Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The topic addressed—health monitoring and safety assessment of retaining structures through theoretical innovation and experimental validation—is both timely and relevant, particularly in the context of structural resilience and risk management. However, before this manuscript can be considered for publication, it requires substantial revisions to strengthen its scientific rigor, clarity, and methodological transparency. The following comments are intended to guide the authors in refining their work and enhancing its contribution to the field.

• Please consider enriching the introduction by incorporating a broader international bibliography to contextualize the research within global developments in structural health monitoring.
• Section 3.1: The experimental scheme lacks photographic evidence or a scheme of the test setup, which would strengthen the clarity of the section. The audience would benefit from this additional information.
• Section 3.2: This reviewer suggests that the five conditions mentioned in this section be detailed.
• Section 3.2: It would be worth it to insert Table 2 before Figure 1 to distinguish the data better.
• Figure 1: Please provide a more comprehensive graph to detail the results. If the authors notice, different colors are used to identify the different conditions, and at the same time, the vertical axis depicts only one condition. It confuses the understanding of the preliminary results discussed.
• Line 192: A discrepancy has been detected, suggesting the influence of complex factors. Could you please provide more details about the possible factors?
• Section 3.2 (2): Table 3, Point 3, Condition 4 actually confirms that no significant residual energy is present in the higher bands; however, the values discussed between lines 206 and 208 are not immediately apparent. Please provide a parallel graph or table to show the actual energy distribution, ensuring consistency with the analysis in Section 3.2 (1).
• Line 215: Looks like this is a subtitle, but it should follow a sequence. Please fix it or reorganize the section. Additionally, please note that the discussion here is not well-structured.
• Line 232: Same comments as Line 215.
• Tables 4, 5, 6, and 7: Please revise the text format of the column associated with a L/m ratio of 1.2.
• Section 3.2: This section would benefit from additional statistical graphs to effectively represent the results.
• Table 8: Same comment as Tables 4, 5, 6, and 7.
• Lines 323-324: The authors mention that "the remaining service life under this damage state was predicted to be approximately 120 days." Could you please include an explanation of the calculated value?
• Some ideas may sound repetitive, so this issue should be addressed. Just one example here: Lines 392-393 and Lines 406-407.
• Overall, the manuscript would benefit from the inclusion of additional statistical graphs to reinforce the analysis and improve data interpretation. Additionally, the absence of images or diagrams of the experimental test setup limits the reader’s understanding of the methodology—visual documentation would significantly enhance transparency and reproducibility.

Author Response

Comments 1: Please consider enriching the introduction by incorporating a broader international bibliography to contextualize the research within global developments in structural health monitoring.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have enriched the introduction by adding several recent international studies to better situate our work within the global context of SHM. This change can be found in the Introduction section (Page 1, Paragraphs 2-3). The added references include, for example:
"[5]. Bertola and Bruehwiler (2024) proposed a systematic framework... [6]. Meanwhile, the application of piezoelectric materials... (Ju et al., 2023)... [7]. Experimental datasets, such as the one provided by de Sousa and Machado (2024)... [8]. Furthermore, the integration of machine learning techniques... (Rajeswari et al., 2024)..."

Comments 2: Section 3.1: The experimental scheme lacks photographic evidence or a scheme of the test setup, which would strengthen the clarity of the section. The audience would benefit from this additional information.

Response 2: Thank you for this suggestion. We agree with this comment. Therefore, we have added a new figure (Figure 1) detailing the experimental setup and field installation. This change can be found in Section 3.1.2, Experimental Equipment Configuration (Page 6, after the equipment list). The figure caption reads:

"Figure 1. Experimental setup and field installation. (a) Sensor grid layout, (b) Individual sensor installation, (c) Simulated damage drilling, (d) Data acquisition system."

Comments 3: Section 3.2: This reviewer suggests that the five conditions mentioned in this section be detailed.

Response 3: Thank you for this suggestion. We agree with this comment. Therefore, we have added a new table (Table 2) explicitly defining the five experimental damage scenarios, including the damage simulation method, description, and stiffness perturbation coefficient. This change can be found in Section 3.1.3, Experimental Condition Design (Page 7, before the description of excitation methods).

"Table 2. Definition of experimental damage scenarios... Condition 1: No drilling, Baseline (no damage), α=0.00 ... Condition 5: Drill 4 holes, Severe damage, α=-0.05"

Comments 4: Section 3.2: It would be worth it to insert Table 2 before Figure 1 to distinguish the data better.

Response 4: Thank you for this suggestion. We agree with this comment. Therefore, we have reordered the content as recommended. The detailed damage condition table (now Table 2) is placed in Section 3.1.3, and the energy ratio data (now Table 3) is presented before the corresponding figures (Figure 2) in Section 3.2.1 to improve the logical flow.

Comments 5: Figure 1: Please provide a more comprehensive graph to detail the results. If the authors notice, different colors are used to identify the different conditions, and at the same time, the vertical axis depicts only one condition. It confuses the understanding of the preliminary results discussed.

