Evaluation of Dynamic Tensions of Single Point Mooring System under Random Waves with Artificial Neural Network

Abstract

Real-time monitoring of the mooring safety of floating structures is of great significance to their production operations. A deep learning model is proposed here, based on the long short-term memory (LSTM) artificial neural network. Firstly, the numerical simulation is carried out with the single-point mooring system of a Floating Production Storage and Offloading (FPSO) as the training data of LSTM. Then the proposed LSTM is performed. Finally, taking the motion of FPSO which is not encountered by LSTM neural network model as input, we predict the mooring line tension with this model. Here, one FPSO in the South China Sea is taken as a research case, hydrodynamic and mooring models are established, and the network structure and hyper-parameters of the LSTM model are determined. The prediction results of the LSTM under different combinations of wind, wave, and current are compared with the calculation results of AQWA software. The model constructed here can well predict the mooring line tension of different combinations of wind, wave and current.

1. Introduction

Offshore oil production in medium-depth water is mainly performed through floating production systems in the South China Sea, such as semi-submersible platforms or FPSO. The marine environment served by these platforms is extremely complex and harsh. Once an accident occurs, it will cause serious economic losses and environmental pollution. A mooring system is a positioning device for a platform or a ship that can limit the platform to remain relatively static within a certain range under the action of external loads. Therefore, it is important to monitor the tension response of the mooring line to prevent potential damage. However, the marine environment in which the platform works is harsh, and monitoring equipment such as inclinometers and tensiometers are prone to failure; moreover, their long-term maintenance and service costs are also very expensive.

The purpose of designing the mooring system is to fix the floating body at a certain position and restrict the movement of the floating body. Therefore, we can calculate the tension of the mooring system based on the movement of the floating body. Compared with testing equipment such as dynamometers, GPS is mounted on a floating upper deck and is less exposed to seawater erosion. Thus, GPS is more reliable and stable and can obtain more accurate data [1]. Therefore, by taking the position of the floating body as the excitation condition and using finite element software to calculate the response of the mooring line, the nonlinear behavior of the mooring system can be accurately calculated. However, the finite-element calculation software is not only slow in calculation speed but also unable to calculate the tension of the mooring line in real time; therefore, the rapid monitoring of the mooring system is based on the movement of the floating body and has become a problem worthy of study [2].

With the rapid development of machine learning, artificial neural networks (ANNs) have been applied to research in the field of ocean engineering. Queau et al. [3] used the back propagation (BP) network to study the fatigue behavior of catenary riser in the case that only the static load is considered while the inertia or damping is ignored. A quadratic Volterra model with a finite nonlinear memory effect was introduced and applied to the time-series prediction of a slender marine structure exposed to the Morison load [4]. Mak et al. [5] used the machine learning approaches to estimate the relative wave direction based on the time histories of six-degrees-of-freedom ship motions. Chaves et al. [6] predicted the tension, curvature, and fatigue life of the flexible pipeline based on the combinations of dynamic finite element analyses and ANN. Guo et al. [7] developed an LSTM-based machine learning model to predict the heave and surge motions of a semi-submersible.

It can be seen that ANN not only can compute complex relationships but also predict future performance; therefore, some scholars apply ANN to the research of mooring lines. Lin and Liu [8] built a deep learning model to study the contributing factors of the maximum mooring tension of the floating wind turbine system in tensioned mooring and relaxation mooring. Li and Choung [9] analyzed and studied the fatigue damage of the mooring line of the OC4 floating wind turbine system based on the artificial neural network method of the multilayer feed-forward neural network and the BP learning scheme. Janas et al. [10] established a convolutional neural network (CNN) model and trained it through historical image data and numerical simulation results to recognize mooring line failures under non-extreme sea conditions.

LSTM is a special neural network that not only can deal with sequence problems but also solve problems such as gradient explosion during training [11]; it can predict time series accurately for many different tasks, such as weather conditions [12,13], ocean temperature [14], stock prices [15], and ship motion [16,17].

