Estimating the Purse Seine Net Geometry during a Hauling Operation Using a Data Assimilation Method

Abstract

The dynamics of fishing nets can be estimated by modeling and numerically computing the forces acting on them. However, the dynamic models of fishing nets are highly nonlinear owing to the significant influence of hydrodynamic forces acting on the net. Therefore, if there are unknown parameters that define the state of motion in the model, it is often difficult to achieve high accuracy in the numerical simulations of fishing gear and evaluate its dynamics. To address this issue, a method is proposed for estimating these unknown parameters by integrating a nonlinear Kalman filter into a fishing net dynamics model. This study aimed to estimate the hauling velocity of large- and medium-sized purse seine fishing nets, which can be a challenging parameter to measure. The calculations are based on the data obtained from a research operation conducted by the Marine Fisheries Research and Development Center in 2019 using the purse seine fishing vessel “Taikei Maru No. 1”. The time series of the hauling-net velocity was estimated based on the results of the estimation experiment. These results allowed the estimation of the hauling velocity and calculation of the net dynamics during the hauling process. This shows that net dynamics simulation is possible even with unknown parameters.

1. Introduction

The most commonly utilized types of fishing gear at fishing sites are those employing nets, such as the purse seine and trawl nets [1,2]. Nevertheless, despite the prevalence of the use of net fishing gear, the movements and geometries of these nets are not readily discernible, rendering their operation arduous. In addition, nets are constructed from flexible materials, such as netting and ropes, which deform significantly when submerged and, therefore, require a high degree of expertise to operate effectively. To address these issues, several research institutions have devised methodologies for visualizing the geometry and dynamics of the net fishing gear using mathematical models. O’Neill conducted a numerical study of the trawl cod-end geometry [3]. Lee successfully visualized the trawl and seine nets using the mass-of-springs method [4]. Lader et al. investigated the hydrodynamic forces acting on a net sheet from waves and currents [5]. Balash et al. researched the hydrodynamic characteristics and added the mass of plane nets in steady and oscillating flows [6]. Bi et al. investigated the drag force changes caused by biofouling [7]. Martin et al. proposed a Lagrangian approach for coupled numerical simulations in the analysis of flow around a net, albeit restricted to a fixed net [8]. Moreover, our research group has successfully calculated the dynamics and loads of the net fishing gear using a lumped mass model [9,10,11,12]. To create a numerical model of the fishing gear, we developed the NaLA system, which comprises three main components: a computer-aided design (CAD) component for creating a 3D model of the design of the fishing gear, a numerical kernel component for numerically computing the equation of motion using the model, and a graphical component for visualizing the computational results using OpenGL. The NaLA system was employed to analyze the underwater dynamics of a range of fishing gear, including trawl nets, purse seines, gill nets, drift nets, and net cages, during operation [12,13,14].

Furthermore, the data regarding the operation of warps to apply tension to the net fishing gear, the location of the towing vessel, and environmental information, such as the current vectors, are essential for calculating the hydrodynamic forces acting on the net fishing gear [15,16]. Consequently, if this information is not available, the precision of the numerical simulation is compromised. The industry strongly advocates the development and implementation of technologies to automatically control fishing nets and achieve the desired underwater geometry for designers and operators [17]. Hence, our research group proposed a methodology for approximating unknown parameters within a mathematical model of net dynamics with the objective of regulating the net to the desired state by integrating state-estimation techniques and the NaLA system [18]. This approach can be extended to estimate the missing operational and flow field data, which are essential for numerical simulations, by applying an analogous algorithm. A purse seine gear is distinguished by its dynamics. In the purse seine operation, a net is deployed to enclose the shoal during the shooting phase. Subsequently, during the hauling phase, the purse seine is tightened by hauling its wire, and the shoal is pulled toward the hull as the net is brought inside the vessel. Given the rapid changes in netting dynamics during the shooting stage, the development of simulation technology for netting dynamics using the NaLA system has focused on visualizing these dynamics.

Takagi et al. employed the NaLA system to visualize the net dynamics from shooting to pursing during an actual netting operation and examined the effect of mesh size on sinking dynamics [14]. Lee et al. proposed an optimal shooting point for fish movement based on the results of numerical simulations [19]. Tang et al. corroborated the alteration in net dynamics during shooting due to the discrepancy in the mesh size and direction of the current in tank experiments [20]. Research has also been conducted to improve the performance of the numerical simulations of purse seine nets. Kim et al. examined the differences in dynamics under different current conditions [21]. Zhou et al. examined the effects of currents on a net and proposed an optimal design method [22]. These studies only calculated the dynamics of a purse seine net from shooting to the end of pursing; the calculations of the dynamics during hauling have not been realized in previous studies.

