Research on Bearing Fault Diagnosis Method Based on MESO-TCN

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper can be improved by considering the followings:

1) The paper should be rewritten following the style of MDPI journals. Highlights and main findings are redundant which can be combined/integrated in to the abstract. 

2) Fault diagnosis has been a popular topic, and fruitful results are reported. The references are insufficient. The introduction session should be much enhanced by discussing recent machine-learning based diagnosis approaches such as federated learning based diagnosis, for instance,  An optimized updating adaptive federated learning for pumping units collaborative diagnosis with label heterogeneity and communication redundancy (https://doi.org/10.1016/j.engappai.2025.110724);  

A Federated Learning Based Fault Diagnosis in UAV-Reliable Sensor Network (10.1109/INDICON59947.2023.10440782)

The research challenges and research motivation of the paper should be highlighted. 

3) Some formulas don't appear well. The authors should double check to ensure the format of the formulas are correct. 

4) In figure 10, the recognised accuracy is 100% which is not realistic in real scenarios. I suggest the authors to use industrial data to further validate the approaches. 

5) The format of the references should be consistent with the style of the journal. 

6) None of the references come from this journal, showing weak relevance of the paper to the journal. 

7) Robustness of the paper to the data with noises should be better discussed and explained. 

8) The resolution of Figure 6 should be much improved. 

9) There are many results on bearing fault diagnosis. Why they are deserved to be further investigated compared with the existing works.

Author Response

COMMENTS TO THE AUTHOR(S)

1)The paper should be rewritten following the style of MDPI journals. Highlights and main findings are redundant which can be combined/integrated in to the abstract.

A：Thank you very much for your constructive suggestion. According to your advice, we have revised the manuscript to fully align with the style of MDPI journals. Specifically, we carefully reviewed and refined the abstract to make it more concise and informative. The previously redundant “Highlights” and “Main Findings” sections have been removed and their core contents have been integrated into the abstract to avoid duplication. The abstract now directly summarizes the key contributions and results of our work, in line with MDPI formatting standards. Please see lines 23–40 in the revised manuscript.

2)Fault diagnosis has been a popular topic, and fruitful results are reported. The references are insufficient. The introduction session should be much enhanced by discussing recent machine-learning based diagnosis approaches such as federated learning based diagnosis, for instance,  An optimized updating adaptive federated learning for pumping units collaborative diagnosis with label heterogeneity and communication redundancy (https://doi.org/10.1016/j.engappai.2025.110724); A Federated Learning Based Fault Diagnosis in UAV-Reliable Sensor Network (10.1109/INDICON59947.2023.10440782)

The research challenges and research motivation of the paper should be highlighted.

A：Thank you very much for your insightful suggestions. In response:

We have enriched the Introduction section by adding a discussion on recent machine learning-based diagnosis methods, particularly those involving federated learning. Specifically, two recent studies were cited to support the enhancement:

– [12] An optimized updating adaptive federated learning for pumping units collaborative diagnosis with label heterogeneity and communication redundancy (Engineering Applications of Artificial Intelligence, 2025)

– [13] A Federated Learning Based Fault Diagnosis in UAV-Reliable Sensor Network (IEEE INDICON, 2023)

These have been integrated into the sixth paragraph of the Introduction.

We have also explicitly highlighted the main research challenges in rolling bearing diagnosis, such as signal redundancy, insufficient deep modeling ability, and reliance on empirical parameter settings (paragraph 5).

The research motivation for proposing MESO-TCN is clarified accordingly, as an integrated solution addressing these challenges through entropy-based screening, multi-scale modeling, and adaptive parameter optimization (end of paragraph 5 and beginning of paragraph 6).

All references have been reformatted to comply with MDPI citation style (e.g., [1], [2], ...).

We sincerely hope these revisions address your concerns. The revised content can be found on lines 101–137 of the manuscript..

3)Some formulas don't appear well. The authors should double check to ensure the format of the formulas are correct.

A：Thank you for your careful review. We have thoroughly checked all mathematical formulas in the manuscript. The formulas have now been re-edited using the standard MS Word equation editor to ensure consistent formatting, proper alignment, and correct rendering.

