Investigation on Bearing Characteristics for Critical Fittings of Transmission Lines Undergoing Coupled Ice–Wind Loads

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

see the attached

Comments for author File: Comments.pdf

Author Response

Responses to comments of reviewer 1

A FEM is used for any application in this manuscript.

(1) There is not much information for modeling. A representative UHV transmission line was selected as the research objective with not enough implementation. There is no relevance with FEM's outcomes with the plots provided.

Response: We sincerely thank the reviewer for this valuable comment. We fully agree that additional modeling details are essential for enhancing the clarity and reproducibility of the FEM procedure. In the revised manuscript, we have added a detailed description of the finite element model, including the modeling parameters, boundary conditions, material properties, and loading configurations.

To address this comment, Figure. 2 has been updated to include more detailed information about the FEM model. In addition, two new paragraphs and several explanatory sentences have been added to Section 2.1, which are highlighted in red for clarity.

 

(2) Which is the target and the innovation of this research?

Response: The target of this research is to evaluate and predict the damage risk of critical fittings in ultra-high-voltage (UHV) transmission lines under complex coupled ice-wind conditions. The innovation of this study lies in the establishment of a systematic FEM-based analysis framework that integrates bundled conductors, jumper structures, and fittings to accurately capture the mechanical responses under combined static and dynamic loads. Furthermore, a high-throughput simulation dataset was constructed, and a damage risk assessment model based on a Multi-Layer Feedforward Deep Neural Network (MLF-DNN) was developed. This approach enables precise prediction of stress responses and damage risks, significantly enhancing the efficiency and intelligence of structural safety evaluation for UHV transmission lines.

 

(3) Which is the journal?  Infrastructures ? the templates says Sustainability

Response: The intended journal is Infrastructures. The inconsistency with the Sustainability template resulted from an oversight during manuscript preparation and has been fully corrected in the revised version.

 

(4) Figure 11, the developed MLF-DNN model consists of an input layer, two hidden layers, and an output layer. etc...

Response: Thank you for the comment. Yes. Figure 11 shows the structure of the developed MLF-DNN model, which includes an input layer, two hidden layers, and an output layer. Seven key influencing factors, including ice thickness (T), wind speed (V), wind direction angle (α), non-uniform icing degrees on windward (U₁) and leeward (U₂) sub-conductors, ice-shedding ratio (R), and non-uniform ice-shedding state (S), were selected based on typical engineering scenarios, as summarized in Table 3. The input layer contains seven nodes corresponding to these parameters, while the output layer includes four nodes (MA₁, MA₂, MB₁, MB₂) representing the maximum stresses of jumper spacers A and B under static and dynamic conditions. The description of the model has been clarified in Section 3.2, and Figure 11 has been updated accordingly.

 

(5) There is no clear connection of different parts in this research study.  Instead, use bullets to show innovation and separately show a scientific paper regarding the different tools being used.

Response: Thank you for the valuable suggestion. To improve the logical connection and readability of the paper, the Introduction section has been restructured with clear secondary subsections: 1.1 Background, 1.2 Literature Review, and 1.3 Contribution and Organization of this Paper.

In Section 1.3, the main innovations of this research are now presented in bullet points to clearly highlight the contributions, followed by a concise paragraph describing the overall organization of the paper. This modification enhances the logical coherence among different parts of the study and makes the novelty of the work more explicit. The revised structure and descriptions can be found in the updated Introduction section of the manuscript.

 

(6) There is no such clear evidence for the programs being used, only plots.

Response: We appreciate the reviewer’s comment. In this study, the finite element (FEM) simulations were conducted using ABAQUS 2023, and the data-driven modeling, training, and validation of the MLF-DNN were performed in Python with the TensorFlow and Scikit-learn libraries.

To clarify this information, corresponding descriptions have been added to Section 2.1 and Section 4.2 of the revised manuscript, specifying the software environment and computational tools used to ensure methodological transparency and reproducibility.

Reviewer 2 Report

Comments and Suggestions for Authors

This work investigates the damage characteristics of transmission line fittings under coupled ice‒wind loads via finite element modeling and deep learning. However, several critical shortcomings must be addressed by the authors.

1) The conclusion that ice accretion dominates over wind is not new, aligning qualitatively with established field knowledge (e.g., CIGRE TB 291, 2019). The term “damage characteristics” is misleading, as the dataset only includes von Mises stress—not fracture, fatigue life, or residual strength.

