To overcome the complication of jetty pile design process, artificial neural networks (ANN) are adopted. To generate the training samples for training ANN, finite element (FE) analysis was performed 50 times for 50 different design cases. The trained ANN was verified with another FE analysis case and then used as a structural analyzer. The multilayer neural network (MBPNN) with two hidden layers was used for ANN. The framework of MBPNN was defined as the input with the lateral forces on the jetty structure and the type of piles and the output with the stress ratio of the piles. The results from the MBPNN agree well with those from FE analysis. Particularly for more complex modes with hundreds of different design cases, the MBPNN would possibly substitute parametric studies with FE analysis saving design time and cost.
Mooring dolphins are usually constructed when it would be impractical to extend the shore to provide access points to moor vessels. A typical mooring dolphin consists of a platform and several piles supporting the platform, which is so-called jetty. The vertical or battered piles are driven into the seabed. In design practice, deciding whether and where to use the vertical or battered piles is important issue. In the practical design process, the arrangement, the number, and the inclination of the piles are tentatively decided based on previous design experiences and then confirmed through finite element (FE) analysis. Therefore, building and analyzing lots of FE models adopting trial and error process are needed to find the optimum design.
Many researches have been performed to help designers to make decisions. An experimental study showed that the pile group effect is an important factor to resist horizontal loads [
To overcome the complication of jetty pile design originated from mutual interaction among a number of design parameters, artificial neural networks (ANN) have been introduced in geotechnical engineering [
The jetty design process involves, as mentioned above, searching for the optimum pile pattern which results in the most effective pile usage within feasible design region. The internal forces of the piles of jetty structure subjected to horizontal mooring load vary unexpectedly depending on the inclination of the piles and deployment pattern of piles. Therefore, developing ANN, the input data to ANN are decided as horizontal load exerting on the jetty platform and the information of jetty piles, such as arrangement and inclination of piles, and the output results as the stress ratios of piles to confirm the feasibility of design candidate. Whole concept of methodology adopted in this paper is summarized in Figure
Methodology of design process using ANN.
To construct the ANN architecture with predefined input and output layers, type of ANN, the number of hidden layers and neurons in each hidden layer, and type of transfer function for each layer should be determined. So in this research, because of the complexity of the problem, multilayer back-propagation neural network (MBPNN) with two hidden layers, shown in Figure
Neural network structure.
Though the number of hidden layers of the MBPNN is determined as two, the performance of the MBPNN will vary depending on the number of neurons in hidden layers. Regarding the number of neurons in each hidden layer, however, there is no general rule to determine. Thus, in this study several neural network architectures with different number of neurons are examined for the best performance and generalization to new data based on the K-fold cross-validation method [
In this study, a mooring dolphin which was designed for a real project is used. Variations of the pile layout which had been proposed from the early design stage were also considered. The main purpose of the project was to design and build a liquefied natural gas (LNG) terminal at a port area so that the gas product would be transmitted from floating storage and regasification unit (FSRU) to natural gas network onshore by pipelines. The dimension of the platform is 16 m in length, 10 m in width, and 2 m in thickness. The platform is made of reinforced concrete and its piles are made of steel. The plan and elevation view of the testbed mooring dolphin are shown in Figure
Mooring dolphin for U-project.
The material properties of C35/45 concrete for the platform are shown in Table
Material properties of concrete.
Unit weight of concrete (dry/submerged) | kN/m3 | 23/13.19 |
Unit weight of RC (dry/submerged) | kN/m3 | 24/14.19 |
Cylinder strength of RC ( |
N/mm2 | 35 |
Cube strength of RC ( |
N/mm2 | 45 |
Modulus of elasticity ( |
kN/mm2 | 29 |
Poisson’s ratio ( |
0.2 |
Material properties of S355 steel.
Thick. |
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Yield strength (MPa) | 355 | 345 | 345 | 335 | 325 | 315 | 295 |
Tensile strength (MPa) | 460–620 | ||||||
Modulus of elasticity ( |
205 kN/mm2 | ||||||
Shear modulus ( |
80 kN/mm2 | ||||||
Poisson’s ratio ( |
0.3 |
The expected largest FSRU at the mooring dolphin has a capacity of 266,000 m3 and the largest LNG carrier has a capacity of 177,400 m3. Maximum mooring force is calculated as 3750 kN. Dead loads are listed in Table
Dead load.
