WTConv–TimesNet for Road Icing State Classification with IWOA-Based Hyperparameter Optimization

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1) Lines 142-148

Figure 1 needs to be described more precisely. In particular, when describing the framework and its general operation in the text, the components shown in this figure (e.g., model input data, TimesBlock, etc.) should be used.

2) Formulas (6), (7)

I suggest specifying the shape of the outputs H and X, as is done for X in formula (4).

3) 4.1 Hyperparameter Optimization Results

I recommend providing a link to the original source describing the IWOA method used, as well as specifying the tool (library) for implementing this method that the authors used in their work.

I think a justification is also needed here for why the authors use validation loss as the objective function for hyperparameter optimization, rather than quality metrics such as accuracy.

4) Furthermore, I suggest that at the beginning of Section 4, the authors indicate the technological tools used to conduct their experiments. Specifically, I recommend indicating the programming language and main libraries, as well as the software environment and hardware used to conduct the experiments.

5) I believe the article lacks a Discussion section, where quantitative results would be discussed in comparison with those demonstrated by other researchers mentioned in the Introduction. This section could also formulate the limitations of the proposed method, as well as offer practical conclusions and recommendations for implementing the proposed model in road icing detection processes in real-world conditions.

Author Response

1)Lines 142-148Figure 1 needs to be described more precisely. In particular, when describing the framework and its general operation in the text, the components shown in this figure (e.g., model input data, TimesBlock, etc.) should be used.

Thank you for this valuable comment. In the revised manuscript, we have provided a more precise description of Figure 1 in Section 2.1 (Page 4, Lines 160–169). The revised text now explicitly explains the general workflow by referring directly to the components shown in the figure, including the raw time-series data, model input data, the TimesNet backbone, stacked TimesBlocks, the transformation from 1D space to 2D space, the WTConv module, the Adaptive Aggregation module, and the Softmax classification layer. Furthermore, in Lines 170–172, we added a supplementary statement linking Figure 1 to Table 1, which further clarifies the layer-wise structure of the proposed framework. As a result, the description of the framework is now more consistent with Figure 1 and easier for readers to follow.

2)Formulas (6), (7)I suggest specifying the shape of the outputs H and X, as is done for X in formula (4).

Thank you for your valuable suggestion. In the revised manuscript, we explicitly specified the output shapes in Equations (6) and (7) in Section 2.3, Page 6, Lines 233–240. Specifically, after defining the reshaped feature tensorin Equation (4) (Lines 220–221), we further clarified that the intermediate feature tensor in the wavelet domain is given asin Equation (6) (Lines 233–235), and that the reconstructed output is given as in Equation (7) (Lines 237–240). In addition, the explanatory text following Equation (7) was refined in Lines 241–242 to improve notational clarity and consistency. These revisions make the tensor-shape definitions in the WTConv formulation more explicit and consistent with the notation introduced earlier in the manuscript.

3)4.1 Hyperparameter Optimization Results I recommend providing a link to the original source describing the IWOA method used, as well as specifying the tool (library) for implementing this method that the authors used in their work . I think a justification is also needed here for why the authors use validation loss as the objective function for hyperparameter optimization, rather than quality metrics such as accuracy.

Thank you for this valuable comment. In the revised manuscript, we addressed this issue in two places. First, in Section 2.4 (Page 7, Lines 262–269), we clarified the methodological origin of the adopted IWOA framework by explicitly linking it to prior WOA improvement studies, from which the nonlinear convergence factor and adaptive weight strategy were derived. Second, in Section 4.1 (Page 12, Lines 402–407), we specified that the hyperparameter optimization was implemented in Python using PyTorch with a self-developed search routine. We also added an explanation for selecting validation loss as the optimization objective, noting that it provides a smoother and more sensitive optimization signal than accuracy, which is discrete and may remain unchanged across candidate configurations during the early search process.

4)Furthermore, I suggest that at the beginning of Section 4, the authors indicate the technological tools used to conduct their experiments. Specifically, I recommend indicating the programming language and main libraries, as well as the software environment and hardware used to conduct the experiments.

