Semi-Active Heave Compensation for a 600-Meter Hydraulic Salvaging Claw System with Ship Motion Prediction via LSTM Neural Networks

: Efﬁciently salvaging shipwrecks is of the utmost importance for safeguarding shipping safety and preserving the marine ecosystem. However, traditional methods ﬁnd it difﬁcult to salvage shipwrecks in deep water. This article presents a novel salvage technology that involves multiple hydraulic claws for directly catching and lifting a 2500-ton shipwreck at 600 m depth. To ensure lifting stability, a semi-active heave compensation (SAHC) system was employed for each lifter to mitigate the effects of sea waves. However, the response delays arising from the hydraulic, control, and ﬁltering systems resist the heave compensation performance. Predicting the barge motion to mitigate measuring and ﬁltering delays and achieve leading compensation is necessary for the salvage. Therefore, a multivariate long short-term memory (LSTM) based neural network was trained to forecast the barge’s heave and pitch motions, exhibiting satisfactory results for the next 5 s. According to the results of numerical simulations, the proposed LSTM-based motion predictive SAHC system demonstrates remarkable effectiveness in compensating for shipwreck motion.


Introduction
Nowadays, the demand for resources has led to a rapid expansion in both marine trade and scientific exploration, resulting in the construction of larger and more numerous vessels and offshore facilities. Unfortunately, it has also led to a significant increase in serious shipping incidents, with approximately 1000 such incidents occurring each year, which poses a threat not only to the marine ecosystem but also to the safe navigation of other vessels [1]. Therefore, removing these wrecks as quickly as possible is crucial to mitigate their impact on the environment and marine transportation.
Shipwrecks in shallow regions can be salvaged through traditional methods, including reestablishing buoyancy by attaching salvage pontoons around the hull and draining water from closed cabins or providing extra lifting force by floating cranes [2]. These methods, however, have obvious flaws. For instance, severely damaged shipwrecks cannot be drained to the extent necessary to achieve appropriate buoyancy, and fragile structures are also challenging to hoist using a floating crane. Furthermore, the majority of mono-hull or sheer-leg floating cranes in use currently lack the lifting capacity necessary to handle large shipwrecks weighing more than 10,000 tons [3]. For larger shipwrecks, a salvage technique named twin-barge synchronous lifting can be used. China's Shanghai Salvage Bureau successfully salvaged the integral Korean M.V. Sewol from a 44 m depth by using weight, which limits its load capacity. SAHC combines PHC and AHC to overcome these limitations, resulting in a structure that boasts both high load capacity and excellent compensating effects. Currently, high-precision compensators with large load capacities are primarily implemented using SAHC solutions. For example, Niu et al. presented an SAHC system for a 3000 m, 200-ton lifting winch, and full-scale experiments demonstrated a 92.9% displacement compensation efficiency [17]. Quan et al. performed a scale model test of an SAHC for deep-sea tethered ROV, the test results indicated that SAHC has better efficiency in dealing with load resonance at critical depth than PHC [18]. Moreover, many novel control algorithms were designed to enhance the performance of SAHC systems, such as the nonlinear controller by Do et al., the model-predictive controller by Woodacre et al., and the H infinity robust controller by Zhang et al. [19][20][21], etc. For safety and steady working, it is essential to apply SAHC in deep water claw salvage operations. However, electro-hydraulic systems will be subject to various delay factors, the most significant of which comes from measurement noise filtering. The hydraulic control systems' frequency response and the uncertainty in the sea waves can also contribute a lot. There is a need to predict the vessel's motion and implement advance heave compensation to make up for the system delays.
Based on theoretical differences, there are three distinct approaches for predicting ship motion: Kalman filtering, time series, and machine learning neural network [22]. Kalman filtering methods necessitate the accurate hydrodynamic model of the vessel, which limits their practical implementation [23,24]. Time-series methods are more suitable for engineering predictions, as they rely only on historical and current motion data of the vessel rather than its system model. Several time-series models, including the classic auto-regressive (AR) model, and its extensions such as auto-regressive moving average (ARMA) and autoregressive integrated moving average (ARIMA), are widely used [25][26][27]. However, ship motion exhibits non-stationary and nonlinear features, which conflict with the assumptions of stationary and explicit relationships between input and output datasets [28]. Neural networks possess the ability to effectively fit nonlinear systems without prior knowledge and can also manage multi-input multi-output predictions. When compared to traditional feed-forward neural networks, recurrent neural networks (RNNs), particularly those represented by long short-term memory (LSTM), demonstrate superior performance in capturing correlations between input motion sequences [29,30]. The studies in predicting semi-submersible and FPSO motion based on LSTM neural network presented by Guo et al. showed very good performance [31][32][33].
In this paper, a multi-claw shipwreck salvaging system for 600 m deep water with LSTM-based motion predicting SAHCs is presented. The SAHCs aimed to achieve a stable shipwreck salvage process for deep water. The LSTM-based neural network was mainly used to predict the barge's heave and pitch motions in the next few seconds and tackle time delays raised by hydraulic and noise filtering systems. In Section 2, the working principle of the salvage system are described, and each part is mathematically modeled. In addition, the barge's heave and pitch motion data under nine different sea conditions are also obtained in Section 2 through hydrodynamic simulation, for network training and simulation inputting. In Section 3, the predictive neural network model is designed and tested for finding the best structure. Finally, numerical simulations based on mathematical models, including the shipwreck's 2-DOF dynamic, lifting slings, SAHCs, and controller are carried out for validation and evaluation purposes in Section 4. From the simulation results, some key contributions could be drawn out:

•
The system delays introduced by the hydraulic SAHC system and the noise filtering system seriously affect the compensation of the SAHCs to the shipwreck motion; • The delay introduced by noise filtering is commonly significant. In this study, the hydraulic control system alone has a delay of 0.6 s, which can reach more than 3 s when filtering is present; • When facing deep water, the effect of PHC is insignificant because the lifting slings are already sufficiently flexible. However, applying SAHC can effectively reduce the shipwreck's motion; • The proposed LSTM-based neural network can effectively predict the heave and pitch motions of the barge 5 s into the future based on the historical data, which is sufficient for the compensation system; • Motion prediction is necessary for systems lagged by noise filtering. SAHC without motion prediction is invalid when the noise exists.