2) The FE model validation is inadequate. The validation of the six-bundle 720 mm² conductor system relies solely on ground-wire subspan tests (Ø 9.5 mm), which are orders of magnitude different in stiffness, sag, and boundary conditions. Material nonlinearity (e.g., plastic hardening, low-temperature embrittlement of the ZL102 alloy), bolt preloading, contact nonlinearity, and wear-induced geometry changes are entirely omitted, compromising model accuracy.

3) Wind loads are applied as static pressure, ignoring aerodynamic damping, wake-induced vibration, and galloping torque—rendering the claim that "wind has minor influence" unsubstantiated under dynamic conditions. Ice shedding is simulated via sudden gravity reduction, neglecting adhesive fracture energy, asymmetric shedding sequences, and multispan propagation effects.

4) The MLF-DNN framework employs straightforward regression without a new architecture, feature engineering, or physics-informed constraints. It must be benchmarked against at least two additional algorithms (e.g., gradient boosting, physics-informed NN) to prove superiority. The absence of interaction terms, dimensionality reduction, or uncertainty quantification (epistemic/aleatory) further weakens its utility.

5) Full-scale mechanical tests advertised in the manuscript are missing. The sandbag test on a ground wire only calibrates jump height and does not generate damage or validate FE stress predictions at critical locations (e.g., end lugs, clevis holes). Static tensile/bending tests on actual jumper-spacer samples with/without ice sleeves are essential to support claims.

6) Class-imbalance issues (only 6% of samples exceed yield) bias accuracy metrics (R²) toward low-stress majorities. Precision‒recall curves for yield‒exceedance classification and uncertainty bands (via Monte Carlo/Bayesian NN) are mandatory for risk-based decisions. The stress outputs must be converted to reliability indices or failure probabilities via material strength distributions.

Author Response

Responses to comments of reviewer 2

This work investigates the damage characteristics of transmission line fittings under coupled ice‒wind loads via finite element modeling and deep learning. However, several critical shortcomings must be addressed by the authors.

(1) The conclusion that ice accretion dominates over wind is not new, aligning qualitatively with established field knowledge (e.g., CIGRE TB 291, 2019). The term “damage characteristics” is misleading, as the dataset only includes von Mises stress—not fracture, fatigue life, or residual strength.

Response: Thank you for this insightful comment. We agree that the dominance of ice accretion over wind load is consistent with existing field knowledge. In this study, our objective is not merely to restate this qualitative understanding but to provide a quantitative analysis of the stress response and potential damage tendency of critical fittings under coupled ice–wind actions through refined FEM simulations and data-driven modeling.

The term “damage characteristics” in this context refers to the mechanical response features—specifically, the stress distribution and concentration patterns—that indicate potential damage risks rather than direct fracture or fatigue failure parameters. To avoid misunderstanding, relevant descriptions have been clarified throughout the manuscript.

To address thes, a new subsection 1.3 “Contribution and Organization of this Paper” has been added to clearly highlight the novelty of this work, including the integration of FEM-based analysis with an MLF-DNN risk assessment model and the construction of a high-throughput simulation dataset for quantitative damage evaluation.

 

(2) The FE model validation is inadequate. The validation of the six-bundle 720 mm² conductor system relies solely on ground-wire subspan tests (Ø 9.5 mm), which are orders of magnitude different in stiffness, sag, and boundary conditions. Material nonlinearity (e.g., plastic hardening, low-temperature embrittlement of the ZL102 alloy), bolt preloading, contact nonlinearity, and wear-induced geometry changes are entirely omitted, compromising model accuracy.

Response: We appreciate the reviewer’s valuable comment. We fully acknowledge that the ground-wire ice-shedding test (Ø 9.5 mm) differs from the six-bundle 720 mm² conductor system in stiffness, sag, and boundary conditions. In this study, the ground-wire test was not intended to serve as a direct quantitative validation but rather as a mechanical behavior reference to verify the correctness of the modeling approach—particularly the dynamic response pattern and the ice-shedding jump mechanism—under comparable physical phenomena. This approach ensures the reasonableness of the FEM modeling and loading methodology within a controllable experimental framework.