Obviously, with the continuous advancement of computer technology and algorithms, the LSTM network is used in the prediction of mooring line tension [18]. Chung et al. [19] studied a damage detection method of tension leg platform mooring line based on deep neural network. Sidarta et al. [20,21] built a neural network model and used the platform’s six degrees of freedom and platform mass to predict mooring line tension and identify mooring line damage. Guarize et al. [22] used a combination of neural network and finite element method to analyze the response of mooring line and riser. Saad et al. [23] used Multilayer Perceptron (MLP) and LSTM networks to build models, based on the comparison between measured motion and predicted motion, to predict mooring line failures and compared the performance of the two models. Qiao et al. [24] used the internal turret FPSO as the research object and constructed the LSTM model, taking the 6-DOF (degrees of freedom) motion of the ship as the input label, and the tension of the mooring line as the output label. The accuracy of the model’s prediction of mooring line tension under given sea conditions was studied. However, the study only considered the conditions of winds, waves, and currents in the same direction.

The inner turret FPSO has a wind vane effect, and the floating body will rotate 360° around the turret under the action of environmental loads. To remove the influence of the wind vane effect on the yaw motion, this paper takes the 5-DOF of the FPSO as the input and the mooring line tension as the output result and builds an LSTM model to study the prediction of the mooring line tension. At the same time, the paper also studies the working conditions of different wind, wave, and current directions.

The content here is arranged as follows: Section 2 describes the methods and formulas; Section 3 describes the main dimensions of FPSO, single point mooring system, and working conditions of the FPSO; Section 4 describes the verification of hydrodynamic and mooring models, the construction of LSTM models, and the parameters settings; and Section 5 describes the analysis of the LSTM model’s prediction results for multiple working conditions.

2. Methodology for the Tensions Evaluation of Single Point Mooring System

The hydrodynamic and mooring model is established based on the given FPSO. The LSTM model is trained and built according to the AQWA time-domain calculation results to achieve the purpose of calculating the mooring line tension based on the motion of the ship. The specific process is shown in Figure 1. Firstly, establish hydrodynamic and mooring models according to the actual ship. Then carry out the time-domain calculation with corresponding wind, wave, and current environmental conditions to provide samples for training the LSTM network. The next step is to train the data with the LSTM model. Finally, predict the mooring line tension with the random motion, which is not encountered by LSTM neural network model.

2.1. Theory of LSTM Neural Network

The LSTM neural network is a special recurrent neural network that learns long-term dependent information through repeated structure design. The LSTM neural network not only has the large loop of the external neural network but also the self-loop of the “cell state” of the LSTM itself. The self-loop is controlled by the gate structure processed by three sigmoid activation functions (as shown in Figure 2): The forget gate ($f_t$) determines which part of the memory needs to be forgotten according to the current input, the output at the previous moment, and the offset of the gate; the expression is shown in Equation (1). The input gate ($i_t$) supplements the latest memories; the expressions are shown in Equations (2) and (3). The output gate ($o_t$) determines the output of the moment according to the latest state of the current moment, the output of the previous moment, and the input of the current moment; the expressions are shown in Equations (5) and (6). Equation (4) is the cell state ($C_t$) at time t [11].

$$f_t=\sigma \left(W_f\left[h_{t-1},X_t\right]+b_f\right)$$

(1)

$$i_t=\sigma \left(W_i\left[h_{t-1},X_t\right]+b_i\right)$$

(2)

$$C_t^0=\tan \mathrm{h}\left(W_C\left[h_{t-1},X_t\right]+b_C\right)$$

(3)

$$C_t=i_t\cdot C_t^0+f_t\cdot C_{t-1}$$

(4)

$$o_t=\sigma \left(W_o\left[h_{t-1},X_t\right]+b_o\right)$$

(5)

$$h_t=o_t\cdot \tanh \left(C_t\right)$$

(6)

where $\sigma$, $tanh$, is the activation function; $h_{t-1}$ is the output at t − 1 second; $X_t$ is the input at t second; and $W_f$, $W_i$, $W_C$, and $W_o$ are their respective weights. When the LSTM model is applied to mooring line tension prediction, $h_t$ represents all predicted future mooring line tension.