Specifically, we revised several formulas such as Formula (1), (2), (10), and (11), which had formatting or clarity issues. All equations now conform to MDPI’s formatting standards. We sincerely appreciate your attention to this detail and have made sure that the formulas now appear correctly throughout the paper.

4)In figure 10, the recognised accuracy is 100% which is not realistic in real scenarios. I suggest the authors to use industrial data to further validate the approaches.

A：Thank you for your valuable suggestion. We agree that 100% accuracy is rarely achievable in real-world industrial applications. In our current work, the result shown in Figure 10 is obtained under controlled experimental conditions using the Xi’an Jiaotong University bearing dataset, which has relatively clean signals and well-labeled fault types. To address this concern, we have introduced an additional validation experiment using the PRONOSTIA bearing dataset, which is a widely recognized industrial-level benchmark designed to simulate realistic operating conditions such as variable loads and natural degradation.

The comparative experimental results of MESO-TCN and other baseline models on the PRONOSTIA dataset are now presented in Section 4.4 of the revised manuscript. MESO-TCN achieves a highest average accuracy of 96.73%, along with significant improvements in F1-score, precision, and recall compared to traditional TCN and CNN variants, thereby validating the model’s effectiveness in more complex and noisy industrial environments.

5)The format of the references should be consistent with the style of the journal.

A：Thank you for your suggestion. We have carefully revised all references in the manuscript to ensure full consistency with the citation and formatting guidelines of the Machines journal. Specifically, we adopted the numbered style [1], [2], … in both in-text citations and the reference list, as required by MDPI. We have also ensured the correct order, punctuation, journal abbreviations, and DOI links. The updated reference formatting now fully aligns with the journal’s specifications.

6)None of the references come from this journal, showing weak relevance of the paper to the journal.

A：Thank you very much for your insightful comment. In the revised manuscript, we have carefully reviewed and ensured the inclusion of relevant literature from Machines. Specifically, we have cited two recent studies published in Machines:

Reference [1]: Zhang, M., Liu, J., & Chen, H. “Knowledge Transfer-Based Ensemble Learning Method for Intelligent Fault Diagnosis with Few Labeled Samples,” Machines, 10(12), 1071, 2022.

Reference [3]: Wang, S., Fan, Y., & Zhang, Y. “A Multi-Branch Attention Feature Learning Network with Meta-Learning for Intelligent Fault Diagnosis,” Machines, 11(3), 332, 2023.

These works are directly related to our proposed MESO-TCN model and provided significant inspiration for the development of our method. We have further emphasized their relevance and contributions in the Introduction section of the revised manuscript. The reference formatting has also been unified to strictly comply with MDPI standards. We sincerely appreciate your helpful suggestion..

7)Robustness of the paper to the data with noises should be better discussed and explained.

A：We sincerely thank the reviewer for this valuable comment. To better address the robustness of our method against noisy data, we have added relevant discussion and verification in the revised manuscript. Specifically, we introduced the PRONOSTIA bearing degradation dataset, which is a widely acknowledged industrial dataset characterized by variable working conditions and naturally occurring noise. This dataset effectively reflects the challenges present in real-world scenarios. The diagnostic performance of the proposed MESO-TCN model on this dataset is detailed in the experimental section (Section 3.5), where the model achieved a high accuracy of 96.73%, along with superior F1-score, precision, and recall compared to other baseline models. These results demonstrate that our method maintains strong robustness and diagnostic capability under noisy and complex conditions.

8)The resolution of Figure 6 should be much improved.

A：We sincerely thank the reviewer for the helpful suggestion. In response, we have replaced Figure 6 with a higher-resolution version in the revised manuscript to ensure better clarity and readability. The updated figure enhances the visibility of key features and labels, and we have carefully checked its rendering quality in the final layout to meet publication standards.

9)There are many results on bearing fault diagnosis. Why they are deserved to be further investigated compared with the existing works.

A：We sincerely thank the reviewer for this important question. It is true that numerous studies have been conducted on bearing fault diagnosis in recent years. However, through a detailed review of the existing literature, we observe that several challenges remain in practical engineering applications, which justify further investigation:

(1) Insufficient robustness to signal noise and redundancy: Many existing models directly use raw vibration signals as input, which often contain redundant components and high-frequency noise. This leads to unstable diagnostic results and reduced generalization capability. Our method introduces a multi-entropy-based feature screening strategy combined with EEMD decomposition, which systematically enhances the quality of diagnostic features.

