Study on Strain Field Reconstruction Method of Long-Span Hull Box Girder Based on iFEM
and Tao Zhang 1,2Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsOverall Assessment:
This paper presents an interesting and valuable application of the inverse Finite Element Method (iFEM) for strain field reconstruction of a long-span hull box girder. The combination of physical test data with virtual sensor data is a novel approach that enhances the practical applicability of iFEM in ship structural health monitoring. The methodology is sound, and the results demonstrate good accuracy in reconstructing strain fields across different parts of the box girder.
Originality and Novelty :
- Novel application: The use of iFEM for a long-span hull box girder is innovative and relevant to the field of ship structural health monitoring.
- Comprehensive approach: The integration of physical test data with virtual sensor data provides a more robust reconstruction method.
- Detailed methodology: The paper provides a clear explanation of the iFEM formulation and its application to shell structures.
- Experimental validation: The use of a physical model test to validate the reconstruction results adds credibility to the findings.
- Visual representation: The strain field visualizations effectively illustrate the reconstruction results.
Suggestions for Improvement:
- Literature review: While the background provided is adequate, a more comprehensive review of recent advancements in iFEM applications for marine structures would strengthen the paper's context.
- Error analysis: The discussion of errors, particularly for points near the neutral axis, could be expanded. A more in-depth analysis of the sources of these errors and potential mitigation strategies would enhance the paper.
- Practical implications: The conclusion could be strengthened by discussing the practical implications of this work for real-world ship structural health monitoring applications.
- Future work: The paper would benefit from a brief discussion of potential future research directions based on the findings presented.
- Data presentation: Some of the tables and figures could be streamlined or combined for better readability. For instance, Tables 3 and 4 could potentially be combined.
- Methodology justification: The choice of iQS4 elements could be better justified, perhaps by comparing it briefly with other potential element types.
Technical Comments:
- The penalty parameter (λ = 10^-4) used in the iFEM formulation should be further justified. How sensitive are the results to this parameter?
- The influence of the number and placement of sensors on the reconstruction accuracy could be discussed more thoroughly.
- The limitations of the current approach, particularly for more complex ship structures, should be addressed.
- English language and clarity: The manuscript would benefit from thorough editing to improve grammar, syntax, and overall clarity. Some sentences are awkward or unclear, which can hinder understanding.
Author Response
Comments 1：[Novel application: The use of iFEM for a long-span hull box girder is innovative and relevant to the field of ship structural health monitoring.]
Response 1: [It has been supplemented in the first part of the literature 23, 23, and marked blue.]
Comments 2：[Comprehensive approach: The integration of physical test data with virtual sensor data provides a more robust reconstruction method.]
Response 2: [The measuring points 6-10 on the port are arranged at the neutral axis position. Near the neutral axis of the box girder, the strain gradient becomes smaller, and the strain value gradually approaches zero. At the same time, the structure is easily affected by external disturbance, measurement accuracy and material micro-inhomogeneity, which leads to the amplification of experimental measurement errors. The reconstruction process is influenced by iFEM algorithm, and the recognition degree of low strain region is low, which continues to expand the reconstruction error. And is added after Table 3 and marked in blue.]
Comments 3：[Practical implications: The conclusion could be strengthened by discussing the practical implications of this work for real-world ship structural health monitoring applications.]
Response 3: [In this study, a large number of experimental data are used to reconstruct the strain field of long-span hull box girder and present it visually, which can quickly evaluate the stress state of hull structure in complex sea conditions, prevent potential structural damage and ensure the safety of ship structure. And it is supplemented in the conclusion.]
Comments 4：[Future work: The paper would benefit from a brief discussion of potential future research directions based on the findings presented.]
Response 4: [ In the future, iFEM has a broad prospect in the field of ship and ocean engineering health monitoring.The research directions that need to be further improved may include improving the rapidity and computational efficiency of the algorithm, optimizing the sensor layout strategy, and verifying its accuracy and reliability under more complex load conditions, so as to further enhance the safety of ship structures and improve the life cycle. And it is supplemented in the conclusion.]
Comments 5：[Data presentation: Some of the tables and figures could be streamlined or combined for better readability. For instance, Tables 3 and 4 could potentially be combined.]
Response 5: [Table 3 shows the data of 45 measuring points and Table 4 shows the data of 15 verification points. How to merge the two tables may cause confusion. If these two tables are merged, it may cause confusion.]
Comments 6：[Methodology justification: The choice of iQS4 elements could be better justified, perhaps by comparing it briefly with other potential element types.]