2.2. Normalization of the Neural Network

The LSTM model built here takes the 5-DOF of the floating body as the input, and the mooring line tension as the output. The unit and magnitude of the input and output data are inconsistent; to make the LSTM model predict more accurately, the data need to be normalized. In the same way, the data calculated by LSTM must be denormalized to get the data we want. The normalization method used here is the Min–Max scaling normalization, and its expression is shown in Equation (7) where, x is the original data, $x_{min}$ is the minimum value of the data, and $x_{max}$ is the maximum value of the data.

$$x_i=\frac{x-x_{min}}{x_{max}-x_{min}}$$

(7)

2.3. Indicators of Calculation Accuracy

Here, three kinds of error evaluation indicators are used: root mean square error (RMSN), average absolute error (MAE), and average absolute error percentage (MAPE). As shown in Equations (8)–(10), n is the total number of samples, $t_i$ is the number i actual value, and $f_i$ is the number i predictive value.

$$RMSN=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{\left(t_i-f_i\right)}^2}}{n}}$$

(8)

$$MAE=\frac{{\displaystyle \sum _{i=1}^n\left|t_i-f_i\right|}}{n}$$

(9)

$$MAPE=\frac{{\displaystyle \sum _{i=1}^n\frac{\left|t_i-f_i\right|}{t_i}}\times 100}{n}$$

(10)

The prediction precision can be judged by comparing the maximum, minimum, and average value of the LSTM predicted value data sets and the AQWA calculated value data sets.

2.4. Training Data of LSTM Neural Network

The training set, validation set, and test set of the LSTM neural network were calculated by AQWA software. Equation (11) was solved by this software in the time domain.

$${\displaystyle \sum _{j=1}^6\left[\left(M_{ij}+m_{ij}\right)x_j\left(t\right)+{\displaystyle {\int }_0^t{R}_{ij}\left(t-\tau \right){\dot{x}}_j\left(\tau \right)d\tau +C_{ij}{\dot{x}}_j\left(t\right)+K_{ij}{x}_j\left(t\right)}\right]=F_i\left(t\right)}$$

(11)

where i is in the range from 1 to 6; $M_{ij}$ is the mass matrix of floating structure; $m_{ij}$ is the added mass matrix; $R_{ij}$ is the hysteresis function matrix; $C_{ij}$ is the viscous damping matrix; $K_{ij}$ is the static recovery stiffness matrix of the FPSO; and $F_i\left(t\right)$ is the force on the FPSO, including mooring force, wind force, current force, wave force, riser force, and so on.

Here, only mooring force, wind force, current force, and wave force are considered. The wave forces on the FPSO are calculated by the boundary element method on the diffraction theory [25]. Because the FPSO ship structure is similar to VLCC (very large crude carrier), the wind forces and current forces on the FPSO are calculated by API (American Petroleum Institute) standard [26]. The mooring forces on the FPSO are calculated by lumped mass method [27]. The 5-DOF and nine mooring line tension, which were calculated by AQWA software, were selected as training data of the LSTM neural network.

3. FPSO and Single-Point Mooring System with the Environment

3.1. FPSO and Mooring System

An FPSO in the South China Sea was taken as the research object to verify the proposed LSTM network prediction mooring system. The specific parameters of the FPSO are shown in

Table 1. Ship’s main dimensions.

Name	Value	Unit	Name	Value	Unit
Overall length	261.6	m	Distance between center of gravity and 0 station (m)	125	m
Molded length	250	m	Distance between gravity center and ship bottom (m)	14	m
Beam molded	46	m	Roll radius of gyration (m)	15.2	m
Molded depth	24.6	m	Pitching radius of gyration (m)	62.5	m
Load draught	16.5	m	Yaw radius of bowing (m)	62.5	m
Water discharge	176,000	t	Distance from turret to 0 station (m)	232	m

. The inner turret FPSO is a 150,000 DWT (dead weight ton) single bottom double-shell structure. The single-point permanent mooring mode is adopted, and the average water depth is 105 m.