System Modeling and Analysis
Establishing a mathematical model of a system is fundamental for conducting numerical simulations. This section provides a detailed description of the salvage system and establishes mathematical models for each component to facilitate subsequent numerical simulations. Additionally, this section includes a hydrodynamic analysis to obtain the motion data of the barge in various sea states. The resulting datasets will be used to train the neural network and serve as inputs for the numerical simulations in subsequent sections. Figure 1 shows a schematic diagram of the multi-claw salvage system with SAHCs. The system consists of a salvage barge anchored to the water surface above the target shipwreck, deploying salvage claws at spaced intervals in the longitudinal direction. A synchronous strand jack lifting system, similar to that used in the salvage operations of the M.V. Sewol and the Kursk submarine, is used for shipwreck lifting [4,7]. This system comprises multiple hydraulic jacks that can work independently or be synchronized under computer control and is commonly used in the construction and marine industries [34]. However, this article mainly focuses on the predictive heave compensation system's effect on a 600 m depth payload, disregarding the lifting effect and not considering the hydraulic jacks' function. The proposed LSTM-based neural network can effectively predict the heave and pitch motions of the barge 5 s into the future based on the historical data, which is sufficient for the compensation system; • Motion prediction is necessary for systems lagged by noise filtering. SAHC without motion prediction is invalid when the noise exists.

System Modeling and Analysis
Establishing a mathematical model of a system is fundamental for conducting numerical simulations. This section provides a detailed description of the salvage system and establishes mathematical models for each component to facilitate subsequent numerical simulations. Additionally, this section includes a hydrodynamic analysis to obtain the motion data of the barge in various sea states. The resulting datasets will be used to train the neural network and serve as inputs for the numerical simulations in subsequent sections. Figure 1 shows a schematic diagram of the multi-claw salvage system with SAHCs. The system consists of a salvage barge anchored to the water surface above the target shipwreck, deploying salvage claws at spaced intervals in the longitudinal direction. A synchronous strand jack lifting system, similar to that used in the salvage operations of the M.V. Sewol and the Kursk submarine, is used for shipwreck lifting [4,7]. This system comprises multiple hydraulic jacks that can work independently or be synchronized under computer control and is commonly used in the construction and marine industries [34]. However, this article mainly focuses on the predictive heave compensation system's effect on a 600 m depth payload, disregarding the lifting effect and not considering the hydraulic jacks' function. As mentioned earlier, a vessel operating in sea waves will experience motion in six DOFs. Generally, the anchoring system can limit the salvage barge's translational and rotational DOFs parallel to the water surface, such as surge, sway, and yaw, but it is unable As mentioned earlier, a vessel operating in sea waves will experience motion in six DOFs. Generally, the anchoring system can limit the salvage barge's translational and rotational DOFs parallel to the water surface, such as surge, sway, and yaw, but it is unable to effectively restrict heave, roll, and pitch. Since the lifting devices on the barge are distributed longitudinally, the heave and pitch of the barge will cause a more significant vertical displacement at each lifter point. Therefore, an SAHC is installed between each strand jack and the barge deck. The compensation system will measure the real-time heave and pitch motions of the barge, calculate the vertical displacement of each lifting point, and control the SAHC cylinders to action. The cylinders will adjust their length to reverse the displacement caused by the heave and pitch motions, ensuring that the lifters remain stable during the salvaging process.

Claw Salvaging System
This study considers a shipwreck model with a submerged weight of 2500 tons and dimensions of 90 × 20 × 8 m (L w × B w × H w ). Nine salvage claws are symmetrically distributed along the longitudinal direction with a 10 m interval for salvage. Each claw weighs 240 tons and can provide a load capacity of 500 tons. Each lifting sling consists of eight 50 mm wire ropes, with a total weight of approximately 54 tons for the 600 m length. Therefore, the static load of each lifting sling is 518 tons, and the static load of each SAHC and lifter needs to be added to the sling weight, which is a total of 572 tons. To ensure safe operation, a salvage barge similar to the one used in the Sewol ferry salvage operation was chosen, which has dimensions of 140 × 56 × 8.88 m (L b × B b × H b ) and a displacement of 26,159 tons, with more specific parameters recorded in [4].

Mathematical Modeling
To perform a numerical simulation of the system, it is necessary to establish a mathematical model that can accurately describe the system's dynamic and motion laws. The salvage system consists of two rigid bodies: the salvage barge and the shipwreck. In the simulation, the heave and pitch motions of the barge, which are obtained from the hydrodynamic analysis, will serve as the input signals for the numerical simulation. The motion of the shipwreck, sling tensions, and compensation systems will be iteratively calculated in response to barge motion inputs. The main focus of the simulation results will be the heave and pitch motions of the shipwreck and the tension variations in the slings.
Before establishing the mathematical model, certain simplifying assumptions should be considered:

1.
Neglecting the dynamic effect of the shipwreck on the barge motion, since the barge has a larger inertia; 2.
Considering the lifting sling as a linear spring model without banding and tilting; 4.
Ideal gas with isothermal compression in the accumulators; 5.
Only the heave and pitch motions are considered for both the barge and shipwreck.