(ton/m3) | RC | Concrete | Mortar | Steel | Rubble | Fill sand | Sea water |
---|---|---|---|---|---|---|---|
Dry | 2.45 | 2.30 | 2.15 | 7.85 | 0.8 | 2.0 | 1.025 |
Submerged | 1.45 | 1.30 | 1.15 | 6.85 | 1.8 | 1.0 |
Appurtenance loads.
Nonstructural member | Loads | Remark |
---|---|---|
Q.R.H | 49 kN/EA | Vertical load |
Cone type fender (1800 H (F0.3) or equivalent) | 196 kN/EA | |
Handrail | 0.285 kN/m | |
Grating | 0.838 kN/m2 |
For the load combination, BS6349-2 [
The location of the virtual fixity points was computed by various methods: Chang’s method, AASHTO, Hansen’s method, and L-pile method. The pile penetration depth under the maximum tensile force was also computed by the Japanese bridge construction standard (2002), API recommended practice 2A-WSD, AASHTO, and Broms’ analysis method. Based on those methods, it turned out that the penetration depth of 5 m into the bedrock would provide a fixed boundary condition at the bedrock level.
Ten different configurations of jetty pile pattern are considered in this study depending on whether vertical or battered, if inclined, the batter direction, and the number of piles (Figure
Patterns of piles (circle means vertical pile and circle with triangle means battered pile).
Pattern 1 (proposed design)
Pattern 2
Pattern 3
Pattern 4
Pattern 5
Pattern 6
Pattern 7
Pattern 8
Pattern 9
Pattern 10
Finite element modes of Pattern 1 and Pattern 2.
After analyzing 50 FE models of mooring dolphins, the ratios of maximum stress to allowable stress of each pile were obtained under given loading condition as shown in Figure
Maximum stress ratio of each pile.
Pattern 1 (proposed design)
Pattern 2
Pattern 3
Pattern 4
Pattern 5
Pattern 6
Pattern 7
Pattern 8
Pattern 9
Pattern 10
In Pattern 1, the absolute values of the stress ratio are all less than unity except Pile 5. Pile 5 shows the maximum compressive stress and Pile 8 shows the maximum tensile stress. Pattern 2, whose piles are all vertical, shows compressive stress and most of the stress ratios are greater than unity.
When Pile 5 is absent (Pattern 3), the tensile stress of Pile 8 becomes bigger than that of the proposed design (Pattern 1). In Pattern 3, the compressive force on Pile 5 in Pattern 1 redistributes to the adjacent piles. Considering all stress ratios and the number of piles, Pattern 3 can be considered as more improved design than the proposed one. Pile 11 of Pattern 4 is compressive within 90% of applied force but it turns to be tensile when the mooring force is equal to or more than 100%. In this case, the absence of Pile 8 causes a rapid stress change in Pile 11 and design of reinforcing bars in concrete platform is difficult; therefore Pattern 4 shall be avoided.
When it is compared to Pattern 1, Pile 4 of Pattern 5 remains tensile. However, Piles 4 and 8 of Pattern 1 change to be compressive in Pattern 5, while Piles 5 and 11 become tensile. The use of vertical piles in Pattern 5 makes stress sign changed. All absolute values of stress ratio of Pattern 5 are less than unity. In this point of view, Pattern 5 is more effective than the proposed design. With absence of Pile 5, Pattern 6 shows slightly higher stress than Pattern 5. Similar to Pattern 4, the absence of Pile 8 causes rapid stress change in Pile 11 of Pattern 7. Pattern 7 shows higher compressive stress than Pattern 5.
The stress ratios of Patterns 8, 9, and 10 are similar to those of Patterns 5, 6, and 7 but they are not compatible for horizontal load direction change.
The first neuron of the input layer is assigned for load condition, and the other input neurons take the information of piles. To distinguish the battered and the vertical piles, the numbers “1” and “2” are assigned as neuron input values for each pile. To the location where pile is absent, the number “0” is assigned to the corresponding input neuron. For the value of mooring force corresponding to the value of input neuron 1 which is very big compared with the values of the other input neurons might lead to a failure of MBPNN training, the mooring force is normalized to the mooring force of 3750 kN. Table
Example of neuron inputs for neural network training process.