Modeling and meshing are built in AQWA software with the specific form in Figure 3. The FPSO model grid unit is 1 m with the total 10,344 elements. The coordinate origin is located at the water surface, between the stern vertical line length and draft line intersection point. The x-axis is along the length direction of the floating body to the bow, the y-axis is along the width direction of the floating body to the starboard, and the z-axis is vertical upward. In general, the mesh element covers the wet surface, and the size of the mesh element is less than 1/7 of the incident wavelength.

The mooring system consists of nine mooring lines grouped into three clusters with three mooring lines, as shown in Figure 4. The angle is 5 degrees between the mooring lines in each cluster. The angle is 120 degrees between clusters. The composition and physical properties of each mooring line are shown in

Table 2. Mooring line components.

Segments (from Top to Bottom)	Length of #1–6 (m)	Length of #7–9 (m)	Drag Coefficients		Added Mass Coefficients
			Normal Direction	Tangential Direction	Normal Direction	Tangential Direction
LCS	50	51	2.4	1.15	1	0.5
CE	2.62	-	1.2	0.025	0.5	0.5
LWS	496	-	1.2	0.025	1	0.5
CE	2.62	-	1.2	0.025	1	0.5
UCS1	140	300	2.4	1.15	1	0.5
UCS2	100	50	2.4	1.15	1	0.5
UCS3	10	10	2.4	1.15	1	0.5
CE	2.62	2.62	1.2	0.025	1	0.5
UWS	206	206	1.2	0.025	1	0.5
CE	2.62	2.62	1.2	0.025	0.5	0.5

and

Table 3. Properties of mooring line components.

Components	Grade	Diameter (mm)	Dry Weight (kg/m)	Wet Weight (kN/m)	Breaking Strength (kN)	Axial Stiffness (kN/m)
LCS	R3 Studless	173	599	5.11	20,120	1,497,950
LWS/UWS	Spiral Strand	130	86.7	0.69	17,000	1,544,000
UCS1/3	R3S Studless	145	420.5	3.59	16,960	1,343,000
UCS2	R3S Studless	145	1140	9.74	16,960	1,343,000
CE	-	270	1039.3	9.62	-	1,540,000

. In the table, the LCS represents the lower chain section, the CE represents the connecting element, the LWS represents the lower wire rope section, the UWS represents the upper wire rope section, and the UCS represents the upper chain section. UCS1, UCS2, and UCS3 are made of the same material, and there are 17 weights on the UCS2. In Table 3, the UCS2 data are treated equivalently.

3.2. Working Environment Conditions

The working conditions of numerical simulation data used here are described in the following cases. Single condition (Case 1): JONSWAP irregular wave with 2 m significate wave height, NPD wind spectrum. The angle is 15° between the wind direction and wave direction. The angle is 45° between the current direction and wave direction, as shown in

Table 4. Description of Case 1.

Working Condition Number	10003
Wave type	JONSWAP
Wave direction (°)	75
Wave height (m)	2
Peak period (s)	11.2
Peak factor	3.3
Current velocity (m/s)	0.75
Current direction (°)	120
Wind spectrum	NPD
Wind speed (m/s)	18
Wind direction (m/s)	90

. Working condition 10003 is the time domain tension data of the ship with 5-DOF and nine mooring lines for 3 h. The value interval is 1 s. The first 7000 are behavior training sets of the data, and the rest are the validation sets. The first five columns are the input data of the neural network, and the rest are the output data labels.

Multiple working conditions (Case 2): significate wave height of 1 m, peak period of 11.2 s, peak factor of 3.3, wind speed of 3 m/s, and current velocity of 0.15 m/s, as shown in

Table 5. Description of Case 2.

	Working Condition Number	Environmental Load Direction
Significate Wave height of 1 m Peak period of 11.2 s Peak factor of 3.3 Wind speed of 3 m/s Current velocity of 0.15 m/s	AD1–AD13	The wind, current, and wave are in the same direction; the wave direction is from 0° to 180°, with an interval of 15°.
	AD14–AD26	The angle between the wind direction and the wave direction is 30°; the angle between the current direction and the wave direction is 45°; and the wave direction is from 0° to 180°, with an interval of 15°.
	AD27–AD39	The angle between the wind direction and the wave direction is 30°; the angle between the current direction and the wave direction is 60°; and the wave direction is from 0° to 180°, with an interval of 15°.