It should be noted that, in real engineering environments, direct validation of hardware load-bearing behavior under complex coupled ice–wind conditions is extremely challenging due to the large scale, environmental variability, and measurement limitations of transmission lines. Meanwhile, because the complete conductor–jumper–fitting system involves highly nonlinear contact and multi-body interactions, an overly detailed full-scale model would become computationally prohibitive. Therefore, appropriate simplifications were adopted to balance computational efficiency and mechanical fidelity.

In response to the reviewer’s suggestion, Section 2.1 has been further revised to include a detailed description of the FEM model configuration (as shown in Figure 2) and to clarify the modeling assumptions and limitations. These updates strengthen the transparency, interpretability, and credibility of the model while preserving its capacity for high-throughput simulation and data-driven risk assessment.

 

(3) Wind loads are applied as static pressure, ignoring aerodynamic damping, wake-induced vibration, and galloping torque—rendering the claim that "wind has minor influence" unsubstantiated under dynamic conditions. Ice shedding is simulated via sudden gravity reduction, neglecting adhesive fracture energy, asymmetric shedding sequences, and multi-span propagation effects.

Response: We sincerely thank the reviewer for this valuable comment. We fully agree that, under real operating conditions, wind loads involve complex dynamic effects such as aerodynamic damping, wake-induced vibration, and galloping torque, while the ice-shedding process may also include adhesive fracture energy release and multi-span propagation behaviors.

 

In this study, the wind load was simplified as a steady-state pressure distribution to focus on the quantitative comparison of mechanical responses under wind, icing, and ice-shedding conditions. This simplification allows for isolating the relative contribution of different load types and ensures the computational efficiency required for large-scale FEM simulations and high-throughput data generation. Therefore, the statement that “wind has minor influence” refers specifically to quasi-static stress responses rather than fully dynamic aerodynamic interactions.

We acknowledge that a more complete simulation that considering aerodynamic damping, galloping torque, and transient adhesive fracture mechanics, would further improve the physical fidelity of the model. However, such analyses require coupling fluid–structure interaction simulations, which may beyond the scope of the present risk-assessment-oriented framework. In future work, we plan to enrich and refine the model by incorporating aerodynamic–structural coupling, multi-span dynamic propagation, and adhesive fracture energy effects to enhance its applicability and predictive accuracy under realistic ice–wind environments.

In response to this comment, additional clarifications, including a new paragraph at the end of Sections 2.1 and a new paragraph at the end of Section 3, have been added to describe the assumptions and applicability of the static wind load and simplified ice-shedding treatments, thereby clarifying the study’s scope and outlining directions for future improvement.

 

(4) The MLF-DNN framework employs straightforward regression without a new architecture, feature engineering, or physics-informed constraints. It must be benchmarked against at least two additional algorithms (e.g., gradient boosting, physics-informed NN) to prove superiority. The absence of interaction terms, dimensionality reduction, or uncertainty quantification (epistemic/aleatory) further weakens its utility.

Response: We sincerely thank the reviewer for this valuable and constructive comment. We acknowledge that the MLF-DNN framework used in this study follows a conventional regression structure without introducing physics-informed constraints or complex feature engineering. The purpose of this work is to establish a data-driven baseline model capable of effectively capturing the nonlinear mapping between multiple ice–wind parameters and the stress responses of critical fittings.

In response to the reviewer’s suggestion, two additional benchmark algorithms，including Random Forest (RF) and XGBoost, were introduced for comparative analysis. The corresponding results are presented in Table 4, showing that the proposed MLF-DNN model achieves the best overall performance with R² = 0.961, MSE = 0.006, and MAE = 0.019, outperforming both RF and XGBoost. These results confirm the superior capability of MLF-DNN in learning complex nonlinear relationships and providing higher predictive accuracy and generalization under coupled ice–wind conditions.

We fully agree that incorporating physics-informed constraints, interaction feature extraction, and uncertainty quantification could further improve the model’s interpretability and robustness. These aspects have been added to the Conclusion section as directions for future research, where hybrid physics–machine learning models will be developed for more reliable risk-oriented prediction.

 

(5) Full-scale mechanical tests advertised in the manuscript are missing. The sandbag test on a ground wire only calibrates jump height and does not generate damage or validate FE stress predictions at critical locations (e.g., end lugs, clevis holes). Static tensile/bending tests on actual jumper-spacer samples with/without ice sleeves are essential to support claims.