Thank you for this valuable suggestion. In the revised manuscript, we included a dedicated description of the experimental environment at the beginning of Section 4 (Page 11, Lines 392–397). The revised text now specifies the programming and software environment, including Python 3.8.5, PyTorch 2.2.0, and CUDA 11.8, as well as the hardware platform, including an Intel Core i5-12600K CPU, an NVIDIA GeForce RTX 3080 Ti GPU with 12 GB memory, and 32 GB RAM. We also clarified that all models were trained and evaluated under identical hardware and software conditions to ensure the fairness and reproducibility of the reported results.

5)I believe the article lacks a Discussion section, where quantitative results would be discussed in comparison with those demonstrated by other researchers mentioned in the Introduction. This section could also formulate the limitations of the proposed method, as well as offer practical conclusions and recommendations for implementing the proposed model in road icing detection processes in real-world conditions.

Thank you for this valuable comment. In the revised manuscript, we addressed this issue in two parts. First, we strengthened the quantitative discussion at the end of Section 4.4 (Page 16, Lines 500–524) by explicitly comparing the proposed model with several representative methods (BiLSTM, TCN, Transformer, and TSMixer) in terms of both predictive performance and computational cost, and by discussing their respective strengths and limitations in modeling road icing time series. Second, we added a dedicated Section 4.5, “Discussion and Limitations” (Pages 16–17, Lines 525–557), where we now explicitly summarize the main limitations of the proposed method, including computational complexity, limited dataset diversity, the lack of isolated evaluation under stronger sensor disturbances or abnormal environmental fluctuations, and the absence of explicit spatial interaction modeling. We further included future research directions and a practical statement clarifying that the proposed framework is more suitable for real-world road monitoring scenarios with available multi-source sensing data and a need for reliable recognition of transitional icing states.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors propose an improved TimesNet network integrated with wavelet transform convolution. Compared with the baseline TimesNet model, it achieves an improvement of more than 6%.

Remarks:

1) Regarding keywords, can this be reworked or broken down into smaller elements - road icing state recognition

2) The text very often contains "we propose...". It may be better to write a scientific article in the third person.

3) A more detailed description of the arguments should be added to the formula. For example, for formula 2, not all variables are described, and one can only guess.

4) Line 169 - "K th−period " or "k th−period ". Check the case again (upper, lower)

5) For Figure 3, it is worth adding an explanation of the color values.

6) It would be very good to add the architecture of the proposed approach in the paper, for example, specific layers with input and output dimensions. This would emphasize the author's contribution to the novelty

Overall, the work is well structured and presented, particularly with regard to the experiments. These comments should be taken into account.

Author Response

• Regarding keywords, can this be reworked or broken down into smaller elements - road icing state recognition

Thank you for this helpful suggestion. In the revised manuscript, we updated the keyword list in Page 2, Lines 54–55 to improve clarity and conciseness. Specifically, the original keyword “road icing state recognition” was reworked into smaller and more focused terms, and the revised keywords are now given as: road icing; icing state classification; multivariate time series; TimesNet; wavelet transform convolution; hyperparameter optimization. This revision makes the keywords more precise and improves the discoverability of the manuscript.

• The text very often contains "we propose...". It may be better to write a scientific article in the third person.

Thank you for this helpful suggestion. In the revised manuscript, the wording has been carefully polished to reduce the repeated use of first-person expressions such as “we propose” and to improve the overall academic style. In particular, the most visible statements in the Abstract, Introduction, methodology description, and conclusion have been revised into third-person or passive constructions where appropriate. This revision makes the presentation more consistent with the style of a scientific article.

• A more detailed description of the arguments should be added to the formula. For example, for formula 2, not all variables are described, and one can only guess.