. The 35 working conditions were randomly selected as the training sets, with the remaining four used as prediction sets. In each environmental working condition, there are 10,000 s of hull 5-DOF movement and nine mooring line tension time history data. The value interval is 1 s, so there are 10,000 rows and 14 columns in total. Take the first 7000 rows of each working condition and stitch them together to obtain the training sets of the neural network; the remaining 3000 rows of data are stitched into the verification sets; and the first five columns (surge, sway, heave, roll, and pitch) are used as input data, and the mooring line tensions are used as output result labels. The splicing sequence is shown in

Table 6. Splicing of Case 2.

Splicing Order
First row	AD5	AD3	AD17	AD27	AD6	AD24	AD4
Second row	AD33	AD37	AD34	AD12	AD25	AD14	AD31
Third row	AD39	AD11	AD18	AD16	AD29	AD22	AD9
Fourth row	AD23	AD1	AD38	AD28	AD21	AD30	AD20
Fifth row	AD2	AD13	AD19	AD36	AD26	AD15	AD8

, from the first row to the fifth row stitched together.

There are two conditions set: Case 1 is a single combination of wind, wave, and current that is used to study the hyperparameters of LSTM model and the accuracy of LSTM model in single condition; and Case 2 is the combination of the same wind, wave, and current with different directions that is used to study the generalization ability of LSTM model.

4. Preliminary Process for the Evaluations

4.1. Validation of the Mooring Model

To verify the accuracy of the initial layout of the entire system, we established FPSO mooring models in AQWA and SIMO software and performed static balance calculations; the calculation results are shown in

Table 7. Comparison of pre-tension.

Line	L1	L2	L3	L4	L5	L6	L7	L8	L9
AQWA (kN)	256	256	256	256	256	256	258	258	258
SIMO (kN)	260	260	260	260	260	260	260	260	260
Error (%)	1.56	1.56	1.56	1.56	1.56	1.56	0.78	0.78	0.78

. The SIMO results show that the pre-tension of every single mooring line is 260 kN, and the AQWA calculation results show that the pre-tension of Mooring Lines 1 to 6 is 256 kN, with an error of 1.56%; the pre-tension of Mooring Lines 7 to 9 is 258 kN, with an error of 0.78%. The difference between the AQWA calculation result and the SIMO calculation result is mainly caused by the equivalent treatment of the connectors. The deviation is within the ideal range, so the model is considered accurate.

4.2. LSTM Model Design

The Keras’ LSTM layer is used to construct a many-to-many LSTM model. By referring to previous research conclusions [24,28], we see that the deep learning model is built with a three-layer LSTM loop layer and a fully connected output layer. The training is carried out with the following data set: (the number of samples sent, the time step of the loop core expansion, the number of input features) as input, (the number of samples sent, the number of labels output) as the output.

Considering the time step as a sensitive factor, the hyperparameters, such as learning rate, number of training rounds, and batch size, are kept consistent in order to study the influences. The working condition 10003 is taken as an example for optimization. Its network layout is shown in

Table 8. Neural network parameters of working condition 10003.

Number	1	2	3	4	5
LSTM_0	25	15	20	30	35
LSTM_1	100	100	100	100	100
LSTM_2	100	100	100	100	100
Dense	9	9	9	9	9
Time step	25	15	20	30	35
Dropout	0.3	0.3	0.3	0.3	0.3
Learning rate	0.01	0.01	0.01	0.01	0.01
batch_size	256	256	256	256	256
epochs	20	20	20	20	20

.

The Case 1 data were transferred into the LSTM model for training. The errors were calculated corresponding to different time steps according to the input results of the working conditions.

As shown in

Table 9. Error result statistics of working condition 10003.

Number	1	2	3	4	5
RMSN	6.02	6.80	7.17	6.12	6.76
MAE	4.26	5.26	5.25	4.43	5.03

, the root mean square error and average absolute error of number 1 are the smallest, indicating that the time-step model has acceptable performance. It can be found that 25 time steps are relative to the best performance from the error analysis results.

