the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 Sep 2026
Review article: A review of dynamic response analysis methods for transmission tower-line systems under ice-wind hazards
Abstract. Ice-wind hazards pose serious threats to transmission tower-line systems (TTLS), and dynamic response analysis is indispensable for elucidating the failure mechanisms of TTLS and guiding effective disaster mitigation strategies. This review elaborates on a series of dynamic response analysis methods for TTLS, covering analytical and mechanics-based methods, numerical simulation methods, stochastic and statistical methods, and methods based on artificial intelligence (AI) that show increasing potential to enhance predictive performance and computational efficiency. Detailed analyses are conducted on the fundamental assumptions, solution procedures, and uncertainty modeling of the various methods, as well as their respective methodological limitations. Finally, this review identifies key challenges associated with modeling, computation, and uncertainty quantification. Future research directions are proposed to advance intelligent and resilience-oriented strategies for the sustainable development of TTLS subjected to ice-wind loads.
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RC1: 'Comment on ms-2026-169', Anonymous Referee #1, 13 Oct 2026
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AC1: 'Reply on RC1', Bingzhao Qiu, 05 Nov 2026
We sincerely thank you for your positive evaluation of our manuscript and your constructive suggestions. We appreciate your recognition of the manuscript's organization, methodological comparisons, and discussion of future research directions. We have carefully considered all seven comments and provide our point-by-point responses below.
Comment 1: In Section 1.3, the authors are encouraged to briefly clarify the literature selection criteria and search strategy to improve the reproducibility of the review.
Response: Thank you for this valuable suggestion. As described in Section 1.3, the literature was retrieved from the Web of Science Core Collection for the period 1990-2025 using combinations of keywords related to ice, wind, dynamic response, transmission towers, and overhead lines. Studies focusing exclusively on meteorological processes or static ice-load estimation without relevance to tower-line dynamic response were excluded. We agree that the search and screening procedures could be described more explicitly. We will further clarify the search strategy and literature selection criteria to improve the transparency and reproducibility of the review.
Comment 2: Sections 2 and 3 both discuss nonlinear finite element analysis. The distinction between mechanics-based formulations and numerical simulation methods could be clarified.
Response: Thank you for pointing this out. The two sections are intended to address different aspects of dynamic response analysis. Section 2 focuses on the mechanical formulations and assumptions used to represent structural behavior, including geometric and material nonlinearities, while Section 3 emphasizes numerical discretization and computational approaches, such as FEM, FDM, and FVM. Nevertheless, we acknowledge that nonlinear finite element analysis involves both mechanical modeling and numerical implementation, which may cause some overlap. We will clarify this distinction and improve the transitions between the two sections to avoid unnecessary repetition.
Comment 3: In Table 4, linear analytical and nonlinear mechanics-based methods are grouped together, although their computational efficiency and nonlinear capabilities differ considerably. This comparison could be refined.
Response: We appreciate this insightful comment. We agree that linear analytical and nonlinear mechanics-based methods have different computational characteristics and capabilities, and their combined presentation in Table 4 may obscure these differences. We will refine the comparison by distinguishing the two subcategories and describing their respective advantages and limitations more accurately, particularly in terms of computational efficiency and nonlinear response analysis.
Comment 4: In Fig. 4, the evaluation scores are based on qualitative judgments. A brief explanation of the scoring criteria would improve the clarity of the comparison.
Response: Thank you for this helpful suggestion. The qualitative scores in Fig. 4 are intended to summarize the relative characteristics of the four methodological categories based on the discussions in Sections 2-5, rather than to provide an absolute quantitative ranking. We agree that the evaluation criteria should be explained more clearly. We will further specify the basis and interpretation of the qualitative scores for the six evaluation indicators. In particular, we will clarify that a higher score on the data-requirements axis indicates greater data demand, whereas higher scores on the other axes indicate stronger capabilities.
Comment 5: Section 5 could more clearly distinguish established AI applications in transmission tower-line systems from emerging methods with potential future applications.
Response: Thank you for this important comment. We agree that distinguishing demonstrated applications from emerging research directions would improve the clarity of Section 5. Existing studies have applied machine learning and deep learning techniques to transmission-line icing prediction, aerodynamic characterization, and related response prediction problems. In contrast, approaches such as physics-informed learning, neural operators, and graph-based learning remain at relatively early stages of application to the dynamic response of transmission tower-line systems under coupled ice-wind hazards. We will make this distinction more explicit and clarify the current applicability and future potential of these approaches.