Response 6: [In order to adapt to different structural forms and physical models, different inverse elements need to be constructed. At present, iCS8 and iQS4 are often used in the reconstruction of deformation field of offshore structures. iCS8 is suitable for constructing inverse shell elements of curved structures such as submarines and cylinders. Because the strain studied in this paper is in a linear changing stage, and the top, side and bottom plates are flat, and the influence of shear deformation on the structure is considered. And supplemented in section 2.1 and marked in blue.]
Technical Comments 1：[The penalty parameter (λ = 10^-4) used in the iFEM formulation should be further justified. How sensitive are the results to this parameter?]
Response 1: In principle, because the matrix is complete, it will be singular if the transverse shear component is not added. In the case of a missing in-situ strain component, the corresponding weighting constant is set to be small.There are related deductions and explanations in the literature[25-27]. If repeated in this paper, the core concerns may become scattered, so the related literature is supplemented.
Technical Comments 2：[The influence of the number and placement of sensors on the reconstruction accuracy could be discussed more thoroughly.]
Response 2: [The number and position of sensors are very important to the accuracy of strain field reconstruction by inverse finite element method. The more sensors there are, the higher the reconstruction accuracy is, but it also increases the calculation cost and prolongs the calculation time. The reasonable arrangement of sensor positions can significantly improve the reconstruction effect, especially in the stress concentration area, which can effectively capture key data and reduce the reconstruction error. Therefore, optimizing the number and location of sensors is the key to improve the accuracy of strain reconstruction. It is supplemented in Section 5.1 and marked in blue.]
Technical Comments 3：[The limitations of the current approach, particularly for more complex ship structures, should be addressed.]
Response 3: [For more complex ship structures, it may be influenced by complex loads, various boundary conditions, various materials and other coupling factors, which makes it more difficult to reconstruct the strain field. At present, the influence of single load and multi-load coupling on the reconstruction accuracy of strain field is also being explored, and the follow-up research will continue to analyze and improve the reconstruction effect of strain field.]
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe article is interesting from both a scientific and a practical point of view. The combination of numerical analysis and experimental studies, especially for large objects, is extremely valuable. In the opinion of the reviewer, the article is suitable for publication; however, several elements should be developed that would benefit the quality of the publication.
1. Describe the numerical model in more detail (section 3), provide more analysis parameters, etc.
2. The experimental part should also be described in more detail, a drawing of the tested elements would be useful, etc.
3. It would be a good idea to present the results of the research and numerical analysis and discuss the main developments in separate sections.
4. The most important conclusions should be summarised as a bulleted list.
Author Response
Comments 1:[Describe the numerical model in more detail (section 3), provide more analysis parameters, etc.]
Response 1:[Related contents have been supplemented in the third part and marked in red, and the front view of the loading model has been supplemented
The model material of the hull box girder studied in this paper is Q235 steel, with a total length of 12.5m, a width of 1.5m and a height of 0.8m. The model is divided into two loading sections, two changeover portions, one test section and two tooling occupation section, which are symmetrically distributed along the length with the test section as the center. In numerical simulation, the thickness of the top plate is 5.55mm, the other three plates are 5.75mm, the elastic modulus is set to 205GPa, and Poisson's ratio is 0.3.
When the model boundary is set, two simple supports are set at the top plate to limit the vertical movement of the model, and different upward thrust forces are applied to the tooling loading section at the top of the model. During the test, there are two 4000kN hydraulic cylinders at the bottom of the model, which work together on a horizontal cross bar, and the top of the model is fixed by a fixture, which contacts the top plate of the box girder in a semi-circular arc to realize the four-point bending loading test of the model. Figure. 3 is a schematic front view of model loading.
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Comments 2:[The experimental part should also be described in more detail, a drawing of the tested elements would be useful, etc.]
Response 2:[Related content has been supplemented in the four part and marked in red.
The experimental model adopts two kinds of sensor acquisition technologies, strain gauge and optical fiber. In this paper, only the acquisition results of strain gauge sensor are used as the input of strain field reconstruction, and the results of optical fiber sensor are not collected. In this paper, the information acquisition process based on strain gauge is to connect the strain gauge and the acquisition instrument through 9-core cable to realize the collection and transmission of structural strain information, and then reconstruct the strain field of the structure after processing the collected results. The main process of structural strain information acquisition is shown in Figure 6.]
Comments 3:[It would be a good idea to present the results of the research and numerical analysis and discuss the main developments in separate sections.]
Response 3:[Related content has been supplemented in the third part and marked in red.