Barge-Shipwreck Motion Analysis
As shown in Figure 2, the barge and the shipwreck have their local coordinate systems, represented as X b O b Z b and X w O w Z w , respectively. The heave displacements relate to the initial time and are denoted as z b (t) and z w (t) for the barge and the shipwreck, respectively. The pitch angles are denoted as θ b (t) and θ w (t), respectively. The origin positions of all lifter points in X b O b Z b and the positions of all lifted points in X w O w Z w are assumed to be known and denoted as where the superscript represents the number of the lifting sling, and the subscript represents the position component.

Lifting Sling Tensions
Each lifting sling performs as a linear spring model, whose tension should relate to its elongation. Due to the assumption that lifting slings remain vertical, each elongation at any time only equals the differential between the vertical displacements of its top and lower end-point. Denoting the compensation displacements of SAHCs are xc = [xc 1 , xc 2 , …, xc i ] T , then the elongations of all slings can be expressed as where ΔBz are the vertical displacements of the points B related to its origin point Bo, and the same for ΔWz. They can be calculated by Then, the sling tensions are expressed as where ks is the equivalent stiffness of a single lifting sling.

Shipwreck Heave and Pitch Dynamics
The shipwreck is subjected to four main forces: buoyancy, gravity, sling tensions, and water resistance. During the lifting process, uneven sling tensions will cause translational When the barge and shipwreck motions occur, the new positions can be calculated by where T is the spatial transformation matrix. The term 1 = [1 1 . . . 1] T is one's vector with i elements, whose purpose is to homogenize the position matrices B o and W o , allowing them to undergo heave transformations by T matrix. It should be emphasized that the vacancies in the matrix are all 0, with omission for brevity. The spatial transformation matrix T includes heave and pitch transformations and is a function of the heave displacement and pitch angle, that is

Lifting Sling Tensions
Each lifting sling performs as a linear spring model, whose tension should relate to its elongation. Due to the assumption that lifting slings remain vertical, each elongation at any time only equals the differential between the vertical displacements of its top and lower end-point. Denoting the compensation displacements of SAHCs are x c = [x c 1 , x c 2 , . . . , x c i ] T , then the elongations of all slings can be expressed as where ∆B z are the vertical displacements of the points B related to its origin point B o , and the same for ∆W z . They can be calculated by Then, the sling tensions are expressed as where k s is the equivalent stiffness of a single lifting sling.

Shipwreck Heave and Pitch Dynamics
The shipwreck is subjected to four main forces: buoyancy, gravity, sling tensions, and water resistance. During the lifting process, uneven sling tensions will cause translational and rotational accelerations in the heave and pitch motions. Firstly, the dynamic equation describing the heave motion of the shipwreck can be given by where k add is the additional mass factor, m w is the mass of the shipwreck, D z is the drag coefficient, F b is the buoyancy, and g is the acceleration due to gravity. The drag force in the heave direction is proportional to the square of an object's heave velocity. It also depends on the water density, ρ sea , and the projected area perpendicular to the object's velocity direction. In fluid mechanics, the drag force is mainly comprised of pressure drag resulting from the difference in pressure between the front and back of the object, and a portion of the friction drag from the sides. The drag coefficient is given by where C D is a shape coefficient. The dynamic equation describing the shipwreck's pitch motion can be given as where I w is the moment of inertia for the pitch motion of the shipwreck, D r is the drag torque of pitch motion, and T is the torque vector on the shipwreck's rotation center caused by the sling tensions.
The sling tension torque can be expressed by where n x = [1 0] T is a normal vector along the x-axis, and is the Hadamard product, which multiplies two vectors element-wise. Since torque is related to both force and the length of the moment arm, the shipwreck will experience different values of drag torque at different turning radii. In order to calculate this, the total drag torque will be obtained through the integration of the drag torque at each turning radius. For an infinitesimal element of length dr located at a distance r from the center of the shipwreck's pitch rotation, its normal velocity is Then, its normal drag force can be expressed as By substituting the normal velocity, its drag torque can be expressed as Finally, the pitch drag torque can be integrated as from which D r = 1/64C D ρ sea B w L w 4 can be obtained.