Response: We sincerely thank the reviewer for this critical and constructive comment. We fully acknowledge that the sandbag ice-shedding test on the ground wire was mainly designed to calibrate the jumping height and dynamic response characteristics rather than to reproduce actual damage evolution or validate stress values at specific critical points such as end lugs or clevis holes.

Due to the large scale, complex structure, and high voltage level of the actual jumper spacer assembly, it is extremely challenging to perform full-scale destructive mechanical tests under realistic ice–wind environments. As a result, the present study primarily relies on numerical modeling and comparative validation to capture the dominant mechanical behaviors and evaluate damage risk trends.

To address this limitation, a detailed explanation has been added to the first paragraph of Section 2.2, clarifying the validation purpose and scope of the sandbag test. In addition, a new paragraph has been added at the end of Section 3, outlining future work involving static tensile and bending tests on full-scale or reduced-scale jumper spacer samples, with and without ice sleeves, to experimentally verify the FEM-predicted stress concentrations at critical regions and to further enhance the practical reliability of the proposed risk assessment model.

 

(6) Class-imbalance issues (only 6% of samples exceed yield) bias accuracy metrics (R²) toward low-stress majorities. Precision‒recall curves for yield‒exceedance classification and uncertainty bands (via Monte Carlo/Bayesian NN) are mandatory for risk-based decisions. The stress outputs must be converted to reliability indices or failure probabilities via material strength distributions.

Response: We sincerely thank the reviewer for this valuable comment. After re-examining the dataset, we confirmed that no class-imbalance issue exists, since all samples were generated using the Latin Hypercube Sampling (LHS) method, ensuring uniform coverage across the entire parameter space. Each combination of key factors—including ice thickness (T), wind speed (V), and wind direction angle (α)—represents a unique continuous sample rather than a discrete classification label. Therefore, the model deals with continuous regression outputs (stress values) instead of categorical prediction, and the concern of bias toward low-stress majorities does not apply.

To illustrate this, a new Figure 11 has been added, showing the sample distribution in two- and three-dimensional spaces, which clearly demonstrates the uniformity of the dataset generated by the LHS method. The uniform sampling ensures that the stress responses corresponding to different combinations of parameters are well represented, thereby guaranteeing the generalization capability and fairness of model training.

In addition, a note has been added in Section 4.1 to clarify that the dataset represents a continuous mapping problem without class-imbalance characteristics. The updated figure and explanation enhance the transparency of data preparation and strengthen the validity of the subsequent MLF-DNN modeling results.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript presents a well-organized and technically solid study addressing the damage risk assessment of critical fittings in UHV transmission lines under complex ice-wind conditions. The topic is highly relevant to the reliability and safety of modern power transmission systems, especially in high-altitude or extreme weather regions. The methodology that combining finite element modeling, high-throughput simulation, and deep neural network is novel and well-motivated. The results are clearly presented and provide valuable insights for practical engineering applications. Overall, the paper is of good scientific quality and merits publication on the respected “Infrastructures” after minor revisions.

The following comments is presented to improve the manuscript.

1. Provide more information on the sampling strategy (e.g., the choose reasons of parameter ranges for ice thickness, wind speed, shedding rate in Table 3) to enhance reproducibility.
2. Some figures should benefit from higher resolution and clearer labeling, particularly for stress contour plots, such as Figure 6.
3. In Section 2.2, the validation of modeling method using the ice-shedding test is very important for the innovation of the work, please fulfill the detail information of the test model.
4. A few grammatical and stylistic corrections would improve fluency (e.g., UHVDC in third paragraph of page 3 was not given the definition).

     5. Some more references corresponding to the work should be added. 

Author Response

Responses to comments of reviewer 3

The manuscript presents a well-organized and technically solid study addressing the damage risk assessment of critical fittings in UHV transmission lines under complex ice-wind conditions. The topic is highly relevant to the reliability and safety of modern power transmission systems, especially in high-altitude or extreme weather regions. The methodology that combining finite element modeling, high-throughput simulation, and deep neural network is novel and well-motivated. The results are clearly presented and provide valuable insights for practical engineering applications. Overall, the paper is of good scientific quality and merits publication on the respected “Infrastructures” after minor revisions.

The following comments is presented to improve the manuscript.

(1) Provide more information on the sampling strategy (e.g., the choose reasons of parameter ranges for ice thickness, wind speed, shedding rate in Table 3) to enhance reproducibility.