Input neuron | Remark | |
---|---|---|
Number | Assigned value | |
1 | 1.0 | Normalized value of horizontal mooring force to 3750 kN |
2 | 1.0 | Pile 1: battered |
3 | 1.0 | Pile 2: battered |
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12 | 2.0 | Pile 11: vertical |
13 | 2.0 | Pile 12: vertical |
In this study, MBPNN, with two hidden layers, utilizing back-propagation process is used. To obtain the training samples, five load cases—70%, 80%, 90%, 100%, and 110% of mooring force of 3750 kN—are applied to 10 different pile patterns of jetty structures. The combination of 10 jetty pile patterns and 5 load cases makes 50 training cases in total. Table
Example of training samples.
Cases | Input neuron (load and information of each pile) | ||||||||
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1 |
2 |
3 |
4 |
5 |
|
11 |
12 |
13 | |
1 | 0.7 | 1 | 1 | 1 | 1 |
|
1 | 1 | 1 |
2 | 0.7 | 2 | 2 | 2 | 2 |
|
2 | 2 | 2 |
3 | 0.7 | 1 | 1 | 1 | 1 |
|
1 | 1 | 1 |
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48 | 1.1 | 1 | 1 | 1 | 2 |
|
1 | 1 | 1 |
49 | 1.1 | 1 | 1 | 2 | 0 |
|
1 | 1 | 1 |
50 | 1.1 | 1 | 1 | 1 | 2 |
|
1 | 1 | 1 |
Cases | Output neuron (stress ratio of each pile) | |||||||
---|---|---|---|---|---|---|---|---|
1 |
2 |
3 |
4 |
5 |
|
11 |
12 | |
1 | −0.364 | −0.363 | −0.364 | 0.302 | −0.727 |
|
−0.307 | −0.305 |
2 | −0.877 | −0.877 | −0.877 | −0.847 | −0.847 |
|
−0.771 | −0.771 |
3 | −0.547 | −0.548 | −0.547 | 0.404 | 0.404 |
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−0.399 | −0.397 |
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48 | −0.750 | −0.751 | −0.750 | 0.737 | 0.737 |
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0.573 | 0.574 |
49 | −0.788 | −0.787 | −0.788 | 0.856 | 0.856 |
|
0.651 | 0.651 |
50 | −0.863 | −0.864 | −0.863 | 0.831 | 0.830 |
|
0.613 | 0.616 |
Since the performance and generalization of MBPNN to new design data will vary depending on the number of neurons in hidden layers, four different topologies of MBPNN with different number of neurons in hidden layers are examined:
The neural network toolbox provided by commercial program MATLAB was used to construct and for training of MBPNN models. The Levenberg-Marquardt method with back-propagation process was adopted for the optimization algorithm for training. The Levenberg-Marquardt method is considered to be effective for the complicated MBPNN for the fastest training [
In the Levenberg-Marquardt method, the optimum weights and biases are searched using
The successful performance of the Levenberg-Marquardt method depends on the choice of
Table
RMSE of each MBPNN model from K-fold cross-validation.
Round | MBPNN model | |||
---|---|---|---|---|
13-15-15-12 | 13-10-10-12 | 13-7-15-12 | 13-15-10-12 | |
1 | 0.0130 | 0.0986 | 0.0482 | 0.1205 |
2 | 0.0606 | 0.0125 | 0.0796 | 0.0118 |
3 | 0.0192 | 0.0086 | 0.1495 | 0.0238 |
4 | 0.0295 | 0.0046 | 0.0675 | 0.0264 |
5 | 0.1138 | 0.0986 | 0.1181 | 0.0078 |
6 | 0.1733 | 0.0383 | 0.1607 | 0.0413 |
7 | 0.0147 | 0.0346 | 0.1218 | 0.1053 |
8 | 0.1147 | 0.0643 | 0.0791 | 0.0730 |
9 | 0.1396 | 0.0461 | 0.1098 | 0.2451 |
10 | 0.0052 | 0.0258 | 0.0343 | 0.0131 |
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Averaged | 0.0684 | 0.0432 | 0.0969 | 0.0668 |
After fixing the architecture of the MBPNN, the MBPNN was trained again with all the training samples. The training process was completed at 147 epochs, as shown in Figure
Training performance.
