Machine Learning-Based Mooring Failure Detection for FPSOs: A Two-Step ANN Approach

Abstract

This study presents a two-step artificial neural network (ANN) approach for detecting mooring failures in a spread-moored floating production storage and offloading (FPSO) vessel using platform motion data. Synthetic statistical data generated from time-domain simulations were utilized as input features. The first-step ANN determines whether the mooring system is intact or a failure has occurred within a specific mooring group. If a failure is detected, the second-step ANN identifies the exact failed mooring line within the group. Hyperparameter optimization was performed using Bayesian and random search methods, and multiple input variable sets were evaluated. The results indicate that the mean values of platform motions, particularly surge and yaw, play a crucial role in accurately identifying mooring failures. Additionally, selecting the top 10 features based on mutual information can be a way to improve detection accuracy. The proposed two-step ANN approach outperformed the single-step ANN method, achieving higher classification accuracy and reducing misclassification between mooring lines. These findings demonstrate the potential of machine learning for near-real-time mooring integrity monitoring, offering a practical and efficient alternative to traditional inspection methods.

1. Introduction

Reliability of mooring systems in marine and offshore structures is a crucial issue in maintaining both operational safety and efficiency in dynamic ocean environments. Mooring line failures, caused by many reasons, such as environmental loads, material degradation, or structural fatigue, can have severe consequences, such as compromised station-keeping and progressive riser failure, potentially leading to environmental hazards. As one example, historical data from 2001 to 2011 indicate that mooring failures were responsible for eight major incidents and 21 overall failures, many of which resulted in riser damage [1]. This underscores the pressing need for accurate and robust mooring failure detection systems.

Conventional integrity management strategies, as outlined in DNV-RP-F116 [2], encompass risk assessment, integrity planning, inspection and monitoring, structural evaluation, and necessary intervention or repair. In particular, mooring inspection and monitoring has traditionally relied on visual assessments [3], sensor-based monitoring using load cells for direct tension measurement [4] or inclinometer-derived tension estimates [5], and indirect evaluations via Global Positioning System (GPS), differential GPS (DGPS), and inertial measurement unit (IMU) data that track platform drift and motion patterns [6]. However, visual inspections are periodic, require costly equipment such as remotely operated vehicles (ROVs) and underwater robots, and do not facilitate real-time monitoring. Meanwhile, sensor-based methods demand the installation of monitoring devices such as a load cell on each mooring line, and GPS-based techniques face challenges in accurately diagnosing failures without advanced detection algorithms. The complexity further escalates in extreme environmental conditions where nonlinear interactions between the platform and environmental forces make deterministic modeling highly challenging.

To address current limitations in mooring failure monitoring, data-driven approaches leveraging machine learning (ML), such as artificial neural networks (ANNs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), and long short-term memory (LSTM) networks, have emerged as promising solutions, offering enhanced accuracy, adaptability, and near-real-time assessment capabilities for offshore mooring integrity. By utilizing GPS or floater-motion sensor data without relying on wet sensors on lines, ML models can effectively detect and classify underwater mooring failures.

This study investigated the feasibility of a data-driven, two-step ANN approach for detecting mooring failures of a spread-moored floating production storage and offloading (FPSO) vessel using vessel motion data. Several factors motivated the proposed two-step ANN approach. First, the application of ANNs in ocean engineering has shown promising results in addressing a range of challenges, including the estimation of directional wave spectra [7,8], current profiles [9], and green water events [10]. In particular, when relying on scalar variables, such as motion statistics, ANNs are well-suited to event detection and classification tasks [11]. Second, the two-step approach helps address current challenges in failure monitoring of the specific mooring configurations. Recent studies have demonstrated the effectiveness of ML-based methods in identifying and localizing failures across various offshore floating structures, including conventional oil and gas platforms [11,12,13,14,15], floating offshore wind turbines [16], floating solar panels [17], and underwater tunnels [18]. While the identification of a failed mooring line is generally more straightforward in taut mooring systems, particularly when employing statistical indicators [19], it remains considerably more challenging in catenary configurations [20]. Furthermore, in spread-moored systems with catenary lines, the close spacing between neighboring lines within each group complicates the task of pinpointing the exact line that has failed. The approach proposed in this study addresses these challenges by first isolating the failing group of lines, thereby narrowing the search space before identifying the specific failed line.