Nevertheless, the net dynamics during the hauling stage have yet to be visualized. This is because of the lack of a device, such as a wire length meter, to measure the amount of net hauled in the time series. This hinders the determination of the submerged netting area. Therefore, this study introduces a net-hauling algorithm that incorporates net elements into a simulation system for the purse seines by using a conventional NaLA system. The objective is to examine the net dynamics during the hauling stage by estimating the hauling velocity, thereby approximating the numerical simulation results to the actual net area dynamics. In this implementation, state-estimation techniques are integrated with the NaLA system, which allows the estimation of unknown parameters in a mathematical model of net dynamics. Therefore, this study assessed the potential of extending this integration technique. Previous studies have only calculated the net dynamics from shooting to the end of pursing. However, in the field of fisheries, an estimation of the net dynamics during the hauling process is also required. Therefore, in this study, we estimated the hauling velocity, which is difficult to measure, and also newly estimated the net dynamics in the hauling process. In other words, we attempted to estimate the dynamics of the net with unknown parameters. The current simulation technology does not allow the calculation of net dynamics during the hauling of purse seine nets because of the inability to measure hauling velocity. To address this limitation, data assimilation techniques were employed to estimate the hauling velocity and reproduce the actual net dynamics during the hauling process.

2. Materials and Methods

2.1. Numerical Model for Estimating the Deformation of a Purse Seine Net

In this study, we employed the same numerical dynamic model of the fishing nets used in the NaLA system developed by our research group. This is a lumped-mass model in which the net fishing gear is represented by lumped-mass points and massless springs. The equation of motion for these mass points is expressed as Equation (1):

$$\left({\mathit{M}}_n+{\sum }_{k=1}^2\left[{\mathit{C}}_{nk}∆{\mathit{M}}_{nk}{\mathit{C}}_{nk}^T\right]\right){\mathit{\alpha }}_n={\mathit{T}}_n+{\sum }_{k=1}^2\left({\mathit{C}}_{nk}{\mathit{F}}_{nk}\right)+{\mathit{W}}_n+{\mathit{B}}_n,$$

(1)

where M_n and ΔM_nk are used to denote the mass and the added mass of the mass point n. The matrix C_nk is used to transform the local coordinate system into a global coordinate system. The symbol a_n denotes the acceleration of the mass n. The symbols T_n, F_nk, W_n, and B_n denote the tension, hydrodynamic force, gravitational force, and buoyancy force acting on the mass n, respectively.

The NaLA system was developed with a particular focus on the calculation of net dynamics from the shooting stage to the end of pursing. This study introduces a novel algorithm for calculating net-hauling dynamics. In purse seine operations, the net is hauled at an arbitrary velocity using a net-hauling apparatus such as a power block. The nets are returned to the deck for storage. The aforementioned hauling process indicates whether each mass point is stored in the vessel. In each calculation step, the length of the hauled net, l (m), is established as the reference length to determine the mass point that should be stored in the vessel. The length of the net hauled, denoted by l_t, at time t (s) is expressed in Equation (2) via the net-hauling velocity v_k at computation time t, with a time step of Δt (s).

$$l_t=\sum _{k=0}^t{v}_k·∆t$$

(2)

When the length of the net hauled is l, the position coordinates of the mass point i, whose horizontal distance from the vessel is equal to or less than l, are set to the same value as the position coordinates of the vessel (Figure 1). Given that the total lengths of the floating and the sinker ropes differ in an actual net, it is not possible to haul them at the same velocity. Instead, the crew members must adjust their velocities to approximate uniformity. For simplicity, it is assumed that the floating and sinker ropes do not undergo expansion or contraction, and that the net is hauled in a uniform manner on both the float and sinker rope sides for the same length as the float rope.

2.2. Integrating the Ensemble Kalman Filter into the NaLA System

The hauling net velocity is estimated as an unknown parameter by integrating the NaLA system using a data assimilation method. The estimation process is illustrated in Figure 2. The geometry of the net from time t to time t + 1 is calculated using a numerical dynamic model of the NaLA system, which is employed as a simulation value in the data assimilation method. The actual net is observed at three points in its center, with depth sensors installed for this purpose. Subsequently, the hauling net length is calculated based on the aforementioned simulation and the measurement values, along with the estimated hauling net velocity derived from the data assimilation method. The hauling net length is used to calculate the net dynamics from the time t to the time t + 1.

