Prediction of ultimate bearing capacity of Tubular T-joint under fire using artificial neural networks

Safety Science 50 (2012) 1495–1501

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Prediction of ultimate bearing capacity of Tubular T-joint under fire using artificial neural networks Jixiang Xu ⇑, Jincheng Zhao, Zhenseng Song, Minglu Liu Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e

i n f o

Article history: Received 15 December 2011 Received in revised form 2 January 2012 Accepted 15 February 2012 Available online 17 March 2012 Keywords: Ultimate bearing capacity Tubular T-joint Artificial neural network Finite element analysis Fire

a b s t r a c t An artificial neural network (ANN) model is developed for the prediction of the ultimate bearing capacity of tubular T-joint under fire. The input parameters of the network are composed of the diameter ratio (b), the wall thickness ratio (s), the diameter–thickness ratio (c) and the temperature (T). The output parameter is composed of the ultimate bearing capacity. In this paper, the training and testing data of the neural network are obtained using the finite element program ABAQUS. The network is trained by 216 dataset and tested by 27 dataset. In the process of training of the network, the Levenberg-Marquardt back-propagation algorithm is adopted. The ‘tansig’ function is adopted in the hidden layer, and the ‘purelin’ function is adopted in the output layer. The results predicted by ANN are compared with the results simulated by finite element method (FEM). These results show that the prediction of the ultimate bearing capacity using the network model is accurate and effective. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.

1. Introduction It is well known that the tubular T-joints are widely used in offshore platform and complex steel structures. As a component of bearing capacity of structure, the tubular T-joint plays a very important role. Although a number of parameters have great influence on the mechanical behavior of the tubular T-joint, such as the material property, the temperature, the size of the tubular T-joint and the applied load, the theory of the mechanical behavior of tubular T-joint under fire is still not fully developed. In recent years, the finite element analysis is widely used to obtain the mechanical behavior of load bearing structure under fire. Although the finite element analysis can be used to predict the mechanical behavior of the tubular Tjoint, the process becomes time consuming and inefficient for the numerous tubular T-joints, and a large number of calculations are necessary. On the contrary, the artificial intelligence (AI) method can reduce the computational cost and time, thus the ANN for the prediction of the mechanical behavior of tubular T-joint under fire becomes increasingly important. In recent years, some researchers solve a lot of civil engineering problems using artificial neural network (ANN) models (e.g., Wang et al., 2011; Yang et al., 2006; Lee, 2011). Abdullateef et al. (2002) developed neutral network model in order to predict the fire resistance of similar columns under fire by observing various factors. Richard et al. (2006) presented a modification of the original GRNNFA model for multi-dimensional prediction problems, and ⇑ Corresponding author. Tel.: +86 21 34207998; fax: +86 21 62933082. E-mail addresses: [email protected], [email protected] (J. Xu).

prediction problems, and predicted the velocity and temperature profiles at the center of the doorway in a single compartment fire by using ANN techniques. Erdem (2010) predicted the ultimate moment capacity of reinforced concrete (RC) slabs under fire by using ANN. Zhao (2006) presented a strength model of steel columns under fire using the artificial neural network. Hozjan et al. (2007) presented an alternative approach to the prediction of the mechanical behaviors of steel frame material under fire using ANN. Cachim (2011) predicted the temperatures in timber under fire using ANN. Lee et al. (2004) developed new and novel ANN model, denoted as GRNNFA, for predicting parameters in compartment fires. In this paper, the ANN model of the ultimate bearing capacity of the tubular T-joints under fire is developed. In order to test the robustness of the ANN model, the results generated by the finite element analysis program ABAQUS, are compared with the results obtained by ANN. These results show that the prediction of the ultimate bearing capacity using the network model is accurate and effective. In addition, the ANN needs almost no additional computational cost and time for the prediction of the ultimate bearing capacity of the T-joints, than the finite element method (FEM) needs. The developed ANN model can be used to predict the fire ultimate bearing capacity of similar structures. 2. Methods 2.1. Finite element model In order to obtain the training and testing data of the ultimate bearing capacity of the T-joints under fire, the numerical simulations