Comment 6: The caption of Fig. 2 could be revised to more clearly describe the annual publication trends.
Response: Thank you for this suggestion. We agree that the current caption does not adequately describe the information presented in Fig. 2. We will revise it to: "Annual publication trends in research related to ice-wind hazards affecting transmission tower-line systems from 1990 to 2025, based on the Web of Science Core Collection." This description will more clearly convey the content and scope of the figure.
Comment 7: The authors are encouraged to check the consistency of abbreviations and terminology throughout the manuscript, particularly in the tables.
Response: Thank you for this careful observation. We agree that consistent terminology and abbreviations are important for the readability of a review article. We will systematically check the abbreviations and technical terms throughout the manuscript, particularly in Tables 1-4, to ensure that they are consistently defined and used. We will also standardize the terminology related to ice-wind hazards, dynamic response analysis, and the different methodological categories.
We sincerely appreciate the reviewer's constructive comments, which will help us further improve the clarity, consistency, and overall quality of the manuscript.Citation: https://doi.org/10.5194/ms-2026-169-AC1
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AC1: 'Reply on RC1', Bingzhao Qiu, 05 Nov 2026
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RC2: 'Comment on ms-2026-169', Anonymous Referee #2, 30 Oct 2026
This manuscript reviews dynamic response analysis methods for transmission tower-line systems under ice–wind hazards, covering mechanics-based formulations, numerical simulations, stochastic approaches, and artificial intelligence. The topic is relevant, and the comparative tables provide a useful overview of the available methods. The discussion of resilience also broadens the engineering perspective of the review. However, the literature selection, methodological classification, and critical synthesis require further improvement.
1.Section 1.3 provides the database, keywords, publication period, and general exclusion criteria. Please additionally report the exact search date, complete Boolean search expressions, and a clearer screening procedure to improve the reproducibility of the bibliometric analysis.
2. Although Section 2.2 distinguishes mechanical formulations from the numerical discretization methods reviewed in Section 3, the relationships among the different methodological levels could be made clearer. A schematic illustrating how mechanical models, numerical solvers, and uncertainty propagation methods can be combined would improve the organization of the review.
3. Sections 3.1 and 3.3 discuss non-uniform icing, conductor galloping, and tower–conductor coupling. Please strengthen the comparative synthesis by explaining the capabilities and limitations of representative methods in capturing these mechanisms.
4. Please clarify the scoring criteria and supporting evidence used for the qualitative comparison in Fig. 4. The broad statements in Table 4 should also account for differences within each category; for example, Category 1 includes nonlinear formulations but is collectively described as having limited capability for strong nonlinearity.
5.Please strengthen the connection between structural dynamic responses and the functionality and recovery concepts discussed in Section 6.2, preferably using representative examples from the reviewed literature.
6. The discussion of computational efficiency could be enriched by considering reduced-order modeling approaches for complex assembled structures. The authors may consider citing the following studies on the Mode Weighting Method as relevant methodological background and discussing their potential applicability and limitations for tower-line systems: https://doi.org/10.1016/j.engstruct.2024.118226；
https://doi.org/10.1016/j.engstruct.2026.122511.Citation: https://doi.org/10.5194/ms-2026-169-RC2 -
AC2: 'Reply on RC2', Bingzhao Qiu, 05 Nov 2026
We sincerely thank you for your positive evaluation of our manuscript and your constructive comments. We appreciate your recognition of the relevance of the topic, the comparative overview of existing methods, and the discussion of resilience. Your suggestions are valuable for improving the methodological organization, critical analysis, and overall clarity of the review. We have carefully considered all six comments and provide our point-by-point responses below.
Comment 1: Section 1.3 provides the database, keywords, publication period, and general exclusion criteria. Please additionally report the exact search date, complete Boolean search expressions, and a clearer screening procedure to improve the reproducibility of the bibliometric analysis.
Response: Thank you for this valuable suggestion. We agree that providing more detailed information on the literature retrieval and screening procedures would improve the reproducibility of the bibliometric analysis. As described in Section 1.3, the literature was retrieved from the Web of Science Core Collection for the period 1990-2025 using combinations of keywords related to ice, wind, dynamic response, transmission towers, and overhead lines. We will further improve this section by reporting the verified search date and complete Boolean search expressions, and by clarifying the literature screening procedure, including the relevance criteria and treatment of excluded records. These additions will make the bibliometric analysis more transparent and reproducible.