SAHC
A single SAHC system consists of two integrated cylinders for load bearing, an active hydraulic system with a 3-position 4-way proportional valve for continuous flow rate control, and a passive power system with multiple gas accumulators, as illustrated in Figure 3. The integrated cylinder has a compact structure with three isolated chambers, two active chambers with the same effective areas, and a passive chamber. The active chambers are linked to the proportional valve for active displacement control, while the passive chamber is connected to gas accumulators for payload bearing. The hydraulic system as a whole is divided into a passive part and an active part. The working pressure of the passive chambers and accumulators is mainly generated by gas compression, which is caused by the displacement of the cylinder. According to Boyer's law, that the state of an adiabatic gas can be expressed as P1V1 n = P2V2 n , the passive working pressure can be derived as where P0 is the initial pressure of the accumulators, V0 is the total gas volume in the accumulators, Ap is the effective area of the passive chamber, and n is the adiabatic index.
The initial pressure of the accumulators should support the combined weight of the shipwreck mw and the lifting sling ms, which is The active part functions as a cylinder system controlled by a proportional valve, enabling continuous regulation of the speed and motion direction of the cylinder by adjusting the valve opening. The area of each active chamber is denoted as Aa, and the oil pressure and flow rate of the inlet chambers are denoted as P1 and q1, respectively. The oil pressure and flow rate of the outlet chambers are denoted as P2 and q2, respectively. The positive direction of the flow rate is defined as the flow direction when cylinder extension (xc > 0). Then, considering the oil compression, the flow continuity equations of two active chambers can be expressed as where V1 = V10 + Aaxc and V2 = V20 − Aaxc are the oil volumes of the inlet and outlet chambers, V10 = V20 are the initial oil volumes of the inlet and outlet chambers, and βe is the oil bulk modulus.
Additionally, the flow rates across the proportional valve are related to the valve opening xv, which can be expressed as where Cd is the orifice flow coefficient, ω is the throttle area gradient, ρoil is the oil density, and sgn(·) is the sign function. The hydraulic system as a whole is divided into a passive part and an active part. The working pressure of the passive chambers and accumulators is mainly generated by gas compression, which is caused by the displacement of the cylinder. According to Boyer's law, that the state of an adiabatic gas can be expressed as P 1 V 1 n = P 2 V 2 n , the passive working pressure can be derived as where P 0 is the initial pressure of the accumulators, V 0 is the total gas volume in the accumulators, A p is the effective area of the passive chamber, and n is the adiabatic index.
The initial pressure of the accumulators should support the combined weight of the shipwreck m w and the lifting sling m s , which is The active part functions as a cylinder system controlled by a proportional valve, enabling continuous regulation of the speed and motion direction of the cylinder by adjusting the valve opening. The area of each active chamber is denoted as A a , and the oil pressure and flow rate of the inlet chambers are denoted as P 1 and q 1 , respectively. The oil pressure and flow rate of the outlet chambers are denoted as P 2 and q 2 , respectively. The positive direction of the flow rate is defined as the flow direction when cylinder extension (x c > 0). Then, considering the oil compression, the flow continuity equations of two active chambers can be expressed as where V 1 = V 10 + A a x c and V 2 = V 20 − A a x c are the oil volumes of the inlet and outlet chambers, V 10 = V 20 are the initial oil volumes of the inlet and outlet chambers, and β e is the oil bulk modulus. Additionally, the flow rates across the proportional valve are related to the valve opening x v , which can be expressed as where C d is the orifice flow coefficient, ω is the throttle area gradient, ρ oil is the oil density, and sgn(·) is the sign function.
Since the response speed of the spool is significantly faster than the action frequency of the hydraulic system, the dynamic characteristics of the spool can be neglected. The pressures in the two chambers can be determined by solving a first-order nonlinear differential equation system that combines the continuity equations of the hydraulic cylinder and the flow equations of the valve, concerning the piston displacement x c and the valve opening x v . These equations can be solved iteratively in the numerical simulation.
Finally, the dynamic equation that describes the piston motion of the SAHC can be expressed as m c ..
where m c is the total mass of the piston and attachments, and b c is the damping coefficient of the compensator. Afterward, the compensating displacements of all the SAHCs will continue to update the sling tensions, completing the closed loop of the numerical calculation.

Barge Motion Hydrodynamic Analysis
The objective of the hydrodynamic analysis is to generate time-series data of the salvage barge's heave and pitch motions under various sea conditions. The majority of these data will be used to train a motion predictive LSTM neural network, while the remaining data will serve as input for the numerical simulation of the barge's motion. Figure 4 illustrates the chosen sea conditions according to the actual wave scatter statistics and their dataset purposes, where the wave parameters are described by JONSWAP [35]. The sequence data for each sea condition will comprise 2000 s of time-series data for the barge's heave and pitch motions, sampled at intervals of 0.1 s.
Since the response speed of the spool is significantly faster than the action fre of the hydraulic system, the dynamic characteristics of the spool can be neglect pressures in the two chambers can be determined by solving a first-order nonlin ferential equation system that combines the continuity equations of the hydraulic and the flow equations of the valve, concerning the piston displacement xc and th opening xv. These equations can be solved iteratively in the numerical simulation Finally, the dynamic equation that describes the piston motion of the SAHC expressed as where mc is the total mass of the piston and attachments, and bc is the damping co of the compensator.
Afterward, the compensating displacements of all the SAHCs will continue to the sling tensions, completing the closed loop of the numerical calculation.

Barge Motion Hydrodynamic Analysis
The objective of the hydrodynamic analysis is to generate time-series data of vage barge's heave and pitch motions under various sea conditions. The majority data will be used to train a motion predictive LSTM neural network, while the rem data will serve as input for the numerical simulation of the barge's motion. Figure trates the chosen sea conditions according to the actual wave scatter statistics a dataset purposes, where the wave parameters are described by JONSWAP [35]. quence data for each sea condition will comprise 2000 s of time-series data for the heave and pitch motions, sampled at intervals of 0.1 s. In the hydrodynamic analysis, only the head sea condition is applied, since focus on the heave and pitch motions of the barge. For simulated shipwreck w static downward force equal to the shipwreck gravity is exerted under the barge. tion, a four-point mooring system is also applied to keep the barge stable [36]. Oth parameters of the barge and the mooring system are listed in Table 1 below.  Figure 5 shows the response amplitude operators (RAOs) of the salvage barg In the hydrodynamic analysis, only the head sea condition is applied, since we just focus on the heave and pitch motions of the barge. For simulated shipwreck weight, a static downward force equal to the shipwreck gravity is exerted under the barge. In addition, a four-point mooring system is also applied to keep the barge stable [36]. Other major parameters of the barge and the mooring system are listed in Table 1 below.  Figure 5 shows the response amplitude operators (RAOs) of the salvage barge's motions in different wave periods, obtained through hydrodynamic analysis. It is observed that the pitch motion exhibits a peak value at around 12 s, indicating its significant influence during this wave period. Although time-domain motion figures can also be provided, due to their vast number only the figures of the testing set are presented in Figure 6. that the pitch motion exhibits a peak value at around 12 s, indicating its significant influence during this wave period. Although time-domain motion figures can also be provided, due to their vast number only the figures of the testing set are presented in Figure 6.

LSTM-Based Barge Motion Prediction
The LSTM neural network is an upgraded version of the traditional recurrent neural network (RNN). Unlike feed-forward neural networks, the traditional RNN can utilize its previous step information as internal memory for the current network. This allows it to extract time features from the input sequence, making it more suitable for time-series prediction. Its parameter size is only related to the feature size of the sequential input data, but not the time length, giving it the advantage of allowing different sequential lengths in the same network. However, the information of the data far from now may be lost in the internal memory with each iteration, and problems such as gradient vanishing and exploding may occur during the backpropagation process, decreasing the accuracy and applicability of the traditional RNN. To address these issues, long short-term memory (LSTM) was proposed, with the key improvement being the addition of a memorization and forgetting mechanism in the recurrent processing.