In the proposed two-step ANN approach, the first step classifies the overall system status, determining whether the mooring system is intact or a failure has occurred within a specific mooring group. If a failure is detected among one of the lines, the first-step ANN identifies the group that includes a failed mooring line. In the second step, a group-specific ANN further pinpoints the exact failed mooring line within the identified group. To validate this framework, synthetic data from time-domain dynamic simulations of a spread-moored FPSO vessel were employed. Furthermore, multiple ANN architectures were evaluated using diverse input variable sets, incorporating extended statistical metrics beyond the conventional mean and standard deviation to identify the optimal features for improving model performance and accuracy.

This paper is structured into five sections. Section 2 introduces the numerical model, environmental datasets, and selected input variables. Section 3 details the ANN architecture and the process of optimizing hyperparameters. In Section 4, the results are analyzed, comparing the proposed two-step ANN approach with the one-step method. Finally, Section 5 summarizes the main findings and discusses the direction of future research.

2. Big-Data Collection from Numerical Simulation

2.1. Design Particulars of Moored FPSO and Numerical Model

A spread-moored FPSO vessel was selected as the numerical model [21], as shown in Figure 1. The system consisted of an FPSO platform, 12 mooring lines arranged in a spread configuration, and a single steel catenary riser, with detailed design specifications provided in

Table 1. Design particulars of an FPSO platform.

Parameter	Value	Unit
Length between perpendicular	310	m
Breadth	47.17	m
Depth	28.04	m
Draft	18.90	m
Displacement	240,869	MT
Center of gravity above base	13.30	m
Roll radius of gyration at COG *	14.77	m
Pitch radius of gyration at COG	77.47	m
Yaw radius of gyration at COG	79.30	m
Heave natural period	14.62	s
Roll natural period	12.88	s
Pitch natural period	11.79	s

* COG: Center of gravity.

and

Table 2. Design particulars of mooring lines and riser.

Parameter	Value				Unit
	Mooring Lines			Steel Catenary Riser
	Segment 1 (Chain)	Segment 2 (Polyester)	Segment 3 (Chain)
Length	120	2290	90	2800	m
Diameter *	9.52	16.0	9.52	25.4	cm
Mass/unit length	189.2	20.4	189.2	131.0	kg/m
Axial stiffness	9.12 × 105	2.79 × 104	9.12 × 105	3.34 × 106	kN
Bending stiffness	-	-	-	2.25 × 104	kNm2
Torsional stiffness	-	-	-	1.84 × 104	kNm2
Added mass coefficient **	1.0	1.0	1.0	1.0	-
Drag coefficient	2.4	1.2	2.4	1.0	-
Minimum breaking load ***	9035.14	4363.95	9035.14	-	kN

* For the mooring lines, it was the nominal diameter. ** Equivalent diameter was used to consider these coefficients. *** Minimum breaking load for chain is based on the R4 grade.

. The generic FPSO vessel was employed. The mooring lines were divided into four mooring groups, each containing three lines. Figure 1 illustrates the layout of these mooring groups along with the numbering scheme for individual lines. Each mooring line featured a chain–polyester–chain composition.

Extensive time-domain simulations were carried out using OrcaFlex version 11.4 [22], a widely recognized commercial software, to generate a comprehensive synthetic dataset encompassing both intact and failure conditions.

