Multiscale computation on feedforward neural network and recurrent neural network

doi:10.1007/s11709-020-0691-7

Frontiers of Structural and Civil Engineering

2020, Vol. 14

Issue (6): 1285-1298 https://doi.org/10.1007/s11709-020-0691-7

本期目录

Multiscale computation on feedforward neural network and recurrent neural network

Bin LI, Xiaoying ZHUANG(

)

Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

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Abstract：

Homogenization methods can be used to predict the effective macroscopic properties of materials that are heterogenous at micro- or fine-scale. Among existing methods for homogenization, computational homogenization is widely used in multiscale analyses of structures and materials. Conventional computational homogenization suffers from long computing times, which substantially limits its application in analyzing engineering problems. The neural networks can be used to construct fully decoupled approaches in nonlinear multiscale methods by mapping macroscopic loading and microscopic response. Computational homogenization methods for nonlinear material and implementation of offline multiscale computation are studied to generate data set. This article intends to model the multiscale constitution using feedforward neural network (FNN) and recurrent neural network (RNN), and appropriate set of loading paths are selected to effectively predict the materials behavior along unknown paths. Applications to two-dimensional multiscale analysis are tested and discussed in detail.

Key words： multiscale method constitutive model feedforward neural network recurrent neural network

收稿日期: 2020-02-19 出版日期: 2021-01-12

Corresponding Author(s): Xiaoying ZHUANG

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2020, 14(6): 1285-1298.
Bin LI, Xiaoying ZHUANG. Multiscale computation on feedforward neural network and recurrent neural network. Front. Struct. Civ. Eng., 2020, 14(6): 1285-1298.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-020-0691-7
https://academic.hep.com.cn/fsce/CN/Y2020/V14/I6/1285

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Fig.10

material	$E (MPa)$	$E t (MPa)$	$ν$	$σ s (MPa)$
M	$1 × 105$	$2 × 104$	0.3	200
B	$1 × 105$	$1 × 104$	0.3	100

Tab.1

Fig.11

experiment number	layers number	learning rate	mini-batch size	dropout rate	accuracy
1	4	$1 e − 2$	16	0.75	0.767
2	4	$1 e − 3$	32	0.85	0.838
3	4	$1 e − 4$	64	0.95	0.856
4	5	$1 e − 2$	32	0.95	0.866
5	5	$1 e − 3$	64	0.75	0.866
6	5	$1 e − 4$	16	0.85	0.870
7	6	$1 e − 2$	64	0.85	0.867
8	6	$1 e − 3$	16	0.95	0.933
9	6	$1 e − 4$	32	0.75	0.895
parameter	6	$1 e − 3$	32	0.95

Tab.2

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Fig.13

experiment number	GRU layers	FNN layers	learning rate	dropout rate	accuracy
1	1	1	$1 e − 3$	0.75	0.817
2	1	2	$1 e − 4$	0.85	0.800
3	1	3	$1 e − 5$	0.95	0.681
4	2	1	$1 e − 4$	0.95	0.840
5	2	2	$1 e − 5$	0.75	0.660
6	2	3	$1 e − 3$	0.85	0.938
7	3	1	$1 e − 5$	0.85	0.521
8	3	2	$1 e − 3$	0.95	0.949
9	3	3	$1 e − 4$	0.75	0.828
parameter	2	3	$1 e − 3$	0.95

Tab.3

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