Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In my opinion, the article is interesting, and the discussion of the proposed analytical methods and practical system solutions leaves no room for doubt. I can only congratulate the author on the effort put into writing this article and on the results achieved, which can be applied in practice.

Author Response

Comment 1:
In my opinion, the article is interesting, and the discussion of the proposed analytical
methods and practical system solutions leaves no room for doubt. I can only
congratulate the author on the effort put into writing this article and on the results
achieved, which can be applied in practice.

Response 1:
Thank you sincerely for your positive and encouraging feedback. We greatly appreciate
your recognition of both the methodological rigor and the practical relevance
of the proposed system.
Your comments confirm the importance of bridging analytical modeling with realworld
deployability, which is a central objective of this work. We are particularly
encouraged that the applicability of the proposed approach to practical scenarios has
been clearly perceived.
We remain committed to further strengthening the manuscript in line with the
reviewers’ suggestions and believe that your feedback contributes significantly to
improving the overall quality and impact of this work.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. While the model fits within ESP32 constraints, how would the system scale when monitoring larger networks with significantly more valves and sensors? Would memory and latency remain acceptable?
2. The anomaly detection relies on a ROC-optimized threshold ε. How sensitive is system performance to this threshold, and how would it be adapted in dynamic or noisy real-world environments?
3. Given the black-box nature of the MLP, how can the model’s predictions be interpreted or validated against physical hydraulic principles in safety-critical scenarios?
4. Consider citing "Neural network-enhanced internal leakage analysis for efficient fault detection in heavy machinery hydraulic actuator cylinders" to strengthen the motivation for using neural networks in hydraulic fault detection.
5. The comparison is made primarily between linear regression and an MLP. Why were more advanced nonlinear baselines (e.g., decision trees, random forests, or gradient boosting) not included to provide a more comprehensive benchmark?
6. The used model is static and trained offline. How does the system handle long-term drift in sensor data or evolving hydraulic conditions without online learning or periodic retraining?

Author Response

Comment 1: While the model fits within ESP32 constraints, how would the system scale when monitoring larger networks with significantly more valves and sensors? Would memory and latency remain acceptable?

Response 1: Thank you for this important and insightful comment regarding the scalability of the proposed system.

To address this concern, we have added a dedicated section entitled "Scalability Analysis for Larger Valve Networks" in the revised manuscript (5.8. Scalability Analysis for Larger Valve Networks). This new section provides a detailed evaluation of how the proposed HydroNeuro framework behaves when extended to larger hydraulic systems.

More specifically, we investigated a 10-valve configuration using a simulation-based dataset constructed via a fractional factorial design (2^(10-5) = 32). This approach reduces the combinatorial space from 1024 to 32 configurations (a 96.9% reduction) while preserving the dominant hydraulic interactions, ensuring experimental tractability without sacrificing representativeness.

From an embedded deployment perspective, we analyzed both memory footprint and inference latency:

• Memory scalability: The converted model size increases only from 4.06 KB (4 valves) to 4.44 KB (10 valves), corresponding to an increase of 8.53%, demonstrating sub-linear growth with respect to the number of inputs. This confirms that the model remains well within ESP32 memory constraints even as the system scales.
• Latency scalability: The computational cost grows approximately linearly with input dimensionality, primarily affecting the first dense layer. Even when increasing from 4 to 10 valves, the additional number of operations remains limited, and the inference time stays compatible with real-time monitoring requirements.

Overall, this analysis demonstrates that both memory usage and latency remain acceptable and controlled as the system scales. The combination of a compact MLP architecture and an efficient experimental design ensures that the HydroNeuro framework can be extended to larger hydraulic networks without violating embedded constraints.

This clarification has been added to the manuscript to strengthen the discussion on scalability and real-world deployment feasibility.

Comment 2: The anomaly detection relies on a ROC-optimized threshold epsilon. How sensitive is system performance to this threshold, and how would it be adapted in dynamic or noisy real-world environments?

Response 2: Thank you for this valuable comment regarding the sensitivity and adaptability of the anomaly detection threshold.

To address this point, we have revised Section 4 (Experimental Setup and Practical Validation) to include a more rigorous and explicit formulation of the threshold selection process within a statistically grounded residual-based framework.

In the updated manuscript, the anomaly detection threshold is no longer treated as a purely ROC-optimized parameter. Instead, it is defined using the statistical properties of the residual error under normal operating conditions:

epsilon = mu_deltaP + 3 * sigma_deltaP

where delta_P = |P_r - P_r_hat| represents the prediction residual. This formulation follows the three-sigma principle, allowing the threshold to directly reflect the intrinsic variability of the system.

Sensitivity analysis. We acknowledge that system performance is inherently sensitive to the threshold value. This sensitivity is now explicitly characterized through ROC analysis (AUC = 0.9231), which illustrates the trade-off between detection rate and false alarm rate. The selected operating point achieves a high true positive rate while maintaining acceptable false alarm levels, demonstrating that the chosen threshold provides a balanced compromise.

Adaptation to real-world conditions. To ensure robustness in dynamic and noisy environments, the revised framework naturally supports adaptive strategies. In particular, the threshold can be updated by re-estimating the residual statistics during normal operation phases, enabling:

• adaptation to sensor noise variations,
• compensation for slow hydraulic drift,
• robustness to environmental fluctuations.

Additionally, the methodology can be extended using sliding-window statistics or periodic recalibration procedures, ensuring that the detection mechanism remains reliable over long-term deployment.

Overall, this revision clarifies that the threshold is not a fixed empirical parameter but a data-driven and adaptable quantity, improving both the robustness and the practical applicability of the proposed anomaly detection system.

This clarification has been incorporated into Section 4 of the revised manuscript.

Comment 3: Given the black-box nature of the MLP, how can the model's predictions be interpreted or validated against physical hydraulic principles in safety-critical scenarios?

Response 3: Thank you for this important and insightful comment

The inherent black-box nature of the Multilayer Perceptron (MLP) is acknowledged, particularly in the context of safety-critical hydraulic applications. However, although the proposed model does not explicitly incorporate physical laws into its structure or training objective, its predictions have been rigorously validated to ensure consistency with established hydraulic principles.