Comment 2: Although Section 2.2 distinguishes mechanical formulations from the numerical discretization methods reviewed in Section 3, the relationships among the different methodological levels could be made clearer. A schematic illustrating how mechanical models, numerical solvers, and uncertainty propagation methods can be combined would improve the organization of the review.
Response: Thank you for this helpful suggestion. We agree that a schematic would help clarify the relationships among the different methodological levels. The mechanical formulations discussed in Section 2 describe the governing physical behavior of transmission tower-line systems, while the numerical methods in Section 3 provide computational approaches for solving the corresponding governing equations. The stochastic and statistical methods in Section 4 can then be integrated with these models to quantify uncertainties in environmental loading, structural properties, and dynamic responses. We will introduce a schematic illustrating these relationships and the potential integration of mechanical models, numerical solvers, and uncertainty propagation methods. This will provide a clearer overview of how the reviewed approaches complement one another in dynamic response analysis.
Comment 3: Sections 3.1 and 3.3 discuss non-uniform icing, conductor galloping, and tower-conductor coupling. Please strengthen the comparative synthesis by explaining the capabilities and limitations of representative methods in capturing these mechanisms.
Response: We appreciate this insightful comment. We agree that a more explicit comparison of representative numerical methods would strengthen the critical analysis. FEM is particularly suitable for modeling the geometrically nonlinear behavior of conductors, tension redistribution, and tower-conductor interactions, whereas FVM is primarily employed to characterize aerodynamic effects associated with irregular ice shapes, flow separation, and wind-induced loading. However, FEM generally requires prescribed or separately calculated aerodynamic forces, while FVM alone cannot fully represent the structural dynamic response without coupling with an appropriate structural solver. We will strengthen the discussion in Sections 3.1 and 3.3 by comparing the capabilities and limitations of these approaches in capturing non-uniform icing, conductor galloping, and tower-conductor coupling, with particular attention to their complementary roles and computational requirements.
Comment 4: Please clarify the scoring criteria and supporting evidence used for the qualitative comparison in Fig. 4. The broad statements in Table 4 should also account for differences within each category; for example, Category 1 includes nonlinear formulations but is collectively described as having limited capability for strong nonlinearity.
Response: Thank you for this important observation. We agree that the qualitative comparison should more clearly distinguish the characteristics of different methods within each category. In particular, Category 1 includes both linear analytical approaches and nonlinear mechanics-based formulations, which differ substantially in their capabilities for representing nonlinear behavior and in their computational requirements. We will refine Table 4 to better reflect these differences and clarify the corresponding descriptions in Fig. 4. We will also provide a more explicit explanation of the qualitative scoring criteria and their supporting methodological evidence, while emphasizing that the comparison represents relative characteristics rather than an absolute quantitative ranking. These improvements will enhance the consistency and transparency of the comparative analysis.
Comment 5: Please strengthen the connection between structural dynamic responses and the functionality and recovery concepts discussed in Section 6.2, preferably using representative examples from the reviewed literature.
Response: Thank you for this constructive suggestion. We agree that establishing a clearer connection between structural dynamic responses and system functionality would improve the engineering relevance of Section 6.2. Dynamic response indicators, such as conductor displacement, cable tension, member stress, and tower deformation, provide important information for assessing structural damage and potential functional degradation. For example, studies of ice-shedding-induced dynamic responses and tower-line fragility under combined wind and ice loading provide useful evidence for understanding how structural responses may contribute to damage and service disruption. We will strengthen Section 6.2 by incorporating representative examples from the reviewed literature and clarifying the relationship between structural response, damage assessment, and functionality loss. We will also distinguish structural response assessment from system-level recovery, which additionally depends on operational conditions and restoration measures.
Comment 6: The discussion of computational efficiency could be enriched by considering reduced-order modeling approaches for complex assembled structures. The authors may consider citing the following studies on the Mode Weighting Method as relevant methodological background and discussing their potential applicability and limitations for tower-line systems: https://doi.org/10.1016/j.engstruct.2024.118226; https://doi.org/10.1016/j.engstruct.2026.122511.