LSTM-Based Motion Predictive Neural Network
The LSTM is a variant of RNN which has three tunable gates: the input gate, the forget gate, and the output gate [37]. As shown in Figure 7, the input gate, denoted by it, determines which information from the input should be added to the cell state, while the that the pitch motion exhibits a peak value at around 12 s, indicating its significant influence during this wave period. Although time-domain motion figures can also be provided, due to their vast number only the figures of the testing set are presented in Figure 6.

LSTM-Based Barge Motion Prediction
The LSTM neural network is an upgraded version of the traditional recurrent neural network (RNN). Unlike feed-forward neural networks, the traditional RNN can utilize its previous step information as internal memory for the current network. This allows it to extract time features from the input sequence, making it more suitable for time-series prediction. Its parameter size is only related to the feature size of the sequential input data, but not the time length, giving it the advantage of allowing different sequential lengths in the same network. However, the information of the data far from now may be lost in the internal memory with each iteration, and problems such as gradient vanishing and exploding may occur during the backpropagation process, decreasing the accuracy and applicability of the traditional RNN. To address these issues, long short-term memory (LSTM) was proposed, with the key improvement being the addition of a memorization and forgetting mechanism in the recurrent processing.

LSTM-Based Motion Predictive Neural Network
The LSTM is a variant of RNN which has three tunable gates: the input gate, the forget gate, and the output gate [37]. As shown in Figure 7, the input gate, denoted by it, determines which information from the input should be added to the cell state, while the

LSTM-Based Barge Motion Prediction
The LSTM neural network is an upgraded version of the traditional recurrent neural network (RNN). Unlike feed-forward neural networks, the traditional RNN can utilize its previous step information as internal memory for the current network. This allows it to extract time features from the input sequence, making it more suitable for time-series prediction. Its parameter size is only related to the feature size of the sequential input data, but not the time length, giving it the advantage of allowing different sequential lengths in the same network. However, the information of the data far from now may be lost in the internal memory with each iteration, and problems such as gradient vanishing and exploding may occur during the backpropagation process, decreasing the accuracy and applicability of the traditional RNN. To address these issues, long short-term memory (LSTM) was proposed, with the key improvement being the addition of a memorization and forgetting mechanism in the recurrent processing.

LSTM-Based Motion Predictive Neural Network
The LSTM is a variant of RNN which has three tunable gates: the input gate, the forget gate, and the output gate [37]. As shown in Figure 7, the input gate, denoted by i t , determines which information from the input should be added to the cell state, while the forget gate f t controls which information should be discarded from the cell state. The output gate o t regulates how the information in the cell state should affect the output at the next time step. With the cooperation of these three gates, the LSTM network can retain and forget the previous data information, and decide which information to add or output based on the current input data, thus better handling long-term dependencies in time series. The formulas of an LSTM cell are shown below: where W and b are the weights and bias matrices of a network cell, respectively, σ(·) is the sigmoid active function, g t is the cell gate, c t is a recurrent cell state that is responsible for recording long-term relationships, and h t is the hidden state and also the cell output. For each W and b, the first subscript annotates the vector it multiplies, with x representing the input vector x and h representing the hidden state h. The second subscript indicates which gate it belongs to, including i (input gate), f (forget gate), g (cell gate), and o (output gate). forget gate ft controls which information should be discarded from the cell state. The output gate ot regulates how the information in the cell state should affect the output at the next time step. With the cooperation of these three gates, the LSTM network can retain and forget the previous data information, and decide which information to add or output based on the current input data, thus better handling long-term dependencies in time series. The formulas of an LSTM cell are shown below: where W and b are the weights and bias matrices of a network cell, respectively, σ(·) is the sigmoid active function, gt is the cell gate, ct is a recurrent cell state that is responsible for recording long-term relationships, and ht is the hidden state and also the cell output.   Figure 8 illustrates the structure of the proposed LSTM-based motion predictive neural network. For motion prediction, we expect the predictive neural network could accept the historical sequences of the barge's heave and pitch motions, then output their predicted future sequences. Therefore, an LSTM recurrent layer aimed at inputting the sequential vectors of each step, containing one heave and one pitch datapoint, is first constructed in the network. The input size for the LSTM layer is n × 2, which represents two features in one recurrent step and a total of n input steps. Although the sequence length allowed by LSTM is arbitrary, only the equal length is used for training and testing in this paper. By repeatedly self-iterating, the LSTM layer fully extracts the dependent information of the motion sequences and gives the final step's hidden state as the layer output, which is a vector with a length equal to the LSTM cell size. Then, containing past information, the layer output will pass three fully connected layers and be reshaped to an output vector combining the sequential predictions of the heave and pitch. For this paper, we set the predictive horizon as far as a fixed 5 s, meaning that the network outputs future  Figure 8 illustrates the structure of the proposed LSTM-based motion predictive neural network. For motion prediction, we expect the predictive neural network could accept the historical sequences of the barge's heave and pitch motions, then output their predicted future sequences. Therefore, an LSTM recurrent layer aimed at inputting the sequential vectors of each step, containing one heave and one pitch datapoint, is first constructed in the network. The input size for the LSTM layer is n × 2, which represents two features in one recurrent step and a total of n input steps. Although the sequence length allowed by LSTM is arbitrary, only the equal length is used for training and testing in this paper. By repeatedly self-iterating, the LSTM layer fully extracts the dependent information of the motion sequences and gives the final step's hidden state as the layer output, which is a vector with a length equal to the LSTM cell size. Then, containing past information, the layer output will pass three fully connected layers and be reshaped to an output vector combining the sequential predictions of the heave and pitch. For this paper, we set the predictive horizon as far as a fixed 5 s, meaning that the network outputs future sequential data of 50 points heave then 50 points pitch at one time (m = 50). By splicing the output tensor, the predictive motion sequences could be obtained. sequential data of 50 points heave then 50 points pitch at one time (m = 50). By splicing the output tensor, the predictive motion sequences could be obtained. The major layer parameters of the proposed network are listed in Table 2, where the size of the LSTM cell is 1024 and the sizes of the first two fully connected layers are 512. The size of the last fully connected layer is 100, which is used to reshape the output tensor. The trained process uses the Adam method with a decaying learning rate to ensure accuracy. The entire training set was shuffled into mini-batches and repeated training for 20 epochs, with an initial learning rate of 0.0001 and a decay of 0.4 times after every 4 epochs. Fully connected layer P × 512 5 Fully connected layer P × 512 6 Output layer P × 2m