An ensemble Kalman filter (EnKF) was employed as the data assimilation method to estimate the control parameters [23,24,25]. In the context of the EnKF, the state vector is expressed as in Equation (3) with the introduction of an expanded system.

$${\mathit{z}}_t={\left[{{\mathit{x}}_t}^T, {\theta }_t\right]}^T$$

(3)

The unknown parameter, designated as θ_t, represents the velocity of the hauling net. In this study, the hauling net velocity fluctuated and was assumed to be updated sequentially. The system model is expressed as follows:

$${\mathit{z}}_t={\mathit{f}}_t\left({\mathit{z}}_{t-1}, {\mathit{v}}_t\right).$$

(4)

In Equation (4), the function f_t represents the net dynamics model of the NaLA system, whereas the vector v_t denotes a normally distributed system noise vector with a mean of 0 and a variance of σ_v². The observation model is presented in Equation (5), which depicts a normally distributed observation noise vector with a mean of 0 and a variance of σ_w².

$${\mathit{y}}_t=\left[\begin{array}{cc}\mathit{I}& \mathbf{0}\end{array}\right]{\mathit{z}}_t+{\mathit{w}}_t=\mathit{H}{\mathit{z}}_t+{\mathit{w}}_t$$

(5)

An EnKF was applied to the system model expressed in Equation (4), and the observation model is represented in Equation (5). An ensemble of system noise was generated using random numbers, and the ensemble of N state vectors was then updated in the prediction step using Equation (6).

$${{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)}={\mathit{f}}_t\left({{{\widehat{\mathit{z}}}^{-}}_{t-1}}^{\left(i\right)}, {{\mathit{v}}_t}^{\left(i\right)}\right)$$

(6)

The predicted value of z_t⁽ⁱ⁾ is given by the function f_t of the previous value z_t⁽ⁱ⁻¹⁾ and the current value v_t⁽ⁱ⁾. Subsequently, the unknown hauling velocity parameter is estimated through the filtering step, as outlined in Equations (7)–(11):

$$\overline{{{\widehat{\mathit{z}}}^{-}}_t}={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)},$$

(7)

$${{\check{\mathit{w}}}_t}^{\left(i\right)}={{\mathit{w}}_t}^{\left(i\right)}-{\displaystyle \frac{1}{N}}{\sum }_{j=1}^N{{\mathit{w}}_t}^{\left(j\right)}.$$

(8)

R_t is calculated as follows:

$${\widehat{\mathit{R}}}_t={\displaystyle \frac{1}{N-1}}{\sum }_{j=1}^N{{\check{\mathit{w}}}_t}^{\left(j\right)}{{\check{\mathit{w}}}_t}^{\left(j\right)T}.$$

(9)

K_t can be expressed as follows:

$${\mathit{K}}_t=\left({\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^N\left({{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)}-\overline{{{\widehat{\mathit{z}}}^{-}}_t}\right){\left(\mathit{H}{{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)}-\mathit{H}\overline{{{\widehat{\mathit{z}}}^{-}}_t}\right)}^T\right){\left({\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^N\left(\mathit{H}{{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)}-\mathit{H}\overline{{{\widehat{\mathit{z}}}^{-}}_t}\right){\left(\mathit{H}{{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)}-\mathit{H}\overline{{{\widehat{\mathit{z}}}^{-}}_t}\right)}^T+{\widehat{\mathit{R}}}_t\right)}^{-1}.$$

(10)

Thus, the final term is expressed as follows:

$${{\widehat{\mathit{z}}}_t}^{\left(i\right)}={{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)}+{\mathit{K}}_t\left({\mathit{y}}_t+{{\check{\mathit{w}}}_t}^{\left(i\right)}-\mathit{H}{{{\widehat{\mathit{z}}}^{-}}_t}^{\left(i\right)}\right).$$

(11)

Subsequently, as indicated in Equation (12), the hauling velocity was employed in the calculation of the NaLA system to regulate the net dynamics during the hauling phase of the simulation.

$${\mathit{X}}_t={\mathit{f}}_t\left({\mathit{X}}_{t-1}, {\widehat{\theta }}_{t-1}\right)$$

(12)

In Equation (12), X_t−1 represents the three-dimensional position vector of all the mass points in the numerical net model employed in the NaLA system. In addition, θ_t−1 denotes the estimated unknown hauling velocity parameter.

