A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy

doi:10.1007/s11709-021-0767-z

Front. Struct. Civ. Eng.

2021, Vol. 15

Issue (6) : 1453-1479 https://doi.org/10.1007/s11709-021-0767-z

RESEARCH ARTICLE

A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy

Huy Q. LE^1,², Tam T. TRUONG^1,⁴, D. DINH-CONG^3,⁴, T. NGUYEN-THOI^1,⁴(

)

¹. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
². Faculty of Civil Engineering, Ho Chi Minh City University of Transport, Ho Chi Minh City 700000, Vietnam
³. Division of Construction Computation, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
⁴. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam

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Abstract

This paper proposes a new Deep Feed-forward Neural Network (DFNN) approach for damage detection in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. In the proposed approach, the DFNN model is developed based on a data set containing 20 000 samples of damage scenarios, obtained via finite element (FE) simulation, of the FG-CNTRC plates. The elemental modal kinetic energy (MKE) values, calculated from natural frequencies and translational nodal displacements of the structures, are utilized as input of the DFNN model while the damage locations and corresponding severities are considered as output. The state-of-the art Exponential Linear Units (ELU) activation function and the Adamax algorithm are employed to train the DFNN model. Additionally, in order to enhance the performance of the DFNN model, the mini-batch and early-stopping techniques are applied to the training process. A trial-and-error procedure is implemented to determine suitable parameters of the network such as the number of hidden layers and the number of neurons in each layer. The accuracy and capability of the proposed DFNN model are illustrated through two distinct configurations of the CNT-fibers constituting the FG-CNTRC plates including uniform distribution (UD) and functionally graded-V distribution (FG-VD). Furthermore, the performance and stability of the DFNN model with the consideration of noise effects on the input data are also investigated. Obtained results indicate that the proposed DFNN model is able to give sufficiently accurate damage detection outcomes for the FG-CNTRC plates for both cases of noise-free and noise-influenced data.

Keywords damage detection deep feed-forward neural networks functionally graded carbon nanotube-reinforced composite plates modal kinetic energy

Corresponding Author(s): T. NGUYEN-THOI

Just Accepted Date: 24 September 2021 Online First Date: 16 November 2021 Issue Date: 21 January 2022

Cite this article:

Huy Q. LE,Tam T. TRUONG,D. DINH-CONG, et al. A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy[J]. Front. Struct. Civ. Eng., 2021, 15(6): 1453-1479.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-021-0767-z
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I6/1453

Fig.1 ?(a) Architecture of a typical DFNN model; (b) operators at jth node, ith hidden layer.

Fig.2 ?(a) Uniform distribution (UD); (b) functionally graded V-distribution (FG-VD); (c) orientation angle of fibers.

Tab.1 ?Comparison of the first six non-dimensional natural frequencies of the FG-CNTRC plates

Fig.3 ?(a) Geometry of the FG-CNTRC plates; (b) numbering of the elements discretized.

edge	SSSS	CSSS	CCCC	CFCF
top	$u = w = β y = 0$	$u = w = β y = 0$	$u = v = w = β x = β y = 0$	–
bottom	$u = w = β y = 0$	$u = w = β y = 0$	$u = v = w = β x = β y = 0$	–
left	$v = w = β x = 0$	$u = v = w = β x = β y = 0$	$u = v = w = β x = β y = 0$	$u = v = w = β x = β y = 0$
right	$u = w = β y = 0$	$v = w = β x = 0$	$u = v = w = β x = β y = 0$	$u = v = w = β x = β y = 0$

Tab.2 ?Restraints of the degrees of freedom corresponding to the boundary conditions

Tab.3 ?The mse values

(× 10 ? 4)

for different pairs of AF/Op (3-[200], 3000 epochs, batch size of 160)

Fig.4 ?Loss values

(× 10 ? 4)

among pairs of AF/Op: (a) training data; (b) validating data.

Fig.5 ?Well-performed pairs of AF/Op: (a) training data; (b) validating data; (c) ratios of val_loss value to loss value.

Fig.6 ?The training history of the different pairs: (a) [ReLU/RMSprop]; (b) [LeakyReLU/Adam]; (c) [ELU/RMSprop]; (d) [ELU/Adam]; (e) [ELU/Adamax]; (f) [ELU/Nadam].

Tab.4 ?Validation loss values

(× 10 ? 4)

according to different associations of [NoL-NoN]

Fig.7 ?The training history of the architecture using five hidden layers and 600 nodes per each layer: (a) loss values; (b) accuracy values.

Tab.5 mse values and accuracy values of different settings of the batch size

Tab.6 ?Training results of the DFNN model

Tab.7 ?Two damage scenarios of the FG-CNTRC plate discretized into 100 elements

Fig.8 ?One damage occurrence with the severity of 19.84% assumed at the 80th element.

Fig.9 ?Detected results of the first case of the first scenario for the UD plates in different boundary conditions: (a) SSSS: mse = 2.606e?07;mse_noise = 6.591e?05; (b) CSSS:mse = 4.511e?07;mse_noise = 1.055e?04; (c) CCCC:mse = 4.809e?07;mse_noise = 2.323e?05; (d) CFCF:mse = 7.080e?07;mse_noise = 3.504e?05.