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Nomenclature D d B t

Outer diameter of the chord tube Outer diameter of the brace tube Wall thickness of the chord tube Wall thickness of the brace tube

b

s c T

Diameter ratio (d/D) Wall thickness ratio (t/B) Diameter–thickness ratio (D/2B) Temperature

Table 1 Finite element analysis models of tubular T-joints with different parameters. Models

D (mm)

d (mm)

B (mm)

t (mm)

h

SPC1 SPC2 SPC3 SPC4 SPC5 SPC6 SPC7 SPC8 SPC9 SPC10 SPC11 SPC12 SPC13 SPC14 SPC15 SPC16 SPC17 SPC18 SPC19 SPC20 SPC21 SPC22 SPC23 SPC24 SPC25 SPC26 SPC27

1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200

240 360 480 600 720 840 960 1080 1200 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600

25 25 25 25 25 25 25 25 25 60 40 30 24 20 17.14 15 13.33 12 25 25 25 25 25 25 25 25 25

15 15 15 15 15 15 15 15 15 30 20 15 12 10 8.57 7.5 6.67 6 5 7.5 10 12.5 15 17.5 20 22.5 25

90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90

Note: SPC denotes pressure branch pipe.

of the T-joints are carried out using the finite element analysis program ABAQUS, the analysis models of the T-joints with different parameters are shown in Table 1. The finite element model of the tubular T-joint is shown in Fig. 1. A four-node doubly curved shell element with six degrees of freedom per node (S4R) is adopted in the finite element model. Along the direction of the shell element thickness, five Gauss integration points are used. The size of the model is consistent with experimental sample. In this paper, the stress–strain relationship of steel at high temperature can reference Eurocode 3 and the temperature effect of material is also considered. The boundary conditions of the finite element model are consistent with the test sample (e.g., Jin et al., 2011). As shown in Fig. 1, the right side of the chord tube is constrained in the direction (X, Y, Z), the left side of the chord tube is only constrained in the direction Y. The concentrated load is imposed on the center of the brace tube.

Fig. 1. Model and boundary conditions of finite element analysis.

2.3. Artificial neural network Artificial neural network (ANN) is a branch of artificial intelligence. The ANN is a mathematical model imitating human brain function such as memorizing, x1 studying, reasoning and performing massively parallel computations. It consists of a number of processing neurons. A simple artificial neural model is shown in Fig. 4. In Fig. 4, where li is the internal state of the neuron i; hi is the threshold; xj is the input signal; wij is the weight for input xj; si is the control signal. In this paper, the supervised error Back-Propagation (BP) network is developed to predict the ultimate bearing capacity of the tubular T-joints under fire. In order to obtain the network with strong robustness, the training process of the network is necessary. The steps of the training process are summarized as follows: Step 1: The number of nodes in the input layer, nodes in the hidden layer and nodes in the output layer is determined by input–output data pairs (X, Y). The weights (wij, wjk) are initialized, the threshold vectors (a, b) in the hidden and output layer are also initialized. The learning rate and the activation function of the neurons are obtained. Step 2: According to the input vector X, the weight on the connection of th input and jth neuron is obtained. The threshold vector a and the output H of the hidden layer are obtained, the formula is given by: n X

Hj ¼ f

! wij  aj

j ¼ 1; 2; . . . ; l

ð1Þ

i¼1

where l is the number of nodes in the hidden layer; f is the activation function in the hidden layer and it is given as follows:

1 1 þ ex

2.2. Validation of finite element model

f ðxÞ ¼

In order to verify the accuracy of the finite element model, the experiments of the tubular T-joints have been performed in the literature (e.g., Jin et al., 2011). As shown in Figs. 2 and 3, the results obtained by the finite element analysis are very close to the experiment results. Therefore, the training and testing data of the ANN, obtained by the finite element analysis, are feasible and accurate.