Figures 4 and 5 present numerical simulations conducted using the finite element software Abaqus. The primary goal of these simulations is to guide the placement of measurement points in the experimental model. The strain distribution on the port exhibits a trend from the top to the bottom, transitioning from a positive high-strain zone to a low-strain zone, and then to a negative high-strain zone. Accordingly, strain sensors are placed in each of these zones. Additionally, strain data from virtual sensors within the model are used to supplement the experimental data from the physical model.]
Comments 4:[The most important conclusions should be summarised as a bulleted list.]
Response 4:[The conclusion has been summarized and revised as required.]
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe study concludes that combining Inverse Finite Element Method (IFEM) technology with physical test data can accurately reconstruct strain fields in long-span hull box girders, crucial for ship safety. The reconstruction errors were minimal, indicating the effectiveness of this approach for structural health monitoring in large marine structures, thus improving the reliability and safety of hull assessments. The reviewer found the novelty of this research, but some comments should be responded before it accepted.
1. In Introduction, the author explains the box girders subjected to several type of load. But some information missing, such as what types of deformation can occur in ships due to long-term cyclic loads and short-term high loads, and how do these affect ship safety? This should be described in Introduction.
2. The literature study of box girder have been done by Putranto et al (2024 and 2023). These reference can be included in the first paragraph in Introduction.
3. In Section 4, what is the significance of the strain field symmetry along the longitudinal section of the box girder under four-point bending conditions?
4. In Figure 18 and 19, what is the significance of the relative error range (-3.31% to 2.52%) between the measured and reconstructed values at the measuring point?
5. Conclusions can be improved. No suggestion for future work found.
Author Response
Comments 1:[In Introduction, the author explains the box girders subjected to several type of load. But some information missing, such as what types of deformation can occur in ships due to long-term cyclic loads and short-term high loads, and how do these affect ship safety? This should be described in Introduction.]
Respose 1:[It has been supplemented in the first part of the article and marked green.
Long-term cyclic loads and short-term high loads can cause various types of deformations in ships, including bending, torsional deformations, and fatigue damage. Long-term cyclic loads, such as those induced by repeated wave stresses, can lead to material fatigue, gradually weakening the structural integrity. On the other hand, short-term high loads, such as those resulting from impacts or extreme weather events, may cause localized buckling, plastic deformation, or even sudden structural failure. These deformations not only compromise the structural integrity of the ship but also pose significant risks to its durability and safety. Therefore, it is crucial to account for these factors in ship design and maintenance.]
Comments 2:[The literature study of box girder have been done by Putranto et al (2024 and 2023). These reference can be included in the first paragraph in Introduction.]
Respose 2:[It has been supplemented in the first part of the article and marked green.
Putranto T took the hull box girder as the research object, and ultimate strength predictions obtained from equivalent single layer (ESL) approach are compared to full three-dimensional finite element method (3D FEM) and the international association of classification societies (IACS) incremental-iterative method. The comparison between different methods is provided in terms of longitudinal bending moment and cross sectional stress distribution. Overall, ESL approach yields good agreement compared to the 3D FEM results in predicting the ultimate strength of ship hull girder while providing up to 3 times computational efficiency and ease of modeling[19,20]]
Comments 3:[In Section 4, what is the significance of the strain field symmetry along the longitudinal section of the box girder under four-point bending conditions?]
Respose 3:[It has been supplemented in the four part of the article and marked green.
Under the condition of four-point bending, by analyzing the numerical simulation results, it is found that the distribution of strain field of box beam is symmetrical in the middle longitudinal section and symmetrical in the middle transverse section. Therefore, the distributed optical fiber sensor and strain sensor are set in two symmetrical areas along the longitudinal section, and the main purpose is to form mutual verification of the acquisition accuracy of the two sensing acquisition technologies. The collected data show that the accuracy of the two sensing acquisition technologies is high in the linear stage of the structure, but only the strain gauge acquisition technology is used for related research in this study.]
Comments 4:[In Figure 18 and 19, what is the significance of the relative error range (-3.31% to 2.52%) between the measured and reconstructed values at the measuring point?]
Respose 4:[This error range is a summary of the reconstruction errors of all points on the bottom surface. Due to the definition of Equation 27, the relative error may be negative, which means that the reconstruction value is less than the measured value.]
Comments 5:[Conclusions can be improved. No suggestion for future work found. ]
Respose 5:[At the end of the article, the future research direction is added.
In the future, iFEM has a broad prospect in the field of ship and ocean engineering health monitoring.The research directions that need to be further improved may include improving the rapidity and computational efficiency of the algorithm, optimizing the sensor layout strategy, and verifying its accuracy and reliability under more complex load conditions, so as to further enhance the safety of ship structures and improve the life cycle.]
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe quality of the paper has been significantly improved. I recommend this paper for publication.