Thank you for this valuable suggestion. In the revised manuscript, we added more detailed explanations of the variables and arguments used in the formulas, with particular attention to Equation (2) and the surrounding mathematical notation. Specifically, in Section 2.2 (Page 5, Lines 187–193), we now explicitly define the period-related variables,and the reshaped tensor. We also refined the descriptions around Equation (1) (Page 5, Lines 183–186) and Equation (3) (Page 6, Lines 197–203) to improve the clarity of the input dimensions, extracted features, learnable parameters, and activation function. Furthermore, additional clarifications were added to the WTConv and IWOA formulations in Page 6, Lines 233–242 and Page 7–8, Lines 270–302 to improve the consistency and readability of the mathematical presentation.

• Line 169 - "K th−period " or "k th−period ". Check the case again (upper, lower)

Thank you for pointing this out. In the revised manuscript, we checked and unified the notation related to  and  in Section 2.2 (Page 5, Lines 187–193). Specifically, is now consistently used to denote the number of selected dominant periods, whereas is used as the index of the period scale. Accordingly, the related expressions in the text were revised to consistently use “the  period scale ” rather than mixing upper- and lower-case notation. This revision removes the ambiguity between  and  and improves notational consistency throughout the manuscript.

• For Figure 3, it is worth adding an explanation of the color values.

Thank you for this helpful suggestion. In the revised manuscript, we added an explicit explanation of the color values for Figure 3 in Section 3.2 (Page 10, Lines 364–367). Specifically, the text now clarifies that the color scale represents Pearson correlation coefficients ranging from −1 to 1, where positive values indicate positive correlations, negative values indicate negative correlations, and larger absolute values correspond to stronger relationships. This revision makes the interpretation of Figure 3 clearer for readers.

• It would be very good to add the architecture of the proposed approach in the paper, for example, specific layers with input and output dimensions. This would emphasize the author's contribution to the novelty

Thank you for this helpful suggestion. In the revised manuscript, we added a layer-wise architecture table in Section 2.1 to provide a clearer description of the proposed IWOA–TimesNet–WTConv framework. Specifically, in Page 4, Lines 169–172, we added a statement explaining that the layer-wise input and output shapes of the main modules are summarized in Table 1. The newly added Table 1 (Page 5, beginning at Line 174) explicitly lists the major architectural components together with their corresponding input and output dimensions, including the Input projection, FFT-based period discovery, 1D-to-2D reshaping, WTConv, Adaptive aggregation, Residual connection, GELU, Dropout, Flatten, and Fully connected layer. This addition makes the structure and implementation details of the proposed model more explicit and helps better highlight the architectural design and novelty of the proposed approach.

Reviewer 3 Report

Comments and Suggestions for Authors

The article is devoted to the classification of road icing using WT and IWOA. However, I have a number of comments, the answers to which will allow to improve the perception of the obtained results.

1.WTConv has long been used for classification. Specify the difference.

2.Equations (17),(19)-(21) need to be eliminated because they are well known.

3.The IOWA algorithm has a drawback that consists in capturing local minima, which leads to incorrect estimation. How to eliminate this drawback.

4.Show how your approach will work under conditions of artifacts: changes in lighting and contrast. How is this artifact eliminated and how does it affect the accuracy of classification.

5.In Table 3.4, compare the computational costs in FLOPS.

6.There is no Discussion section where it is necessary to state the limitations of the approach and the prospects for further research.

7.In the Introduction, the advantage of using WT should be more clearly substantiated, for example, Huan, W et al Haar wavelet-based classification method for visual information processing systems.

8.References should be expanded and supplemented to enhance the relevance of the research conducted.

Author Response

1.WTConv has long been used for classification. Specify the difference.

Thank you for this important comment. In the revised manuscript, we clarified more explicitly that WTConv itself is an existing wavelet-based convolution framework, rather than a standalone module newly proposed in this study. Specifically, in the Introduction (Page 3, Lines 95–101), we added a clearer background statement indicating that previous studies have already demonstrated the effectiveness of wavelet-based classification and that the WTConv framework has been reported as an existing wavelet-domain convolution approach. We then clarified in Page 3, Lines 110–117 that the contribution of the present work does not lie in proposing WTConv itself, but in integrating WTConv into the TimesNet backbone by replacing the original Inception convolution and incorporating it into a periodic time-series modeling framework for road icing state classification.