Step 3: According to the output H in the hidden layer, the connection weight wjk, the threshold vector b and the output O are obtained, the formula is given by:

Ok ¼

l X j¼1

Hj wjk  bk

ð2Þ

k ¼ 1; 2 . . . ; m

ð3Þ

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Fig. 2. Comparison of failure mode of the tubular T-joint (experiment and FEM).

350

)

300

Applied force (

Step 6: According to the prediction error of the network, the thresholds of the network are updated, the formulas are given by:

SP1(Test) SP1(FEM) SP3(Test) SP3(FEM)

aj ¼ aj þ gHj ð1  Hj Þ

m X

wjk ek

j ¼ 1; 2; . . . ; l

ð7Þ

k¼1

bk ¼ bk þ ek

k ¼ 1; 2 . . . ; m

ð8Þ

Step 7: If the algorithm iterations have been not finished, it will return to the step 2. 2.3.1. The number of nodes of the hidden layer As we know, the number of nodes in the hidden layer plays a very important role to predict the accuracy. Therefore, it is very important for reasonably determining the number of nodes in the hidden layer. In generally, the number of nodes in the hidden layer can be determined by the following formulas;

250 200 150 100 50 0 0

10

20

30

40

50

60

70

80

90

100

Vertical displacement (mm) Fig. 3. Comparison of vertical displacement-ultimate bearing capacity of the tubular T-joint (experiment and FEM).

l< n1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l < ðm þ nÞ þ a a 2 ð0; 10Þ

ð10Þ

l ¼ log2 n

ð11Þ

ð9Þ

where n is the number of nodes in the input layer; m is the number of nodes in the output layer. In practical problem, the optimal number of nodes of the hidden layer is determined by the trial-and-error method after the approximate range of nodes of hidden layer is determined.

x1 μi

x2

Σ

x3

θi

yi

wij

xj

si

xn

Fig. 4. Simple artificial neural model.

Step 4: According to the predicted output O and the desired output Y, the error of the network is given by:

ek ¼ Y k  OK

k ¼ 1; 2 . . . ; m

ð4Þ

Step 5: According to the prediction error of the network, the weights are updated, the formulas are given by:

wij ¼ wij þ gHj ð1  Hj ÞxðiÞ

m X

wjk ek i ¼ 1; 2; . . . ; n; j ¼ 1; 2; . . . ; l

k¼1

ð5Þ wjk ¼ wjk þ gHj ð1  Hj Þek

j ¼ 1; 2; . . . ; l; k ¼ 1; 2 . . . ; m

where g is the learning rate.

ð6Þ

2.3.2. The selection of the input and output parameters It is very difficult to identify all the parameters influencing on the prediction of the ultimate bearing capacity of the tubular Tjoints under fire. However, all of the influencing factors are not independent and some of them are strongly correlated. Thus, it is unnecessary to input all the parameters. In this paper, the dimensionless parameters are considered as the main influence factors of the tubular T-joints, the input parameters of the network are composed of the diameter ratio (b), the wall thickness ratio (s), the diameter–thickness ratio (c) and the temperature (T). The output parameter is composed of the ultimate bearing capacity. All of the input and output parameters are shown in Table 2. The validating and test samples of the BP network are shown in Table 3. 2.3.3. Network architecture In order to predict the ultimate bearing capacity of the tubular T-joints under fire, the neural network is developed. The ANN network consists of one input layer, one hidden layer and one output layer. The input layer consists of four neurons, the output layer consists of one neuron, the hidden layer consists of 11 neurons. The network architecture is shown in Fig. 5. 2.4. Comparative studies between ANN and FEM In this study, the Network is trained by 216 dataset and tested by 27 dataset. In the process of training, the Levenberg-Marquardt

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Table 2 All of the input and output samples of the tubular T-joints. Models

b

s

c

SPC1 SPC2 SPC3 SPC4 SPC5 SPC6 SPC7 SPC8 SPC9 SPC10 SPC11 SPC12 SPC13 SPC14 SPC15 SPC16 SPC17 SPC18 SPC19 SPC20 SPC21 SPC22 SPC23 SPC24 SPC25 SPC26 SPC27