This validation is performed by systematically comparing the predicted pressures with experimentally measured values obtained from a controlled hydraulic system. The resulting residuals provide a physically interpretable metric, as they directly reflect deviations from expected hydraulic behavior. Under normal operating conditions, these deviations remain bounded, while significant discrepancies indicate physically meaningful anomalies such as leaks or obstructions.

Furthermore, the model is not intended to operate as a fully autonomous decision-making system. Instead, it is integrated within a supervised operational framework that includes additional control and verification mechanisms. In this framework, model outputs are continuously monitored and assessed against observed system responses, ensuring that any potentially inconsistent or unreliable predictions are detected before triggering decisions.

In this context, hydraulic principles are not embedded within the model itself but are used as an external reference for validation and interpretation. This approach preserves the flexibility of the data-driven model while ensuring that its predictions remain consistent with fundamental physical behavior, which is essential for safe and reliable deployment.

Comment 4: Consider citing "Neural network-enhanced internal leakage analysis for efficient fault detection in heavy machinery hydraulic actuator cylinders" to strengthen the motivation for using neural networks in hydraulic fault detection.

Response 4: Thank you for this helpful suggestion. We agree that the proposed reference further strengthens the motivation for using neural networks in hydraulic fault detection.

In response, we have added the suggested citation to the Introduction section of the revised manuscript and highlighted its relevance to our work. The following sentence has been included:

"Recent studies have also demonstrated the effectiveness of neural networks for internal leakage detection in hydraulic actuator cylinders of heavy machinery, achieving efficient fault classification through supervised learning on pressure and vibration signals [zhang2023leakage]."

This addition reinforces the relevance of data-driven and neural approaches for hydraulic fault diagnosis and further supports the methodological choices adopted in this study.

Comment 5: The comparison is made primarily between linear regression and an MLP. Why were more advanced nonlinear baselines (e.g., decision trees, random forests, or gradient boosting) not included to provide a more comprehensive benchmark?

Response 5: We sincerely thank the reviewer for this insightful and constructive comment. We fully agree that limiting the comparison to a single baseline (linear regression) is not sufficient to comprehensively demonstrate the effectiveness and positioning of the proposed approach.

To address this point, we have introduced a new subsection entitled "5.5. Extended Model Comparison and Embedded Deployment Analysis", which is clearly highlighted in red in the revised manuscript.

In this new section, we extend the comparative analysis by including several additional classical and widely used machine learning models, namely:

• Decision Tree
• Random Forest
• 1D Convolutional Neural Network (1D-CNN)

These models were selected to represent different families of learning approaches commonly used for tabular regression tasks and to provide a broader evaluation framework.

We provide a detailed and rigorous comparison based on:

• Standard regression metrics (MSE, RMSE, MAE, R^2)
• A normalized Custom Score for cross-model comparison
• Statistical validation using a permutation test (MLP vs. Random Forest, p = 0.3281), confirming that performance differences are not statistically significant

Beyond predictive accuracy, we further extend the analysis to include embedded deployment considerations, which constitute a central contribution of this work. In particular, we evaluate each model in terms of:

• Memory footprint and representation structure
• Computational complexity and inference latency
• Firmware integration constraints on ESP32 microcontrollers

This analysis reveals that, although tree-based models (Decision Tree and Random Forest) achieve performance comparable to the MLP, their branching-heavy structure leads to inefficient and complex firmware representations. Similarly, the 1D-CNN introduces additional computational overhead without providing meaningful accuracy gains for this low-dimensional, non-sequential problem.

In contrast, the proposed MLP uniquely combines:

• High predictive accuracy
• Compact and efficient representation (TensorFlow Lite Micro format)
• Deterministic and low-latency inference
• Seamless integration into embedded systems

Therefore, the extended comparison demonstrates that the superiority of the proposed approach is not only based on predictive performance, but also on its optimal trade-off between accuracy and deployability, which is critical for real-time embedded hydraulic monitoring systems.

We believe that this addition significantly strengthens the manuscript by providing a more comprehensive, fair, and application-oriented comparison framework, fully addressing the reviewer's concern.

Comment 6: The used model is static and trained offline. How does the system handle long-term drift in sensor data or evolving hydraulic conditions without online learning or periodic retraining?

Response 6: Thank you for this important comment regarding long-term robustness and system adaptability.

We acknowledge that the proposed HydroNeuro model is trained offline and operates as a static predictor during deployment. To address potential long-term drift in sensor measurements and evolving hydraulic conditions, we have extended the revised manuscript by adding a dedicated subsection entitled "5.9. Long-Term Robustness and Model Maintenance Strategy."

In this updated section, we clarify that the system does not rely on continuous online learning, but instead adopts a monitoring-driven, event-based maintenance strategy specifically designed for resource-constrained embedded environments.

More precisely, the framework leverages the residual-based anomaly detection mechanism not only for fault detection but also as a proxy indicator of model validity over time. A sustained increase in residual error, bias, or false alarm rate is interpreted as evidence of a distribution shift caused by sensor drift or changes in hydraulic conditions.

When such degradation is detected, the system triggers a two-stage maintenance procedure:

• Sensor recalibration: The sensing chain is re-evaluated using a stable hydraulic reference to compensate for offset drift, gain variation, and environmental influences.
• Offline model retraining: A new dataset is collected under updated operating conditions, and the model is retrained using the same structured experimental protocol before redeployment.

This event-driven retraining strategy ensures that adaptation occurs only when statistically justified, thereby avoiding unnecessary computational overhead while preserving deterministic execution and real-time reliability on the ESP32 platform.

We intentionally avoid continuous online learning due to embedded system constraints, including limited memory, strict timing requirements, and the need for predictable execution. The adopted approach therefore represents a practical trade-off between adaptability and deployability.

Additionally, we note that the framework can be further extended to incorporate sliding-window statistical updates or periodic recalibration cycles, enhancing robustness in highly dynamic environments.