Network Training and Testing
The datasets used in the predictive neural network are shown in Figure 4, consisting of eight sequences for training and one for testing. The test set data is not used for training due to the difficulty in obtaining on-site sea state information during actual salvaging operations. The training sets are randomly shuffled and split into input and output tensor pairs. The output tensor size is fixed at 100 elements, with 50 elements of the sequential heave and 50 elements of the sequential pitch. To evaluate the effect of input tensor length, networks with varying lengths of input sequences are first trained and tested.
The root-mean-square error (RMSE) performance of the networks was evaluated and the results are presented in Figure 9. Each evaluation was averaged over multiple training sessions. The left side of the figure shows the predictive performance of the networks with different input time sizes for varying prediction horizons, while the right side displays the corresponding error box plots. It is expected that the prediction errors of all the networks increase with the prediction horizon. The best prediction performance for heave is achieved with the input time sizes of 25 s and 30 s, while the former is better for pitch prediction. Therefore, it can be concluded that an input time size of 25 s, which represents an input length of 250 points, is more suitable for improving the prediction accuracy of the proposed neural network. The major layer parameters of the proposed network are listed in Table 2, where the size of the LSTM cell is 1024 and the sizes of the first two fully connected layers are 512. The size of the last fully connected layer is 100, which is used to reshape the output tensor. The trained process uses the Adam method with a decaying learning rate to ensure accuracy. The entire training set was shuffled into mini-batches and repeated training for 20 epochs, with an initial learning rate of 0.0001 and a decay of 0.4 times after every 4 epochs. Table 2. Layer parameters of the LSTM-based predictive neural network, with the mini-batch size denoted by p.

Network Training and Testing
The datasets used in the predictive neural network are shown in Figure 4, consisting of eight sequences for training and one for testing. The test set data is not used for training due to the difficulty in obtaining on-site sea state information during actual salvaging operations. The training sets are randomly shuffled and split into input and output tensor pairs. The output tensor size is fixed at 100 elements, with 50 elements of the sequential heave and 50 elements of the sequential pitch. To evaluate the effect of input tensor length, networks with varying lengths of input sequences are first trained and tested.
The root-mean-square error (RMSE) performance of the networks was evaluated and the results are presented in Figure 9. Each evaluation was averaged over multiple training sessions. The left side of the figure shows the predictive performance of the networks with different input time sizes for varying prediction horizons, while the right side displays the corresponding error box plots. It is expected that the prediction errors of all the networks increase with the prediction horizon. The best prediction performance for heave is achieved with the input time sizes of 25 s and 30 s, while the former is better for pitch prediction. Therefore, it can be concluded that an input time size of 25 s, which represents an input length of 250 points, is more suitable for improving the prediction accuracy of the proposed neural network.
After fixing the input length (n = 250) and the prediction length (m = 50), the predictive neural network is fully trained and the results of continuous motion prediction for the testing set are presented. Figure 10 displays the sequential input and prediction output curves at a specific moment, while Figure 11 shows the continuous rolling predictions for the barge's heave and pitch, with prediction horizons of 0.5 s, 2 s, and 5 s. Although the 5 s prediction shows some deviations at the peaks compared to the ground-truth data, it is still considered acceptable.   After fixing the input length (n = 250) and the prediction length (m = 50), the predictive neural network is fully trained and the results of continuous motion prediction for the testing set are presented. Figure 10 displays the sequential input and prediction output curves at a specific moment, while Figure 11 shows the continuous rolling predictions for the barge's heave and pitch, with prediction horizons of 0.5 s, 2 s, and 5 s. Although the 5 s prediction shows some deviations at the peaks compared to the ground-truth data, it is still considered acceptable. After fixing the input length (n = 250) and the prediction length (m = 50), the predictive neural network is fully trained and the results of continuous motion prediction for the testing set are presented. Figure 10 displays the sequential input and prediction output curves at a specific moment, while Figure 11 shows the continuous rolling predictions for the barge's heave and pitch, with prediction horizons of 0.5 s, 2 s, and 5 s. Although the 5 s prediction shows some deviations at the peaks compared to the ground-truth data, it is still considered acceptable.

Simulation Results and Analysis
In this section, the numerical simulation of the salvage system is implemented for testing the compensation and motion prediction performance. The involved numerical models were introduced in Section 2.2. The simulation parameters which have not yet been mentioned are listed in Table 3. Furthermore, the heave compensation system uses traditional PID controllers for position closed-loop control, which can ensure the basic dynamic tracking ability of the compensation cylinders.
The working process of the predictive compensation system can be summarized as follows: first, the heave and pitch signals of the barge are measured. Next, the LSTM-based neural network is used to predict the future heave and pitch values according to the historical sequential signals. Then, the predicted results are transformed into displacement compensation values for each SAHC through coordinate transformation. Finally, the controllers are ordered to perform the necessary compensation actions on the SAHCs.
It is important to reiterate that the purpose of barge motion prediction is to compensate for the hysteresis in the compensation system, which may arise from various factors such as the PID controller, hydraulic system response, dynamic characteristics of the salvage system, and filtering process of the motion measurements. However, we believe that the filtering process of the sensor has a greater impact. Therefore, in the following analysis, we will consider the effects of both situations, with and without measurement noise.