Response: Thank you for recommending these relevant studies. We agree that reduced-order modeling provides an important direction for improving the computational efficiency of nonlinear dynamic analysis. The Mode Weighting Method (MWM) presented in the suggested studies offers an efficient approach to constructing low-dimensional dynamic models of complex assembled structures while retaining important modal characteristics. Such approaches provide useful methodological insights for the efficient modeling of transmission tower-line systems, particularly when repeated dynamic analyses are required. However, their applicability to tower-line systems under coupled ice-wind hazards requires further investigation, especially regarding geometric nonlinearity, sag-tension effects, tower-conductor coupling, and time-varying icing conditions. We will incorporate the two recommended references into the discussion of reduced-order modeling and further clarify their potential applicability and limitations in the context of transmission tower-line dynamic analysis.
We sincerely appreciate the reviewer's thoughtful and constructive comments. These suggestions will help us improve the methodological clarity, comparative depth, and engineering relevance of the manuscript.Citation: https://doi.org/10.5194/ms-2026-169-AC2
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AC2: 'Reply on RC2', Bingzhao Qiu, 05 Nov 2026
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RC3: 'Comment on ms-2026-169', Anonymous Referee #3, 30 Oct 2026
This manuscript reviews methods for analyzing the dynamic response of transmission tower-line systems under combined ice and wind hazards. It covers analytical and mechanics-based methods, numerical simulations, stochastic and statistical methods, and artificial intelligence approaches. The manuscript provides a useful overview of the subject and discusses the implications for system resilience. The topic is relevant, and the review is generally well organized. I recommend major revision before the manuscript can be considered for publication. The authors are encouraged to address the following comments:
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Please consider adding keywords such as “conductor galloping” or “numerical simulation” to better reflect the content of the manuscript.
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Please check that all abbreviations, such as TTLS, FEM, and PIML, are defined when they first appear in the text.
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At the beginning of Section 4, please briefly explain the main purposes of stochastic methods in the analysis of ice–wind hazards.
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At the end of Section 5.2, please add a brief summary of the main challenges in applying deep learning to the dynamic response analysis of transmission tower-line systems under combined ice and wind loads.
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In Section 5.2, the authors may consider discussing neural-network-based reconstruction of dynamic time histories as a related research direction. For example, the following study reconstructs bedrock motion from surface ground motion. Its application differs from the transmission tower-line problem and should be identified as a cross-domain example: Ji D, Chen Y, Li C, et al. BMINN: A neural network for bedrock motion inversion from ground motion. Engineering Geology, 2026, 374: 109110. https://doi.org/10.1016/j.enggeo.2026.109110.
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Please explain the basic idea of physics-informed machine learning in simpler terms so that readers without an artificial intelligence background can more easily understand it.
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In Figure 5, please clarify the meaning of the functionality variable \(q(t)\), for example, whether it represents structural serviceability or electricity delivery capability.
Citation: https://doi.org/10.5194/ms-2026-169-RC3 -
AC3: 'Reply on RC3', Bingzhao Qiu, 05 Nov 2026
We sincerely thank you for your positive evaluation of our manuscript and your constructive comments. We appreciate your recognition of the relevance of the topic, the organization of the review, and its discussion of system resilience. We agree that the suggested improvements will help enhance the clarity, completeness, and accessibility of the manuscript. We have carefully considered all seven comments and provide our point-by-point responses below.
Comment 1: Please consider adding keywords such as “conductor galloping” or “numerical simulation” to better reflect the content of the manuscript.
Response: Thank you for this helpful suggestion. We agree that the proposed keywords would better reflect the main research topics covered in the review. We will revise the keyword list to include "Conductor galloping" and "Numerical simulation", while retaining the essential keywords describing transmission tower-line systems, ice-wind hazards, and dynamic response analysis.
Comment 2: Please check that all abbreviations, such as TTLS, FEM, and PIML, are defined when they first appear in the text.
Response: Thank you for this careful observation. We agree that clear and consistent definitions of abbreviations are important for improving readability. We will systematically check the abbreviations throughout the manuscript to ensure that each abbreviation is properly defined upon its first occurrence and used consistently thereafter, particularly in the tables and figure captions.
Comment 3: At the beginning of Section 4, please briefly explain the main purposes of stochastic methods in the analysis of ice-wind hazards.