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

24 24 24 24 24 24 24 24 24 10 15 20 25 30 35 40 45 50 20 20 20 20 20 20 20 20 20

UBC 20 °C

200 °C

300 °C

400 °C

500 °C

600 °C

700 °C

800 °C

900 °C

1492 2038 2712 3259 3887 4493 5605 7016 8086 15,136 7762 4762 3063 2226 1694 1338 1096 899 3401 3404 3470 3474 3474 3474 3474 3474 3476

1480 2024 2692 3235 3838 4430 5528 6934 8006 15,052 7720 4732 3036 2201 1673 1321 1069 886 3369 3374 3438 3448 3448 3448 3446 3446 3448

1470 2008 2668 3199 3791 4377 5461 6855 7951 14,948 7654 4686 3002 2173 1652 1299 1052 873 3335 3338 3400 3408 3409 3408 3408 3408 3408

1350 1843 2444 2931 3474 4006 4999 6277 7275 13,724 7022 4292 2752 1993 1514 1194 967 801 3054 3058 3120 3124 3124 3122 3122 3122 3122

1071 1462 1938 2325 2756 3177 3957 4963 5710 10,784 5542 3398 2184 1582 1202 948 769 636 2423 2428 2475 2478 2476 2476 2476 2476 2476

699 951 1263 1515 1799 2072 2579 3235 3701 7000 3602 2212 1423 1034 786 621 504 416 1586 1584 1612 1614 1614 1614 1614 1614 1614

340 465 616 739 878 1014 1260 1589 1834 3470 1774 1084 693 502 380 299 242 199 775 774 787 788 788 788 788 788 788

154 210 279 336 401 463 575 728 832 1580 806 492 314 227 172 136 110 91 356 354 358 358 358 358 358 358 358

60 82 109 131 160 186 233 301 360 714 342 200 123 85 62 50 40 34 139 138 140 140 140 140 140 140 140

Note: SPC denotes pressure branch pipe.

IW 2 ¼ ½ 0:8591 0:6947 0:3598 0:7267 0:7168 0:6003 0:2147 0:0861 0:6754 0:9887 0:5430 

back-propagation algorithm is adopted. The epochs are 2000. The momentum coefficient of the network training is 0.95, the learning rate is 0.3, the target error is 1e10. The ‘tansig’ function is adopted in the hidden layer, and the ‘purelin’ function is adopted in the output layer. The graphical comparison between the results obtained by FEM and ANN is given in Fig. 6. As shown in this figure, the results predicted by ANN are very close to the results obtained by FEM. 3. Results After the ANN training is finished, the weight and threshold value matrices of the network are obtained. In here, IW1 is the weight matrix of the weight values between the input layer neurons and the hidden layer neurons; IW2 is the weight matrix of the weight values between the hidden layer neurons and the output layer neurons; b1 is the threshold vector of the hidden layer neurons; b2 is the threshold vector of the output layer neuron. These weight matrices corresponding to the ANN model are given below. 2 3 2 3 0:6507 1:1264 1:8989 1:0967 2:5496 6 2:0104 1:4936 0:2455 0:4094 7 6 2:0397 7 6 7 6 7 6 0:4018 1:4772 1:5984 1:2657 7 6 1:5298 7 6 7 6 7 6 7 6 7 6 0:2736 1:9066 0:3681 1:6295 7 6 1:0198 7 6 7 6 7 6 2:2864 0:2549 0:9452 0:5610 7 6 0:5099 7 6 7 6 7 6 7 1 6 7 IW 1 ¼ 6 0:8585 2:3176 0:0543 0:6239 7 b ¼ 6 0 7 6 7 6 7 6 0:9765 1:3297 1:2816 1:4616 7 6 0:5099 7 6 7 6 7 6 1:4850 0:7530 1:6155 1:0577 7 6 1:0198 7 6 7 6 7 6 7 6 7 6 1:6817 1:8978 0:2210 0:1478 7 6 1:5298 7 6 7 6 7 4 1:3228 1:2570 1:7188 0:4652 5 4 2:0397 5