Therefore, the hyperparameters of the network model are determined with the following parameters: number of training epochs is 20, batch size is 256, number of network layers is 5, discard rate is 0.3, learning rate is 0.01, loss function is MSE, activation function is tanh, optimizer is Adam.

5. Cases Study of Tension Prediction with LSTM

5.1. The Same Condition Verification

The prediction result of this case is compared with the time-domain calculation result of AQWA to further verify its accuracy. The tension comparison for Mooring Line 2 is shown in Figure 5 for the calculated and the predicted results. Within a wave period, the mooring force predicted by LSTM is in good agreement with that calculated by AQWA, except the amplitude points. The reason why the prediction accuracy of amplitude points is low is that there are less data for amplitude points in the training data, and the change characteristics were not learned by the neural network model completely. The calculation results of the LSTM model and the AQWA results are statistically analyzed in

Table 10. Result statistics of mooring tensions in Case 1.

Line	Max			Min			Mean
	AQWA (kN)	LSTM (kN)	Error (%)	AQWA (kN)	LSTM (kN)	Error (%)	AQWA (kN)	LSTM (kN)	Error (%)
1	347.4	330.7	4.81	247.9	249.2	0.52	296.2	295.8	0.14
2	379.3	359.95	5.1	260.3	262.4	0.81	316.6	316.6	0
3	410.8	389.3	5.23	272.3	275.7	1.25	337.1	337.9	0.24
4	559.3	539.2	3.59	408.4	406.1	0.56	480.3	478.2	0.44
5	582	555.5	4.55	422.1	423.7	0.38	493.8	494.1	0.06
6	601.1	571.4	4.94	434.3	442.3	1.84	504.7	507.6	0.57
7	381.3	361.3	5.25	273	274.8	0.66	313.5	313.3	0.06
8	351.1	335.1	4.56	259.7	261.1	0.54	294.5	295	0.17
9	321.9	310.5	3.54	245.8	247.3	0.61	276.3	276.6	0.11

. The maximum values of the result predicted by LSTM neural network are smaller than those calculated by AQWA, the minimum values of the result predicted by the LSTM neural network are larger than those calculated by AQWA, and the average values are very close. This is because the LSTM neural network has a more accurate prediction value at general points than at amplitude points. In general, the maximum error of LSTM neural network prediction results is 5.25%, which is within the allowable range of engineering. Therefore, it proves that the proposed LSTM neural network model can predict a single short-term working condition.

5.2. The Different Conditions Verification

5.2.1. Validation Sets Prediction

In Case 2, the prediction results are compared with the validation set obtained from AQWA, as shown in

Table 11. Result statistics of case2.

Line	Max			Min			Mean
	AQWA (kN)	LSTM (kN)	Error (%)	AQWA (kN)	LSTM (kN)	Error (%)	AQWA (kN)	LSTM (kN)	Error (%)
1	277.1	270.2	2.49	211.4	217.6	2.93	249.4	249.7	0.12
2	275.9	270.9	1.81	211.4	217.6	2.93	249.7	250.0	0.12
3	275.5	272.1	1.23	211.7	217.6	2.79	250.1	250.5	0.16
4	303.1	288.7	4.75	228.6	231.9	1.44	256.2	256.6	0.16
5	307.7	291.4	5.29	229.6	232.0	1.05	256.3	256.8	0.20
6	312.5	295.8	5.34	229.5	231.5	0.87	256.4	256.8	0.16
7	292.9	286.8	2.08	222.7	228.3	2.51	251.9	251.5	0.16
8	291.1	285.1	2.06	222.4	226.7	1.93	251.6	251.0	0.24
9	288.9	283.0	2.04	222.1	225.0	1.31	251.1	250.5	0.24

. Although the maximum values predicted by the LSTM neural network are smaller than those calculated by AQWA, and the minimum values predicted by the LSTM neural network are larger than those calculated by AQWA, the average values of the two results are closer than the result of the single working condition. This is because, with the increase of training data, the LSTM neural network can better learn the change characteristics of mooring line tension. It can be found that the long short-term memory neural network model is reliable to predict the mooring tension.

