Determination of Anchor Drop Sequence during Vessel Anchoring Operations Based on Expert Knowledge Base and Hydrometeorological Conditions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper reports on the development of an algorithm for the definition of an achor drop sequence for ship's station keeping. The algorithms seems to be sufficiently generalistic to account for various weather conditions and sea states and for various characteristics of the ship. This makes it a valuable tool for automating anchor placement and safer station keeping features. The paper is well written, with good quality figures. My main criticism is that the manuscript provides limited description of the actual algorithm and almost no results or validation of the algorithm. The literature review on station keeping is also quite sparse and would benefit from a more thorough revision.

I am listing below comments which the authors must incorporate in order to make the mansucript suitable for publication.

Major comments:

1 - please try and avoid repetitions in the opening sentence of the abstract: the word "position" appears three times in the same sentence and 7 times in just the first 4 lines. I recommend using alternative terms such as "station keeping", "set-point regulation" (when mediated by a controller) and similar.

2 - the last 3 lines of the abstract contain informatin that don't belong to the abstract. The reader will not mind what programming languages are used. The authors should edit the final remark of the abstract to summarily report the results of the proposed method.

3 - none of the papers cited with reference to dynamic positioning are actually focussed on the theme of dynamic positioning. The literature on the topic is quite broad and more recent and focussed work should instead be referenced for reader's convenience. I recommend the authors to review recent work where explicity knowledge of the wave disturbances can be incorporated in the disturbance rejection control, for example in Walker et al., 2021, "Experimental validation of wave induced disturbances for predictive station keeping of a remotely operated vehicle"; Walker et al., 2020, "Impact of thruster dynamics on the feasibility of ROV station keeping in waves", OCEANS 2020; Chellapurath et al., 2021, "Analysis of station keeping performance of an underwater legged robot", IEEE/ASME TMech and finally Koch, 2017, “Model Predictive Control for Six Degrees-of-Freedom Station-Keeping of an Underwater Vehicle-Manipulator System,” Ph.D. dissertation, KTH Royal Institute of Technology.

4 - line 169 "distribution of wind pressure", do you actually mean pressure or do you mean force?

5 - what is term "q" in eq. 1-6? I am assuming this is somewhat connected to the wind and current speed. Please clarify and consider discerning between the wind flow speed and the current flow speed to avoid confusion. Make sure the dimensions are correct here: if the A-terms are m^2 and K is dimensionless, then q should be kg/(m*s^2)? that looks strange.

6 - with reference to eq. 1-6 I don't understand why the authors cannot simply use a quadratic drag foce of the type Fx = 0.5*density*Cd*A*ux^2 with A being the cross section of the ship projected on the x plane. And the same for the y direction. Wouldn't this be easier?

7 - eq. 7-20 are extremely hard to read and interpret. Where are these definitions coming from? please cite. This is not the conventional way of estimating wave forces from a wave spectrum on a hull, it would be relevant for the reader to understand what rationale lies behind this definition.

8 - in section 3.1 the authors are providing "examples" of what the rules should be. Why don't they provide the actual rules used in their algorithm and express it based on the terms defined in the section 2.1.1, 2.1.2 and 2.1.3?

9 - line 317 "To achieve this, click on the globe icon, and upon pressing it, the silhouette of the ship will appear. Drag the ship's silhouette to the selected geographic coordinates". This is not a tutorial on how to set up Unity, this kind of step-by-step description don't belong in a manuscript.

10 - the process to estimate anchor drop sequence is only described in the results section. Why? this should be part of the "rules" used to define the anchor drop algorithm. I think the authors should revise this.

11 - the manuscript does not contain any actual result. It would be beneficial to have some comparison of how the algorithm developed works in comparison with an expert personnel or some evidence of applying the algorithm to a real-world ship in order to assess its efficacy.

12 - is the algorithm developed available to the readers for testing? the authors should include reference to a github page where the code can be accessed and used.

Minor comments:

- line 150 "position keep", change to "station keeping"

- line 151 "which consists of..."

- line 170 "torsional moment" around the z-axis, I assume. You might want to call this the Yaw moment

- line 174-178 and following, please correct the editing of the units currently defined as "[m2]"

Author Response

Reviewer 1:

This paper reports on the development of an algorithm for the definition of an achor drop sequence for ship's station keeping. The algorithms seems to be sufficiently generalistic to account for various weather conditions and sea states and for various characteristics of the ship. This makes it a valuable tool for automating anchor placement and safer station keeping features. The paper is well written, with good quality figures. My main criticism is that the manuscript provides limited description of the actual algorithm and almost no results or validation of the algorithm. The literature review on station keeping is also quite sparse and would benefit from a more thorough revision.

Dear Reviewer 1,

We would like to express our gratitude for the time devoted to the review the article. The comments made by the respected Reviewer will certainly improve the quality of the content presented and the legibility of the proposed publication. The main corrections in the paper and our responds to the Reviewer’s comments are as follow:

Please try and avoid repetitions in the opening sentence of the abstract: the word "position" appears three times in the same sentence and 7 times in just the first 4 lines. I recommend using alternative terms such as "station keeping", "set-point regulation" (when mediated by a controller) and similar.

We sincerely thank the esteemed reviewer for the feedback and for providing various alternatives for the word "position." We have carefully considered the suggestions and implemented changes throughout the abstract. Currently, it is formulated as follows:

Presently, the most common technique for maintaining a ship's location is dynamic positioning, which uses a series of thrusters to hold its position. This method is resilient to moderate hydro-meteorological conditions, eliminating the need for extensive preliminary steps before initiating positioning operations. An alternative approach involves station keeping using a set of anchors, where thrusters are not employed, necessitating careful planning of the anchorage in light of hydro-meteorological conditions. Presently, in vessels using this anchoring method, the captain determines the order of anchor drops, taking into account the prevailing weather conditions, the ship's manoeuvring abilities, and vessel Capability Plots. This article introduces a novel algorithm that uses sensor-acquired weather data and a cognitive knowledge base to establish the best sequence for anchor drops. This innovation represents a significant stride towards the automation of the anchoring process. By using the anchorage planning algorithm presented in the publication, it has been possible to reduce the time required for anchor deployment by about 52% due to the preparation of the anchor deployment strategy in port. A reduction in energy consumption of about 8% was also achieved.

We hope that the revised abstract meets the expectations of the esteemed reviewer.

The last 3 lines of the abstract contain informatin that don't belong to the abstract. The reader will not mind what programming languages are used. The authors should edit the final remark of the abstract to summarily report the results of the proposed method.