For the FPSO vessel, hydrodynamic coefficients and wave forces were first determined through a potential-theory-based 3D radiation/diffraction analysis in the frequency domain [23], which has been widely adopted in many numerical studies to compute both hydrostatic/hydrodynamic coefficients and wave excitation forces [24,25,26]. The Cummins equation [27] was the time-domain formulation for solving FPSO dynamics, which includes both first and second-order wave forces:

$$(M+A(\infty ))\ddot{X}(t)+K_{H}X(t)=F_W(t)+F_{WD}(t)+F_C(t)+F_D(t)+F_S(t),$$

(1)

where the matrices, M, $A(\infty )$, and $K_H$, denote mass, the added mass at the infinite frequency, and the total stiffness, which is a summation of hydrostatic and gravitational restoring coefficients, respectively. The vector, $X$, represents displacements in 6 degrees of freedom (6DOF). The load vectors on the right-hand side, $F_W$, $F_{WD}$, $F_C$, $F_D$, and $F_S$, denote the first-order wave-excitation load, the second-order wave drift load, the convolution-integral-based radiation-damping load, the viscous drag load due to wind and current, and the coupling load from the interaction between FPSO and mooring lines or riser at their connection positions. $A(\infty )$, $K_H$, $F_W$, $F_{WD}$, and $F_C$ were determined from frequency-domain analysis while considering the correspondence between frequency-domain and time-domain equations of motion [28]. $F_{WD}$ was first acquired by Newman’s approximation, in which off-diagonal terms of the difference-frequency quadratic transfer function (QTF) can approximately be obtained by combining diagonal terms. In addition, diagonal terms of QTF for calculation of $F_{WD}$ were further modified using Aranha’s solution for the inclusion of wave drift damping [29]. Moreover, Oil Companies International Marine Forum (OCIMF) formulations were utilized to evaluate wind and current loads on the FPSO platform [30]. In this report, drag forces were modeled as being proportional to the square of the fluid velocity, and direction-dependent drag coefficients were provided based on the fluid flow direction. Furthermore, there exist no relative translational motions between FPSO and mooring line/riser at the connection position since they are tightly connected, which results in $F_S$ being the constraint force.

The lumped mass method was adopted to model mooring lines and riser. In this method, a continuous line is discretized into a certain number of nodes and elements. A node includes all physical properties of a line, such as the mass, damping, and wave load, whereas the massless element represents the elastic behaviors of the line via linear axial, bending, and torsional springs. Euler struts, where the Euler load depends on the bending stiffness ($EI$), were used to model the slack behavior and compression of mooring chains. Since the chains were modeled with zero bending stiffness, they had no resistance to compression, resulting in zero axial stiffness under compression. The wave load on the line was calculated using the Morison equation, which is typically valid for slender bodies relative to the wavelength. For a moving body, the Morison equation includes three force components: added mass, inertia, and drag, representing radiation, diffraction, and viscous drag effects, respectively. While radiation force consists of added mass and radiation-damping forces, the Morison equation neglects the radiation-damping force, which is acceptable for slender structures. Mooring line failure was modeled by removing a single mooring line from the coupled platform model, thereby simulating the post-failure steady-state condition rather than capturing transient responses.

For each case, a one-hour simulation was performed with a time step of 0.25 s. An additional 400 s was used as ramping time to ensure a smooth transition to a steady-state response; however, this period was excluded from the data.

The generic FPSO platform has been validated against scaled experiments in the wave tank under wind, wave, and current loads [31] and has been utilized in a variety of previous studies. The line dynamics in OrcaFlex has been confirmed through experiments and comparison against an in-house program [32,33].

2.2. Environmental Data

Wind, wave, and current data were gathered from two primary online sources: ERA5, the fifth-generation atmospheric reanalysis dataset from ECMWF [34], and HYCOM, the Hybrid Coordinate Ocean Model [35]. These datasets were retrieved for a location at 10° N latitude and 56° W longitude, situated in the North Sea region of South America. ERA5 provided wave and wind data spanning 2018 to 2021, while HYCOM contributed surface current velocity data from 2012 to 2015.