Simulation Results and Analysis
In this section, the numerical simulation of the salvage system is implemented for testing the compensation and motion prediction performance. The involved numerical models were introduced in Section 2.2. The simulation parameters which have not yet been mentioned are listed in Table 3. Furthermore, the heave compensation system uses traditional PID controllers for position closed-loop control, which can ensure the basic dynamic tracking ability of the compensation cylinders. The working process of the predictive compensation system can be summarized as follows: first, the heave and pitch signals of the barge are measured. Next, the LSTMbased neural network is used to predict the future heave and pitch values according to the historical sequential signals. Then, the predicted results are transformed into displacement compensation values for each SAHC through coordinate transformation. Finally, the controllers are ordered to perform the necessary compensation actions on the SAHCs.
It is important to reiterate that the purpose of barge motion prediction is to compensate for the hysteresis in the compensation system, which may arise from various factors such as the PID controller, hydraulic system response, dynamic characteristics of the salvage system, and filtering process of the motion measurements. However, we believe that the filtering process of the sensor has a greater impact. Therefore, in the following analysis, we will consider the effects of both situations, with and without measurement noise.

Influence of Lead/Lag Compensation
Before testing the effectiveness of predictive heave compensation, the time-delay characteristics of the SAHC system without motion prediction were analyzed. The simulation results are presented in Figure 12, which demonstrates the effect of changing the time position of the barge signal input to the SAHC system. A positive value on the horizontal axis indicates that the compensation amount lags behind the actual movement of the barge, and a negative value indicates that the compensation amount is ahead of the actual movement of the barge. By analyzing the standard deviation changes in the shipwreck motion in each corresponding case, it can be concluded that both the compensation lag and premature lead compensation can intensify the motion of the wreck. Furthermore, it was found that the minimum motion result was obtained at 0.6 s of lead compensation, rather than 0 s. This indicates that the system has a 0.6 s delay from the barge motion measurement to the SAHC's displacement acting, highlighting the importance of motion prediction and advancing compensation. Before testing the effectiveness of predictive heave compensation, the tim characteristics of the SAHC system without motion prediction were analyzed. Th lation results are presented in Figure 12, which demonstrates the effect of chang time position of the barge signal input to the SAHC system. A positive value on th zontal axis indicates that the compensation amount lags behind the actual movem the barge, and a negative value indicates that the compensation amount is ahead actual movement of the barge. By analyzing the standard deviation changes in th wreck motion in each corresponding case, it can be concluded that both the compe lag and premature lead compensation can intensify the motion of the wreck. Furthe it was found that the minimum motion result was obtained at 0.6 s of lead compen rather than 0 s. This indicates that the system has a 0.6 s delay from the barge measurement to the SAHC's displacement acting, highlighting the importance of prediction and advancing compensation.

Predictive Compensation without Measuring Noise
Based on the barge motion without noise pollution, this section simulates an pares the heave and pitch time-domain motions of the barge in different heave co sation modes: non-compensation, PHC mode, original SAHC mode without pred and SAHC mode with prediction. The results are displayed in Figure 13, from wh following conclusions can be drawn: In the absence of heave compensation, the heave and pitch motions of the ship are significant. Even with the passive mode, only the pitch motion is slightly wea This limited performance is primarily due to the reduced sling stiffness of the length, and cannot be further reduced by the PHCs.
Compared to the non-compensation condition, the original SAHC mode witho tion prediction can significantly reduce both the heave and pitch motions of th

Predictive Compensation without Measuring Noise
Based on the barge motion without noise pollution, this section simulates and compares the heave and pitch time-domain motions of the barge in different heave compensation modes: non-compensation, PHC mode, original SAHC mode without prediction, and SAHC mode with prediction. The results are displayed in Figure 13, from which the following conclusions can be drawn: time is switched to 1 s, the motions become significant, which is consistent with the results shown in Figure 12.

Predictive Compensation with Measuring Noise
In this section, it is assumed that the motion signal of the barge is contaminated by white noise and should be filtered before being input into the predictive neural network. Therefore, a second-order low-pass filter is used to filter the motion signal, and its transfer function is given by ( ) where ωn is the cut-off frequency, whose value is set as ωn = 0.8. Figure 14 presents a comparison between the original data of the barge's heave and pitch, the noisy data, and the filtered data. The filtering process introduces a delay of approximately 2.5 to 3 s to the original data. It should be noted that this delay can be further reduced by using a better filter, such as the Kalman filter. The filtered data is input into the neural network for motion prediction, and the predicted result is used as the expected compensation amount of the SAHC system. The final Figure 13. Simulation results of the barge motions without measuring noise, including the compensation conditions of non-compensation, PHC mode, SAHC mode without motion prediction (original), and SAHC mode with motion prediction (pts denotes t seconds prediction).
In the absence of heave compensation, the heave and pitch motions of the shipwreck are significant. Even with the passive mode, only the pitch motion is slightly weakened. This limited performance is primarily due to the reduced sling stiffness of the 600 m length, and cannot be further reduced by the PHCs.
Compared to the non-compensation condition, the original SAHC mode without motion prediction can significantly reduce both the heave and pitch motions of the shipwreck, with standard deviation (STD) decrements of about 67.59% and 53.77%, respectively. Furthermore, when motion predictions are applied, the motion STDs are further reduced by about 66.89% and 68%, with a 0.6 s prediction. However, when the prediction time is switched to 1 s, the motions become significant, which is consistent with the results shown in Figure 12.