We thank the honourable reviewer for his suggestion on the abstract. In the view of the previous comment, we have decided to rewrite the abstract. In the new version, we have omitted information about the programming languages used and focused on highlighting the results obtained from the analyses.

None of the papers cited with reference to dynamic positioning are actually focussed on the theme of dynamic positioning. The literature on the topic is quite broad and more recent and focussed work should instead be referenced for reader's convenience. I recommend the authors to review recent work where explicity knowledge of the wave disturbances can be incorporated in the disturbance rejection control, for example in Walker et al., 2021, "Experimental validation of wave induced disturbances for predictive station keeping of a remotely operated vehicle"; Walker et al., 2020, "Impact of thruster dynamics on the feasibility of ROV station keeping in waves", OCEANS 2020; Chellapurath et al., 2021, "Analysis of station keeping performance of an underwater legged robot", IEEE/ASME TMech and finally Koch, 2017, “Model Predictive Control for Six Degrees-of-Freedom Station-Keeping of an Underwater Vehicle-Manipulator System,” Ph.D. dissertation, KTH Royal Institute of Technology.

We would like to express our gratitude to the esteemed reviewer for noting the absence of relevant publications in the literature review. We have thoroughly examined the titles recommended by the reviewer. Their content is exceptionally insightful, aligning seamlessly with the thematic focus of our work. Citations to the referenced articles have been incorporated into our manuscript.

 

Line 169 "distribution of wind pressure", do you actually mean pressure or do you mean force?

Thank you for bringing attention to the error in the translation of notations in the equations. We appreciate your clarification, and indeed, the intended expression is "distribution of wind force." We have incorporated the corrected version into the article.

What is term "q" in eq. 1-6? I am assuming this is somewhat connected to the wind and current speed. Please clarify and consider discerning between the wind flow speed and the current flow speed to avoid confusion. Make sure the dimensions are correct here: if the A-terms are m^2 and K is dimensionless, then q should be kg/(m*s^2)? that looks strange.

We thank the esteemed reviewer for highlighting the lack of explanation regarding the coefficient 'q.' The coefficient 'q' takes the following form in the mathematical model of forces stemming from the wind:

The mathematical model for forces from sea currents similarly features the following formula:

The explanations for each coefficient 'q' have been included in the revised version of the manuscript.

With reference to eq. 1-6 I don't understand why the authors cannot simply use a quadratic drag foce of the type Fx = 0.5*density*Cd*A*ux^2 with A being the cross section of the ship projected on the x plane. And the same for the y direction. Wouldn't this be easier?

Many thanks for the suggestion given by the respected reviewer. The notation of the mathematical models for the forces generated by wind and sea current is taken from the book 'Handbook of Marine Craft Hydrodynamics and Motion Control', authored by Thor I. Fossen.

Figure 1. The mathematical models presented by Thor I. Fossen

 

The mathematical model of sea current force is presented in DNV documents.  (link to the document https://home.hvl.no/ansatte/gste/ftp/MarinLab_files/Litteratur/DNV/rp-h103_2011-04.pdf)

Figure 2. The mathematical model for sea current force

Since we use the same notation for mathematical models in studies and documentation, we decided to use it also in our manuscript in order to standardise the formulas related to Capability Plots.

Eq. 7-20 are extremely hard to read and interpret. Where are these definitions coming from? please cite. This is not the conventional way of estimating wave forces from a wave spectrum on a hull, it would be relevant for the reader to understand what rationale lies behind this definition.

Thank you for pointing out the ambiguities. The model for forces originating from ocean waves, as presented in the publication, is found in a document from the DNV classification society titled "Assessment of station keeping capability of dynamic positioning vessels" (link to the document: https://standards.dnv.com/explorer/document/7E231C260D4846DF8DF3CBA12A2229D4/5; reference 32 in our manuscript). This document introduces guidelines regarding mathematical models used for determining the Capability Plot. Currently, the document is accessible only to users with an account on the DNV platform. Therefore, we have included an image below with an excerpt from the document related to the mathematical model of ocean waves.

Figure 3. The mathematical model for sea waves

 

In section 3.1 the authors are providing "examples" of what the rules should be. Why don't they provide the actual rules used in their algorithm and express it based on the terms defined in the section 2.1.1, 2.1.2 and 2.1.3?

We appreciate the valuable feedback from the esteemed reviewer. The examples of rules in Chapter 3.1, were developed, among other considerations, based on the mathematical models presented in the publication. Due to the substantial number of rules in the cognitive knowledge base, a selection was made to present key elements related to anchoring planning.

For instance, the rule suggesting the course of the vessel relative to the wind direction was implemented as follows:

IF ( wind angle of attack on the hull == 90°) THEN

(set the proposed course of the ship to 90° or 270°)

 

Algorithm code for the above rule:

 

public void CheckWindDirectionValue()

{

   if (WindDirection.text != "")

      {

        if (double.TryParse(WindDirection.text, out TempValue))

            {

     if (double.Parse(WindDirection.text)>=0 && double.Parse(WindDirection.text)<=360)

         { HeadingText.text = TempValue.ToString() + "°";}

         else { HeadingText.text = 0.ToString("°");}

             }

             else { WindDirection.text = 0.ToString(); }

        }

        else

        { WindDirection.text = 0.ToString();}

    }

 

Rule designating the maximum extent of the safe anchor drop area:

 

IF (depth == 15 m AND anchor LB == SELECTED ) THEN
(show anchor deployment field for anchor LB) AND

(set the maximum anchor deployment distance to 1000 m – depth)

 

Algorithm code for the above rule:

 

public void CheckDepthValue()

    {

        if (DepthText.text != "")

        {

            if (double.TryParse(DepthText.text, out TempValue))

            {

                if (double.Parse(DepthText.text) <= 0)

                { DepthText.text = 0.ToString();}

            }

            else

            { DepthText.text = 0.ToString();}

        }

        else

        { DepthText.text = 0.ToString();}

 

        DepthTemp = float.Parse(DepthText.text.Replace('.', ','));

if (IsLDPanel)                 NumberLDAnchor.transform.parent.gameObject.GetComponent<CreateAreaForAnchor>().SetNewHandleData();

       

        if (IsPDPanel)

            NumberPDAnchor.transform.parent.gameObject.GetComponent<CreateAreaForAnchor>().SetNewHandleData();

        if (IsLRPanel)

            NumberLRAnchor.transform.parent.gameObject.GetComponent<CreateAreaForAnchor>().SetNewHandleData();

        if (IsPRPanel)

            NumberPRAnchor.transform.parent.gameObject.GetComponent<CreateAreaForAnchor>().SetNewHandleData();

    }

Line 317 "To achieve this, click on the globe icon, and upon pressing it, the silhouette of the ship will appear. Drag the ship's silhouette to the selected geographic coordinates". This is not a tutorial on how to set up Unity, this kind of step-by-step description don't belong in a manuscript.