To further make this distinction explicit, we revised the contribution statement (Page 4, Lines 130–145) to state that the novelty of this study lies in the architecture integration and task adaptation, namely redesigning the original TimesNet temporal feature extraction process with wavelet-based operations for multivariate road icing time-series classification, rather than introducing WTConv as a new generic convolution module. In addition, in Section 2.1 (Page 4, Lines 154–168) and Section 2.3 (Page 6, Lines 213–218), we further clarified that WTConv is used here as a task-oriented replacement for the original Inception convolution module in TimesNet, with the purpose of strengthening multiscale time-frequency representation and improving the characterization of high-frequency and non-stationary variations during road icing evolution. These revisions make the novelty boundary of the manuscript more precise and transparent.

2.Equations (17),(19)-(21) need to be eliminated because they are well known.

Thank you for this constructive suggestion. We agree that these evaluation metrics are standard and do not need to be presented in equation form in this manuscript. In the revised manuscript, we removed Equations (17) and (19)–(21) together with their related explanatory text, and rewrote Section 3.3, “Evaluation Metrics” (Page 11, Lines 383–390) as a concise textual description. The revised section now briefly explains the use of Accuracy, Precision, Recall, F1-score, macro-averaged metrics, and confusion matrices without listing their mathematical formulas. This revision improves the readability and presentation of the manuscript.

3.The IOWA algorithm has a drawback that consists in capturing local minima, which leads to incorrect estimation. How to eliminate this drawback.

Thank you for this important comment. We agree that whale optimization algorithms may suffer from premature convergence and may become trapped in local optima, which can negatively affect the reliability of hyperparameter estimation. In the revised manuscript, we clarified in Section 2.4 and Section 4.1 how the adopted IWOA alleviates this drawback rather than completely eliminating it. Specifically, in Section 2.4 (Page 7, Lines 262–269), we added a clearer explanation that the introduced nonlinear convergence factor helps maintain stronger global exploration in the early search stage, while the adaptive weight strategy improves the balance between exploration and exploitation during iteration. In addition, in Page 8, Lines 299–306, we further clarified that the use of Xrand(t)X_{rand}(t)Xrand​(t) increases population diversity and enhances the ability of the algorithm to move away from local optima. To complement this mechanism-based explanation, in Section 4.1 (Page 12, Lines 409–417; Page 13, Lines 426–427), we also refined the convergence discussion to indicate that the proposed IWOA exhibits a relatively efficient and stable search process in the hyperparameter space. Accordingly, the revised manuscript now emphasizes that the adopted strategy reduces the risk of being trapped in local optima and alleviates premature convergence, rather than claiming complete elimination of this drawback.

4.Show how your approach will work under conditions of artifacts: changes in lighting and contrast. How is this artifact eliminated and how does it affect the accuracy of classification.

Thank you for this valuable comment. We would like to clarify that the proposed method operates on multi-source environmental sensor time-series data, rather than visual images. Accordingly, variations in lighting and contrast are represented in the present framework through environmental measurements—most directly through illumination intensity—instead of being treated as image artifacts. To make this point explicit, we revised Section 3.1 (Page 9, Lines 310–317) to state that illumination intensity is included in the raw monitoring data and is jointly learned with the other sensor variables. Furthermore, in Section 4.5 (Pages 16–17, Lines 538–554), we now explicitly acknowledge that the independent quantitative effect of stronger sensor disturbances or abnormal environmental fluctuations on classification accuracy has not yet been separately evaluated. The revised manuscript therefore clarifies both how such disturbances are represented in the current framework and that a more targeted robustness analysis will be conducted in future work.

5.In Table 3.4, compare the computational costs in FLOPS.

