Development of deep neural network model to predict the compressive strength of FRCM confined columns

doi:10.1007/s11709-022-0880-7

Front. Struct. Civ. Eng.

2022, Vol. 16

Issue (10) : 1213-1232 https://doi.org/10.1007/s11709-022-0880-7

RESEARCH ARTICLE

Development of deep neural network model to predict the compressive strength of FRCM confined columns

Khuong LE-NGUYEN^1,², Quyen Cao MINH¹, Afaq AHMAD³, Lanh Si HO^1,⁴(

)

¹. Department of Civil Engineering, University of Transport Technology, Hanoi 100000, Vietnam
². Faculty of Arts and Design, University of Canberra, Bruce ACT 2617, Australia
³. Department of Civil Engineering, University of Engineering and Technology, Taxila 47080, Pakistan
⁴. Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima 739-8527, Japan

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Abstract

The present study describes a reliability analysis of the strength model for predicting concrete columns confinement influence with Fabric-Reinforced Cementitious Matrix (FRCM). through both physical models and Deep Neural Network model (artificial neural network (ANN) with double and triple hidden layers). The database of 330 samples collected for the training model contains many important parameters, i.e., section type (circle or square), corner radius r_c, unconfined concrete strength f_co, thickness n_t, the elastic modulus of fiber E_f, the elastic modulus of mortar E_m. The results revealed that the proposed ANN models well predicted the compressive strength of FRCM with high prediction accuracy. The ANN model with double hidden layers (APDL-1) was shown to be the best to predict the compressive strength of FRCM confined columns compared with the ACI design code and five physical models. Furthermore, the results also reveal that the unconfined compressive strength of concrete, type of fiber mesh for FRCM, type of section, and the corner radius ratio, are the most significant input variables in the efficiency of FRCM confinement prediction. The performance of the proposed ANN models (including double and triple hidden layers) had high precision with R higher than 0.93 and RMSE smaller than 0.13, as compared with other models from the literature available.

Keywords FRCM deep neural networks confinement effect strength model confined concrete

Corresponding Author(s): Lanh Si HO

Just Accepted Date: 13 September 2022 Online First Date: 30 November 2022 Issue Date: 29 December 2022

Cite this article:

Khuong LE-NGUYEN,Quyen Cao MINH,Afaq AHMAD, et al. Development of deep neural network model to predict the compressive strength of FRCM confined columns[J]. Front. Struct. Civ. Eng., 2022, 16(10): 1213-1232.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0880-7
https://academic.hep.com.cn/fsce/EN/Y2022/V16/I10/1213

Fig.1 Equivalent circular cross-section.

model	analytical expressions	No.
Ortlepp’s model [32]	$f cc f co = 1 + 0.27 × f lu f co + 5.55 × (f lu f co) 2 ? 3.51 × (f lu f co) 3$	(1)
	$σ lu = k e × b + h b h × a f × n f × f fu$	(2)
	$k e = 1 ? b n 2 + h n 2 3 A c$	(3)
ACI 549.4-13 [31]	$f cc f co = f co + 3.1 κ a f lu f co$	(4)
	$f lu = (2 n f A f E f ε fe) / (2 n f A f E f ε fe) (b 2 + h 2) (b 2 + h 2) 0.5$	(5)
	$κ a = (b h) 2 [1 ? (b h) b n 2 + (h b) h n 2 3 A g]$	(6)
	$κ b = (h b) 2 [1 ? (b h) b n 2 + (h b) h n 2 3 A g]$	(7)
	$ε fe = min (ε fu; 0.012)$	(8)
Ombres’s model [7]	$f cc f co = 1 + 0.913 (f lu f co) 0.5$	(9)
	$f lu = 12 k e k θ ρ f E f ε fu$	(10)
	$k e = 0.25 [(ρ f E f f co) 0.3 ? 1]$	(11)
	$k θ = 1 1 + 3 tan ? θ$	(12)
Triantafillou’s model [22]	$f cc f co = 1 + 1.9 (f lu f co) 1.27$	(13)
	$f lu = k e b + h b h t f E f ε fu$	(14)
	$k e = 1 ? b n 2 + h n 2 3 A c$	(15)
de Caso’s model [33]	$f cc f co = 1 + 2.87 (f lu f co) 0.775$	(16)
de Caso’s model [33]	$f lu = 2 E f ε fu t f n f D$	(17)
Colajanni’s model [23]	$f cc f co = 2.254 1 + 7.94 f lu f co ? 2 f lu f co ? 1.254$	(18)
	$f lu = 12 ρ f E f ε fu k e$	(19)
	$k e = 1 ? (b ? r c) 2 + (h ? r c) 2 3 A g$	(20)
Fossetti’s model [26]	$f cc f co = 6.46 η ? 0.86 ρ + 3.47 η ? 0.28$	(21)
	$η = E c ρ f E f$	(22)
	$ρ = 2 r / l$	(23)

Tab.1 Summary of the strength models used in this study

Fig.2 Simplified mathematical function of ANN.

Tab.2 Parameters details in the database for FRCM

Fig.3 Histogram with a normal distribution fit. (a) area (mm² × 10⁴); (b) l/h; (c) θ (°); (d) f_co (MPa); (e) ε_co (%); (f) f_uo (MPa); (g) ε_uo (%); (h) f_cm (MPa); (i) f_tm (MPa); (j) E_m (GPa); (k) f_fu (MPa); (l) E_f (GPa); (m) ρ = 2r/l; (n) ρ_f = 4t_fn/l; (o) a_f (mm²/m).

Tab.3 Detail of the hyper-parameter of LM used for modeling the ANN models

Fig.4 Local minima and over-fitting problem. (a) Local and global error; (b) over-fitting problem.

Fig.5 K-Fold cross-validation.

Tab.4 Double Layers ANN Models with all Parameters for FRCM

Tab.5 Triple Layers ANN Models with all Parameters for FRCM

Fig.6 ANN models predictions for the FRCM using the database with all 15 input parameters. (a) Double layers; (b) triple layers.

Fig.7 ANN models error for the FRCM. (a) ANN with double layers; (b) ANN with triple layers.

Fig.8 Multi-correlation between input variables and output.

Fig.9 The score of input variables.

Tab.6 Double Layers ANN Models with all Selected for FRCM

Tab.7 Triple Layers ANN Models with all Selected for FRCM

Fig.10 ANN models predictions for the FRCM using the database with selected input parameters. (a) Double layers; (b) triple layers.

Fig.11 ANN models error for the FRCM. (a) Double layers; (b) triple layers.

Tab.8 Comparison of D-ANN and T-ANN with 4 classical models (primary parameters for the three ML models)

Fig.12 Prediction results for the FRCM of other models. (a) Decision tree model; (b) SVM model; (c) Gaussian process model; (d) XGBoost model.

Tab.9 Results of comparison of D-ANN and T-ANN with 4 classical models

Fig.13 Comparison of predictions between ANN models and physical models for FRCM.

Fig.14 Normal distribution of ratios for the case of FRCM.

Fig.15 Range limits of ratios for the FRCM.

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