This clarification has been incorporated into the revised manuscript to explicitly describe how the system maintains performance under long-term real-world operating conditions.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. In Section 3.2, the discussion regarding Analysis of Variance (ANOVA)and ROC analysis is overly brief. It is recommended to supplement the complete results of ANOVA and the full process of ROC analysis.
2. In Section 3.7, the descriptions of the various operations are too brief.It is recommended to expand them appropriately.
3. In the “Model training and optimization”subsection of Section 3.7, the MLR baseline should correspond to Equation (8), and MLP should correspond to Equation (10). There are errors in the text, suggested revision.
4. Equation (7) and Equation (13) (the Gaussian-based data augmentation formula) are duplicated. It is recommended to delete one of them and renumber all equations in the paper accordingly.
5. The values of Test MSE in Figure 5 are inconsistent with those in the text and Table 1. In addition, the decimal point (.) in the title of Figure 5 was incorrectly written as a comma (,). It is recommended to check and revise them.
6. The statement in Section 5.3 that “The MLR does not require iterative training” conflicts with the epoch loss curve of the linear regression model shown in Figure 7. It is recommended to check and revise accordingly.
7. The quality of the figuresand tables in the paper needs to be improved. For example, the left part of Figure 7 is incompletely captured, the bottom border of Figure 8 is missing and there is an extra "width=" above Table 2. It is recommended to check and revise them accordingly.
8. The division of the dataset is not clearly specified in the paper. It is recommended to elaborate on the splitting ratio and method of the training set and test set.
9. In terms of comparison with other methods, this paper only compares with the linear regression model, which cannot fully demonstrate the superiority of the proposed method. It is recommended to add other classical comparison methods.
10. Thispaper only verifies the ideal situation of single leakage and single blockage. It is recommended to supplement the cases of multi-branch leakage, multi-branch blockage and mixed faults.

Author Response

Comment 1: In Section 3.2, the discussion regarding Analysis of Variance (ANOVA) and ROC analysis is overly brief. It is recommended to supplement the complete results of ANOVA and the full process of ROC analysis.

Response 1: We sincerely thank the reviewer for this insightful and constructive comment. We fully agree that a more detailed presentation of the ANOVA analysis and the ROC evaluation process significantly strengthens the scientific rigor and interpretability of the manuscript. This remark has been particularly valuable in helping us enhance both the statistical depth and the clarity of our contribution.

To address this point, we have introduced a new dedicated section entitled:

"4.1. Experimental Design Refinement and Statistical Modeling"

which is clearly highlighted in red in the revised manuscript.

In this new section, we substantially extend the statistical analysis by:

• Providing a refined and augmented experimental design, transitioning from the initial fractional factorial design to an enriched 13-configuration dataset. This improvement ensures better coverage of the hydraulic operating space and enhances the identifiability of both main effects and interaction terms.
• Presenting a complete ANOVA-based decomposition of the pressure response model, including:
  • explicit modeling of main and interaction effects,
  • quantitative evaluation of variance explained (with R^2 = 0.987 and adjusted R^2 = 0.924),
  • statistical significance testing of each factor (p < 0.05),
  • identification of dominant hydraulic contributors (notably valve V2),
  • and interpretation of significant interaction effects (particularly V2:V3) from a physical standpoint.
• Strengthening the physical interpretation of the statistical results by explicitly linking the estimated coefficients to hydraulic flow behavior, ensuring consistency with established fluid dynamics principles.
• Clearly discussing statistical limitations, particularly the reduced residual degrees of freedom, in order to provide a transparent and scientifically balanced interpretation of the results.
• Expanding the ROC analysis framework by detailing the full anomaly detection pipeline, including:
  • definition of the residual-based anomaly score,
  • statistical derivation of the detection threshold using the three-sigma rule,
  • explicit reporting of distribution parameters,
  • and comprehensive evaluation using ROC curves.
• Reporting quantitative performance metrics, including:
  • Area Under the Curve (AUC = 0.9231),
  • True Positive Rate (98.31%),
  • False Positive Rate (25.36%), thus providing a complete and reproducible assessment of detection performance.

Overall, this addition significantly improves the statistical completeness, methodological transparency, and scientific robustness of the manuscript. We believe that these enhancements fully address the reviewer's concern and substantially enrich the quality of the work.

Comment 2: In Section 3.7, the descriptions of the various operations are too brief. It is recommended to expand them appropriately.

Response 2: We sincerely thank the reviewer for this constructive suggestion. We fully agree that the descriptions in Section 3.7 were initially too concise, which could limit the clarity and completeness of the proposed embedded AI pipeline. This remark has been very helpful in improving the pedagogical quality and methodological transparency of the manuscript.

To address this point, we have substantially expanded Section 3.7 by providing a more detailed and structured description of each stage of the pipeline. The updated content is clearly highlighted in red in the revised manuscript.

In particular, the following enhancements have been introduced:

• A more detailed explanation of the data acquisition process, including the introduction of a stabilization window to ensure quasi-steady-state measurements and reduce noise effects.
• A formalization and clarification of the FFD-based experimental design, including the generator relation and defining relation of the fractional factorial structure, as well as its Resolution IV properties and implications on aliasing. The section has also been enriched with a justification of repeated measurements and dataset augmentation.
• The introduction of Gaussian data augmentation, explicitly formulated and motivated as a strategy to improve robustness and generalization under noisy operating conditions.
• A clearer and more explicit presentation of the model training phase, including both the linear MLR baseline formulation and the nonlinear MLP architecture, along with its role in capturing complex hydraulic interactions.
• A detailed description of the model conversion pipeline, from PyTorch to ONNX to TensorFlow Lite Micro, including quantization and deployment constraints for embedded systems.
• An expanded explanation of the edge deployment on ESP32, emphasizing the advantages of local inference in terms of latency reduction, autonomy, and robustness in low-connectivity environments.
• A more comprehensive formulation of the anomaly detection mechanism, including the residual-based decision rule, statistical threshold definition, and interpretation of detected anomalies in terms of hydraulic faults.