0:8510 0:5350 0:6423 2:2534

2:5496

2

b ¼ ½0:5296 In the training process, the change of the error performance of the network is shown in Fig. 7. As shown in Fig. 7, the expected value of the error performance of the network has been reached after 54 iterations, thus the training of the network is finished. The regression analyses of the data are given in Fig. 8, the regression analysis of the training data locates in the top left corner of Fig. 8, from the picture, the correlation coefficient of regression analysis of the training data is 0.99814; the regression analysis of the validating data locates in the top right corner of Fig. 7, from the picture, the correlation coefficient of regression analysis of the validating data is 0.98974; the regression analysis of the testing data locates in the bottom left corner of Fig. 7, from the picture, the correlation coefficient of regression analysis of the testing data is 0.99416; the regression analysis of all the data locates in the bottom right corner of Fig. 7, from the picture, the correlation coefficient of regression analysis of all the data is 0.99591; These correlation coefficients of regression analysis show that the performance of the network is very good. The simulation error of the network is given in Fig. 9. The simulations of the test data are performed using the trained network, then linear regression analysis is carried out between the test data and the results obtained by ANN, the results of linear regression analysis is shown in Fig. 10. As can be seen in Fig. 10, the correlation coefficient between the simulation output and the expected output is very high. The correlation coefficient between them is 0.99848. In addition, for the same tubular T-joint under fire, the required calculation time of the ANN only needs one second, the required calculation time of the FEM needs 2400 seconds. Therefore, for the tubular T-joint under fire, the prediction of the ultimate

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Table 3 The validating and test samples of the BP network. Models

b

s

c

UBC

Models

b

s

c

UBC

SPC1 (200 °C) SPC2 (300 °C) SPC3 (400 °C) SPC4 (500 °C) SPC5 (600 °C) SPC6 (700 °C) SPC7 (800 °C) SPC8 (900 °C) SPC9 (200 °C) SPC10 (300 °C) SPC11 (400 °C) SPC12 (500 °C) SPC13 (600 °C) SPC14 (700 °C)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.5 0.5 0.5 0.5 0.5

0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5

24 24 24 24 24 24 24 24 24 10 15 20 25 30

1480 2008 2444 2325 1799 1014 575 301 8006 14,948 7022 3398 1423 502

SPC15 SPC16 SPC17 SPC18 SPC19 SPC20 SPC21 SPC22 SPC23 SPC24 SPC25 SPC26 SPC27

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

35 40 45 50 20 20 20 20 20 20 20 20 20

172 50 1069 873 3054 2428 1612 788 358 140 3446 3408 3122

(800 °C) (900 °C) (200 °C) (300 °C) (400 °C) (500 °C) (600 °C) (700 °C) (800 °C) (900 °C) (200 °C) (300 °C) (400 °C)

Note: SPC denotes pressure branch pipe.

Hidden layer

1 2 3 Input layer Diameter ratio

1

Wall thickness ratio

2

Diameter-thickness ratio

3

Temperature

4 5

Output layer

6 ultimate bearing capacity

7

4

8 9 10 11 Fig. 5. Back propagation neural network.

Ultimate bearing capacity

15000 Predicted by ANN Obtained by FEM 10000

5000

0

0

5

10

15

20

25

30

Number of test samples Fig. 6. Comparison of UBC predicted by FEM and ANN.

Fig. 7. The change of the error performance of the BP network.

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J. Xu et al. / Safety Science 50 (2012) 1495–1501

Fig. 8. The data regression situation of the BP network.

1000

Simulation error

500

0

-500

-1000

-1500 0

50

100

150

200

250

Number of training samples Fig. 9. The simulation error of the BP network.

bearing capacity using the ANN model is accurate and effective. The training process of the network is shown in Fig. 11. In this paper, the relative error (RE) is used to describe the performance of the network. The formula of calculation of the relative error is given by

RE ¼

jUBCactual  UBCpredict j UBCactual

The relative errors (RE) are given in Table 4.

ð12Þ

Fig. 10. The result of linear regressive analysis.