From the gathered data, wind, wave, and current rose plots are illustrated in Figure 2. The directional convention used in this study was converted to be aligned with that of OrcaFlex, where 0 degrees represents the direction relating to the positive x-axis (i.e., east), and 90 degrees indicates the direction relating to the positive y-axis (i.e., north). The analysis of the data revealed that the most commonly observed wave conditions featured significant wave heights varying from 1 m to 3 m, with peak periods ranging between 6 s and 14 s, and predominant wave directions spanning 180° to 240°. Furthermore, the highest recorded wind speed was 12.65 m/s with a direction of 211°, while its mean directional range also fell between 180° and 240°. Surface currents exhibited a maximum velocity of 1.25 m/s with a direction of 198°, with major directions ranging from 90° to 240°.

2.3. Big Data Collection and Data Description

Figure 3 illustrates the representative training and testing datasets used in the research. In total, 2400 simulations were performed, with the first half corresponding to intact conditions (first 1200 simulations) and the latter half representing line-failure cases (next 1200 simulations). Specifically, the intact-case dataset comprised 900 training simulations and 300 testing simulations, which are marked by black and blue dots in Figure 3, respectively.

To generate the training dataset, key input parameters—including significant wave heights, peak periods, and wave directions—were determined based on the most probable wave conditions. This approach resulted in 75 combinations of wave height and peak period values, coupled with 13 discrete mean wave directions, culminating in 900 simulations. Additional parameters were randomly sampled from their respective probability distributions, with the enhancement parameter and spreading factor varying within the ranges of 1–3 and 2–8, respectively. The multidirectional wave spectra were characterized using the JONSWAP wave spectrum with cosine-s spreading formulations [22]. Likewise, surface current and wind velocities were randomly selected from zero up to their maximum observed values during the study period, with their directions randomly assigned within the recorded ranges as well. The test dataset from 300 simulations was subsequently drawn randomly from the same ranges of wind, wave, and current values used for training.

An additional set of 1200 simulations was conducted to analyze single-line failure scenarios. Given a system with 12 mooring lines, each line was subjected to 100 failure simulations—75 for training and 25 for testing—resulting in a total of 900 training and 300 testing simulations. The environmental conditions for failure cases were identical to those used for intact cases.

It is important to note that this study did not consider the correlation among wind, wave, and current conditions. The purpose of the fine division or random selection was to evaluate the robustness of the ANN regardless of specific combinations of environmental conditions. Since it is worthwhile to investigate the impact of correlated environmental loads on detection performance, future research will address this issue.

3. ANN Architecture

3.1. ANN Architecture: Two-Step Approach

An ANN is a computational model inspired by biological learning processes, which identifies the patterns and relationships between inputs and outputs instead of relying on explicitly defined equations. An example of ANN architecture is presented in Figure 4. An ANN consists of three types of layers: an input layer that takes in data, an output layer that delivers results, and one or more hidden layers that process information between them. As data move through the layers, they are transformed via weighted connections between neurons in neighboring layers. Learning in an ANN involves adjusting these weights and associated biases to maximize the accuracy of the predicted outputs compared with actual ones. The ANN learning mechanism follows a feedforward structure, meaning that data move forward from the input layer through hidden layers before reaching the output layer. Initially, each neuron calculates a weighted sum of its input values $x$, incorporating a bias term $b$. The activation function $f_a(x)$ then determines whether the neuron is activated, which introduces nonlinearity into the system. The output layer produces the predicted output $y$. Through the loss function that compares predicted and actual outputs, weights and biases are updated through backward propagation [36,37].