Thank you for this helpful suggestion. In the revised manuscript, the comparison of computational cost in terms of FLOPs was incorporated into Table 6 in Section 4.4. As shown in Page 15, Lines 496–499, the table was revised to include both predictive performance and computational cost, and three new columns—Total parameters, Trainable parameters, and FLOPs—were added for all compared models. Furthermore, in Page 16, Lines 507–515, we added a dedicated discussion of these results, showing that the proposed IWOA–TimesNet–WTConv model achieves the best classification performance with 513.792K FLOPs, which is substantially lower than that of BiLSTM and Transformer, although moderately higher than that of TCN and TSMixer. These revisions make the trade-off between predictive performance and computational efficiency clearer.

6.There is no Discussion section where it is necessary to state the limitations of the approach and the prospects for further research.

Thank you for this valuable suggestion. In the revised manuscript, we addressed this issue by adding a dedicated Section 4.5, “Discussion and Limitations” (Pages 16–17, Lines 525–554). This section now explicitly summarizes the main limitations of the proposed method, including computational complexity, limited dataset generalization, and the absence of explicit spatial dependency modeling, while also acknowledging that the independent impact of stronger disturbances has not yet been separately quantified. Moreover, the section outlines several directions for future work, including lightweight model design, broader cross-scenario validation, and spatiotemporal collaborative modeling. To maintain coherence, the Conclusion section (Page 17, Lines 560–577) was also revised accordingly so that the discussion of future work is no longer repeated unnecessarily.

7.In the Introduction, the advantage of using WT should be more clearly substantiated, for example, Huan, W et al Haar wavelet-based classification method for visual information processing systems.

Thank you for this helpful suggestion. In the revised manuscript, the motivation for using WT was strengthened in the Introduction (Page 3, Lines 95–101). Specifically, the reviewer-suggested study by Huan et al. was added as Reference [21], and the related WTConv study was cited as Reference [22]. The revised text now states that wavelet-based classification has shown effectiveness in visual information processing systems [21], while wavelet-domain convolution has also been demonstrated to enhance multi-frequency feature extraction in deep architectures [22].

8.References should be expanded and supplemented to enhance the relevance of the research conducted.

Thank you for this valuable suggestion. In the revised manuscript, we expanded and supplemented the references in the Introduction (Page 3, Lines 87–100) to improve the relevance and timeliness of the literature context. Specifically, we added two recent studies on winter road-state prediction—Jang [16] and Ma et al. [17]—in Lines 87–88 to further show that black ice prediction and road surface condition prediction remain active and practically important research topics. In addition, in Lines 95–100, we added Huan et al. [21] to support the methodological motivation for introducing wavelet-based representation, and cited the WTConv study as Reference [22] to further support the use of wavelet-domain convolution for multi-frequency feature extraction in deep architectures. These additions provide a more relevant and up-to-date literature basis for both the application background and the methodological design of the present study.

Reviewer 4 Report

Comments and Suggestions for Authors

This paper introduces IWOA–TimesNet–WTConv, a deep learning framework designed to classify accurately road icing states, using multi-source environmental data. The authors improve upon the standard TimesNet architecture by integrating a wavelet transform convolution (WTConv), which better captures the rapid, high-frequency atmospheric changes and temperature fluctuations that lead to ice formation. To ensure peak performance, they developed an Improved Whale Optimization Algorithm (IWOA) to automate and refine the selection of model hyperparameters. Additionally, the study employs Pearson correlation to identify the most physically relevant features, such as surface temperature and atmospheric pressure, while removing redundant or confounding data. The result is a reproducible workflow that covers raw-data preprocessing, feature construction, feature selection, and model training and evaluation, which provides a basis for road-icing early warning and intelligent road-safety management.