From Table 4, the change range of the relative errors is from 0 to 0.1405. For the tubular T-joints under fire, these analysis results show that the prediction of the ultimate bearing capacity using the ANN model is accurate and effective.

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J. Xu et al. / Safety Science 50 (2012) 1495–1501 Table 4 Comparison of numerical test results for BP ANN. No.

Actual

ANN

RE

No.

SPC1 (200 °C) SPC2 (300 °C) SPC3 (400 °C) SPC4 (500 °C) SPC5 (600 °C) SPC6 (700 °C) SPC7 (800 °C) SPC8 (900 °C) SPC9 (200 °C) SPC10 (300 °C) SPC11 (400 °C) SPC12 (500 °C) SPC13 (600 °C) SPC14 (700 °C)

1480 2008 2444 2325 1799 1014 575 304 8006 14,948 7022 3398 1423 502

1416.3 2066.5 2373.2 2299.7 1776.3 1020.8 497.905 280 8024.8 14,588 6711.9 2953.9 1368.6 566.07

0.0430 0.0291 0.0289 0.01088 0.0126 0.0067 0.1340 0.078 0.0023 0.0240 0.0441 0.1306 0.0382 0.1270

SPC15 SPC16 SPC17 SPC18 SPC19 SPC20 SPC21 SPC22 SPC23 SPC24 SPC25 SPC26 SPC27

(800 °C) (900 °C) (200 °C) (300 °C) (400 °C) (500 °C) (600 °C) (700 °C) (800 °C) (900 °C) (200 °C) (300 °C) (400 °C)

Actual

ANN

RE

172 50 1069 873 3054 2428 1612 788 358 140 3446 3408 3122

187.6460 56.588 1040.8243 857.5441 3251.3 2576 1653.1 808.898 328.6693 159.6745 3123.0 3408.2 3337.3

0.0909 0.1317 0.0263 0.0017 0.0064 0.0061 0.025 0.026 0.0819 0.1405 0.093 0 0.068

the output layer consists of one neuron, the hidden layer consists of 11 neurons. The weight matrices corresponding to the ANN model are obtained. The linear regression analysis is performed between the test data and the results obtained by ANN. It is observed that the correlation coefficient between them is very high. The correlation coefficient between them is 0.99848. The results predicted by ANN are very close to the results obtained by FEM. In addition, for the same tubular T-joint of the tensile brace tube under fire, the required calculation time of the ANN model only needs one second, however, the required calculation time of the FEM needs 2400 seconds. Therefore, for the tubular T-joint under fire, the prediction of the ultimate bearing capacity using the ANN model is accurate and effective. The change range of the relative errors is from 0 to 0.1405. Acknowledgements

Fig. 11. The training process of BP network.

The work presented in this paper was funded by Hi-Tech Research and Development Program of China (863) – ‘‘Security performance assessing technology of offshore platform on active duty under fire and explosion (Granted: 2007AA09Z322)’’ and the independent research project of the State Key Laboratory of Ocean Engineering of Shanghai Jiaotong University (GKZD010049).

4. Discussion

References

As we known that it is a difficult issue to predict mechanical behavior of tubular T-joint because there are a number of parameters which affect its mechanical properties. FEM is a widely used way, but it’s a time consuming and inefficient process and usually cannot meet the requirements during emergencies such as fire. Although AI methods, such as the ANN sometimes can get satisfying results and save computational cost and computing time simultaneously, the deficiencies of the approach are also very obvious, the deficiencies can be summarized as follows: (a) The generation of datasets is time consuming. (b) The accuracy of the prediction of the ANN completely depends on the accuracy of the training samples. According to these deficiencies, the author suggests that more efficient ways of generating training data will need to be investigated. In addition, in order to obtain the accurate prediction, the generation of the accurate training and testing data of the ANN is very important, thus in the process of generating the training and testing data, the right finite element model must be built.

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5. Conclusions In this paper, for predicting the ultimate bearing capacity of the tubular T-joint of the tensile brace tube under fire, the neural network is developed. The input layer consists of four neurons,