Overall, these revisions significantly improve the clarity, completeness, and technical depth of Section 3.7. We believe that the expanded description now provides a much more transparent and comprehensive understanding of the end-to-end embedded AI pipeline, fully addressing the reviewer's concern.

Comment 3: In the "Model training and optimization" subsection of Section 3.7, the MLR baseline should correspond to Equation (8), and MLP should correspond to Equation (10). There are errors in the text; suggested revision.

Response 3: We sincerely thank the reviewer for this careful reading and constructive remark. We fully acknowledge the importance of ensuring consistency between the textual descriptions and the corresponding equations in the manuscript.

In response to this comment, we have carefully revised the "Model training and optimization" subsection in Section 3.7 to correct the indicated inconsistency. The MLR baseline is now explicitly and correctly linked to Equation (8), while the MLP formulation is properly associated with Equation (10), in full consistency with the mathematical definitions provided in the manuscript.

These corrections have been implemented throughout the revised version to ensure coherence between the narrative description and the formal model definitions, thereby improving the clarity and accuracy of the presentation.

We believe that this correction resolves the issue raised by the reviewer and enhances the overall rigor and readability of the manuscript.

Comment 4: Equation (7) and Equation (13) (the Gaussian-based data augmentation formula) are duplicated. It is recommended to delete one of them and renumber all equations in the paper accordingly.

Response 4: We sincerely thank the reviewer for this careful observation. We fully agree that the duplication of the Gaussian-based data augmentation formulation (Equation (7) and Equation (13)) was unnecessary and could lead to confusion in the manuscript.

In response to this comment, we have removed the redundant occurrence of the equation to ensure consistency and avoid repetition. Specifically, the duplicated formulation previously appearing in Section 4.1 "Dataset Characteristics" of the original manuscript has been removed, and only the updated version in Section 4.2 "Dataset Characteristics" (revised manuscript) has been retained.

All equations in the manuscript have been carefully renumbered accordingly to maintain a coherent and consistent mathematical structure throughout the paper.

We believe that this correction improves the clarity, readability, and formal rigor of the manuscript, and fully addresses the reviewer's concern.

Comment 5: The values of Test MSE in Figure 5 are inconsistent with those in the text and Table 1. In addition, the decimal point (.) in the title of Figure 5 was incorrectly written as a comma (,). It is recommended to check and revise them.

Response 5: We sincerely thank the reviewer for this careful and detailed observation. We fully agree that consistency between figures, tables, and textual descriptions is essential to ensure the clarity and reliability of the presented results.

In response to this comment, we have carefully reviewed and corrected the inconsistencies related to the Test MSE values. The figure has been updated accordingly, and all reported values have been harmonized across the manuscript, including Figure 5 in the original version, which now corresponds to Figure 6 in the revised manuscript.

In addition, the formatting issue in the title of the figure has been corrected by replacing the incorrect decimal separator (comma) with the standard decimal point, ensuring consistency with scientific notation conventions.

All modifications have been clearly highlighted in red in the revised manuscript to facilitate the reviewer's verification.

We believe that these corrections significantly improve the coherence, accuracy, and presentation quality of the results, and fully address the reviewer's concern.

Comment 6: The statement in Section 5.3 that "The MLR does not require iterative training" conflicts with the epoch loss curve of the linear regression model shown in Figure 7. It is recommended to check and revise accordingly.

Response 6: We sincerely thank the reviewer for this careful and pertinent observation. We fully agree that the original statement in Section 5.3 could lead to a misunderstanding when considered alongside the epoch-based loss curves presented in Figure 7.

To address this issue, we have revised both the textual description and the interpretation of the results to ensure full consistency between the methodology and the reported figures.

In the revised manuscript, we clarify that although linear regression admits a closed-form Ordinary Least Squares (OLS) solution, the MLR model in our study is implemented using a gradient-based optimization procedure over multiple epochs. This choice was made to maintain methodological consistency with the MLP training pipeline and to enable a direct and fair comparison of learning dynamics between the two models.

Accordingly, Figure 7 has been updated and now correctly reflects the training behavior of the MLR model, showing a rapid decrease in loss followed by convergence to a plateau around MSE ≈ 0.34. The revised text explicitly explains that this plateau corresponds to the bias-limited performance of the linear model, highlighting its limited expressive capacity in capturing nonlinear hydraulic interactions.

These revisions eliminate the previous inconsistency and provide a clearer, more rigorous interpretation of the comparative results.

Comment 7: The quality of the figures and tables in the paper needs to be improved. For example, the left part of Figure 7 is incompletely captured, the bottom border of Figure 8 is missing and there is an extra "width=" above Table 2. It is recommended to check and revise them accordingly.

Response 7: We sincerely thank the reviewer for this careful and constructive comment regarding the quality of the figures and tables. We fully agree that clear and properly formatted visual elements are essential for the readability and overall quality of the manuscript.

In response, we have thoroughly revised all figures and tables and addressed each point raised:

• Figure 7: The figure has been replaced with a corrected and higher-quality version. The new figure is properly rendered, with all elements (including the left part, axes, labels, and curves) fully visible and clearly presented.
• Figure 8: The missing bottom border has been fixed by correcting the figure formatting and export settings, resulting in a complete and well-framed visualization.
• Table 2 (now Table 6 in the revised manuscript): The extraneous "width=" artifact has been removed. The table has been reformatted using a corrected LaTeX structure to ensure proper alignment and consistency with the rest of the manuscript.

In addition, we conducted a comprehensive review of all figures and tables to ensure consistent formatting, proper alignment, and high-resolution rendering throughout the manuscript.

These revisions significantly improve the visual clarity and overall presentation quality of the paper. We appreciate the reviewer's attention to detail, which has helped us strengthen the manuscript.

Comment 8: The division of the dataset is not clearly specified in the paper. It is recommended to elaborate on the splitting ratio and method of the training set and test set.