2.3. Operation Data

The operational data employed in this study were procured from a research operation conducted on an overseas purse seine fishing vessel, Taikei Maru No. 1, in 2019 by the Marine Fisheries Research and Development Center. The positions of the vessel and the skiff boat were recorded using GPS sensors throughout the operation. The lengths of the purse wire, towing wire pay-out, and roll-up were calculated by recording the number of rotations of each winch. The current velocity and direction, which are necessary for calculating the hydrodynamic forces acting on the purse seine net, were recorded using a current meter fitted to the vessel. The average values between the start of the shooting and the end of the pursing were used. The purse seine nets utilized in the operation predominantly had a mesh size of 30 mm. Depth sensors were affixed to the net to record the observations of the local net dynamics. A Star Oddi DST centi-TD depth sensor was utilized; its installation position is shown in Figure 3. Given that the underside of the net was drawn up to the deck following the completion of the pursing process, the depth sensors were positioned at the center of the net to facilitate the measurement of the net dynamics during the hauling operation.

2.4. Estimation of Hauling Velocity

An experiment was conducted using the estimation system constructed in Section 2.2 to estimate the unknown parameters of the hauling velocity and bring the results of the numerical simulation closer to the actual net dynamics. The initial value of the hauling velocity, which is a control parameter, was set to 0.44 ms⁻¹ because it was deemed that the net might not initiate the hauling process if the velocity was set to 0.0 ms⁻¹. Accordingly, the velocity was calculated by dividing the total length of the net by the time interval between the commencement and conclusion of the hauling. The computation interval was set to 1.0 s for each step, and the number of ensembles was set to 10. The distribution of the system noise was set to have a mean of 0.0 and a standard deviation of 5.0 × 10⁻⁵.

3. Results

3.1. Estimated Hauling Velocity and Length of Hauling Net

Figure 4 illustrates the time series variation in the estimated hauling rate. The gray areas in Figure 4 and Figure 5 represent the interval between the commencement of the shooting and the conclusion of the hauling, whereas the white area represents the period during which the netting velocity was estimated and controlled. The hauling velocity exhibited a range of 0.43 to 0.49 ms⁻¹ from the commencement of hauling to approximately 2500 s. At approximately 2500 s, the hauling velocity exhibited a notable increase, subsequently fluctuating between 0.55 and 0.65 ms⁻¹ until approximately 3500 s. At approximately 4000 s, the velocity stabilized at approximately 0.60 ms⁻¹. In addition, a slight change in the slope was observed, as shown in Figure 5, indicating an increase in the hauling velocity at approximately 2500 s.

3.2. Results of the Dynamic Simulation Using the Estimated Net-Hauling Velocity

The estimated hauling velocity was used to calculate the net dynamics during hauling. Figure 6 shows the visualized net dynamics, which show that the hauling operation is reproduced as the mass points constituting the net are taken into the vessel during the transition from state (a) to state (c). Figure 7 shows a depth comparison between the estimated results and the actual net dynamics. During the hauling process, the nets were hauled in the order of #3, #2, and #1. Figure 7c shows that the changes in the estimated net dynamics and the actual net depth were generally in agreement. Figure 7b shows that the estimated net dynamics for site #2 were greater than the observed depth. Figure 7a also shows that the estimated net dynamics for #2 were deeper than the observed depth for approximately 4000 s. Figure 7a shows that the depth of the estimated net dynamics was greater than the observed depth until approximately 4000 s. Figure 7 shows that at all the sensor attachment points, the simulation results show a depth of 0 m earlier than those for the actual net. Such results can also be observed in Figure 6c, where a faster hauling velocity generates a stronger tension on the net, resulting in a straight line as the net is taken up by the deck.

Based on these results, and by integrating the EnKF and NaLA systems, we estimated the hauling net velocity, which is an unknown parameter, and the net dynamics during the hauling process. From the comparison of depths, it appears that the hauling velocity was affected by the difference between the depth of the net obtained from the simulation results and the actual depth of the net at the end of the pursing before the start of the hauling velocity estimation. The average difference in depth between the positions #1 and #3 was 18.1 m. The difference between the hauling net depth obtained from the simulation results before the start of the estimation and the actual net depth may be due to the current velocity and errors in the net dynamics model. We attempted to reproduce the entire net dynamics by estimating the hauling velocity, including these differences; however, in this experiment, it was difficult to achieve high accuracy for the attachment positions #1–#3 by only estimating the hauling velocity. This issue can be addressed by improving the accuracy of the net dynamics model of the NaLA system and the input current vector.