We appreciate the suggestion from the esteemed reviewer. We acknowledge that the particular passage may have sounded like a tutorial; however, our intention was to illustrate the manner of declaring the specified position. In line with the reviewer's suggestion, the indicated sentence has been edited, and it now reads as follows: "The target position is defined in the section Operation point." We sincerely hope that the revised text meets the approval of the esteemed reviewer.

The process to estimate anchor drop sequence is only described in the results section. Why? this should be part of the "rules" used to define the anchor drop algorithm. I think the authors should revise this.

We would like to express our gratitude for pointing out the absence of a description regarding the anchor deployment sequence. We agree that in Chapter 3.1, Cognitive Knowledge Base, there is a missing part related to the description of the subsequent stages of anchoring operations. To address this, we have added the following excerpt to fill the gap:

 

In order to implement the algorithm presented in the publication on the ship, the rules for the anchor deployment process were integrated into the cognitive knowledge base. Throughout the operation, the algorithm dynamically assesses the ongoing anchor deployment stage, adjusting the rules accordingly. The various stages of anchor deployment, with concise examples of the associated rules, are described as follows:

 

Stage 1: Loading the planned anchorage into the ship's control system in the form of waypoints.

Stage 2: Set the course for the first anchor and adjust the declared speed.

IF (ship course != target course) THEN

(adjust the rudder to achieve the desired course)

IF (ship speed != target speed) THEN

(increase the main propeller RPMs to achieve the desired speed)

 

Stage 3: Stop the vessel at the designated drop point for the first anchor.

IF (ship position == first anchor position ± 5 meters) THEN

(stop engines and keep position)

 

Stage 4: Begin to slacken the anchor rope until it touches the seabed.

IF(anchor line tension > 0) THEN

(anchor has not touched seabed. Loosen the anchor rope )

 

On the ship, the anchor winches operators followed the rule that the length of anchor rope should be twice the depth. Therefore, a similar rule can be applied:

IF(anchor rope length < 2*depth) THEN

(anchor has not touched seabed. Loosen the anchor rope)

 

Stage 5: When the tension of the anchor line reaches 0 or the appropriate length of the anchor rope has been released, begin to move slowly towards the next anchor. At this stage, it is crucial to observe whether the tension of the anchor rope is increasing. If not, it indicates that the anchor has not successfully engaged the seabed. In such a scenario, the vessel should be maneuverer directly over the anchor (positioning the ship precisely above the anchor) and pull in it. Subsequently, repeat stage 4:

IF(anchor line tension > 2kN) THEN

(adjust the rudder to achieve the course for next anchor) AND

(increase the main propeller RPMs to achieve the desired speed)

 

IF(anchor line tension < 2kN) THEN

(return to the anchor drop point) AND

(pull in the anchor) AND

(return to stage 4)

Stages 1 to 5 should be repeated for each subsequent anchor.

 

Stage 6: At this point, all anchors have been dropped. The ship should be moved to the target point.

IF(anchor LB ==dropped) AND

(anchor RB == dropped) AND

(anchor LS == dropped) AND

(anchor RS == dropped) THEN

(turn off main engine) AND

(pull in the anchor ropes until the ship is at the desired point)

 

At each of the above stages, it may turn out that environmental conditions differ from those declared during anchorage planning. In such a case, based on the anchors already deployed, the algorithm will suggest modifications to the anchorage.

The manuscript does not contain any actual result. It would be beneficial to have some comparison of how the algorithm developed works in comparison with an expert personnel or some evidence of applying the algorithm to a real-world ship in order to assess its efficacy.

We sincerely appreciate this observation. In accordance with the reviewer's suggestion, we have decided to include a real ship navigation scenario to illustrate the differences between anchoring planned by the captain and anchoring planned by the algorithm. We have added Chapter 4.2 to our manuscript, in which we compare two navigation situations. The content of the aforementioned chapter is as follows:

• The comparison of the planned anchor dropping sequence in the anchorage planning tool and on the actual ship

In chapter 3.2, navigation scenarios modelled in Unity3D have been considered to demonstrate the capabilities of the anchor planning tool and the developed cognitive knowledge base. While carrying out research on a real ship, the process of anchor planning and deployment by the ship's captain was documented using the user interface of the anchor-based positioning system. Figure 15 shows a screenshot of the interface with all anchor-related data.

 

Figure 4. Screenshot of captain's anchorage planning

The user interface from the figure 15 consists of two main sections:

• Left Side: On the left side, all parameters related to the vessel's movement and position are displayed. This section also includes anchor-related data, such as the distance of the anchor from the ship and the length of the anchor line.
• Right Side: On the right side, there are symbols representing the ship and anchors. In the presented scenario in figure 15, the anchors are shown to be out of range.

 

Characteristics related to environmental conditions, such as the speed and angle of attack of the wind and sea current on the ship's hull, were also recorded. These were used to reconstruct the environmental conditions during anchorage planning by the algorithm. Figure 16 depicts the relationship between sea current speed and the operational time.

 

Figure 5. Sea current speed and angle

Figure 17 depicts the relationship between wind speed and the operational time.

 

Figure 6. Wind speed and angle

In figure 15, it can be observed that individual anchors are not dropped at equal distances from the ship. This uneven distribution may result in poorer position holding during abrupt changes in wind speed. Figure 18 illustrates a simplified diagram of the anchor positions around the ship, along with their respective distances.

Figure 7. Captain's anchorage plan

To compare the anchorage planned by the captain with that generated by the algorithm, a new anchorage was developed in Unity3D, incorporating hydrometeorological data extracted from figures 15-17. Following the sequence outlined in chapter 3.2 for anchorage planning, the arrangement of anchors depicted in Figure 19 is obtained.

 

Figure 8. Anchorage arrangements according to the algorithm

 

 

 

 

 

Figure 20 illustrates a simplified diagram of anchorage from figure 19.

 

Figure 9. The anchorage plan proposed by the algorithm.

The difference between the two is that the algorithm has determined equal distances to drop anchors from the vessel and deployed them evenly around the vessel. In contrast, the anchors deployed by the captain are at different distances and angles to the vessel.

 

During anchor planning, the algorithm took into account a stability factor (0.16) that determines the relationship between the stability of holding position and energy consumption. According to this coefficient, it determined the distance of the anchors from the vessel to be approximately 0.1 nautical miles (about 200 meters). The master also deployed the anchors at approximately 0.1 nautical miles. Despite the short anchor deployment time and low energy consumption, the close distance of the anchors to the vessel makes the vessel's position less resistant to frequent changes in wind speed. Additionally, with this anchor deployment, the vessel's ability to change its position is limited.