This study introduces a two-step ANN-based methodology for evaluating mooring line failure integrity, as depicted in Figure 5. As explained before, the ANN framework consists of an input layer, multiple hidden layers, and an output layer. As input features, statistical parameters calculated from time history data of 6DOF motions were utilized, including the mean, standard deviation, spectral moments, and spectral bandwidth, among others. Various input parameter combinations are detailed in Section 3.2 (Feature Selection). In the initial step, the ANN performs classification to determine the system’s condition, identifying whether it remains intact or a failure has occurred within one of the four mooring groups. If a failure is detected, this first-step ANN further pinpoints the affected mooring group. Subsequently, the second step involves four distinct ANN models, each specifically trained to diagnose the precise mooring line failure within the identified group, pinpointing the specific failed mooring line.

3.2. Feature Selection

Selecting appropriate input features is critical for developing high-performing ANNs. In this regard, this study examined seven different combinations of input variables in the input layer, as outlined in

Table 3. Selected cases from the combinations of input variables.

Case #	Input Variables
1	Mean and standard deviation of 6DOF motions
2	Mean and standard deviation of 6DOF motions Environmental data (wave, wind, and current)
3	Mean and standard deviation of 6DOF motions Additional 113 features
4	Mean and standard deviation of 6DOF motions Additional 113 features Environmental data (wave, wind, and current)
5	Mean and standard deviation of surge, sway, and yaw motions
6	Mean and standard deviation of heave, roll, and pitch motions
7	Top 10 highly correlated inputs from mutual information maps

. First, means and standard deviations were considered. When one of the mooring lines fails on the spread-moored FPSO platform, the vessel’s mean position shifts dramatically due to the resulting imbalance in mooring stiffness. In other words, when one of the mooring lines fails, the imbalance in stiffness causes a noticeable shift in the mean values, depending on the location of the failed mooring line and the directions of environmental loads. This imbalance in stiffness also impacts the vessel’s dynamic behavior. Figure 6 provides additional evidence that mooring failure leads to substantial changes in mean values. Moreover, as shown in Figure 7, although standard deviations also show some variations, the magnitude of these changes is relatively minor compared to the pronounced shifts in mean values. Furthermore, the planar motions—surge, sway, and yaw—are particularly sensitive to mooring failure, given the mooring configuration.

Next, while prior studies on mooring failure detection primarily utilized mean and standard deviation as input features, this study explored the significance of additional statistical parameters that have been widely employed in ocean engineering and can be calculated from the 6DOF motions (Mode# 1–6), 3DOF angular velocities (Mode# 7–9), and 3DOF translational accelerations (Mode# 10–12) of the platform. The expanded dataset included not only means and standard deviations but also zeroth, second, and fourth spectral moments, zero-crossing and crest-to-crest periods, cross-correlations of dominant coupling modes, spectral bandwidths, one-tenth max values, and relative standard deviation computed as the standard deviation of other motions divided by that of surge motion. These additions introduced 113 extra features beyond the conventional mean and standard deviation of 6DOF motions. In our separate study using the same platform and environmental conditions for inverse wave estimation by ANN, these statistical parameters notably enhanced the accuracy of wave parameter estimation [21]. For wave estimation, the dynamics of the platform tend to be more important than statics, while mooring failure detection heavily relies on the statics of the platform, as can also be observed in Figure 6 and Figure 7. In this regard, it is interesting to see whether these additional parameters can help improve the performance of the ANN. Additionally, the study assessed the sensitivity with regard to additional environmental parameters on accuracy by including significant wave height, peak period, wave direction, wind speed and direction, and surface current speed and direction as additional inputs. Furthermore, the means and standard deviations from both the planar motion-only and nonplanar motion-only cases were included. Motions resulting from mooring line failure are typically more sensitive to in-plane translational and yaw rotational motions. By including cases where planar and nonplanar motions were used as inputs (Cases 5 and 6), the dominant factors contributing to the identification of line failure were better isolated and understood.