Response 8: We sincerely thank the reviewer for this important and constructive comment. We fully agree that clearly specifying the dataset splitting strategy is essential to ensure the transparency and reproducibility of the experimental protocol.

To address this point, we have added a new paragraph entitled "Dataset Splitting and Experimental Protocol" in Section 4.2 (Dataset Characteristics), which is clearly highlighted in red in the revised manuscript.

In this addition, we explicitly describe the data preparation and splitting procedure. The dataset is first randomly shuffled to eliminate any ordering bias related to the sequence of experimental acquisition. It is then divided into 80% for training (1,069 samples) and 20% for testing (267 samples), out of a total of 1,336 samples.

We also provide a detailed justification for this choice. The 80% training portion ensures that the models have sufficient data to learn both linear and nonlinear relationships between valve states and nodal pressures, while the 20% test set allows for a reliable evaluation on unseen data. Furthermore, the random shuffling step guarantees that both subsets contain representative operating conditions rather than being influenced by the chronological structure of the dataset.

Finally, we clarify that this 80/20 split follows standard practices in machine learning and provides a balanced trade-off between model training and unbiased performance evaluation, particularly for datasets of moderate size.

We believe that this addition significantly improves the clarity, rigor, and reproducibility of the manuscript, and we thank the reviewer for highlighting this important aspect.

Comment 9: In terms of comparison with other methods, this paper only compares with the linear regression model, which cannot fully demonstrate the superiority of the proposed method. It is recommended to add other classical comparison methods.

Response 9: We sincerely thank the reviewer for this insightful and constructive comment. We fully agree that limiting the comparison to a single baseline (linear regression) is not sufficient to comprehensively demonstrate the effectiveness and positioning of the proposed approach.

To address this point, we have introduced a new subsection entitled "5.5. Extended Model Comparison and Embedded Deployment Analysis", which is clearly highlighted in red in the revised manuscript.

In this new section, we extend the comparative analysis by including several additional classical and widely used machine learning models, namely:

• Decision Tree
• Random Forest
• 1D Convolutional Neural Network (1D-CNN)

These models were selected to represent different families of learning approaches commonly used for tabular regression tasks and to provide a broader evaluation framework.

We provide a detailed and rigorous comparison based on:

• Standard regression metrics (MSE, RMSE, MAE, R^2)
• A normalized Custom Score for cross-model comparison
• Statistical validation using a permutation test (MLP vs. Random Forest, p = 0.3281), confirming that performance differences are not statistically significant

Beyond predictive accuracy, we further extend the analysis to include embedded deployment considerations, which constitute a central contribution of this work. In particular, we evaluate each model in terms of:

• Memory footprint and representation structure
• Computational complexity and inference latency
• Firmware integration constraints on ESP32 microcontrollers

This analysis reveals that, although tree-based models (Decision Tree and Random Forest) achieve performance comparable to the MLP, their branching-heavy structure leads to inefficient and complex firmware representations. Similarly, the 1D-CNN introduces additional computational overhead without providing meaningful accuracy gains for this low-dimensional, non-sequential problem.

In contrast, the proposed MLP uniquely combines:

• High predictive accuracy
• Compact and efficient representation (TensorFlow Lite Micro format)
• Deterministic and low-latency inference
• Seamless integration into embedded systems

Therefore, the extended comparison demonstrates that the superiority of the proposed approach is not only based on predictive performance, but also on its optimal trade-off between accuracy and deployability, which is critical for real-time embedded hydraulic monitoring systems.

We believe that this addition significantly strengthens the manuscript by providing a more comprehensive, fair, and application-oriented comparison framework, fully addressing the reviewer's concern.

Comment 10: This paper only verifies the ideal situation of single leakage and single blockage. It is recommended to supplement the cases of multi-branch leakage, multi-branch blockage and mixed faults.

Response 10: Thank you for this relevant remark.

To address this point, we have added a new subsection entitled "5.7. Detection Performance Discussion" in the revised manuscript.

In this section, we clarify that although the experimental validation focuses on single-fault scenarios (single leakage and single blockage), the proposed HydroNeuro framework is not limited to these cases. The system incorporates a sequential sector-wise diagnostic strategy, which allows it to isolate faulty branches by activating each branch individually after anomaly detection and analyzing the corresponding pressure response.

We explicitly explain that this mechanism naturally extends to:

• multi-branch leakage,
• multi-branch obstruction,

since each branch is evaluated independently during the diagnostic phase.

In addition, we discuss the more challenging case of mixed faults (simultaneous leakage and obstruction in different branches). We clarify that, while the system can still perform localization in most practical situations, there exists a rare edge case where opposing hydraulic effects may compensate, leading to reduced anomaly observability under single-point pressure sensing. This limitation, its physical explanation, and possible future improvements (e.g., multi-sensor configurations) are now clearly stated in the manuscript.

These additions strengthen the methodological clarity and better position the proposed approach with respect to complex real-world fault scenarios.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors This paper presents HydroNeuro, a framework that integrates hydraulic domain knowledge, statistical experimental design, and lightweight neural networks for anomaly detection in agricultural hydraulic systems. The authors demonstrate an original approach to reducing experimental data volume through fractional factorial design and Hamming weight criteria. This strategy minimizes water consumption and mechanical stress on infrastructure. The deployment of a quantized MLP model on an ESP32 microcontroller using TensorFlow Lite for Microcontrollers achieves high prediction accuracy. The system detects anomalies with over 96% accuracy while maintaining low energy consumption and inference latency around 8 ms. The work represents a complete solution covering data collection through autonomous operation under limited connectivity.   Despite promising results, the methodology requires substantial clarification. Key concerns are listed as follows: 1. The physical dataset contains only 36 samples, expanded to 36,000 through aggressive Gaussian augmentation. Without sensitivity analysis of the noise parameter and ablation studies, overfitting to statistical artifacts remains a risk. 2. The manuscript lacks details on MLP architecture, including justification for layer depth and width, regularization techniques, and early stopping strategy. 3. The procedure for selecting the anomaly detection threshold and splitting data into training and testing sets is insufficiently described, hindering reproducibility assessment. 4. The study omits comparison with modern alternatives such as 1D-CNN, Isolation Forest, or autoencoders, limiting evaluation within the context of TinyML anomaly detection methods. 5. Transition to field deployment requires discussion of model robustness to long-term sensor drift and the need for periodic retraining without human intervention.