(2) Lack of adaptive hyperparameter tuning mechanisms: Deep learning models, including TCN variants, usually rely on empirically set hyperparameters (e.g., learning rate, number of channels). Such manual tuning may not guarantee optimal performance under diverse operating conditions. To address this, our work incorporates an improved whale optimization algorithm (IWOA) to achieve automatic and efficient hyperparameter optimization.

(3) Limited performance under complex and heterogeneous conditions: Existing models often exhibit performance degradation when applied to different datasets or real-world industrial signals. We validate our approach not only on the Xi’an Jiaotong University dataset but also on the PRONOSTIA dataset, demonstrating the superior adaptability and robustness of our model under varying noise and domain conditions.

In summary, by integrating feature screening, multi-scale modeling, and adaptive optimization, our method offers a more comprehensive and practically applicable solution to the persistent challenges in bearing fault diagnosis.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript introduces a new algorithm for diagnosis of bearing faults using a neural network. It uses a Multi-Entropy Screening and Optimization Temporal Convolutional Network (MESO-TCN). The algorithm integrates signal preprocessing. It uses an ensemble empirical mode decomposition (EEMD), feature selection, and an extended temporal convolutional network (ETCN). The feature selection uses a hybrid entropy measures for find the relevant features. The ETCN is optimized by some process designated as an “improved whale optimization algorithm” (IWOA). It is inspired by the firefly algorithm. Two benchmark datasets are used. The first, Xi’an Jiaotong University and the second from Southeast University. These datasets are used to demonstrates the classification performance. There is also discussion on their robustness and generalization abilities.

I have read the manuscript and have these comments:

1. The literature background is very limited. Please improve it by more approaches for bearing fault type diagnosis such as “Zero-fault-shot learning for bearing spall type classification by hybrid approach” and “Rolling element bearing diagnostics—A tutorial “.
2. Why the authors choose just two datasets? There are many other publicly available datasets such as Paderborn university dataset, CRWU dataset etc.
3. The algorithm includes many ingredients. It is not clear whatever each ingredient is necessary. For example, is the IWOA is necessary, or a simpler approach will also work? Please include in the revised version a breakdown of the contribution of each ingredient of the algorithm to the results.
4. For real application, what is the complexity of inference time?
5. Please write more details on how the datasets were split into training, validation and test sets. Furthermore, how the paper accommodates the problem of test-training leakage?
6. There are many hyperparameters in this work, such as entropy threshold and number of IMF components. Please provide a hyperparameters sensitivity analysis.
7. As far as I remember there are many other papers that were utilized their algorithm on Xi’an Jiaotong University dataset. Can you please provide a comparison between your results and their results?
8. Please review small errors such as the citation of [1] that include [1][1].

Author Response

Referee: 2

COMMENTS TO THE AUTHOR(S)

1)The literature background is very limited. Please improve it by more approaches for bearing fault type diagnosis such as “Zero-fault-shot learning for bearing spall type classification by hybrid approach” and “Rolling element bearing diagnostics—A tutorial “.

A：We sincerely thank the reviewer for pointing out the limitations in the literature background. In response to your valuable suggestion, we have revised the Introduction section of the manuscript to incorporate and discuss two representative works:

Zhang et al. (2022) proposed a hybrid meta-learning approach titled “Zero-fault-shot learning for bearing spall type classification by hybrid approach”, which addresses the challenge of bearing fault classification with extremely limited samples. This work inspired our approach to enhancing generalization capability under data-scarce conditions.

Tandon et al. (2020) provided a comprehensive tutorial “Rolling element bearing diagnostics—A tutorial”, which systematically reviewed traditional and modern methods for bearing diagnostics. This reference offered theoretical context and motivated the methodological innovations presented in our study.

These references have been added and discussed in the revised manuscript, specifically in Section 1, Lines 94–110. We believe these additions substantially strengthen the academic background of our work and better align it with recent developments in the field.

2)Why the authors choose just two datasets? There are many other publicly available datasets such as Paderborn university dataset, CRWU dataset etc.

A：Thank you for your valuable comment.