Response: Thank you for this valuable suggestion. Section 4 currently introduces the role of stochastic and statistical methods in characterizing uncertainties associated with ice-wind hazards. We agree that their main purposes could be stated more explicitly. We will refine the opening paragraph to emphasize three primary objectives: characterizing the randomness of ice and wind loads, quantifying the variability of structural dynamic responses, and evaluating structural reliability under uncertain loading conditions. This clarification will provide a clearer introduction to the methods reviewed in the subsequent subsections.
Comment 4: At the end of Section 5.2, please add a brief summary of the main challenges in applying deep learning to the dynamic response analysis of transmission tower-line systems under combined ice and wind loads.
Response: We appreciate this constructive comment. We agree that a summary of the main challenges would provide a more balanced discussion of deep learning applications. We will add a brief paragraph at the end of Section 5.2 highlighting several important challenges, including the limited availability of representative data under coupled ice-wind conditions, difficulties in generalizing models across different structural configurations and loading scenarios, and the limited physical interpretability of purely data-driven predictions. These challenges also motivate the discussion of physics-informed machine learning in Section 5.3.
Comment 5: In Section 5.2, the authors may consider discussing neural-network-based reconstruction of dynamic time histories as a related research direction. For example, the following study reconstructs bedrock motion from surface ground motion. Its application differs from the transmission tower-line problem and should be identified as a cross-domain example: Ji D, Chen Y, Li C, et al. BMINN: A neural network for bedrock motion inversion from ground motion. Engineering Geology, 2026, 374: 109110. https://doi.org/10.1016/j.enggeo.2026.109110.
Response: Thank you for recommending this relevant study. We agree that neural-network-based reconstruction of dynamic time histories represents a valuable research direction. The suggested BMINN study demonstrates the potential of deep learning for reconstructing complete dynamic time histories by combining amplitude prediction with time-frequency feature reconstruction. Although this study focuses on bedrock motion inversion rather than the dynamic response of transmission tower-line systems, it provides useful methodological insights into data-driven time-history reconstruction. We will cite this study in Section 5.2 as a cross-domain example and briefly discuss its potential relevance to reconstructing structural dynamic responses from limited monitoring information, while clearly distinguishing its original application from the ice-wind problem.
Comment 6: Please explain the basic idea of physics-informed machine learning in simpler terms so that readers without an artificial intelligence background can more easily understand it.
Response: Thank you for this helpful suggestion. We agree that a more accessible explanation would benefit readers from different research backgrounds. We will simplify the introductory description in Section 5.3 by explaining that physics-informed machine learning combines data-driven learning with established physical laws. Unlike conventional machine learning approaches that primarily learn relationships from data, physics-informed models incorporate physical constraints, such as governing equations, equilibrium conditions, and boundary conditions, into the learning process. This allows the model to learn from available data while encouraging predictions that are consistent with the underlying physical behavior. We will also briefly explain its potential benefits for transmission tower-line dynamic response analysis.
Comment 7: In Figure 5, please clarify the meaning of the functionality variable q(t), for example, whether it represents structural serviceability or electricity delivery capability.
Response: Thank you for pointing out this ambiguity. In Fig. 5, q(t) is intended to represent the normalized functionality of the transmission tower-line system relative to its pre-hazard operating condition, reflecting its overall ability to maintain electricity transmission service. It is a conceptual indicator of system functionality rather than a direct measure of an individual structural response, such as displacement or stress. Structural damage and loss of serviceability may contribute to functionality degradation, while recovery also depends on repair and restoration processes. We will clarify this definition in the text and figure caption and emphasize that Fig. 5 provides a conceptual illustration of functionality evolution rather than a quantitatively derived recovery curve.
We sincerely appreciate the reviewer's constructive comments and suggestions, which will help us further improve the clarity, technical content, and overall quality of the manuscript.Citation: https://doi.org/10.5194/ms-2026-169-AC3
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Remarks for the editor
(visible to the reviewers only)：
The manuscript addresses a relevant and important topic and provides a comprehensive, well-organized review of existing methods. The extensive literature coverage and discussion of future research directions are valuable. However, the critical comparison of different approaches, methodological classification, and justification of qualitative evaluations require further improvement.
Comments to the author：
The manuscript presents a comprehensive review of dynamic response analysis methods for transmission tower-line systems under ice-wind hazards. The topic is relevant, and the manuscript is generally well organized. The comparison of different approaches and discussion of future research directions are valuable. The following comments are provided for further improvement.