Response 5: Thank you for pointing this out. We agree with this comment. Therefore, we have completely redesigned the figure (now Figure 2 in Section 3.2.1) to improve clarity. The new figure uses a consistent color scheme across all subplots, clearly labels each working condition for all measurement points, and ensures the axes accurately represent the data for each condition, eliminating previous confusion.

Comments 6: Line 192: A discrepancy has been detected, suggesting the influence of complex factors. Could you please provide more details about the possible factors?

Response 6: Thank you for this suggestion. We agree with this comment. Therefore, we have expanded the discussion in Section 3.2.1 (Page 9, Paragraph 2) to include possible factors contributing to the discrepancy between theoretical predictions and actual energy redistribution. The added text is:

"This discrepancy between theoretical predictions and actual energy redistribution suggests the influence of complex factors, such as localized material heterogeneity, sensor coupling effects, and environmental noise. "

Comments 7: Section 3.2 (2): Table 3, Point 3, Condition 4 actually confirms that no significant residual energy is present in the higher bands; however, the values discussed between lines 206 and 208 are not immediately apparent. Please provide a parallel graph or table to show the actual energy distribution, ensuring consistency with the analysis in Section 3.2 (1).

Response 7: Thank you for pointing this out. We agree with this comment. Therefore, we have added a new Table 4 ("Measurement point wavelet packet characteristic frequency band energy ratio difference") in Section 3.2.1 (Page 11). This table clearly quantifies the energy shifts discussed, ensuring consistency with the analysis in the preceding subsection.

Comments 8: Line 215: Looks like this is a subtitle, but it should follow a sequence. Please fix it or reorganize the section. Additionally, please note that the discussion here is not well-structured.

Response 8: Thank you for this suggestion. We agree with this comment. Therefore, we have reorganized Section 3.2.2 by introducing two new subsections: "3.2.2.1 Spatial Distribution Validation of Damage Identification Indicators" and "3.2.2.2 Dynamic Assessment of Damage Severity and Its Correlation with Location" (starting on Page 12). This improves the hierarchical structure and clarity of the discussion.

Comments 9: Line 232: Same comments as Line 215.

Response 9: Thank you for pointing this out. We agree with this comment. Therefore, we have applied the same structural improvement to this part of the text, which is now included under the new subsection 3.2.2.2 (Page 13), ensuring a consistent and logical flow.

Comments 10: Tables 4, 5, 6, and 7: Please revise the text format of the column associated with a L/m ratio of 1.2.

Response 10: Thank you for pointing this out. We agree with this comment. Therefore, we have corrected the formatting in all relevant tables (now Tables 5, 6, 7, and 8 in Section 3.2.2). The column header for the horizontal distance has been standardized to "1.2" with correct numerical alignment throughout.

Comments 11: Section 3.2: This section would benefit from additional statistical graphs to effectively represent the results.
Response 11: Thank you for this suggestion. We agree with this comment. Therefore, we have enhanced Section 3.2 with additional graphical representations. Specifically, the redesigned Figure 2 now more effectively visualizes the energy distribution across conditions and points. Furthermore, the spatial distribution of the Damage Identification Index (DI) is now more clearly represented through the data in Tables 5-8 and the accompanying analysis.

Comments 12: Table 8: Same comment as Tables 4, 5, 6, and 7.

Response 12: Thank you for pointing this out. We agree with this comment. Therefore, we have reformatted Table 8 (now Table 9 in Section 4.1) to ensure consistency in numerical presentation and alignment with the other tables in the manuscript.

Comments 13: Lines 323-324: The authors mention that "the remaining service life under this damage state was predicted to be approximately 120 days." Could you please include an explanation of the calculated value?

Response 13: Thank you for this suggestion. We agree with this comment. Therefore, we have added a detailed explanation in Section 4.2 (Page 16, Paragraph 3) clarifying the basis of this prediction. The added text is:

The forecast is premised on an extrapolation of the observed degradation trend in the anti-overturning stability coefficient . The model posits that the temporal decay of  is linear and driven by cumulative damage, as quantified by the ERSD indicator. The remaining service life is defined as the time period until  is predicted to attain a predetermined failure threshold (with  typically regarded as the critical limit for overturning stability). This computation accounted for the daily degradation rate of the stability coefficient under sustained operational loads (, cf. Section 4.1) but explicitly disregarded the effects of extreme environmental incidents. "

Comments 14: Some ideas may sound repetitive, so this issue should be addressed. Just one example here: Lines 392-393 and Lines 406-407.

Response 14: Thank you for pointing this out. We agree with this comment. Therefore, we have carefully reviewed the manuscript to identify and eliminate repetitive statements. For instance, repetitive ideas in Sections 4.3 and 4.4 have been consolidated or rephrased to improve conciseness and flow.

