# Statutory and Operational Damage Stability by a Monte Carlo Based Approach

*Reviewer 1:*Anonymous

*Reviewer 2:*Anonymous

*Reviewer 3:*Anonymous

**Round 1**

*Reviewer 1 Report
*

The manuscript presents interesting new practical approaches for using Monte-Carlo simulation and non-zonal damage stability for statutory calculations. Although the non-zonal method for calculation of the probability of damages has been developed some time ago, and its benefits are obvious, it not easy to apply it conservative regulatory damage stability calculations, and this paper provides one more step towards more common use of advanced tools.

In general, the paper is well-written, but some parts should be clarified, and small errors need to be corrected. For the presented operational damage stability, some further explanations are needed. A detailed list of comments and questions is provided below.

1. Abstract is quite short, and could be extended.

2. line 17: “…problems are time consuming” is likely referring to the fact that the calculations and analyses are time consuming?

3. Introduction text refers to p_i and s_i without introducing these symbols. Some short explanation on definition of attained subdivision index and its components might be useful

4. Background: “If once” sounds a little strange, maybe simply “when”? The same strange phare is used also elsewhere

5. End of section 3 line 180: “has three major drawbacks” but only 2 bullet points are listed

6. Section 4 heading: it would be better to use the same symbols p_i, r_i and v_i instead of capital letters to avoid confusion

7. “manual damage stability calculation” is a strange term as all calculations are nowadays done with computers.

8. A subsection might be needed after eq. (3). In general, a clearer organization of the paper with use of subsection headers would make the paper easier to read. Therefore, some restructuring of the manuscript is highly recommended

9. Line 333 “to heal this problem” could be “to solve this problem”?

10. Some symbols are not consistent, for example the s-factor is sometimes s_i and sometimes S_i

11. Note in current SOLAS2020 the eq. (4) applies only for ropax ships in the damage cases, where a roro room is involved. In SOLAS2009, and currently for other damage cases, the range and MaxGZ references are different.

12. Eq. (4) could be presented better. Note in the text that range is in deg. Also SOLAS uses symbol K instead of c, which may be slightly confusing. And note that this depends only on the heel angle

13. End of section 7 notes some example computational times. It is not clear what “hydrostatic calculations” mean. How long does it take to calculate the final A-index?

14. Line 412 at end of section 8: “The output the contains” should be “The output contains”

15. Table 1: it would be good to list also the draft values

16. line 431 “but here degrees of freedom” is not clear

17. Font size in Figure 6 is so small, that it is very hard to read

18. The suggestion to interpolate “required A-index” based on the draft is interesting, but it seems to be in conflict with SOLAS Explanatory Notes. Thus some more extensive discussion on this, noting also regulatory aspects, would be useful.

19. Another aspect is the R-index, and if any real operational loading condition would be treated as a partial index, then for passenger ships, it would be required that Ai>0.9R. How would this additional requirement affect the presented case study of EMSA2 Ropax ship?

20. Conclusion section could be extended. E.g. some notes on needs for future research on the topic?

21. Reference list: please check and use a unified style with volume and page numbers. For example, ISP as a journal name is clear, as it likely should be International Shipbuilding Progress.

*Author Response*

Please see attachment

Author Response File: Author Response.docx

*Reviewer 2 Report
*

This is a quite interesting paper addressing the always important issue of damaged stability of ships. In the following, please find a few suggestions along with some requests for clarifications, aiming to help the potential reader.

The definition of p_{i}, r_{i} and v_{i} in lies 52, 53 and 54 might be rephrased so that they correspond to the probability of not extending beyond the corresponding boundary.

It is not clear (or maybe I have missed it) if and how the developed algorithm accounts for the SOLAS provision regarding damages with lower extend below the waterline.

In lines 244 to 246 it is stated that “In this context, it was found most efficient to analyze the nearest, but larger z-value of all the spaces breached by a cuboid”. This is not very clear, and some clarification is needed. For example, what is the meaning of “nearest”? Is this nearest to the hull?

What is the “maximum damage height of each individual damage case” in 248? Is it the maximum height of all damaged compartments? Please add an explanation.

In lines 248 to 249 it is stated that “In the same way, we can obtain the penetration depth for each individual damage case.” Please explain in more detail.

In page 7, regarding the breaches leading to the damage of the steering gear compartment it is stated that they either breach only the main compartment or only the emergency exit. However, one can imagine a hull breach limited in the longitudinal and transverse direction within the extend of the emergency exit but extending vertically both below and above z=9.20m, thus breaching both. What impact has this on the performance of the developed algorithm?

In lines 290 to 291 it is stated that “Damage zones are defined by giving a minimum and a maximum x-value for each damage zone.” Is this information provided by the user or is it obtained automatically by the algorithm?

In line 295 reference is made to the “flooded length of a damage”. Could you please define this term? Is it the length of the breach, or the distance between the most fwg to the most aft limit of all breached compartments, or something else? Is it the same with the “damage length” referenced in lines 297 and 298?

Section extending from line 288 to 309 is quite important in order to understand the way the developed algorithm is working. Unfortunately this section is not easy to follow. It is suggested that it is rewritten in more detail and more clearly.

In lines 381 to 382 it is stated: ”If the majority of these subcases is survived, the damage triangle is plotted in green, if the majority is not survived, the triangle is red.” What is the criterion of survival? Is it s>0, or s=1 or something in between? Green color in Fig. 5 corresponds to majority of s=1, red to majority of s=0 and yellow all other cases? Please explain.