The WTConv module improves classification accuracy by integrating wavelet transform convolution into the TimesNet architecture to strengthen multiscale time-frequency feature extraction. By utilizing Discrete Wavelet Transform, WTConv decomposes input sequences into low-frequency and high-frequency sub-bands. This allows the model to capture high-frequency dynamics and abrupt local variations, such as rapid temperature changes, which are critical for identifying icing state transitions. This enhanced sensitivity to fine-grained variations significantly reduces confusion between adjacent icing stages and improves overall performance while retaining the advantages of TimesNet's periodic modeling. On the other hand,  the IWOA algorithm enhances classification accuracy by jointly optimizing key model hyperparameters, addressing the high parameter sensitivity inherent in road icing scenarios. It introduces a nonlinear convergence factor and an adaptive weight strategy to the standard optimization framework. These modifications improve convergence stability and prevent premature convergence by effectively balancing global exploration and local exploitation.

Experimental results on real-world datasets with icing in roads are classified into four different stages, demonstrate that this integrated approach achieves a high classification accuracy of 98.83%. An ablation study was performed to evaluate the proposed components by progressively integrating WTConv and IWOA into the baseline TimesNet model. The baseline TimesNet achieved 92.72% accuracy but exhibited noticeable confusion between adjacent icing stages, particularly mild and moderate icing. By incorporating the WTConv module, overall accuracy improved to 95.97% and the macro F1-score increased by 6.4%, demonstrating its enhanced ability to capture high-frequency dynamics and multiscale temporal patterns. The final proposed IWOA–TimesNet–WTConv model further increased accuracy to 98.83% and the macro F1-score to 0.9806, representing a total improvement of 6.11% over the baseline. These results confirm that WTConv substantially reduces misclassifications during transitional states, while IWOA-based hyperparameter optimization further sharpens decision boundaries and strengthens the model's discrimination between closely related icing states.

While the proposed model achieves high classification accuracy, the authors highlight several inherent limitations and areas for further development. A significant constraint is the current focus on localized temporal data. For a broad adoption of the model ,the study does not yet incorporate sufficiently variate spatial information or multi-site collaborative modeling, which are necessary to understand icing variations across roads in different geographical regions under several weather conditions. Furthermore, while the model was validated on a real-world dataset, it has not yet undergone online deployment in real-time monitoring systems. Consequently, its operational robustness and computational efficiency in live, practical applications remain untested. The results also emphasize a high sensitivity to hyperparameters, such as network depth and wavelet decomposition levels, necessitating a complex optimization algorithm like IWOA to prevent unstable convergence and misclassification. Additionally, the numerical improvement provided by feature selection was relatively moderate, and the model’s reliance on discrete stage labels may still face challenges in environments where the boundaries between icing states are particularly unclear. Finally, the preprocessing methods for handling missing values through filling strategies could potentially introduce temporal biases if sensor gaps are significant.

Notwithstanding these limitations, the paper represents an actual and valuable contribution to the state-of-the-art in automated road-icing early warning and intelligent road-safety management.

Recommendations for enhancing the final version:

1. The authors state (p. 222): "Conventional hyperparameter tuning strategies based on empirical selection or grid search are computationally inefficient and prone to subjective bias, making them unsuitable for such complex optimization tasks." Please provide some evidence therof, perhaps a comparison of training performed with traditional grid-search parameter tuning and the proposed one.

2. Eq. 13, "e is a natural constant", please clarify if it is Euler's number.

3. Line 270, "NTC temperature" please explain.

4. Line 272 "power supply voltage", this appears to be a mistake (and not used further in the analysis).

5. Eq. 17 I don't think it is necessary to explain what is Pearson correlation to the readers.

6. Fig. 3, Please explain why apparently unrelated variables have a very strong correlation (f.e., Pressure with NTC temperature). Also, why is wind speed not considered?

Author Response

1. The authors state (p. 222): "Conventional hyperparameter tuning strategies based on empirical selection or grid search are computationally inefficient and prone to subjective bias, making them unsuitable for such complex optimization tasks." Please provide some evidence therof, perhaps a comparison of training performed with traditional grid-search parameter tuning and the proposed one.

