A hierarchical system to predict behavior of soil and cantilever sheet wall by data-driven models

doi:10.1007/s11709-022-0822-4

Frontiers of Structural and Civil Engineering

2022, Vol. 16

Issue (6): 667-684 https://doi.org/10.1007/s11709-022-0822-4

本期目录

A hierarchical system to predict behavior of soil and cantilever sheet wall by data-driven models

Nang Duc BUI¹, Hieu Chi PHAN²(

), Tiep Duc PHAM¹, Ashutosh Sutra DHAR²

¹. Institute of Techniques for Special Engineering, Le Quy Don Technical University, Hanoi 100000, Vietnam
². Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, NL A1B 3X5, Canada

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Abstract：

The study proposes a framework combining machine learning (ML) models into a logical hierarchical system which evaluates the stability of the sheet wall before other predictions. The study uses the hardening soil (HS) model to develop a 200-sample finite element analysis (FEA) database, to develop the ML models. Consequently, a system containing three trained ML models is proposed to first predict the stability status (random forest classification, RFC) followed by 1) the cantilever top horizontal displacement of sheet wall (artificial neural network regression models, RANN1) and 2) vertical settlement of soil (RANN2). The uncertainty of this data-driven system is partially investigated by developing 1000 RFC models, based on the application of random sampling technique in the data splitting process. Investigation on the distribution of the evaluation metrics reveals negative skewed data toward the 1.0000 value. This implies a high performance of RFC on the database with medians of accuracy, precision, and recall, on test set are 1.0000, 1.0000, and 0.92857, respectively. The regression ANN models have coefficient of determinations on test set, as high as 0.9521 for RANN1, and 0.9988 for RANN2, respectively. The parametric study for these regressions is also provided to evaluate the relative insight influence of inputs to output.

Key words： finite element analysis cantilever sheet wall machine learning artificial neural network random forest

收稿日期: 2021-08-15 出版日期: 2022-10-20

Corresponding Author(s): Hieu Chi PHAN

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2022, 16(6): 667-684.
Nang Duc BUI, Hieu Chi PHAN, Tiep Duc PHAM, Ashutosh Sutra DHAR. A hierarchical system to predict behavior of soil and cantilever sheet wall by data-driven models. Front. Struct. Civ. Eng., 2022, 16(6): 667-684.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-022-0822-4
https://academic.hep.com.cn/fsce/CN/Y2022/V16/I6/667

Fig.1

Fig.2

Fig.3

Tab.1

Fig.4

Fig.5

Fig.6

No.	L (m)	EI (kN·m²/m)	H_w (m)	H (m)	q (kN/m²)	B (m)	γ_unsat (kN/m³)	γ_sat (kN/m³)	E_oed (kN/m²)	c (kN/m²)	phi (° )	stable	Δ (mm)	not failure?
1	8	44982	40	5	0	0	18	19	23000	41	15	1	33.61	1
2	9	44982	40	5	0	0	18	19	23000	41	15	1	30.12	1
3	10	44982	40	5	0	0	18	19	23000	41	15	1	28.69	1
4	12	44982	40	5	0	0	18	19	23000	41	15	1	28.14	1
5	16	44982	40	5	0	0	18	19	23000	41	15	1	27.97	1
6	8	44982	40	5	0	0	19	20	9958	1	27	0	–	0^*
7	9	44982	40	5	0	0	19	20	9958	1	27	0	–	0^*
8	10	44982	40	5	0	0	19	20	9958	1	27	1	211.68	0^*
9	12	44982	40	5	0	0	19	20	9958	1	27	1	164.33	1
10	16	44982	40	5	0	0	19	20	9958	1	27	1	155.18	1
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
198	10	44982	4	5	10	10	19	19.5	12000	32	22	1	40.67	1
199	12	44982	4	5	10	10	19	19.5	12000	32	22	1	39.1	1
200	16	44982	4	5	10	10	19	19.5	12000	32	22	1	39.14	1

Tab.2

sample #	1		2		…	199		200
sample #	x (m)	y(x) (m)	x (m)	y(x) (m)	…	x (m)	y(x) (m)	x (m)	y(x) (m)
1	0.0000	0.0082	0.0000	0.0061	…	0.0000	0.0140	0.0000	0.0134
2	0.2951	0.0113	0.2951	0.0092	…	0.2951	0.0232	0.2951	0.0234
3	0.2951	0.0113	0.2951	0.0092	…	0.2951	0.0232	0.2951	0.0234
4	0.6264	0.0123	0.6264	0.0104	…	0.6264	0.0251	0.6264	0.0254
5	0.6264	0.0123	0.6264	0.0104	…	0.6264	0.0251	0.6264	0.0254
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
53	55.2219	0.0009	55.2219	0.0009	…	55.2219	0.0019	55.2219	0.0020
54	57.6109	0.0009	57.6109	0.0009	…	57.6109	0.0019	57.6109	0.0019
55	60.0000	0.0009	60.0000	0.0009	…	60.0000	0.0019	60.0000	0.0019

Tab.3

No.	variable	unit	count	min	max
1	L	(m)	200	8	16
2	EI	(kN·m²/m)	200	44982	110250
3	H_w	(m)	200	1	40
4	H	(m)	200	2.5	5
5	q	(kN/m²)	200	0	15
6	B	(m)	200	0	15
7	γ_unsat	(kN/m³)	200	17	19
8	γ_sat	(kN/m³)	200	17.6	20
9	E_oed	(kN/m²)	200	5479	78000
10	c	(kN/m²)	200	1	41
11	$φ$	°	200	15	34

Tab.4

Fig.7

Tab.5

variable	L	EI	H_w	H	q	B	γ_unsat	γ_sat	E_oed	c	$φ$	x
stable	0.3674	–0.0642	0.1327	–0.0832	0.1362	0.1184	–0.0698	–0.1439	0.4293	0.4100	–0.0055	–
Δ	0.3235	–0.0447	0.0012	0.1555	–0.1327	–0.1248	0.0838	0.1510	–0.4126	–0.4753	0.0798	–
y(x)	0.0614	–0.0077	–0.0771	-0.0374	0.2938	0.2575	–0.2399	–0.2714	–0.3055	–0.3830	0.3683	–0.3926

Tab.6

Fig.8

Fig.9

Tab.7

Tab.8

metric	equation	RANN1		RANN2
metric	equation	on train set	on test set	on train set	on test set
mean absolute error	$M A E = 1 n × ∑ i = 1 n \| y i − f i \|$	0.201697	4.531986	0.000288	0.00103
mean squared error	$M S E = 1 n ∑ i = 1 n (y i − f i) 2$	0.11290	49.2773	7.2152e−07	9.6209e−06
coefficient of determination	$R 2 = 1 − ∑ i = 1 n (y i − f i) 2 ∑ i = 1 n (y i − y ¯) 2$	0.9999	0.95212	0.9999	0.9988

Tab.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Tab.10

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