In the upper-right part of Figure 5 one can see the 38 damage zones mentioned in the text. Bellow the ship’s profile one can see a very large number of triangles, starting at or between the limits of the damage zones. How do these triangles occur? Their starting points correspond to the aft and fwd limits of small rooms (e.g. small tanks) located within the limits of the damage zones? The same question applies to the lower part of Figure 5.

In lines 387 to 389 it says: “we have selected a damage zone setup with a damage zone at each transverse WTB of every compartment”. Are these zones specified manually by the user or created automatically by the algorithm? In the latter case, how can one specify the preferred detail of zonification?

Minor syntactical errors can be found throughout the text (e.g. lines 42, 51, 67, 251, 289, 412, 431 and maybe elsewhere).

*Author Response*

See attachment

Author Response File: Author Response.docx

*Reviewer 3 Report
*

The paper presents a methodology to obtain conventional "zonal" results from a set of "non-zonal" calculations for the damage stability assessment of a passenger ship.

Main comments:

1. The main concern about the paper's content is the scope of the research itself. If it is required to provide statutory output in a "zonal" format, why perform a "non-zonal" approach and rework it instead of choosing a "zonal" one directly? What is the benefit of employing a different calculation approach and reconverting the results to an older method? The development of a "non-zonal" damage stability framework has been intended as an alternative/substitutive method to the zonal one (see Bulian, G. et al., 2020. *Probabilistic assessment of damaged survivability of passenger ships in case of groundings or contact*. Ocean Engineering 218, 107396). The author should better clarify the benefits of its proposal.

2. The literature review on damage stability and Monte Carlo simulations is poor and limited until 2019. All recent developments and applications on the topic, available in the open literature, are missing. The author is encouraged to update his bibliography with relevant papers published in high-level journals between 2019 and 2022.

3. In Section 2 (lines 49-54), it is suggested to provide a more detailed description of the damage model used in the non-zonal approach.

4. In Section 2 (line 78), the author introduces the word "zones" without describing it. This is obvious for people dealing with damage stability but not for all journal readers.

5. (line 84) The author mentions a "numerical design environment". What does it specifically mean? Is it perhaps a design calculation framework? Please clarify.

6. (line 89) The author states that the Monte Carlo technique is an efficient solver for damage stability problems. Recent studies show more efficient ways to solve these problems (see Mauro, F., Vassalos, D., 2022. *The influence of damage breach sampling process on the direct assessment of ship survivability*. Ocean Engineering 250, 111008). Such considerations are linked to the bibliography issues raised in point 2.

7. (line 120) Please briefly mention the inconsistencies found by the author and verify if are in line with inconsistencies detected by other authors in the open literature.

8. (line 131) Introduction of a lower vertical limit for collision damages has been already studied and published (Bulian et al. 2019. *Complementing Solas damage ship stability framework with a probabilistic description for the extent of collision damage below the waterline*. Ocean Engineering 186, 106073). Please mention the reference in the text.

9. Please check the CDF for damage penetration in Fig. 2. Is this the standard for lateral penetration given by SOLAS?

10. The author describes the damages as cuboids. Is this modelling assumption in line with SOLAS regulations? The development of a non-zonal approach compliant with zonal assumptions results in damage modelling for side damages different from a box-shaped breach (see relevant literature from 2019 to 2022). Therefore, in case the author uses box-shaped damages, his non-zonal modelling is not comparable with SOLAS modelling and the reconversion process inherits a modelling error. Please clarify the damage shape issue.

Minor comments:

1. The figures throughout the paper have a really bad quality, quantities on the axis are not easily readable, and the same for the legends. The author should improve the figures/graph format in the revised version.

2. The symbols in the text should be all in italics, please revise the format.

3. Equations should be formatted according to the journal template.

4. Please check the style for citations and bibliography.

5. It is suggested to carefully check the English language in the revised version. There are a lot of typo errors and some sentences are hard to read.

*Author Response*

see attachment

Author Response File: Author Response.docx

**Round 2**

*Reviewer 1 Report
*

Firstly, the author is thanked for prompt response to all comments and questions, and for updating the manuscript accordingly.

Some small editorial corrections are still recommended:

1. equations and equation numbering is weird, and not in line with the journal template

2. same for figure captions

3. on page 3, the equation should be right after the paragraph and not after the figure

4. section 4, check the citations, since the reference list contains two papers Bulian et al. (2019). Think that the journal prefers numbered citations [1]... instead of using author name(s) and year...

5. on page 6 and 7 the formatting of the bullet lists is strange

6. after figure 4 the formatting of the text changes

7. section 4.3 line 384: "definition of the damage zones then is then only..." should be "definition of the damage zones is then only..."

8. section 4.4 should not start with a figure, but with a text section referring to the figure after the text.

9. on page 14: "x-Position" should be "x-position"

10. lots of empty space above fiture 10

*Author Response*

Please see attachment and thank you.

Author Response File: Author Response.pdf

*Reviewer 3 Report
*

The author partially addressed the reviewer's comments. It is suggested t better focus on the following two points:

1. Review of the application of Monte Carlo-based methods for damaged stability.

2. effective implementation of changes claimed in the reply. (e.g. the improper nomenclature "numerical model" still appears in the figure captions)

*Author Response*

Please see attachment.

Author Response File: Author Response.pdf