4. Discussion

4.1. Estimation and Application of Hauling-Net Dynamics

By applying the data assimilation method, we estimated the hauling net velocity, which was an unknown parameter, from the net gear dynamics model and observed the resulting net dynamics. The results confirmed that it is possible to estimate the net gear dynamics during the hauling process by feeding back the estimated hauling velocity into the calculation of the net dynamics. The hauling velocity was calculated to be 0.43–0.65 ms⁻¹ with an average of 0.56 ms⁻¹, which is consistent with the expected range. In the previous numerical simulations of net fishing gear, the dynamics could not be calculated unless all the parameters necessary for calculating the load acting on the net were available [26]; however, the dynamics could be estimated, even when there were unknown parameters, as long as some observed values of the net were available. The results of this study suggest that unknown parameters can be estimated using known information on the dynamics of net fishing gear. In previous studies simulating the dynamics of purse seine nets, the time from shooting to the end of pursing was calculated only up to 1800 s. In this study, however, the hauling velocity could be estimated, which made it possible to calculate the net dynamics up to 5800 s, which is the end of the hauling process. In the EU and Scandinavia, for resource management, efforts are being made to release overcaught fish from nets by opening a portion of the net at the end of the hauling phase [27,28]. As the net is lifted, the net volume in the water gradually decreases, and the density of the fish population gradually increases. As an increase in fish population density causes mortality after release, restrictions are placed on the amount of net lifted before release to improve the survival rate of fish. However, because it is technically difficult to accurately determine the net geometry during hauling, there is a lack of evaluation of the appropriate net volume and the hauling rate. The results of this study are expected to serve as a scientific basis for regulating net lifts.

4.2. Unknown Parameter Estimation and Control of Net Fishing Gear Dynamics

In this study, we estimated the unknown parameters necessary to reproduce net dynamics by using the dynamics of a part of the actual net as the observed values. This estimation of unknown parameters can be assumed as a control to make the purse seine net dynamics in the numerical simulation similar to actual net dynamics. If the observed values are not the actual net dynamics but the dynamics and geometry of the control target, it would be possible to estimate the parameters needed to control the net fishing gear. Our research group conducted a basic study on controlling a net gear with an arbitrary geometry by integrating the NaLA and data assimilation methods [18]. Although this investigation used a simple net, the results suggest the possibility of controlling actual net fishing gear, such as the purse seine nets. These results are expected to be useful in the control of net geometry so that the net volume is appropriate for a catch per operation, for example, as in the case of a release when too much is taken up by the turning net, as discussed in Section 4.1. Therefore, it is necessary to promote the research and development of elemental technologies for practical applications. In the proposed method, the estimated unknown parameters were used in the dynamic calculations; however, a mechanism for adjusting the input of the control parameters must be considered when controlling the net fishing gear. Various methods have been proposed for adjusting the inputs, including general control methods such as an on-off control and the proportional–integral–derivative (PID) control. This study enables the estimation of unknown parameters in the numerical simulations of net fishing gear dynamics, and makes a significant contribution to fishery engineering research, where the application of numerical simulation techniques is becoming increasingly important. In addition to the estimation of net dynamics, the results of this study are expected to be applicable to the control of fishing nets and fishing gear.

5. Conclusions

This study successfully developed a methodology for estimating unknown parameters in purse seine net operations, with a specific focus on hauling velocity. This was achieved by integrating the NaLA system with a data assimilation technique employing the EnKF. By accurately estimating the hauling velocity, which is typically challenging to measure in real-world operations, we could effectively simulate the net dynamics during the hauling process. This represents a significant advancement over the previous studies that only calculated the net dynamics up to the end of the pursing stage.

The proposed method demonstrates that, even with incomplete operational data, an effective estimation of unknown parameters is possible as long as some measurements of the dynamics of the net are available. This approach extends the simulation of the net dynamics and provides deeper insights into the hauling process. These insights have important implications for enhancing fishing operations, such as optimizing net design and preventing overfishing during the hauling phase.