Response: We sincerely thank the reviewer for this helpful comment. To improve the transparency and reproducibility of the sampling strategy, detailed explanations regarding the parameter selection principles and range definitions in Table 3 have been added in Section 4.1 (Data Acquisition). Specifically, the selection of each parameter range was determined based on typical engineering scenarios, on-site monitoring data, and safety design criteria for UHV transmission lines in heavy-icing regions such as the Sichuan–Tibet and Yunnan–Tibet corridors.

For example, the ice thickness (T) range of 0–50 mm covers both normal icing and extreme heavy-ice conditions observed in field inspections; the wind speed (V) range of 0–30 m/s corresponds to the measured maximum gusts and design reference speeds in mountainous terrains; and the ice-shedding ratio (R) of 0–100% accounts for the entire de-icing process from initial detachment to complete shedding. In addition, to capture the effects of non-uniform icing and asymmetric ice-shedding, the parameters U₁, U₂, and S were included to represent differential loading between windward and leeward sub-conductors.

These clarifications have been added at the second paragraph of Section 4.1, providing a clear rationale for the parameter configuration and ensuring the reproducibility of the sampling and simulation process.

 

(2) Some figures should benefit from higher resolution and clearer labeling, particularly for stress contour plots, such as Figure 6.

Response: Thank you for the reviewer’s helpful suggestion. In the revised manuscript, Figure 6 and other stress contour plots have been replaced with higher-resolution images and enhanced labeling to improve visual clarity. The contour color scales, stress units, and key structural regions (such as jumper spacers and connection fittings) have been clearly annotated to ensure better readability and accurate interpretation. These updates improve the overall quality and legibility of the figures, making the stress distribution features more distinguishable.

 

(3) In Section 2.2, the validation of modeling method using the ice-shedding test is very important for the innovation of the work, please fulfill the detail information of the test model.

Response: We sincerely thank the reviewer for highlighting this important point. We agree that providing detailed information on the ice-shedding validation test is essential for demonstrating the reliability and innovation of the proposed modeling approach. Accordingly, Section 2.2 has been revised and expanded to include comprehensive descriptions of the experimental setup, subsystem components, and measurement configurations.

The updated text now specifies that the ice-shedding experiment consisted of four main subsystems: the ground wire–suspension string system, the ice-shedding control system, the tension measurement system, and the displacement measurement system. The test model used two consecutive spans (444 m span length and 38 m height difference), with stiff steel frames replacing towers to eliminate deformation effects. The ice-shedding process was simulated using calibrated sandbags held by electromagnets, which were released via a programmable controller to reproduce the sudden loss of ice mass. The tension variation was recorded through load cells (0–10 t range, 10 kg precision), while displacement was captured by a high-resolution optical system using digital cameras and image-processing algorithms.

These details have been fully incorporated into Section 2.2. The revision ensures a more complete understanding of the test model and strengthens the experimental validation supporting the FEM-based simulation framework.

 

(4) A few grammatical and stylistic corrections would improve fluency (e.g., UHVDC in third paragraph of page 3 was not given the definition).

Response: We appreciate the reviewer’s careful reading and helpful suggestion. The grammatical and stylistic issues mentioned have been thoroughly reviewed and corrected throughout the manuscript to enhance overall fluency and readability. In particular, the abbreviation “UHVDC” has now been clearly defined as “Ultra-High-Voltage Direct Current” upon its first appearance in the third paragraph of Section 1. Minor grammatical adjustments and style refinements were also made in several sections to ensure linguistic accuracy and consistency with academic writing standards.

 

(5) Some more references corresponding to the work should be added. 

Response: Thank you for the reviewer’s valuable suggestion. In the revised manuscript, four additional references closely related to ice accretion, ice-shedding dynamics, and the mechanical behavior of transmission components have been added to the Literature Review (Section 1.2) to strengthen the contextual background and scientific relevance of this work.

These include recent studies by Zhang et al. (2025, 2025) on natural icing and anti-icing performance of insulator structures, and by Teng et al. (2025) on the nonlinear dynamic responses of six-bundle conductors under ultra-heavy icing conditions. The added references improve the completeness and timeliness of the literature review and further highlight the novelty and engineering significance of the present research.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

accept as it is. the cover letter is good

Reviewer 2 Report

Comments and Suggestions for Authors

Revised reasonably.