Thank you for this valuable suggestion. In the revised manuscript, we supplemented the discussion with direct experimental evidence. The statement regarding the limitation of conventional empirical tuning and grid search is retained in Section 2.4 (Page 7, Lines 258–260), and an explicit comparison between grid search and the proposed IWOA-based hyperparameter optimization has been added in Section 4.1 (Page 12, Lines 409–417) and presented in Figure 4. The comparison shows that IWOA attains a lower best fitness value (0.2331 vs. 0.2647), higher classification accuracy (0.9837 vs. 0.9638), and faster convergence to the best result (11th vs. 18th iteration). These additions provide direct quantitative evidence that the adopted IWOA strategy is more efficient than conventional grid search for the present task.

2. 13, "e is a natural constant", please clarify if it is Euler's number.

Thank you for this valuable comment. We agree that the original description of  was not sufficiently precise. In the revised manuscript, the explanation following Equation (13) was revised in Section 2.4 (Page 8, Lines 294–295) to explicitly state that  denotes Euler’s number. This change improves the precision and clarity of the mathematical notation.

3. Line 270, "NTC temperature" please explain.

Thank you for this valuable comment. We agree that the term “NTC temperature” required further clarification. In the revised manuscript, the explanation was added at its first occurrence in Section 3.1 (Page 9, Lines 312–314), where it is now explicitly defined as the contact-measured pavement temperature obtained using a negative temperature coefficient (NTC) thermistor. This clarification improves the precision of the variable description and avoids possible confusion with other temperature-related variables in the manuscript.

4. Line 272 "power supply voltage", this appears to be a mistake (and not used further in the analysis).

Thank you for this valuable observation. We agree that the original wording “power supply voltage” was inaccurate and potentially misleading. In the revised manuscript, the term was corrected to “wind speed sensor output voltage” in Section 3.1 (Page 9, Lines 312–317) to accurately describe the recorded signal. Moreover, this variable was not retained for the downstream analysis, as reflected by the revised feature-selection results in Section 3.2 and Table 2, where the compact input feature set used for the subsequent model is summarized. This revision clarifies both the meaning of the signal and its limited role in the present study.

5. 17 I don't think it is necessary to explain what is Pearson correlation to the readers.

Thank you for this valuable suggestion. We agree that the explicit formula for the Pearson correlation coefficient is not necessary for the present manuscript. In the revised version, Equation (17) and the associated explanatory text were removed, and Section 3.2 (Page 10, Lines 353–360) was rewritten in a more concise form. The revised text now states directly that PCC analysis was adopted to measure the linear relationship between candidate features and road icing-state labels, without including the standard equation. This change improves the conciseness and overall presentation of the manuscript.

6. 3, Please explain why apparently unrelated variables have a very strong correlation (f.e., Pressure with NTC temperature). Also, why is wind speed not considered?

Thank you for this valuable comment. In the revised manuscript, we added a more explicit explanation to the discussion of Figure 3 in Section 3.2 (Page 10, Lines 364–377). Specifically, the revised text now clarifies that a strong correlation does not necessarily imply a direct causal relationship. For example, the observed strong correlation between pressure and NTC temperature is interpreted as a joint statistical response to shared winter meteorological conditions and pavement thermal states during icing-prone periods, rather than as a direct physical causal relationship. The text further explains that, under such conditions, atmospheric pressure and NTC-measured pavement temperature tend to vary in opposite directions in the monitored dataset, which leads to the pronounced negative correlation shown in Figure 3.

Regarding wind speed, it was included in the initial candidate feature set and evaluated during the PCC-based feature screening stage. As shown in Table 2 (Page 11, Line 381 onward), its correlation with the road icing-state labels was relatively weak (r = 0.129) compared with the retained variables. Therefore, it was not included in the final compact feature subset discussed in Section 3.2 (Page 10, Lines 376–378) and visualized in Figure 3. These revisions make the interpretation of the correlation heatmap clearer and better justify the exclusion of wind speed from the final selected features.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

I generally agree with the responses to my comments. The changes and additions made have significantly improved the perception of the preserved results.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors provided substantial improvement on the quality of their paper. I have no further concerns.