Author Response

Comment 1: The physical dataset contains only 36 samples, expanded to 36,000 through aggressive Gaussian augmentation. Without sensitivity analysis of the noise parameter and ablation studies, overfitting to statistical artifacts remains a risk.

Response 1: Thank you for this important and insightful comment regarding the dataset size, augmentation strategy, and the potential risk of overfitting to synthetic data.

We would like to first clarify that the previously stated dataset size of 36,000 samples was a typographical error. In the revised manuscript (Section 4.2: Dataset Characteristics), this has been corrected. The actual dataset used for training consists of 1,336 samples, constructed from 36 physical measurements and a controlled augmentation process.

More specifically, the augmentation strategy is not an aggressive or unconstrained expansion, but a structured, state-aware stochastic process. Synthetic samples are generated independently for each of the 13 valve configurations using an adaptive Gaussian noise model, where the variance is derived from empirical statistics and bounded by a minimum physically meaningful noise floor. Additionally, a 3sigma clamping mechanism is applied to prevent unrealistic outliers and preserve physical plausibility.

Regarding the reviewer's concern about overfitting to statistical artifacts, several safeguards have been incorporated:

• State-wise controlled augmentation: Each operating configuration is augmented uniformly (100 samples per state), preventing dataset imbalance and avoiding bias toward specific valve combinations.
• Physically grounded noise modeling: The noise level is not arbitrary but derived from observed variability or a conservative minimum bound, ensuring that synthetic samples remain consistent with real hydraulic behavior.
• Generalization validation: Model performance is evaluated on a held-out test set (20% split), where the MLP demonstrates strong generalization (low test MSE and stable training/validation curves), indicating that the model does not overfit to synthetic noise patterns.
• Implicit robustness check: The close alignment between training and validation errors, together with consistent predictive accuracy across configurations, suggests that the learned mapping reflects underlying physical relationships rather than augmentation artifacts.

Concerning sensitivity to the noise parameter, we acknowledge that this is an important aspect. While an explicit ablation study is beyond the scope of the current work, the adopted adaptive formulation already mitigates sensitivity by:

• tying noise magnitude to empirical statistics when available, and
• enforcing a conservative lower bound when measurements are sparse.

This design avoids both under-perturbation (which could lead to overfitting) and over-perturbation (which could distort physical realism).

To improve clarity and reproducibility, the entire dataset construction and augmentation pipeline --- including formulas, assumptions, and design rationale --- has been explicitly detailed in the revised manuscript.

In summary, the revised version addresses the concern by:

• correcting the dataset size,
• formalizing the augmentation process,
• and demonstrating that the approach remains physically consistent, statistically controlled, and generalizable.

Comment 2: The manuscript lacks details on MLP architecture, including justification for layer depth and width, regularization techniques, and early stopping strategy.

Response 2: We sincerely thank the reviewer for this important remark. We fully agree that a detailed and reproducible description of the MLP architecture is essential for scientific rigor and reproducibility. In response to this comment, we have substantially expanded Section 5.2 (Neural Network Model Evaluation) in the revised manuscript, which now provides explicit and structured justifications for all architectural design choices. The additions directly address the four points raised by the reviewer.

1. Layer Depth and Width Justification. The revised Section 5.2 now explicitly justifies the choice of a compact architecture composed of two fully connected hidden layers with 32 neurons each. Additional experiments reported in the revised manuscript show that deeper configurations (three or more hidden layers) and wider layers were systematically evaluated but discarded, as they increase memory consumption and inference latency without providing measurable improvements in predictive performance for this low-dimensional regression task.

The resulting architecture is therefore an intentional and evidence-based compromise between nonlinear representational capacity and embedded deployability on the ESP32 microcontroller. The final model is formally defined as:

Linear(nb_valves, 32) -> ReLU -> Dropout(0.1) -> Linear(32, 32) -> ReLU -> Linear(32, 1)

2. Regularization Techniques. The revised manuscript introduces a dedicated subsection on activation, optimization, and regularization strategies, detailing three complementary mechanisms that were not fully specified in the original version:

• Dropout regularization: A dropout layer with probability p = 0.1 applied after the first hidden layer to reduce neuron co-adaptation and improve generalization stability.
• L2 regularization: Weight decay with lambda = 1e-5 applied through the Adam optimizer, mitigating overfitting and improving parameter robustness.
• Adaptive learning rate scheduling: A ReduceLROnPlateau strategy with patience of 5 epochs and reduction factor of 0.5, enabling smoother convergence and improved stability in late training stages.

These mechanisms collectively ensure that the proposed MLP is not only compact but also robust to overfitting under constrained embedded learning conditions.

The effectiveness of these regularization mechanisms is further confirmed experimentally through the training and validation loss curves presented in Figure 8 of the revised manuscript. As shown in this figure, the MLP exhibits a continuous and stable decrease in both training and validation MSE over 1000 epochs, converging to MSE < 0.02 well before the final epoch. The close alignment between the training and validation curves throughout the full training horizon confirms the absence of overfitting, validating the combined effect of dropout regularization, L2 weight decay, and adaptive learning rate scheduling. This convergence behavior stands in clear contrast to the MLR baseline, which rapidly saturates at MSE ≈ 0.34, further demonstrating the necessity and effectiveness of the nonlinear regularized architecture proposed in this work.