Comments 15: Overall, the manuscript would benefit from the inclusion of additional statistical graphs to reinforce the analysis and improve data interpretation. Additionally, the absence of images or diagrams of the experimental test setup limits the reader’s understanding of the methodology—visual documentation would significantly enhance transparency and reproducibility.

Response 15: Thank you for these overarching suggestions. We agree with these comments. Therefore, we have addressed them comprehensively. We have included a new Figure 1 illustrating the experimental setup. We have added and improved several graphs, such as the redesigned Figure 2 for energy distribution and the analysis in Section 5.3 involving terrain curvature and ERSD correlation. These additions significantly enhance the visual documentation, data interpretation, and overall reproducibility of the study.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript offers a valuable contribution to structural health monitoring but requires minor refinements to address the points raised above. I recommend minor revisions to improve methodological justification, include comparative analyses, and enhance linguistic clarity. 

Comments for author File: Comments.pdf

Author Response

[The manuscript offers a valuable contribution to structural health monitoring but requires minor refinements to address the points raised above. I recommend minor revisions to improve methodological justification, include comparative analyses, and enhance linguistic clarity.]

Response 1:

Thank you for pointing this out. I/We agree with this comment. Therefore, I/we have added a new paragraph in Section 2.2 to justify the parameter selection for the FOWPT algorithm. This addition can be found on Page 8, in the paragraph following the performance comparison table (Table 1).

"To justify the parameter selection for the FOWPT algorithm, the Daubechies 4 (Db4) wavelet basis and a decomposition level of 4 were adopted. This selection was based on preliminary analyses which indicated that this configuration achieved an optimal balance between high-frequency resolution (critical for capturing crack-induced vibrations in the 4-8 kHz band) and computational efficiency for real-time monitoring applications. The Db4 wavelet is widely recognized for its suitability in structural vibration analysis due to its orthogonality and similarity to structural impulse responses."

Response 2:

Thank you for this suggestion. I/We agree with this comment. Therefore, I/we have enhanced the description of the ERSD indicator in Section 2.3(3) to clarify its physical basis and quantitative capabilities. This addition can be found on Page 9, in the paragraph following the initial introduction of the ERSD indicator.

"The ERSD indicator is formulated to correlate with the reduction in local structural stiffness. A higher ERSD value signifies a greater energy shift from low to high-frequency bands, which is a direct consequence of stiffness degradation (quantified by the perturbation coefficient α). This physical basis allows ERSD to serve not only as a localization tool but also as a quantitative measure of damage severity. The linear correlation with crack width (R² = 0.96) further validates its efficacy as a robust damage metric."

Response 3:

Thank you for this recommendation. I/We agree with this comment. Therefore, I/we have added a new subsection, 5.4 "Comparative Analysis with Conventional Methods", following Section 5.3. This new section, along with its accompanying Table 11, provides a comprehensive performance comparison between the proposed WPCF model and benchmark methods. This addition can be found starting on Page 28.

"5.4 Comparative Analysis with Conventional Methods

To comprehensively evaluate the superiority of the proposed WPCF model, a comparative analysis was conducted against two benchmark methods: (1) a conventional method based on Wavelet Transform (WT) energy features, and (2) the dynamic-only FOWPT-ERSD method without terrain fusion. The performance was assessed using multiple metrics: prediction accuracy (RMSE, MAE, R²), computational efficiency (relative to the WT method), and noise resistance (SNR improvement).

As summarized in Table 11, the proposed WPCF model achieved the highest overall performance. It yielded the most accurate ERSD predictions, with the lowest RMSE (1.26) and MAE (0.98), and the highest goodness-of-fit (R² = 0.84). While the WPCF model incurred a moderate increase in computational time (1.6×) compared to the traditional WT method (1.0×), this is considered a reasonable trade-off for its significant gains in accuracy and robustness. Notably, the FOWPT algorithm itself (even without fusion) already provided substantial improvements in noise resistance and accuracy over the WT method. The WPCF model further enhanced this anti-interference capability, achieving the highest SNR improvement (12.8 dB), which underscores the stabilizing effect of integrating static topographic features.

Table 11. Performance Comparison of Different Damage Identification Methods

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This reviewer thanks the authors for considering the comments. The quality of the manuscript has consistently improved. Only one concern remains regarding the New Figure 2. Please ensure consistency in the number of decimals on the graph, with a maximum of 3 decimal places. This might assist with overcrowding.    

Author Response

Comments 1: This reviewer thanks the authors for considering the comments. The quality of the manuscript has consistently improved. Only one concern remains regarding the New Figure 2. Please ensure consistency in the number of decimals on the graph, with a maximum of 3 decimal places. This might assist with overcrowding.

Response 1: Thank you for this positive feedback and for pointing out this important detail. We agree with this comment. Therefore, we have revised Figure 2 to ensure that all data labels consistently display a maximum of three decimal places. This adjustment has been applied uniformly across the entire figure, which has effectively alleviated the issue of overcrowding and improved visual clarity.