 

The deployment time of anchors also differs in both cases. According to the table 7, the planned deployment time for anchors determined by the algorithm is 73 minutes. In the case of anchor deployment by the captain, it took 94 minutes, but in this case, it took 60 minutes to prepare the anchorage plan. The total time of the operation was 154 minutes. The disparity between these two times arises from the fact that the captain had to first plan the entire anchorage.

 

Table 1. Results of energy consumption analysis between two anchorage plans. Case 1 – Captain’s anchorage plan, Case 2 – Anchorage generated by algorithm

Case	Phase	S [NM]	V [knots]	t  [h]	Wind angle [°]	Env. force  vector (X-axis; Y-axis)	Sum of thrust [kN]	Fuel consumption [l]	Energy consumption [kWh]
1	RB -> LB	0.09	0.29	0.31	66	(3 kN; 41 kN) (5 kN; 33 kN) (0.5 kN; 48 kN)	74	6.75	27.28
	LB -> RS	0.18	0.21	0.9	137		82	36.26	146.55
	RS -> LS	0.11	0.29	0.37	92		76	8.67	35.04
								SUM	208.87
2	RB -> LB	0.14	0.4	0.35	92	(0.5 kN; 48 kN)	76	8.48	34.27
	LB -> RS	0.21	0.4	0.52	137	(5 kN; 33 kN)	82	31.49	127.27
	RS -> LS	0.14	0.4	0.35	92	(0.5 kN; 48 kN)	76	8.53	34.47
								SUM	196.01

According to Table 7, the energy consumption for the anchor deployment planned by the captain was 208.87 kWh. For the algorithm, the energy consumption was 196.01 kWh, which is about 8% less consumption compared to the captain's anchor deployment. This is due to the manual control of the individual anchors by the operator. In addition, the anchor arrangement designed by the algorithm was deployment in 52% less time than that deployment by the operator.

Additionally, we would like to inform you that there was an error in the calculations in Tables 5 and 6. During the calculations, we mistakenly adopted an incorrect ship speed, which affected the results. We have made corrections to the tables.

Table 5:

Phase	S [NM]	V [knots]	t  [h]	Wind angle [°]	Env. force  vector (X-axis; Y-axis)	Sum of thrust [kN]	Fuel consumption [l]		Energy consumption [kWh]
RB -> LB	0.6	0.4	1.5	90	(0.5 kN; 46 kN) (6 kN; 34 kN) (0.5 kN; 46 kN)	137	71.61		318.66
LB -> RS	0.84	0.4	2.1	135		152	156.89		698.16
RS -> LS	0.6	0.4	1.5	90		137	71.64		318.79
							SUM	1335.74

     

Table 6:

Case	Phase	S [NM]	V [knots]	t  [h]	Wind angle [°]	Env. force  vector (X-axis; Y-axis)	Sum of thrust [kN]	Fuel consumption [l]	Energy consumption [kWh]
1	RB -> LB	0.6	0.4	1.5	0	(7.5 kN; 0 kN) (5.2 kN; 34 kN) (7.5 kN; 0 kN)	189	110.41	446.22
	LB -> RS	0.84	0.4	2.1	45		138	170.88	690.62
	RS -> LS	0.6	0.4	1.5	0		189	110.43	446.31
								SUM	1538.13
2	RB -> LB	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.41	446.24
	LB -> LS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	60	118.08	477.23
	LS -> RS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.39	446.15
								SUM	1369.62
3	LB -> RB	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.43	446.32
	RB -> RS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	60	118.11	477.36
	RS -> LS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.42	446.26
								SUM	1369.94
4	LB -> RB	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.39	446.14
	RB -> LS	0.84	0.4	2.1	315	(5.2 kN; 34 kN)	138	170.91	690.76
	LS -> RS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.41	446.24
								SUM	1583.14

 

 

 

 

 

 

 

Is the algorithm developed available to the readers for testing? the authors should include reference to a github page where the code can be accessed and used.

Thank you for this observation. Currently, we are refining our algorithm by incorporating new rules into the cognitive knowledge base. We are committed to delivering a functional solution, so before releasing the algorithm code for testing, we plan to verify the correctness of the new rules in operation. The algorithm code will be made available after successfully completing this process.

 

Minor comments:

- line 150 &quot;position keep&quot;, change to &quot;station keeping&quot;

- line 151 &quot;which consists of...&quot;

- line 170 &quot;torsional moment&quot; around the z-axis, I assume. You might want to call this the Yaw moment

- line 174-178 and following, please correct the editing of the units currently defined as [m2]

Thank you to the esteemed reviewer for drawing our attention to the correct formatting. We have incorporated all the provided comments and suggestions into the publication.

We would like to thank the dear reviewer for his attention and time. The article and abstract have been edited and/or supplemented with missing content in many places. All comments have been taken into account with due care and corrections have been included and marked in the proposed text of the manuscript.

Best Regards

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. Wind force coefficient and sea current force coefficients in Eqs. (1)-(6) should be given.

2. Generally speaking, it is not easy to obtain maximum tension of the anchor line. Then, how are the max tensions given in Table. 3? Line 223 states that Eqs. (24)-(26) will give tension values. However, if the tensions are obtained by calculations, it is quite hard to achieve tensions in practice.

3. In Figure 4 and Figure 5, the green line means the maximum wind speed value. How do the green lines obtained?

4. The paper states that cognitive knowledge base is the key to the proposed anchorage planning. However, are these knowledge rules reasonable? Detailed explanations should be included.

5. In section 3.2 anchorage planning in Unity 3D, very few models are mentioned in the previous sections.

6. The proposed methods should be compared to the traditional ones to show its advantages.

Comments on the Quality of English Language

The quality of English language is OK. In section 3.1, THAN should be THEN.

Author Response

Reviewer 2,

 

Dear Reviewer, thank you very much for posting all the remarks and comments. Based on your comments, we have made extensive modifications to the original manuscript. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important and significant guide to our research. We hope that the implemented changes (based on comments from all Reviewers) will satisfy the Reputable Reviewer enough to accept the proposed paper for publication.

1. Wind force coefficient and sea current force coefficients in Eqs. (1)-(6) should be given.

We sincerely appreciate your opinion. If we understand the esteemed reviewer correctly, the concern relates to the coefficients mentioned by the classification society DNV in their Capability Plots guidelines.