To comprehensively evaluate the proposed MESO-TCN method that integrates multi-entropy feature screening, extended temporal modeling, and parameter optimization, we carefully selected three datasets with complementary characteristics:

The Xi’an Jiaotong University bearing dataset, based on vibration signals, provides standard fault types under controlled conditions, serving as a solid benchmark for time-frequency feature modeling.

The Southeast University acoustic emission dataset, collected using AE sensors, contains complex, non-stationary signals with higher noise levels, thus validating the model's robustness in weak and noisy signal environments.

The PRONOSTIA bearing degradation dataset (newly added in the revised manuscript in response to reviewer comments) simulates realistic industrial conditions with natural degradation, varying loads, and complex noise. This dataset has been widely adopted in bearing life prediction and serves as an industrial-level benchmark.

Each dataset contains multiple health and fault states (e.g., inner/outer race damage, rolling element fault), enabling rich validation of the model across various fault scenarios. As the number of conditions and signals within each dataset is substantial, we chose these three representative datasets to balance experimental coverage and manageability.

We appreciate your suggestion to consider additional datasets such as those from Paderborn University or CWRU. We plan to incorporate these in future research to further extend and validate the generalization capability of the proposed approach.

3)The algorithm includes many ingredients. It is not clear whatever each ingredient is necessary. For example, is the IWOA is necessary, or a simpler approach will also work? Please include in the revised version a breakdown of the contribution of each ingredient of the algorithm to the results.

A：Thank you for your valuable comment. We agree that it is essential to clarify the necessity and individual contribution of each module in the proposed algorithm.

In the revised manuscript, we have carefully addressed this concern by conducting and expanding the ablation study, which is now detailed in Section 3.4 and presented in Table 3. This section evaluates the impact of each core component of our method, including the EEMD decomposition, the mixed entropy feature screening, the extended TCN backbone, and the IWOA-based parameter optimization module.

Specifically, we have added a comparative model named MES-TCN, which retains the same signal preprocessing and network structure as MESO-TCN but removes the IWOA optimization module. Instead, it uses manually set static hyperparameters. This comparison allows us to isolate the contribution of the IWOA module.

The experimental results in Table 3 show that excluding IWOA leads to a notable decrease in accuracy, F1-score, and other performance metrics. This demonstrates that the IWOA-based optimization mechanism plays a critical role in enhancing the stability, convergence, and overall diagnostic performance of the model.

We believe this updated analysis clearly justifies the inclusion of each component and effectively addresses your concern regarding their necessity.

4)For real application, what is the complexity of inference time?

A：We sincerely thank the reviewer for raising this important question regarding the inference time complexity in practical applications.

To address this concern, we have added an additional experimental evaluation using the PRONOSTIA bearing fault dataset, which simulates real industrial conditions. As shown in Table 4 of the revised manuscript, we provide a detailed comparison of multiple models, including inference time (in seconds) along with diagnostic accuracy, F1-score, precision, and recall.

The MESO-TCN model achieves the highest accuracy of 96.73%, with an F1-score of 90.54% and precision of 98.15%, while requiring 231 seconds for the entire training and evaluation process.

In terms of inference complexity, we further clarify:

The actual inference phase (excluding training) is highly efficient and capable of near real-time processing on short time-series signals when run on GPU hardware.

The slightly longer total time is mainly due to the multi-scale structure and entropy-based signal reconstruction, which are essential for enhancing robustness under high-noise industrial environments.

The theoretical computational complexity of inference is approximately O(n × k), where n is the input sequence length and k is the number of parallel convolutional paths. The use of dilated convolutions effectively expands the receptive field with limited parameter growth, maintaining manageable computational costs.

In summary, MESO-TCN achieves a well-balanced trade-off between diagnostic performance and inference efficiency, making it suitable for industrial deployment where diagnostic accuracy is critical.

5)Please write more details on how the datasets were split into training, validation and test sets. Furthermore, how the paper accommodates the problem of test-training leakage?

A：We sincerely thank the reviewer for raising this important question regarding dataset partitioning and the prevention of training-test leakage.