Figure 8 shows mutual information maps with and without intact scenarios. The maps help identify the relationship between inputs and outputs. The map is normalized to a range between 0 and 1. When a value is close to 1, the input is highly correlated with the output, whereas lower values indicate weaker correlation. The findings show that mean values will play an important role in mooring failure detection, especially surge and yaw means. The one-tenth maximum values of surge and yaw motions also show high correlations. Assuming that highly correlated inputs enhance the accuracy of ANN architectures, the top 10 most correlated inputs were selected and tested for performance enhancement. In the first-step ANN, the top 10 highly correlated inputs were chosen based on mutual information with intact scenarios considered (Figure 8a). Meanwhile, in the second-step ANNs, the top 10 highly correlated inputs were selected without considering intact scenarios (Figure 8b).

3.3. Hyperparameter Optimization

The architectures of the ANN used for these tasks incorporated a SoftMax activation function in the output layer, making it ideal for multi-class classification problems. The other hyperparameters—such as the number of layers, neurons per layer, dropout rate to prevent overfitting, and activation functions for the hidden layers—were fine-tuned for each specific architecture.

This study utilized two optimization techniques: Bayesian optimization and random search, which have been widely employed in ANN architecture optimizations. Both methods employed the same search space, as detailed in

Table 4. The search field in the hyperparameter optimizations.

Hyperparameter	Search Field
Number of layers	1–5
Number of neurons	32–512
Dropout	0% or 30%
Activation function	tanh or ReLU

. First of all, Bayesian and random search optimizations were compared at different configurations of 50, 150, and 250. Configuration means one set of hyperparameters generated within the search field given in Table 4. Bayesian optimization can be applied to optimize ANNs by selecting the best hyperparameters. It uses a probabilistic model to predict the performance of different configurations and iteratively chooses the most promising options. This process helps efficiently find the optimal architecture and parameters, leading to improved ANN performance. In contrast, the random search method randomly selected configurations from the search space. Each configuration underwent 10 of the same trials with 1000 epochs to account for variations in accuracy due to the random initialization of weights in the hidden layers, which could lead to different outcomes and potential local minima. The configuration that achieved the best performance across all trials is reported in this study.

The comparison between Bayesian and random search optimizations is presented in

Table 5. Accuracy comparisons between Bayesian and random search optimizations with different sets of hyperparameters (i.e., configurations) for Case 1.

Optimization Method	Configuration	Accuracy (%)
		1st Step	2nd Step				Overall *
			Group 1	Group 2	Group 3	Group 4
Bayesian	50	100.0	62.7	66.7	74.7	56.0	82.5
Random	50	100.0	62.7	65.3	74.7	60.0	82.8
Bayesian	150	100.0	61.3	66.7	77.3	57.3	82.8
Random	150	100.0	66.7	66.7	77.3	58.7	83.7
Bayesian	250	100.0	61.3	69.3	76.0	58.7	83.2
Random	250	100.0	64.0	66.7	78.7	60.0	83.7

* Overall accuracy denotes the combined accuracy of the intact case and one-line failure case in second-step ANN architectures.

. Only Case 1 was tested, as it yielded the highest accuracy among the seven cases, and the details will be explained in Section 4. In general, higher configurations tended to yield higher accuracy, although the difference was minor. Additionally, both methods achieved very similar accuracy, with random search optimization performing slightly better. For random search optimization, there was no significant difference between configurations of 150 and 250. Therefore, the further study adopted random search optimization with a configuration of 150 for hyperparameter optimization.

Both methods were trained on a system equipped with a Tesla A100 GPU featuring 40 GB of VRAM and an AMD EPYC 7402 Rome 2.8 GHz 24-Core CPU. When evaluating the computational cost using 50 configurations, training from the Bayesian approach took approximately 6.5 h and required approximately 11.5% more time to complete compared to the random approach. This is partially explained by the overhead required to pick the best configuration at the beginning of each iteration.