Each vessel equipped with a Dynamic Positioning (DP) system of Class 2 or higher is required to have valid Capability Plots. These plots serve as information for clients, indicating whether a particular vessel can maintain its position under specific hydrometeorological conditions. Client evaluations based on Capability Plots have prompted shipowners to retrofit their vessels to achieve optimal plots. However, this hasn't always translated into improved actual control and position keeping.

Recognizing that Capability Plot analyses ceased to serve as a reliable indicator of position-keeping quality, in 2018, the classification society DNV decided to introduce a division of Capability Plots into five levels. According to the current guidelines, vessels built before 2018 may have Capability Plots at Level 1, while vessels constructed after 2018 must undergo a position-keeping capability analysis in accordance with the five-level classification.

The division of Capability Plots into levels according to DNV standards is outlined on the following webpage: https://www.dnv.com/services/dp-capability-85124.

DP capability level	Level description
Level 1	Level 1 is a prescriptive, quasi static calculation method for documenting ship-shaped mono-hull vessels, based on a static balance of environmental forces and thrust output. To facilitate vessel comparisons, predefined Beaufort-scale-based environmental conditions are used.
Level 2	Level 2 is a more comprehensive quasi static calculation method. It allows for project-specific adjustments and is applicable for all vessel shapes. The Beaufort-scale-based environmental conditions are used.
Level 2 - Site	Same as Level 2 but allows for site-specific environmental data and external forces.
Level 3	The Level 3 method provides more insight into the vessel’s DP capability performance by use of time-domain simulations. It also includes relevant vessel and environmental dynamics. Thus, the calculation provides more information on the station-keeping performance than the other DP capability levels.
Level 3 - Site	Same as Level 3, but allows for site-specific environmental data and external forces.

 

A detailed description of individual levels based on the guidelines of the DNV classification society:

For Level 1:

 The DP Capability plots and numbers shall be presented in form of Wind envelopes (limiting wind speed for given environmental direction) according to the standard DNV GL ST-0111 – Level 1. Below the main requirements:

• Level 1 in ST-0111 is fully prescriptive (requires zero forward speed, summer load line draft, even keel, environmental and actuator forces are calculated from prescriptive formulas, Beaufort weather scale is used, 10% of reserved power for other loads than thrusters).

 

 

For Level 2 :

The DP Capability plots and numbers shall be presented in form of wind envelopes (limiting wind speed for given environmental direction) according to the standard DNV GL ST-0111-Level 2. Below the main requirements that should be defined:

• The calculation shall be performed with zero forward speed, summer load line draft, even keel. For vessels without a defined summer load line draft, the draft shall be the deepest approved operating draft.
• The calculation shall be performed with wind, current and wave drift coefficients specific to the vessel.
• The calculation shall be performed with actuator losses according to the vessel and actuator specific equipment.
• The calculation shall be performed with project specific reserved power for electrical losses, hotel loads and other loads not related to actuators
• The environmental dynamic factors can be taken as 1.5 for wind and waves, 1.05 for current if vessel specific data are not available. Optional: Results can also be presented as thrust and power utilization for given environmental conditions.

 

For Level 2-Site

The DP Capability plots shall be presented in form of wind envelopes (limiting wind speed for given

environmental direction) according to the standard DNV GL ST-0111-Level 2 site. Below the main

requirements that should be defined:

• The wind envelopes shall be calculated for the site-specific operating: table with wind speed,

wave height, wave period needs to be specified. Current speed needs to be specified. Wind, wave

and current direction need to be specified.

• The calculation shall be performed with the draft: draft-name, draft m; trim angle
• The calculation shall be performed with wind, current and wave drift coefficients specific to the

vessel.

• The calculation shall be performed with actuator losses according to the vessel and actuator

specific equipment.

• The calculation shall be performed with project specific reserved power for electrical losses, hotel

loads and other loads not related to actuators

• If external forces are relevant: External forces shall be included (specify from drilling riser, pipes,

etc.)

• The environmental dynamic factors can be taken as 1.5 for wind and waves, 1.05 for current if

vessel specific data are not available.

 

For Level 3

The DP Capability plots shall be presented in form of Wind envelopes (limiting wind speed for given

environmental direction) according to the standard DNV GL ST-0111-Level 3. Below the main

requirements that should be specified:

• The calculation shall be performed with zero forward speed, summer load line draft, even keel.

For vessels without a defined summer load line draft, the draft shall be the deepest approved

operating draft.

• The calculation shall be performed with wind, current and wave drift coefficients specific to the

vessel.

• The calculation shall be performed with actuator dynamics and losses according to the vessel and

actuator specific equipment.

• Simulations shall be in accordance with the vessel power consumption balance.
• The positioning limits shall be 5 meters and 3 degrees. Simulations lengths shall be 3-hours. As

minimum 3 wave realization to be simulated.

• The calculations shall be performed considering either the low-frequency motion when assessing

the vessel positioning against the positioning limits

For Level 3-Site

The DP Capability plots shall be presented in form of Wind envelopes (limiting wind speed for given

environmental direction) according to the standard DNV GL ST-0111-Level 3-site. Below the main

requirements that should be specified:

• The calculation shall be performed the specified load conditions: Operating (or survival, etc.)
• The calculation shall be performed with wind, current and wave drift coefficients specific to the

vessel.

• The calculation shall be performed with actuator dynamics and losses according to the vessel and

actuator specific equipment.

• Simulations shall be in accordance with the vessel power consumption balance.
• The positioning limits shall be specific to the specified operation. Simulations lengths shall be at

least 3-hours. As minimum 3 wave realizations to be simulated.

• The calculations shall be performed considering either the low-frequency motion or the total

motion when assessing the vessel positioning against the positioning limits, according to the

operation requirements.

• If external forces are relevant: External forces shall be included (specify from drilling riser, pipes,

etc.).

• Effect of water depth shall be included if relevant.

The Capability Plot presented in our manuscript represents an analysis at Level 1, therefore, in this case, additional coefficients related to wind force and sea current force are not taken into account.

2. Generally speaking, it is not easy to obtain maximum tension of the anchor line. Then, how are the max tensions given in Table. 3? Line 223 states that Eqs. (24)-(26) will give tension values. However, if the tensions are obtained by calculations, it is quite hard to achieve tensions in practice.

We appreciate the esteemed reviewer for this observation. The data regarding the maximum anchor winch pull, as presented in Table 3, were determined by the manufacturer during the production stage. The values presented in the manuscript are derived from the technical documentation. Unfortunately, we cannot publicly disclose the technical specifications of the anchor winches, as the vessel on which the research was carried out belongs to the Navy. We kindly ask the respected reviewer for understanding. Enclosed is a selected page from the technical documentation.

