, Xiaoying email: zhuang@hot.uni-hannover.de organization: Department of Geotechnical Engineering, Tongji University, Shanghai, China – sequence: 2 givenname: Hongwei surname: Guo fullname: Guo, Hongwei email: guo@hot.uni-hannover.de organization: Chair of Computational Science and Simulation Technology, Faculty of Mathematics and Physics, Leibniz Universität Hannover, Hannover, Germany – sequence: 3 givenname: Naif surname: Alajlan fullname: Alajlan, Naif email: najlan@ksu.edu.sa organization: ALISR Laboratory, College of Computer and Information Sciences, King Saud University, P.O. Box 51178, Riyadh 11543, Saudi Arabia – sequence: 4 givenname: Hehua surname: Zhu fullname: Zhu, Hehua email: zhuhehua@tongji.edu.cn organization: Department of Geotechnical Engineering, Tongji University, Shanghai, China – sequence: 5 givenname: Timon surname: Rabczuk fullname: Rabczuk, Timon email: timon.rabczuk@uni-weimar.de organization: Institute of Structural Mechanics, Bauhaus University Weimar, Weimar, Germany |
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| Snippet | In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits... |
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| SubjectTerms | Activation function Artificial neural networks Autoencoder Bending Boundary conditions Buckling Configuration management Continuity (mathematics) Deep learning Energy method Energy methods Feature extraction Hyperbolic functions Kirchhoff plate Machine learning Plates Potential energy Resonant frequencies Robustness (mathematics) Transfer learning Vibration Vibration analysis |
| Title | Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning |
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