In the revised manuscript, we have added more details to clarify the data splitting strategy:

Dataset Partitioning:

All datasets used in this study were randomly split into three subsets according to the ratio of 7:2:1, corresponding to 70% for training, 20% for validation, and 10% for testing. This splitting strategy was applied consistently to the datasets from Xi’an Jiaotong University, Southeast University (AE signals), and the PRONOSTIA bearing dataset.

The training set is used to fit the model parameters, the validation set is employed for hyperparameter tuning and early stopping, and the test set is strictly reserved for final performance evaluation to ensure objective assessment.

Avoidance of Training-Test Leakage:

To prevent test-training leakage, the following measures were taken:

The raw time-series data were segmented into independent non-overlapping samples before the dataset splitting process. This ensures that adjacent samples derived from the same time window are not distributed across both training and testing sets.

Data shuffling was applied only after segmentation, not before, which avoids sampling continuity leakage.

All results reported in the manuscript are based on the test set, which was never exposed to the model during training or validation phases.

These steps ensure the integrity of our evaluation and the generalizability of the proposed MESO-TCN model.

6)There are many hyperparameters in this work, such as entropy threshold and number of IMF components. Please provide a hyperparameters sensitivity analysis.

A：We sincerely thank the reviewer for pointing out the need to further elaborate on the hyperparameter settings in our study.

In response, we have made the following revisions and additions:

Hyperparameter Specification:

We have explicitly provided the values of key hyperparameters in the final paragraphs of the Model and Training Process section. Specifically, the number of IMF components used after EEMD decomposition is set to 16, and the entropy threshold for feature selection is set to 2200.

Sensitivity Analysis Description:

In the Experimental Results and Discussion section, we added a brief sensitivity analysis to explain how these hyperparameters were selected:

The number of IMF components was chosen based on empirical observations across multiple datasets, where 16 components provided a balance between decomposition granularity and computational efficiency.

The entropy threshold was adjusted within a reasonable range (from 1800 to 2500), and the best performance was observed when set to 2200. We noted that significantly higher or lower values led to either loss of important features or inclusion of noise-dominated components, respectively.

We believe this additional explanation helps to clarify the rationale behind the chosen hyperparameter values and confirms the robustness of the proposed method.

7)As far as I remember there are many other papers that were utilized their algorithm on Xi’an Jiaotong University dataset. Can you please provide a comparison between your results and their results?

A：We sincerely thank the reviewer for raising this important point. To comprehensively demonstrate the performance advantages of the proposed method, we have added a comparative analysis in the revised manuscript that benchmarks our model against several representative methods previously applied to the Xi’an Jiaotong University rolling bearing dataset:

The MTF-CBAM-LCNN method presented in [21] achieved an accuracy of 99.47%.

The approach based on Convolutional Denoising Autoencoder (CDAE) and Bidirectional Long Short-Term Memory (Bi-LSTM) in [22] achieved 88.65%.

The Adaptive Signal Diagnosis Network (ASDN) introduced in [23] achieved 97.42%.

In contrast, the proposed MESO-TCN model in our study reaches a higher average diagnostic accuracy of 99.78%. Moreover, our method exhibits notable advantages in multi-entropy-based feature screening, multi-scale temporal modeling, and parameter optimization using improved WOA, validating its effectiveness and superiority in rolling bearing fault diagnosis tasks..

8)Please review small errors such as the citation of [1] that include [1][1].

A：Many thanks to the reviewers for their suggestions. We have made corresponding changes to the suggestions made.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

• Page 2/Line 52: Bearing fault diagnosis is not confined to wind turbine; it is applicable to all machinery where rolling element bearings are used. Please revise the introduction section accordingly.
• Page 13/Line 361: The manuscript claims to overcome empirically set parameters through the integration of the IWOA algorithm. However, key hyperparameters such as convolution kernel sizes (3, 5, 7), batch size (32), number of training epochs (100), and the use of the Adam optimizer appear to be set empirically without justification or inclusion in the optimization process. This creates a contradiction between the stated goals and the experimental methodology. 
• Page 13/Line 371: The model appears overfitted on the Jiaotong dataset (accuracy = 99.78%) with potential data leakage or excessive parameter tuning. More cross-validation or unseen fault classes could test generalization.
• To validate the claim MESO-TCN performs better than other models, statistical significance testing is required.