 

3. In Figure 4 and Figure 5, the green line means the maximum wind speed value. How do the green lines obtained

 

We sincerely thank you for your question and for bringing to our attention that certain aspects related to Capability Plot may be unclear.

 

The algorithm for determining Capability Plots aims to find the appropriate distribution of thrust forces for the thrusters (in the case of DP systems) or tension of the anchor ropes (in the case of an anchor-based system) to resist the environmental forces acting on the vessel. The operation of the algorithm is as follows:

1. Set the wind angle to 0°.
2. Set the wind speed to 25 m/s and the current speed to 0.75 m/s (according to DNV guidelines).
3. Calculate the environmental force value for the specified wind speed.
4. Find the thrust allocation on the thrusters (or the tension in the anchor ropes) capable of resist the environmental forces.
5. If a suitable force distribution capable of counteracting environmental forces is found, increase the wind speed and repeat steps 3-5. If not, decrease the wind speed and re-peat steps 3-5.
6. Repeat step 5 until the maximum wind speed at which the vessel can keep its position at a given wind angle is obtained. Add the point with the maximum wind value and current angle to the polar plot.
7. Once the maximum wind speed for a given angle has been determined, increase the wind angle by 10°. Repeat steps 2-6.

We hope that the description of how the algorithm works is understandable to the esteemed reviewer. We have also added the same description to the proposed manuscript.

4. The paper states that cognitive knowledge base is the key to the proposed anchorage planning. However, are these knowledge rules reasonable? Detailed explanations should be included.

 

We extend our gratitude to the esteemed reviewer for this question. Over the past 5 years, we have been involved in the design of an anchoring-based positioning system. During this period, we participated in numerous positioning operations, where, in addition to testing algorithms, control systems, and equipment, we had the opportunity to observe the work of the captain and officers. Based on this extensive observation, we have developed a cognitive knowledge base, which has been utilized for the purposes of this publication. Additionally, we would like to present to the esteemed reviewer several photographs taken during our work on the actual vessel.

 

Figure 1. Anchor winch

 

Figure 2. Stern anchor rope roller

 

Figure 3. Stern anchor rope roller2

 

Figure 4. User Interface of an Anchoring-Based Positioning System

 

Figure 5. Navigation bridge

5. In section 3.2 anchorage planning in Unity 3D, very few models are mentioned in the previous sections.

We appreciate the esteemed reviewer for this comment. All mathematical models (equations 1-28) have been directly implemented in the Unity3D environment and were utilized for anchoring planning. An exemplary application of the mathematical models presented in Chapter 2 is the determination of Capability Plots for the cognitive knowledge base. Based on the Capability Plots conducted during shipboard research, the unit received accreditation from the DNV classification society.

6. The proposed methods should be compared to the traditional ones to show its advantages.

We sincerely thank the esteemed reviewer for this suggestion. Indeed, it would be appropriate to include a real ship navigation scenario to illustrate the differences between anchoring planning by the ship's captain and the algorithm. In accordance with the reviewer's suggestion, we have added section 4.2, where we compare two navigation scenarios. The content of the section is as follows:

• The comparison of the planned anchor dropping sequence in the anchorage planning tool and on the actual ship

In chapter 3.2, navigation scenarios modelled in Unity3D have been considered to demonstrate the capabilities of the anchor planning tool and the developed cognitive knowledge base. While carrying out research on a real ship, the process of anchor planning and deployment by the ship's captain was documented using the user interface of the anchor-based positioning system. Figure 15 shows a screenshot of the interface with all anchor-related data.

 

Figure 6. Screenshot of captain's anchorage planning

The user interface from the figure 15 consists of two main sections:

• Left Side: On the left side, all parameters related to the vessel's movement and position are displayed. This section also includes anchor-related data, such as the distance of the anchor from the ship and the length of the anchor line.
• Right Side: On the right side, there are symbols representing the ship and anchors. In the presented scenario in figure 15, the anchors are shown to be out of range.

 

Characteristics related to environmental conditions, such as the speed and angle of attack of the wind and sea current on the ship's hull, were also recorded. These were used to reconstruct the environmental conditions during anchorage planning by the algorithm. Figure 16 depicts the relationship between sea current speed and the operational time.

 

Figure 7. Sea current speed and angle

Figure 17 depicts the relationship between wind speed and the operational time.

 

Figure 8. Wind speed and angle

In figure 15, it can be observed that individual anchors are not dropped at equal distances from the ship. This uneven distribution may result in poorer position holding during abrupt changes in wind speed. Figure 18 illustrates a simplified diagram of the anchor positions around the ship, along with their respective distances.

Figure 9. Captain's anchorage plan

To compare the anchorage planned by the captain with that generated by the algorithm, a new anchorage was developed in Unity3D, incorporating hydrometeorological data extracted from figures 15-17. Following the sequence outlined in chapter 3.2 for anchorage planning, the arrangement of anchors depicted in Figure 19 is obtained.

 

Figure 10. Anchorage arrangements according to the algorithm

 

Figure 20 illustrates a simplified diagram of anchorage from figure 19.

 

Figure 11. The anchorage plan proposed by the algorithm.

The difference between the two is that the algorithm has determined equal distances to drop anchors from the vessel and deployed them evenly around the vessel. In contrast, the anchors deployed by the captain are at different distances and angles to the vessel.

 

During anchor planning, the algorithm took into account a stability factor (0.16) that determines the relationship between the stability of holding position and energy consumption. According to this coefficient, it determined the distance of the anchors from the vessel to be approximately 0.1 nautical miles (about 200 meters). The master also deployed the anchors at approximately 0.1 nautical miles. Despite the short anchor deployment time and low energy consumption, the close distance of the anchors to the vessel makes the vessel's position less resistant to frequent changes in wind speed. Additionally, with this anchor deployment, the vessel's ability to change its position is limited.

 

The deployment time of anchors also differs in both cases. According to the table 7, the planned deployment time for anchors determined by the algorithm is 73 minutes. In the case of anchor deployment by the captain, it took 94 minutes, but in this case, it took 60 minutes to prepare the anchorage plan. The total time of the operation was 154 minutes. The disparity between these two times arises from the fact that the captain had to first plan the entire anchorage.