Fig.10 ?Detected results of the first case of the first scenario for the FG-VD plates in different boundary conditions: (a) SSSS: mse = 1.533e?06;mse_noise = 1.309e?05; (b) CSSS:mse = 3.780e?07;mse_noise = 8.090e?05; (c) CCCC:mse = 5.209e?07;mse_noise = 1.288e?05; (d) CFCF:mse = 9.000e?07;mse_noise = 5.760e?06.

Fig.11 ?Two damage occurrences with severities of 36.56% and 24.91% assumed at the 55th and 65th elements, respectively.

Fig.12 ?Detected results of the second case of the first scenario for the UD plates in different boundary conditions: (a) SSSS: mse = 2.836e?05;mse_noise = 7.249e?05; (b) CSSS:mse = 2.498e?05;mse_noise = 1.913e?04; (c) CCCC:mse = 1.897e?05;mse_noise = 4.355e?05; (d) CFCF:mse = 3.958e?05;mse_noise = 6.969e?05.

Fig.13 Detected results of the second case of the first scenario for the VD plates in different boundary conditions: (a) SSSS: mse = 2.509e?05;mse_noise = 1.210e?04; (b) CSSS:mse = 2.925e?05;mse_noise = 1.049e?04; (c) CCCC:mse = 5.732e?06;mse_noise = 2.798e?05; (d) CFCF:mse = 7.001e?05;mse_noise = 1.815e?04.

Fig.14 ?Three damage occurrences with severities of 67.46%, 59.86%, and 21.38% assumed at the 8th, 59th, and 98th elements, respectively.

Fig.15 Detected results of the final case of the first scenario for the UD plates in different boundary conditions: (a) SSSS: mse = 9.567e?06;mse_noise = 9.793e?05; (b) CSSS:mse = 1.720e?05;mse_noise = 1.530e?04; (c) CCCC:mse = 1.711e?04;mse_noise = 1.891e?04; (d) CFCF:mse = 2.183e?04;mse_noise = 1.345e?03.

Fig.16 Detected results of the final case of the first scenario for the VD plates in different boundary conditions: (a) SSSS: mse = 4.307e?05;mse_noise = 1.064e?04; (b) CSSS:mse = 3.777e?05;mse_noise = 2.828e?04; (c) CCCC:mse = 2.769e?05;mse_noise = 5.157e?04; (d) CFCF:mse = 3.176e?04;mse_noise = 1.117e?03.

Fig.17 ?One damage occurrence with the severity of 44.13% assumed at the 72nd element.

Fig.18 Detected results of the first case of the second scenario for the UD plates in different boundary conditions: (a) SSSS: mse = 1.108e?06; mse_noise = 5.932e?05; (b) CSSS: mse = 7.708e?07; mse_noise = 4.485e?06; (c) CCCC: mse = 3.213e?07; mse_noise = 1.476e?05; (d) CFCF: mse = 7.760e?07; mse_noise = 1.545e?05.

Fig.19 Detected results of the first case of the second scenario for the VD plates in different boundary conditions: (a) SSSS: mse = 7.496e?07;mse_noise = 9.554e?05; (b) CSSS:mse = 5.180e?07;mse_noise = 4.340e?05; (c) CCCC:mse = 3.537e?07;mse_noise = 4.763e?06; (d) CFCF:mse = 9.628e?07;mse_noise = 2.138e?05.

Fig.20 ?Two damage occurrences with severities of 30.96% and 48.44% assumed at the 21st and 85th elements, respectively.

Fig.21 Detected results of the second case of the second scenario for the UD plates in different boundary conditions: (a) SSSS: mse = 3.601e?06;mse_noise = 7.009e?05; (b) CSSS:mse = 1.672e?06;mse_noise = 2.121e?04; (c) CCCC:mse = 2.838e?06;mse_noise = 2.672e?05; (d) CFCF:mse = 7.688e?06;mse_noise = 2.488e?04.

Fig.22 Detected results of the second case of the second scenario for the VD plates in different boundary conditions: (a) SSSS: mse = 6.168e?06;mse_noise = 3.695e?05; (b) CSSS:mse = 3.603e?06;mse_noise = 7.286e?05; (c) CCCC:mse = 3.913e?06;mse_noise = 4.179e?04; (d) CFCF:mse = 3.104e?06;mse_noise = 4.358e?05.

Fig.23 ?Three damage occurrences with severities of 38.61%, 40.50%, and 36.75% assumed at the 37th, 75th, and 79th elements, respectively.

Fig.24 Detected results of the final case of the second scenario for the UD plates in different boundary conditions: (a) SSSS: mse = 4.477e?06;mse_noise = 2.933e?04; (b) CSSS:mse = 2.671e?06;mse_noise = 7.494e?04; (c) CCCC:mse = 3.893e?06;mse_noise = 2.800e?04; (d) CFCF:mse = 3.289e?06;mse_noise = 5.185e?04.

Fig.25 Detected results of the final case of the second scenario for the VD plates in different boundary conditions: (a) SSSS: mse = 2.868e?06;mse_noise = 5.316e?04; (b) CSSS:mse = 2.780e?06;mse_noise = 1.892e?04; (c) CCCC:mse = 2.651e?06;mse_noise = 8.236e?05; (d) CFCF:mse = 3.976e?06;mse_noise = 3.690e?04.

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