Predictive Compensation with Measuring Noise
In this section, it is assumed that the motion signal of the barge is contaminated by white noise and should be filtered before being input into the predictive neural network. Therefore, a second-order low-pass filter is used to filter the motion signal, and its transfer function is given by where ω n is the cut-off frequency, whose value is set as ω n = 0.8. Figure 14 presents a comparison between the original data of the barge's heave and pitch, the noisy data, and the filtered data. The filtering process introduces a delay of approximately 2.5 to 3 s to the original data. It should be noted that this delay can be further reduced by using a better filter, such as the Kalman filter.
where ωn is the cut-off frequency, whose value is set as ωn = 0.8. Figure 14 presents a comparison between the original data of the barge's heave and pitch, the noisy data, and the filtered data. The filtering process introduces a delay of approximately 2.5 to 3 s to the original data. It should be noted that this delay can be further reduced by using a better filter, such as the Kalman filter. The filtered data is input into the neural network for motion prediction, and the predicted result is used as the expected compensation amount of the SAHC system. The final simulation results are presented in Figure 15, which includes the curves for SAHC without heave compensation (as in Figure 13), the SAHC system without motion prediction, and the predictions for 1 s, 3 s, and 4 s. The filtered data is input into the neural network for motion prediction, and the predicted result is used as the expected compensation amount of the SAHC system. The final simulation results are presented in Figure 15, which includes the curves for SAHC without heave compensation (as in Figure 13), the SAHC system without motion prediction, and the predictions for 1 s, 3 s, and 4 s.

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The delay introduced by the filtering process and the presence of noise makes it difficult for the various SAHC systems to completely compensate for the motion of the wreck. However, it was found through simulations that the best compensation effect can be achieved when the prediction time is set to 3 s. If the prediction time is greater or less than this, the compensation effect will be reduced. At this prediction time, the standard deviations of the barge motion are reduced by 44.14% and 43.19% in heave and pitch, respectively, compared to the uncompensated case. This result is lower than the ideal noise-free situation shown in Figure 13, but it is more representative of the actual engineering situation, where noise is expected. Figure 15. Simulation results of the barge motions with measuring noise, including the compensation conditions of non-compensation, SAHC mode without motion prediction (original), and SAHC mode with motion prediction (pts denotes t seconds prediction).

Conclusions
In this paper, a shipwreck salvaging system with multiple hydraulic claws, capable of operating at depths of up to 600 m, is proposed. This system incorporates SAHCs to ensure stable lifting operations. Additionally, a multivariate LSTM-based neural network is introduced for predictive compensation of barge motion. Through hydrodynamic analysis, heave and pitch motion sequences of the working barge in nine different sea conditions were obtained for neural network training and numerical simulation input. In the proposed neural network, the historical heave and pitch sequences of the barge were fed into the LSTM cell and reshaped by several fully connected layers to obtain future motion sequences. The testing results demonstrated that a historical sequential input of 25 s was the most suitable for the neural network to achieve a 5 s sequential prediction. Then, the performance of the SAHC system and the predictive neural network are tested through a The delay introduced by the filtering process and the presence of noise makes it difficult for the various SAHC systems to completely compensate for the motion of the wreck. However, it was found through simulations that the best compensation effect can be achieved when the prediction time is set to 3 s. If the prediction time is greater or less than this, the compensation effect will be reduced. At this prediction time, the standard deviations of the barge motion are reduced by 44.14% and 43.19% in heave and pitch, respectively, compared to the uncompensated case. This result is lower than the ideal noise-free situation shown in Figure 13, but it is more representative of the actual engineering situation, where noise is expected.

Conclusions
In this paper, a shipwreck salvaging system with multiple hydraulic claws, capable of operating at depths of up to 600 m, is proposed. This system incorporates SAHCs to ensure stable lifting operations. Additionally, a multivariate LSTM-based neural network is introduced for predictive compensation of barge motion. Through hydrodynamic analysis, heave and pitch motion sequences of the working barge in nine different sea conditions were obtained for neural network training and numerical simulation input. In the proposed neural network, the historical heave and pitch sequences of the barge were fed into the LSTM cell and reshaped by several fully connected layers to obtain future motion sequences. The testing results demonstrated that a historical sequential input of 25 s was the most suitable for the neural network to achieve a 5 s sequential prediction. Then, the performance of the SAHC system and the predictive neural network are tested through a numerical simulation based on the mathematical models described in Section 2. Based on the results in Section 4, the following conclusions could be drawn out:

•
Passive heave compensation has minimal effects on a shipwreck's motion at this depth; • When the SAHCs are employed without motion prediction, the standard deviations of the shipwreck motion are significantly reduced, by 67.59% in heave and 53.77% in pitch; • In the absence of measurement noise, a 0.6 s predictive compensation to counter system delay further reduces shipwreck motion by 66.89% and 68% in heave and pitch, respectively, compared to the non-prediction case; • SAHCs without prediction exhibit poor compensation effects in the presence of noise pollution in barge motion measurement; • In such scenarios, a 3 s predictive compensation can achieve the best compensating performance, resulting in a reduction in shipwreck motion to 44.14% in heave and 43.19% in pitch.
These results underscore the indispensability of motion prediction in deep-sea shipwreck salvage operations and highlight the good performance of the proposed LSTM-based predictive neural network and SAHC system. In conclusion, the efficacy of the proposed predictive SAHC system for a 600 m multi-claw shipwreck salvaging system has been demonstrated, with potential implications for real-world engineering practices. Future endeavors will entail conducting factory tests in a laboratory wave pool to further validate the system's capabilities. Furthermore, collecting more motion data from actual barges at sea, to enhance the motion predictive network's reliability, is work that this paper did not address and will be incorporated into future research.