4. Results and Discussions

The Results and Discussion section begins by assessing the performance of the two-step ANN architecture through an analysis of various input combinations (Cases 1–7). As mentioned in Section 3.3, we compared Bayesian and random optimizations, and random optimization with 150 configurations was adopted in this section. In this section, overall accuracies, accuracies in first and second-step ANNs, and confusion matrices are presented and discussed. In addition, the accuracies of the best-performing two-step ANNs are compared with that of the single-step ANN that estimates intact or failed line numbers directly through 13 classifications, i.e., one intact and 12 failure cases.

Table 6. Accuracies in first- and second-step ANNs and overall accuracy of various input cases.

Case #	Accuracy (%)
	1st Step	2nd Step				Overall *
		Group 1	Group 2	Group 3	Group 4
1	100.0	66.7	66.7	77.3	58.7	83.7
2	100.0	58.7	80.0	68.0	60.0	83.3
3	100.0	54.7	53.3	64.0	58.7	78.8
4	100.0	53.3	64.0	65.3	66.7	81.2
5	94.7	56.00	65.3	73.3	54.7	75.3
6	71.2	57.3	53.3	53.3	56.0	50.3
7	100.0	68.0	66.7	74.7	60.0	83.7

* Overall accuracy denotes the combined accuracy of the intact case and one-line failure case in second-step ANN architectures.

presents a comparison of accuracy across all cases. Most first-step ANN architectures demonstrated high accuracy, except for Case 6. Specifically, in Cases 1–4 and Case 7, the accuracy reached 100% with random search optimization, whereas Case 6 showed a relatively lower accuracy of 71.2%. The ANN model effectively identified the failure group, making it particularly useful for early failure detection and the prevention of progressive failures.

Conversely, second-step ANN architectures exhibited lower accuracies. As illustrated in the confusion matrix in Figure 9 and Figure 10, which correspond to the best-performing ANN architectures from Cases 1 and 7, misclassifications of line numbers primarily occurred between adjacent lines. The difficulty in pinpointing the exact line number arose from the small mooring interval of 5 degrees. In other words, the dynamic behavior of a single-line failure within one group was very similar to that of another line failure in the same group, leading to occasional misclassification by the second-step ANN model.

Among the evaluated cases, the highest performance was achieved when using inputs that incorporated the mean and standard deviation of 6DOF motions (i.e., Case 1) and the 10 best features exhibiting the strongest correlations based on the mutual information maps, as shown in Figure 8 (i.e., Case 7). According to the mutual information map, mean values, particularly for surge and yaw DOFs, demonstrated a high correlation with output classes. The results further indicate that selecting the most relevant features from the mutual information map (i.e., the top 10 features in this case) played a crucial role in achieving high accuracy, leading to the best overall performance. When the best input features can be straightforwardly identified from known facts, such as 6DOF means for mooring failure detection, constructing the ANN architecture becomes straightforward. However, if identifying the best features is challenging and complex, using a mutual information map to select a certain number of the best features can be an effective approach.

In our mooring failure monitoring framework, changes in 6DOF mean values were critical for detecting mooring failures. These changes can also be clearly observed in the time history plots shown in Figure 6. However, even when using reduced DOF inputs, such as in Case 5, which relies on planar motions, accuracy remained sufficiently high, with the first-step ANN’s accuracy measured at 94.7%. Notably, Case 5 outperformed Case 6, indicating that mooring failure was more strongly correlated with planar motions. This trend is also evident in the mutual information maps and time histories of mean values. Nevertheless, the mutual information map also reveals that nonplanar motions, particularly the mean values of pitch and roll, also exhibited strong correlations with output classes. As a result, utilizing full 6DOF motion inputs led to superior performance.