Author Response

Referee: 3

COMMENTS TO THE AUTHOR(S)

1)Page 2/Line 52: Bearing fault diagnosis is not confined to wind turbine; it is applicable to all machinery where rolling element bearings are used. Please revise the introduction section accordingly.

A：We sincerely thank the reviewer for the insightful comment. In response, we have revised the relevant expression in the introduction section to avoid the misleading impression that bearing fault diagnosis is specific to wind turbines. Specifically, the sentence on Page 2, Line 52 has been modified as follows:

"Rolling element bearings are essential components in various types of rotating machinery, such as wind turbines, motors, pumps, and gearboxes, and their health status directly impacts the operational reliability of such equipment."

This revision broadens the scope of application and better reflects the general relevance of bearing fault diagnosis across diverse industrial machinery. The change has been made in the revised manuscript accordingly.

2)Page 13/Line 361: The manuscript claims to overcome empirically set parameters through the integration of the IWOA algorithm. However, key hyperparameters such as convolution kernel sizes (3, 5, 7), batch size (32), number of training epochs (100), and the use of the Adam optimizer appear to be set empirically without justification or inclusion in the optimization process. This creates a contradiction between the stated goals and the experimental methodology.

A：We sincerely thank the reviewer for the valuable and insightful comment. In this study, we have indeed adopted the Improved Whale Optimization Algorithm (IWOA) to adaptively optimize several critical structural parameters within the ETCN model, including the learning rate, the number of convolutional channels, and the number of convolutional layers. This significantly alleviates the reliance on empirically determined parameter settings and enhances the model's adaptability.

However, as rightly pointed out by the reviewer, certain parameters such as the convolution kernel sizes (3, 5, 7), batch size (32), number of training epochs (100), and the choice of the Adam optimizer were retained as fixed settings based on conventional practices and prior empirical evidence. These choices were made to balance optimization performance and computational cost, and to ensure reproducibility across multiple benchmark datasets. We acknowledge that these hyperparameters could potentially impact performance and appreciate the suggestion. We will consider including more of these in the optimization scope in future work to further improve the comprehensiveness of our approach.

A clarifying statement has been added in Section 3.3 of the revised manuscript to explicitly address this design choice and resolve the perceived contradiction.

3)Page 13/Line 371: The model appears overfitted on the Jiaotong dataset (accuracy = 99.78%) with potential data leakage or excessive parameter tuning. More cross-validation or unseen fault classes could test generalization.

A：We sincerely thank the reviewer for pointing out this critical concern. In response to the potential overfitting issue and concerns regarding generalization, we have taken the following measures and made corresponding revisions in the manuscript:

First, to reduce the risk of overfitting, we have extended the number of training cycles from 10 to 50 epochs, allowing for more robust convergence and avoiding the risk of undertraining or premature stabilization. Furthermore, dropout layers and early stopping strategies are also employed in the training process to mitigate overfitting.

Second, to better evaluate the generalization performance of the proposed method, we have incorporated an additional industrial-grade dataset—the PRONOSTIA bearing failure dataset, which contains natural degradation signals under variable load conditions. This dataset is widely recognized as a benchmark for real-world validation. The experimental results on PRONOSTIA, now included in Section 4.4 of the revised manuscript, demonstrate that the proposed MESO-TCN model achieves a high accuracy of 96.73%, along with significant improvements in F1-score, precision, and recall. This confirms the model’s strong generalization capability beyond the Jiaotong dataset.

These improvements and corresponding analysis have been explicitly included in the revised manuscript in Sections 3.3 and 3.4, and we believe they adequately address the reviewer’s concerns.

4)To validate the claim MESO-TCN performs better than other models, statistical significance testing is required.

A：

We thank the reviewers for their valuable comments on our manuscript. We agree that using only accuracy as an evaluation metric may not be sufficient to fully measure the performance of the model. Therefore, we have supplemented Recall, Precision and F1 Score as additional benchmark performance metrics in the experimental section to evaluate the model's classification effectiveness more comprehensively. The results of the three dataset experiments are shown in the paper.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper has been improved which can be accepted. 

Reviewer 2 Report

Comments and Suggestions for Authors

I read the author responses, they have answered all my questions.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed the concerns raised during the review process, and I therefore recommend the manuscript for publication.