3. Early Stopping Strategy. The revised Section 5.2 now explicitly clarifies the role of convergence control. Although no explicit early-stopping callback is implemented, the validation loss is continuously monitored during training. The adaptive learning rate scheduler effectively serves as an implicit stopping mechanism by progressively reducing the learning rate when validation performance plateaus, thereby preventing unnecessary overfitting while maintaining deterministic training behavior.
4. Training Protocol. The revised manuscript further enriches Section 5.2 by providing a complete description of the training procedure, which was previously underspecified:

• 1000 training epochs with batch size of 32
• Adam optimizer with initial learning rate eta = 1e-2
• Mean Squared Error (MSE) loss function as optimization objective
• k-fold cross-validation, yielding a standard deviation of RMSE below 5% across folds
• Strict separation between training and test sets prior to any model fitting to prevent data leakage

These additions significantly improve the transparency, reproducibility, and methodological completeness of the proposed MLP framework.

Comment 3: The procedure for selecting the anomaly detection threshold and splitting data into training and testing sets is insufficiently described, hindering reproducibility assessment.

Response 3: We sincerely thank the reviewer for this precise and constructive observation. We fully agree that a rigorous and reproducible experimental protocol requires explicit specification of both the anomaly detection threshold selection procedure and the dataset partitioning strategy. Both aspects have been substantially expanded in the revised manuscript, with all additions clearly indicated in red.

1. Anomaly Detection Threshold Selection

The threshold selection procedure is now formally described in Section 5.2 (Neural Network Model Evaluation). The adopted approach is based on a principled statistical residual analysis operating in three sequential steps.

First, the MLP model (architecture 4-32-32-1) is trained exclusively on hydraulically normal operating conditions, defined as configurations yielding a measured pressure Pm > 0.6 bar, ensuring that the learned pressure baseline is not contaminated by anomalous states.

Second, the anomaly score for any new observation is defined as the absolute prediction residual:

delta_P = | P_r - P_r_hat |

where P_r denotes the measured nodal pressure and P_r_hat the MLP prediction under the corresponding valve configuration.

Third, the detection threshold is derived from the empirical residual distribution of the normal training set using the three-sigma rule:

epsilon* = mu_deltaP + 3 * sigma_deltaP

where mu_deltaP = 0.102977 bar and sigma_deltaP = 0.191592 bar are the mean and standard deviation of the absolute residuals computed on the normal training partition, yielding epsilon* = 0.677753 bar. Any new observation producing delta_P > epsilon* is classified as anomalous.

The robustness of this threshold is validated through ROC analysis, which sweeps the decision boundary across the full residual range and computes the True Positive Rate (TPR) and False Positive Rate (FPR) at each operating point. The model achieves AUC = 0.9231, with the selected threshold epsilon* yielding TPR = 98.31% and FPR = 25.36%. The ROC curve is provided in Figure 9 of the revised manuscript. This complete procedure --- from residual computation to threshold derivation and ROC validation --- is now explicitly documented to ensure full reproducibility.

2. Dataset Splitting and Experimental Protocol

The dataset partitioning strategy is now formally described in Section 4.2 (Dataset Characteristics), under the new subsection "Dataset Splitting and Experimental Protocol". The procedure is specified as follows.

Prior to any model fitting, the full augmented dataset of N_total = 1,339 samples is randomly shuffled using a fixed random seed to ensure reproducibility and to eliminate any ordering bias arising from the chronological sequence of experimental acquisition. The shuffled dataset is then partitioned into training and held-out test sets according to an 80/20 ratio:

N_train = 1,071 samples, N_test = 268 samples

This partitioning is justified by three complementary considerations:

• Allocating 80% of the samples to the training set provides both models with sufficient diversity to estimate the nonlinear mapping between valve states and nodal pressures, which is particularly critical for the MLP.
• Reserving 20% as a strictly held-out test set ensures that all reported performance metrics --- MSE, RMSE, MAE, and R^2 --- are computed on data that were never seen during training or hyperparameter selection, providing an unbiased estimate of generalization performance.
• The prior random shuffling guarantees that both subsets contain representative samples drawn from all 13 hydraulic operating states, preventing the chronological clustering of specific configurations in either partition and ensuring that the evaluation is not confounded by acquisition order.

The 80/20 ratio follows widely adopted practice in machine learning for datasets of moderate size and provides a principled compromise between maximizing training diversity and preserving a statistically meaningful evaluation subset. With 268 test samples distributed across 13 operating states, the test set contains approximately 20 samples per state on average, providing sufficient coverage to assess generalization across the full hydraulic operating space.

Comment 4: The study omits comparison with modern alternatives such as 1D-CNN, Isolation Forest, or autoencoders, limiting evaluation within the context of TinyML anomaly detection methods.

Response 4: We sincerely thank the reviewer for this valuable and insightful remark. We fully agree that the inclusion of modern baseline architectures is essential to strengthen both the scientific rigor and the contextual positioning of the proposed approach within TinyML anomaly detection frameworks.

In response to this comment, we have introduced a new Section 5.5 entitled "Extended Model Comparison and Embedded Deployment Analysis" in the revised manuscript. This section provides a systematic and unified evaluation of five representative architectures: the proposed MLP, linear regression, Decision Tree, Random Forest, and a 1D-CNN. The corresponding results are reported in the newly introduced Table 4 and Table 5, which jointly assess predictive performance and embedded deployment feasibility under ESP32 constraints.

We address below the specific models mentioned by the reviewer.

1. 1D-CNN. The 1D-CNN has been explicitly implemented and evaluated within the extended experimental protocol. As reported in Table 4, it achieves performance comparable to the MLP in terms of RMSE and R^2. However, despite this similarity in predictive accuracy, it was not retained for deployment for the following reasons:

• The HydroNeuro input space consists of a low-dimensional, non-sequential binary encoding of valve states, which does not exhibit spatial or temporal locality. Consequently, the inductive bias of convolutional layers is not theoretically aligned with the problem structure.
• The convolutional architecture introduces additional parameterization and computational overhead without measurable gain in predictive performance for this task.
• From a TinyML deployment perspective, the resulting TensorFlow Lite Micro model exhibits higher flash memory consumption and increased inference latency on the ESP32 compared to the MLP.

Therefore, while the 1D-CNN is competitive in accuracy, it is suboptimal under the combined constraint of efficiency and embedded deployability. The MLP remains the most balanced solution in this context.