5.2.2. Test Sets Prediction

The environmental conditions of the test set are consistent with Table 5. The combination form is given in

Table 12. Test set environment combination form.

Condition Number	AD7	AD10	AD32	AD35
Wind direction (deg)	90	135	45	90
Wave direction (deg)	90	135	75	120
Current direction (deg)	90	135	15	60

. The direction is determined with the angle relative to the bow by anticlockwise. The AD7 and AD10 have the same wind wave and current directions. The AD32 and AD35 have a wind and wave angle of 30 degrees, and a current and wave angle of 60 degrees.

The LSTM model trained in Case 2 predicted the mooring tensions of the mooring system in four working conditions of the test set. Take out the test set, AD10 Mooring Line 8, AD35 Mooring Line 4, AD32 Mooring Line 3, AD7 Mooring Line 7 prediction results, and AQWA results to draw the time history curve, and draw the error distribution map for the first 200 s and statistics on the results of 4 test sets. These are shown in Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 and

Table 13. Result statistics of AD10.

Line	Max (kN)		Min (kN)		Mean (kN)		Standard Deviation (kN)
	AQWA	LSTM	AQWA	LSTM	AQWA	LSTM	AQWA	LSTM
1	256.4	251.2	243.4	246.0	250.4	248.8	1.7	1.1
2	256.7	251.8	244.4	247.5	251.1	249.7	1.5	0.9
3	257.2	252.4	245.5	249.1	251.9	250.7	1.4	0.7
4	272.7	271.0	247.2	249.1	259.6	257.4	4.5	4.6
5	272.1	270.2	247.3	249.2	259.3	257.1	4.4	4.4
6	271.4	269.7	247.6	249.9	259.1	257.1	4.2	4.2
7	257.2	253.9	238.7	240.5	247.7	246.3	3.1	2.7
8	257.3	254.4	237.9	238.9	247.2	245.9	3.3	3.0
9	257.2	254.6	237.0	237.6	246.8	245.3	3.5	3.4

,

Table 14. Result statistics of AD7.

Line	Max (kN)		Min (kN)		Mean (kN)		Standard Deviation (kN)
	AQWA	LSTM	AQWA	LSTM	AQWA	LSTM	LSTM	AQWA
1	257.6	253.4	235.2	236.3	246.0	244.1	3.9	3.7
2	257.7	254.1	235.8	236.7	246.4	244.7	3.7	3.7
3	257.9	255.5	236.6	237.1	246.9	245.6	3.6	3.7
4	271.2	267.6	247.0	249.5	258.0	256.8	4.0	3.2
5	272.0	268.2	246.8	249.4	258.2	257.1	4.2	3.4
6	272.9	268.9	246.7	249.2	258.5	257.3	4.4	3.7
7	259.0	256.9	244.6	245.7	252.5	250.6	1.6	1.8
8	258.3	255.9	244.1	245.6	251.8	250.0	1.6	1.7
9	257.5	254.5	243.6	245.4	251.1	249.3	1.6	1.6

,

Table 15. Result statistics of AD35.

AD35	Max (kN)		Min (kN)		Mean (kN)		Standard Deviation (kN)
	AQWA	LSTM	AQWA	LSTM	AQWA	LSTM	AQWA	LSTM
1	277.5	268.7	240.2	241.9	257.8	255.3	6.8	5.4
2	277.7	269.6	240.7	242.2	258.1	256.2	6.7	5.4
3	277.9	271.2	241.0	242.4	258.5	257.3	6.5	5.5
4	275.3	271.1	235.1	238.4	252.1	251.2	6.6	6.0
5	274.4	270.2	234.7	238.0	251.5	250.6	6.6	6.0
6	273.5	269.7	234.6	237.1	250.9	250.0	6.6	6.0
7	262.7	257.4	231.0	233.2	246.9	244.1	5.3	5.1
8	264.0	259.0	231.1	233.6	247.2	244.5	5.4	5.3
9	265.2	260.1	231.2	233.7	247.6	245.0	5.5	5.4

and

Table 16. Result statistics of AD32.