 

Table 1. Results of energy consumption analysis between two anchorage plans. Case 1 – Captain’s anchorage plan, Case 2 – Anchorage generated by algorithm

Case	Phase	S [NM]	V [knots]	t  [h]	Wind angle [°]	Env. force  vector (X-axis; Y-axis)	Sum of thrust [kN]	Fuel consumption [l]	Energy consumption [kWh]
1	RB -> LB	0.09	0.29	0.31	66	(3 kN; 41 kN) (5 kN; 33 kN) (0.5 kN; 48 kN)	74	6.75	27.28
	LB -> RS	0.18	0.21	0.9	137		82	36.26	146.55
	RS -> LS	0.11	0.29	0.37	92		76	8.67	35.04
								SUM	208.87
2	RB -> LB	0.14	0.4	0.35	92	(0.5 kN; 48 kN)	76	8.48	34.27
	LB -> RS	0.21	0.4	0.52	137	(5 kN; 33 kN)	82	31.49	127.27
	RS -> LS	0.14	0.4	0.35	92	(0.5 kN; 48 kN)	76	8.53	34.47
								SUM	196.01

According to Table 7, the energy consumption for the anchor deployment planned by the captain was 208.87 kWh. For the algorithm, the energy consumption was 196.01 kWh, which is about 8% less consumption compared to the captain's anchor deployment. This is due to the manual control of the individual anchors by the operator. In addition, the anchor arrangement designed by the algorithm was deployment in 52% less time than that deployment by the operator.

Additionally, we would like to inform you that there was an error in the calculations in Tables 5 and 6. During the calculations, we mistakenly adopted an incorrect ship speed, which affected the results. We have made corrections to the tables.

Table 5:

Phase	S [NM]	V [knots]	t  [h]	Wind angle [°]	Env. force  vector (X-axis; Y-axis)	Sum of thrust [kN]	Fuel consumption [l]		Energy consumption [kWh]
RB -> LB	0.6	0.4	1.5	90	(0.5 kN; 46 kN) (6 kN; 34 kN) (0.5 kN; 46 kN)	137	71.61		318.66
LB -> RS	0.84	0.4	2.1	135		152	156.89		698.16
RS -> LS	0.6	0.4	1.5	90		137	71.64		318.79
							SUM	1335.74

     

Table 6:

Case	Phase	S [NM]	V [knots]	t  [h]	Wind angle [°]	Env. force  vector (X-axis; Y-axis)	Sum of thrust [kN]	Fuel consumption [l]	Energy consumption [kWh]
1	RB -> LB	0.6	0.4	1.5	0	(7.5 kN; 0 kN) (5.2 kN; 34 kN) (7.5 kN; 0 kN)	189	110.41	446.22
	LB -> RS	0.84	0.4	2.1	45		138	170.88	690.62
	RS -> LS	0.6	0.4	1.5	0		189	110.43	446.31
								SUM	1538.13
2	RB -> LB	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.41	446.24
	LB -> LS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	60	118.08	477.23
	LS -> RS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.39	446.15
								SUM	1369.62
3	LB -> RB	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.43	446.32
	RB -> RS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	60	118.11	477.36
	RS -> LS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.42	446.26
								SUM	1369.94
4	LB -> RB	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.39	446.14
	RB -> LS	0.84	0.4	2.1	315	(5.2 kN; 34 kN)	138	170.91	690.76
	LS -> RS	0.6	0.4	1.5	0	(7.5 kN; 0 kN)	189	110.41	446.24
								SUM	1583.14

 

Once again many thanks the Respected Reviewer for his valuable insights and time. All comments have been taken into account with due care and corrections have been included and marked in the proposed text of the manuscript.

Best Regards

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The new version has contained some improvements according to the reviews. However, some aspects are not still covered as follows.

 

1. In the sea current force model, the coefficients Kx, Ky, KM are still not given.

 

2. The authors try to obtain respective tension values for the anchor winches from Eqs. 26-28. However, in Eqs. 26-28, there are totally 4 tension values, namely, LB, RB, LS, RS, it seems impossible to obtain 4 unknowns values from 3 equations.

 

3. Eqs (26)-(28) gives anchor’s tension values. And Table 3 also gives anchor tensions. Then what are the relationships between the tension values from the two different methods?

 

3. In Eqs. (23) - (25), how can the values of \alpha, PosX and PosY be obtained?

 

4. The roadmap figure of the proposed anchor planning method should be given.

 

5. The authors explain that, based on this extensive observations from engineering practice, the cognitive knowledge base is obtained. However, this is not persuasive.

Comments on the Quality of English Language

The quality of English language is good.

Author Response

Reviewer 2

The new version has contained some improvements according to the reviews. However, some aspects are not still covered as follows.

 

Dear Reviewer 2,

 

Once again we would like to express our gratitude for the time devoted to the review of our article. The comments made by the respected Reviewer will certainly improve the quality of the content presented and the legibility of the proposed publication. The main corrections in the paper and our responds to the Reviewer’s comments are as following:

 

1. In the sea current force model, the coefficients Kx, Ky, K_M are still not given.

Thank you very much for drawing your attention to this issue. The coefficients K_X, K_Y, K_M are related to the geometric dimensions of the ship's hull. They were determined based on the relationships given in the publication by Thor I. Fossen, 'Marine Craft Hydrodynamics and Motion Control', first edition, 2011. The relationships take the following form:

 

 

 

The individual values of CD_l and CD_t depend on the type of vessel [according to Thor I. Fossen, 'Marine Craft Hydrodynamics and Motion Control', first edition, 2011]:

 

 

 

 

 

In the example presented in the manuscript, values for an 'Offshore Supply Vessel' were assumed. The individual coefficient values depending on the angle of wind incidence on the ship's hull are shown in the

following figure:

 

The coefficients K_X, K_Y, and K_M for sea currents were determined in a similar manner.

 

We have added the above information in the publication:

=======================================================================================

Line: 181 - 192

The hull shape coefficients (K_X, K_Y, and K_M) were determined based on the publication [28]:

	(4)
	(5)
	(6)

where: CD_l – longitudinal resistance coefficient [-]; CD_t – lateral resistance coefficient [-]; - cross-force coefficient [-]; k- rolling moment coefficient [-]

 

The values of CD_l and CD_t depend on the type of vessel. For the above example, it was assumed that CD_l , CD_t = 0.9, k = 1.2, =0.55.

 

The individual values of K_X, K_Y, and K_M are presented in Figure 5.

Figure 1. Ship shape coefficients

=======================================================================================

 

2. The authors try to obtain respective tension values for the anchor winches from Eqs. 26-28. However, in Eqs. 26-28, there are totally 4 tension values, namely, LB, RB, LS, RS, it seems impossible to obtain 4 unknowns values from 3 equations.