Change of gradient and
Cases 3, 15, 27, 39, and 50 were selected for verification of MBPNN training. Table
Simulation results.
Pile number | Number of training cases | |||||||||
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3 | 15 | 27 | 39 | 50 | ||||||
Target | Simul. | Target | Simul. | Target | Simul. | Target | Simul. | Target | Simul. | |
1 | −0.6050 | −0.6051 | −0.6030 | −0.6035 | −0.7580 | −0.7580 | −0.7120 | −0.7117 | −0.7500 | −0.7492 |
2 | −0.6050 | −0.6055 | −0.6030 | −0.6032 | −0.7580 | −0.7588 | −0.7120 | −0.7121 | −0.7510 | −0.7496 |
3 | −0.6050 | −0.6051 | −0.6030 | −0.6035 | −0.7580 | −0.7580 | −0.7120 | −0.7117 | −0.7500 | −0.7492 |
4 | 0.5230 | 0.5227 | 0.6090 | 0.6082 | 0.6680 | 0.6673 | 0.6540 | 0.6537 | 0.6400 | 0.6398 |
5 | 0.5220 | 0.5227 | 0† | 0.0001 | 0.7080 | 0.7092 | 0.6940 | 0.6937 | 0† | −0.0004 |
6 | 0.5230 | 0.5227 | 0.6090 | 0.6082 | 0.6680 | 0.6672 | 0.6540 | 0.6538 | 0.6400 | 0.6399 |
7 | −0.7660 | −0.7649 | −0.7440 | −0.7433 | −0.9210 | −0.9210 | −0.8060 | −0.8057 | −0.9990 | −0.9990 |
8 | 0† | −0.0008 | −0.7490 | −0.7475 | 0† | −0.0004 | −0.8600 | −0.8599 | 0.9600 | 0.9593 |
9 | −0.7660 | −0.7657 | −0.7440 | −0.7432 | −0.9210 | −0.9203 | −0.8060 | −0.8059 | −0.9990 | −1.0010 |
10 | −0.3970 | −0.3963 | 0.4530 | 0.4528 | −0.5100 | −0.5096 | 0.5310 | 0.5302 | −0.5580 | −0.5580 |
11 | −0.3980 | −0.3974 | 0.4520 | 0.4521 | −0.5080 | −0.5093 | 0.5300 | 0.5294 | −0.5600 | −0.5600 |
12 | −0.3970 | −0.3963 | 0.4530 | 0.4528 | −0.5100 | −0.5096 | 0.5310 | 0.5302 | −0.5580 | −0.5580 |
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RMSE | 0.0008 | 0.0004 | 0.0007 | 0.0006 | 0.0005 |
RMSE: root mean squared error.
†No pile at this location.
Through the trained MBPNN, the stress ratios of jetty piles were obtained under different loading conditions which were not included in the training samples. The feasibility of the MBPNN was verified by comparing the results from FE model and the MBPNN. Table
Comparison of stress ratios obtained by MBPNN and FE analysis.
Pile number | Patterns (75% of original mooring force) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | ||||||
Anlys. | ANN | Anlys. | ANN | Anlys. | ANN | Anlys. | ANN | Anlys. | ANN | |
1 | −0.3800 | −0.3803 | −0.9350 | −0.9333 | −0.5710 | −0.5697 | −0.4290 | −0.4297 | −0.5720 | −0.5710 |
2 | −0.3790 | −0.3788 | −0.9350 | −0.9335 | −0.5710 | −0.5701 | −0.4270 | −0.4281 | −0.5730 | −0.5713 |
3 | −0.3800 | −0.3803 | −0.9350 | −0.9333 | −0.5710 | −0.5697 | −0.4290 | −0.4297 | −0.5720 | −0.5710 |
4 | 0.3260 | 0.3259 | −0.9020 | −0.9004 | 0.4330 | 0.4333 | 0.4500 | 0.4486 | 0.4830 | 0.4834 |
5 | −0.7610 | −0.7633 | −0.9020 | −0.9012 | 0† | −0.0004 | −0.8870 | −0.8873 | 0.5120 | 0.5127 |
6 | 0.3260 | 0.3261 | −0.9020 | −0.9004 | 0.4330 | 0.4333 | 0.4500 | 0.4487 | 0.4830 | 0.4834 |
7 | −0.4910 | −0.4885 | −0.8690 | −0.8679 | −0.7360 | −0.7347 | −0.5450 | −0.5442 | −0.6350 | −0.6357 |