AD32	Max (kN)		Min (kN)		Mean (kN)		Standard Deviation (kN)
	AQWA	LSTM	AQWA	LSTM	AQWA	LSTM	AQWA	LSTM
1	276.6	268.0	233.2	233.2	252.9	251.2	7.6	7.5
2	277.2	270.6	233.3	233.3	253.5	252.5	7.8	8.0
3	277.8	273.3	233.6	233.6	254.2	254.0	8.0	8.5
4	275.4	267.8	243.1	247.6	257.8	256.2	5.5	3.7
5	275.2	267.7	243.1	247.5	257.4	255.9	5.6	3.8
6	275.7	268.5	243.0	247.0	257.1	255.6	5.7	4.2
7	266.2	260.6	229.5	232.1	246.4	243.6	6.4	5.9
8	265.8	260.1	229.4	232.2	246.1	243.2	6.2	5.4
9	265.2	258.9	229.3	232.1	245.9	242.7	5.9	4.9

.

In Figure 6 and Figure 8, we showed a comparison chart of the mooring line tension calculated by LSTM and the results of the AQWA calculation; the blue curve represents the AQWA calculated value, and the red curve represents the LSTM predicted value. The prediction results of the AD10 and AD7 test sets are in good agreement with the AQWA calculation results in the low-frequency variation trend. As shown in Figure 7 and Figure 9, the value predicted by LSTM is slightly smaller than the value calculated by AQWA, the two curves vary identically in wave frequency, and the error is kept within 1.8%. As exhibited in Table 13 and Table 14, the maximum values of the result predicted by LSTM neural network are smaller than those calculated by AQWA, the minimum values of the result predicted by LSTM neural network are larger than those calculated by AQWA, and the average values and the standard deviation are very close. In general, the LSTM model built and trained here has high accuracy in predicting the tension of the mooring line and has the same trend in both low frequency and wave frequency when the wind, wave, and current come from the same direction.

In Figure 10 and Figure 12, we showed a comparison chart of mooring line tension calculated by LSTM and the results of the AQWA calculation; the blue curve shows the AQWA calculated value, and the red curve shows the LSTM predicted value. The prediction results of AD35 and AD32 test sets are in good agreement with the AQWA calculation results in the low-frequency variation trend. As shown in Figure 11 and Figure 13, the value predicted by LSTM is close to the value calculated by AQWA, and the error is kept within 1.8%, but the trend of wave frequency variation of the two curves is not very consistent. This could be because the wind, wave, and current are not in the same direction. As exhibited in Table 15 and Table 16, the maximum values of the result predicted by the LSTM neural network are smaller than those calculated by AQWA, the minimum values of the result predicted by the LSTM neural network are larger than those calculated by AQWA, and the average values and the standard deviation are very close. The standard deviations of the AD35 and AD32 are larger than those of the AD10 and AD7 due to the different directions of the wind, wave, and current. In general, the LSTM model built and trained here has high accuracy in predicting the tension of the mooring line and has the same trend in low frequency when wind, wave, and current come from a different direction. Compared with the prediction performance of wind, wave, and current in the same direction, the LSTM neural network model has poor prediction performance in wave frequency variation trend.

6. Conclusions

This paper studied the short-term prediction of the mooring tension of the FPSO inner turret single-point mooring system and used the commercial software AQWA to model and calculate the three-dimensional hull and mooring system. In this way, a data set of hull motion and mooring force was obtained, and then an LSTM neural network was built to train and predict the data set. Using the ship’s 5-DOF data calculated by the AQWA software in the time domain as input data, we obtained the predicted results of the tension and bowing of the nine mooring lines. The following conclusions are obtained through the research of this paper:

(1)

The LSTM model built here performs well in predicting the mooring tension.

(2)

In the prediction of mooring line tension under multiple combinations of wind, wave, and current, the predicted value does not deviate much from the true value, and the prediction result is relatively satisfactory, so the LSTM neural network model can learn the low-frequency trend regardless of whether the wind, wave, and current are in the same direction.

(3)

Here, the research on the prediction of the mooring line tension of the inner turret FPSO can realize the comparative analysis of the real-time measurement data and numerical calculation data at sea to a certain extent and provide a new calculation method for the calculation of the dynamic mooring line tension.