 

Thanks a lot for your comment. We agree with the esteemed reviewer that it is difficult to obtain four unknowns from three equations. Equations (29)-(31) present the main equations, i.e., the sum of the forces generated by the anchor winches on the X-axis must be equal to the sum of the environmental forces acting on the X-axis of the ship (with the opposite sign), the sum of the forces generated by the anchor winches on the Y-axis must be equal to the sum of the environmental forces acting on the Y-axis of the ship (with the opposite sign), and the torque generated by the anchor winches must be equal to the torque generated by the environmental forces (with the opposite sign). To these three main equations, there are added constraints related to the tension generated or the force of the thrusters. The system of equations along with the constraints is as follows.

=======================================================================================

Line 253-282

	(29)
	(30)
	(31)
	(32)
	(33)
	(34)
	(35)
	(36)
	(37)
	(38)
	(39)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To determine the individual values of the tension forces, we utilized the Ipopt library (Interior Point Optimizer) and the MUMPS solver (MUltifrontal Massively Parallel sparse direct Solver). Link to the documentation: https://coin-or.github.io/Ipopt/. The aforementioned solver allows for finding a solution in cases of fewer equations, as it operates on the principle of substituting values into the equations and checking if all conditions are met. The operation of the solver can be described as follows:

1. Based on the constraints, determine initial values, and then substitute them into the system of equations.
2. Check if the obtained values of the tension of each anchor winch are able to balance the given environmental forces. If not, determine a new set of values, substitute them into the equations, and recheck the solution. Repeat until a solution is found.

=======================================================================================

 

We are aware that finding the values of the individual tensions of the anchor winches takes more time with this method, but it allows for finding a solution with fewer equations

 

 

3. Eqs (26)-(28) gives anchor’s tension values. And Table 3 also gives anchor tensions. Then what are the relationships between the tension values from the two different methods?

We sincerely thank you for this question. The analysis of the Capability Plot aims to find the minimum value of the tension of anchor winches or the thrust value of propellers at which the ship can maintain its position while being affected by environmental forces. Table 3 presents the maximum tension of each anchor winch depending on the length of the anchor rope, as provided in the manufacturer's technical data (limit value). Using equations (29)-(39), one can find the minimum tension values of each anchor winch for the given environmental conditions. We have included the appropriate correction in the manuscript

 

=======================================================================================

Line 243 – 248

With the mathematical models of environmental forces and anchor winches defined, the next step is to solve the system of equations comprising equations 29-39 to find the minimum respective tension values for the anchor winches to keep the vessel at the target position. For equations 29-39, it is assumed that the modeled vessel is equipped with 4 anchor winches – 2 located at the bow of the ship and 2 at the stern. The following designations for the anchor winches are assumed:

=======================================================================================

 

 

4. In Eqs. (23) - (25), how can the values of \alpha, PosX and PosY be obtained?

Thank you for this question. PosX and PosY are values indicating the position of each anchor winch on the ship. The parameters were read from the technical documentation. The individual values are given relative to the point Lpp/2.

Figure 3 shows the position of each anchor winch relative to the X and Y axes.

 

The above figure should be interpreted as follows:

for the anchor winch LB: PosX = 32.1 m, PosY = 2.7 m.

for the anchor winch RB: PosX = 32.1 m, PosY = -2.7 m.

for the anchor winch LS: PosX = -34.8 m, PosY = 2.9 m.

for the anchor winch RS: PosX = -34.8 m, PosY = -2.9 m.

 

Based on the ship's position read from the GPS and the position of the anchor winches relative to the point Lpp/2, the geographical position of each anchor winch is determined. During the anchor drop, the system saves the geographical position of the anchor winch and then assigns it to the respective anchor.

Based on the geographical position of the anchor and the anchor winch, the angle α is determined. To better visualize what the angle α is, we have marked this parameter in Figures 19 and 21.

 

 

Figure 19:

 

 

 

 

Figure 21:

 

 

 

 

 

 

 

5. The roadmap figure of the proposed anchor planning method should be given

We thank the esteemed reviewer for this comment. The description of the entire process of anchor deployment has been included in our manuscript. Additionally, we have added arrows on Figure 14 to indicate the successive movements of the ship during the anchor deployment.

 

=======================================================================================

Line 519 - 541

The last element is to establish the sequence of dropping individual anchors. During the course determination, it was mentioned that the vessel presented in the publication is equipped with tunnel thrusters, which do not allow for free movement in the left-right axis when anchors are dropped. To deploy the anchors, the force of the wind must be utilized. Therefore, it is necessary to start deploying the anchors from those on the starboard side. Considering the possible danger of the anchor rope getting entangled in the propulsion screw during forward movement, the program proposed dropping anchor RB first (point 0 on Figure 14). Excluding the possibility of moving forward, the next anchor to be dropped will be anchor LB. The movement of the ship towards anchor LB is indicated by arrow number 1 in Figure 14. With two anchors planned, the algorithm compares the remaining two possible situations: dropping anchor LS as 3 and anchor RS as 4 or dropping anchor RS as 3 and anchor LS as 4. In the case of dropping anchor LS as 3 and moving to anchor RS, the vessel pulls 3 anchor lines and moves upwind only using the tunnel thrusters. 

Figure 2. The final arrangement of elements along with the established sequence of anchor drops

In the case of dropping anchor RS as 3 (arrow 2 in Figure 14) and moving to anchor LS (arrow 3 in Figure 14), also, 3 anchor lines are pulled, but in this case, the vessel moves with the wind. Taking into account environmental conditions and the maneuvering capabilities of the vessel, the algorithm determined the sequence of dropping anchors shown in Figure 14. After deploying all the anchors, the ship should be moved to the operation point using only the anchors (arrow 4 in Figure 14).

 

 

 

 

 

 

 

 

6. The authors explain that, based on this extensive observations from engineering practice, the cognitive knowledge base is obtained. However, this is not persuasive.

 

Dear Reviewer, thank you for your insightful comments. We greatly appreciate the time you have invested and the review conducted at a very high substantive level. The material presented in the manuscript is part of the work we have recently dedicated to developing a system that is continuously updated and improved. The idea behind the developed system is to support navigators during manoeuvres related to anchor deployment, as well as manoeuvring the ship over a given body of water using the anchor system. We are aware that the system is not yet perfect, but we are making every effort to continuously modify and improve it. The application of the developed system with a cognitive knowledge base and visualization interface has already significantly simplified the work of navigators. While this may not fully convince the esteemed reviewer, the presented manuscript describes a method that is applied to real objects and, according to user feedback, is very useful

 

 

Thank You very much once again the Respected Reviewer for his comments and time.

 

Best Regards

Jakub Wnorowski

Andrzej Łebkowski

 

 

Author Response File: Author Response.pdf