Conversely, expanding the input set by including additional statistical variables (Case 3) did not enhance accuracy. A comparison between Cases 3 and 7 further demonstrates that selecting the top 10 features yielded significantly better performance. This finding suggests that introducing a large number of uncorrelated variables may hinder the model’s ability to effectively learn underlying relationships. Therefore, it is essential to focus on variables with strong correlations to the output. As illustrated in Figure 8b, in addition to mean values of certain DOFs, the selected top 10 features in the second-step ANN architectures included the one-tenth maximum values of surge and yaw, the standard deviation of heave, the spectral bandwidth of pitch, and the zeroth spectral moment of heave, all of which exhibited high correlations with output classes.

Additionally, incorporating environmental conditions as inputs did not significantly improve performance and, in some cases, even degraded it, as observed when comparing Case 1 with Case 2. This trend may arise because environmental conditions do not have a direct causal relationship with mooring failure, whereas ship motions are directly linked to the failure mechanism. In other words, while environmental conditions may contribute to performance improvement in certain cases, they are not a key factor in significantly enhancing the accuracy of mooring failure detection.

Finally, the effectiveness of the two-step approach was assessed by comparing the best-performing two-step ANN architecture (Case 1) with the single-step ANN model. In the single-step ANN framework, the intact condition or a failed mooring line with the exact line number was directly assessed, which resulted in 13 output classes; 13 output classes were defined—12 corresponding to individual mooring line failures and one representing intact conditions. The same random search optimization method and configuration number of 150 were chosen for fair comparison. Since Case 1 was considered in single-step ANN, the input features included the mean and standard deviation of 6DOF motions. The confusion matrix is presented in Figure 11. In the confusion matrix, an intact case is marked as class 0, while the output classes 1–12 correspond to failures in mooring lines 1–12. As illustrated in Figure 11, the single-step ANN model yielded an accuracy of 78.1%. There was one instance where the intact case was misclassified as the failed case and there were two instances where failure cases were misclassified as the intact case. In contrast, the two-step ANN achieved 100% accuracy in group classification, ensuring that the system reliably distinguished between intact and failed conditions while also correctly identifying the group containing the failed mooring line. Additionally, the overall accuracy of the two-step ANN model reached 83.7% for Case 1, surpassing that of the single-step approach. These results highlight the advantages of the two-step ANN method, demonstrating its superior accuracy and practicality for mooring failure detection.

5. Concluding Remarks

This study presents a two-step ANN framework for detecting mooring failures in spread-moored FPSO vessels using platform motion data. The proposed method classifies mooring failures in two stages: the first-step ANN determines whether the mooring system is intact or identifies the group containing the failed line, while the second-step ANN pinpoints the exact failed mooring line within the group. Synthetic motion data generated from time-domain dynamic simulations were used as inputs, and various statistical features were evaluated to optimize performance. Two hyperparameter optimization techniques were employed, with random search optimization slightly outperforming Bayesian optimization. The following conclusions were drawn from the results:

• The two-step ANN architecture outperformed the single-step method, achieving an overall accuracy of 83.7% with 100% accuracy in mooring group classification and reducing misclassifications in individual line failures. The single-step ANN suffered from misclassifications, including falsely identifying an intact case as failure and two misclassifications where failure cases were incorrectly classified as intact, while the second-step ANN did not misclassify any intact cases as failures.
• The 6DOF mean values, particularly for surge and yaw motions, were the most critical features for mooring failure detection. Additionally, planar motions were more important than non-planar motions.
• Selecting the best features using a mutual information map can improve model accuracy, highlighting the importance of selecting highly correlated input variables rather than expanding the dataset with uncorrelated features.
• Including environmental conditions as inputs did not enhance performance, reinforcing the idea that platform motion data are the most relevant predictor for mooring failure detection.

In mooring failure detection, while early failure detection is an important aspect, as discussed in this study, multi-line failure is also critical, as the failure of two lines or more negatively influences overall safety. Furthermore, the data used in this study were based on noise-free conditions, and sensor noise could affect accuracy. Future work will explore multi-line failure scenarios, the effects of sensor noise, and further optimization of feature selection to enhance the model’s robustness and applicability in real-world offshore operations.