8 | 0.4590 | 0.4580 | −0.8740 | −0.8727 | 0.6530 | 0.6529 | 0† | 0.0005 | −0.7050 | −0.7038 |
9 | −0.4910 | −0.4790 | −0.8690 | −0.8678 | −0.7360 | −0.7357 | −0.5450 | −0.5437 | −0.6350 | −0.6346 |
10 | −0.3140 | −0.3154 | −0.8190 | −0.8147 | −0.4170 | −0.4168 | −0.3320 | −0.3308 | 0.3820 | 0.3825 |
11 | −0.3160 | −0.3171 | −0.8190 | −0.8146 | −0.4190 | −0.4187 | −0.3320 | −0.3313 | 0.3810 | 0.3814 |
12 | −0.3140 | −0.3154 | −0.8190 | −0.8147 | −0.4170 | −0.4168 | −0.3320 | −0.3308 | 0.3820 | 0.3825 |
RMSE |
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Pile number | Patterns (75% of original mooring force) | |||||||||
6 | 7 | 8 | 9 | 10 | ||||||
Anlys. | ANN | Anlys. | ANN | Anlys. | ANN | Anlys. | ANN | Anlys. | ANN | |
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1 | −0.5900 | −0.5918 | −0.6550 | −0.6556 | −0.5590 | −0.5587 | −0.5750 | −0.5749 | −0.6330 | −0.6336 |
2 | −0.5900 | −0.5912 | −0.6240 | −0.6563 | −0.5600 | −0.5593 | −0.5740 | −0.5747 | −0.6340 | −0.6341 |
3 | −0.5900 | −0.5918 | −0.6550 | −0.6556 | −0.5590 | −0.5587 | −0.5750 | −0.5749 | −0.6330 | −0.6336 |
4 | 0.5610 | 0.5598 | 0.5540 | 0.5540 | 0.4920 | 0.4920 | 0.5680 | 0.5670 | 0.5620 | 0.5615 |
5 | 0† | −0.0001 | 0.5880 | 0.5869 | 0.4920 | 0.4921 | 0† | −0.0001 | 0.5610 | 0.5599 |
6 | 0.5610 | 0.5599 | 0.5540 | 0.5540 | 0.4920 | 0.4920 | 0.5680 | 0.5670 | 0.5620 | 0.5615 |
7 | −0.6840 | −0.6834 | −0.7930 | −0.7928 | −0.6770 | −0.6757 | −0.7130 | −0.7107 | −0.7990 | −0.7973 |
8 | −0.7430 | −0.7420 | 0† | −0.0003 | −0.6830 | −0.6825 | −0.7180 | −0.7158 | 0† | 0.0003 |
9 | −0.6840 | −0.6833 | −0.7930 | −0.7917 | −0.6770 | −0.6750 | −0.7130 | −0.7106 | −0.7990 | −0.7981 |
10 | 0.4350 | 0.4353 | −0.4410 | −0.4396 | 0.3710 | 0.3718 | 0.4200 | 0.4200 | −0.4170 | −0.4161 |
11 | 0.4350 | 0.4344 | −0.4420 | −0.4398 | 0.3700 | 0.3705 | 0.4190 | 0.4192 | −0.4180 | −0.4169 |
12 | 0.4350 | 0.4353 | −0.4410 | −0.4396 | 0.3710 | 0.3718 | 0.4200 | 0.4200 | −0.4170 | −0.4161 |
RMSE |
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RMSE: root mean squared error.
†No pile at this location.
In this paper, the application of MBPNN as a structural analyzer for jetty structures is explored. The framework of MBPNN is defined as the input with the lateral forces on the jetty structure and the type of piles and the output with the stress ratios of the piles. For the highly complex jetty pile patterns the results from the MBPNN show very good agreement with those from FE analysis. With the more training samples and the expansion of input parameters for jetty structure design, the MBPNN shows possibility to replace the repetitive and time-consuming FE analysis. Although only 50 cases have been modeled for study purpose in this paper, the merit of MBPNN would be clearer as the number of cases increases.
The authors declare that there is no conflict of interests regarding the publication of this paper.