2. Isolation Forest and Autoencoders. These approaches were also carefully analyzed but are not included in the quantitative regression benchmark due to fundamental methodological differences with the problem formulation.

The HydroNeuro framework is explicitly defined as a supervised regression problem, where a model learns the mapping f: V -> P_r_hat from labeled valve configurations to continuous pressure values. Anomaly detection is subsequently performed via residual analysis.

• Isolation Forest: This method is inherently unsupervised and relies on partition-based anomaly scoring. It does not model the functional relationship between valve states and pressure and cannot produce deterministic pressure estimates. As a result, its inclusion in regression-based metrics such as RMSE or R^2 would not be methodologically consistent.
• Autoencoders: These models are primarily designed for unsupervised reconstruction error estimation. In our setting, where labeled input-output pairs are available, supervised regression provides a more direct, interpretable, and accurate modeling strategy. Moreover, autoencoders would introduce additional architectural complexity without leveraging the available ground-truth supervision.

For transparency, we explicitly discuss these limitations and exclusions in Section 5.5 of the revised manuscript, ensuring methodological clarity regarding their non-inclusion in the quantitative comparison.

3. TinyML deployment perspective. In addition to performance comparison, the new Section 5.5 introduces a unified evaluation framework that jointly considers predictive accuracy, model complexity, and embedded deployability. This allows a more realistic assessment of each architecture under ESP32 constraints (memory footprint, inference latency, and TFLM conversion overhead). The resulting Table 5 provides a consolidated view of this trade-off, which was not present in the original version of the manuscript.

Overall, these additions significantly strengthen the experimental section by providing a transparent, reproducible, and hardware-aware comparison with both classical and modern machine learning alternatives in the context of TinyML anomaly detection.

Comment 5: "Transition to field deployment requires discussion of model robustness to long-term sensor drift and the need for periodic retraining without human intervention."

Response 5: We sincerely thank the reviewer for this highly relevant and practical observation. We fully agree that long-term robustness and autonomous maintenance are essential requirements for real-world field deployment of embedded AI systems. In response to this comment, we have added Section 5.9 entitled "Long-Term Robustness and Model Maintenance Strategy" in the revised manuscript, which directly addresses both aspects raised by the reviewer.

1. Regarding Long-Term Sensor Drift. As detailed in Section 5.9, the residual-based anomaly detection module is continuously exploited not only for fault detection but also as a real-time indicator of model validity and system stability. In particular:

• A sustained increase in residual error, prediction bias, or false alarm rate is interpreted as evidence of distribution shift, potentially caused by sensor drift, hydraulic aging, or evolving operating conditions.
• When such behavior is detected, an automatic maintenance cycle is triggered, consisting of: (i) sensor recalibration using a stable hydraulic reference state to compensate for measurement drift, and (ii) offline model retraining using an updated dataset reflecting the current system dynamics.

In addition, the anomaly detection threshold is designed to support progressive drift adaptation. As introduced in Section 4.2, the fixed threshold epsilon* = 0.677753 bar (used in the controlled experimental setup) is replaced in field conditions by an adaptive formulation:

epsilon_t = mu^(t)_deltaP + 3 * sigma^(t)_deltaP

where mu^(t)_deltaP and sigma^(t)_deltaP are computed over a sliding window of recently validated healthy states. This adaptive mechanism allows the decision boundary to evolve dynamically with the hydraulic system, ensuring robustness against slow drift while maintaining sensitivity to true anomalies.

2. Regarding Periodic Retraining Without Human Intervention. Section 5.9 further formalizes an autonomous, event-driven retraining strategy that eliminates the need for manual intervention. Unlike fixed-interval retraining schemes, the proposed approach is triggered only when statistically significant degradation is detected, which offers two key advantages:

• It preserves computational efficiency and deterministic execution on the ESP32 platform by avoiding continuous online learning.
• It ensures that retraining is performed only when necessary, based on objective drift indicators, preventing both premature and delayed updates.

The manuscript also highlights that lightweight sliding-window updates can optionally be integrated to further improve adaptability in highly dynamic environments, while preserving embedded constraints such as memory usage and energy efficiency.

3. Consistency with System Architecture. This maintenance strategy is fully aligned with the offline Edge-AI design philosophy of HydroNeuro. As described in Section 3.8, the system operates primarily in a fully embedded mode, with model updates deployed via an Over-The-Air (OTA) mechanism through local Wi-Fi connectivity. This design requires only short and infrequent communication windows, avoiding permanent cloud dependency and ensuring suitability for rural and resource-constrained agricultural environments.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have made revisions and improvements based on the reviewers' comments. I have no further suggestions.

Reviewer 4 Report

Comments and Suggestions for Authors The authors have submitted a substantially revised manuscript. They have comprehensively addressed the comments from the first review round. The training dataset size has been corrected from 36,000 to 1,339 samples. The manuscript now contains a detailed description of the adaptive Gaussian augmentation. This augmentation applies physically justified outlier constraints. The protocol for data partitioning has been formalized. An extended comparison with Decision Trees, Random Forests, and 1D-CNNs has been included. This comparison analyzes the firmware conversion process for the ESP32 microcontroller. The results demonstrate a systematic approach to architectural selection. The selection prioritizes real TinyML deployment constraints over standalone accuracy metrics.   The revised version provides a clear justification for the selected MLP topology. The architecture consists of a 4-32-32-1 layer configuration. Regularization mechanisms are explicitly detailed. These include a dropout layer with a probability of 0.1. The model also uses L2 regularization with a weight decay of 10⁻⁵. An adaptive learning rate scheduler is implemented. The training protocol is fully documented. These measures eliminate overfitting risks on synthetic data. Section 5.9 now addresses long-term system stability. It introduces an event-driven recalibration strategy. It also describes an adaptive threshold update mechanism based on a sliding window. This addition resolves a critical practical issue. The issue involves sensor drift and autonomous maintenance in field conditions. The integration of fractional factorial design, statistically controlled augmentation, and energy-efficient edge deployment strengthens the work. The study offers significant value to the precision agriculture and embedded AI research communities.