Surrogate Model of Hydraulic Actuator for Active Motion Compensation Hydraulic Crane

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The research addresses computational challenges in modeling hydraulic actuators integrated with active motion compensation (AMC) systems, widely used in offshore cranes. These cranes are critical for offshore engineering tasks such as wind turbine maintenance and subsea operations. The complexity of actuator dynamics, described by differential-algebraic equations (DAEs), demands substantial computational resources, especially for real-time control and digital twins. It develops a surrogate model based on artificial neural networks (ANN) to significantly reduce computational compexity while maintaining high accuracy, and provides a rapid dynamics solution suitable for real-time applications such as hardware-in-the loop (HIL) simulations and model predictive control (MPC).

The paper is in good condition and still has some points for improvement:

1. Figures 7 and 8 are only described in basic terms and could benefit from more discussion.
2. No comparative benchmark with alternative models such as Kriging and Recurrent Neural Networks. The authors should provide a benchmark table comparing accuracy, time, memory, and complexity of various surrogate techniques. 
3. The surrogate is validated only on a single-axis actuator. Authors could extend to multi-axis cranes with joint-coupled hydraulic subsystems and test under coupled dynamics from experimental data.
4. No quantification of confidence intervals or robustness under sensor noise or model mismatch. Authors could add Monte Carlo robustness analysis under uncertain input conditions

Author Response

Comments 1:Figures 7 and 8 are only described in basic terms and could benefit from more discussion.

Response 1:Dear Professor, Your question provided significant insight. Figures 7 and 8 illustrate the errors between the method proposed in this study and traditional methods, along with their respective calculation results. Further discussion indeed helps us present our research more comprehensively.
Consequently, we introduced a random perturbation force based on a Gaussian distribution into the load (lines 298-311 in the revised manuscript). This allowed us to obtain the errors and calculation results between the proposed method and traditional methods in the presence of this random perturbation. This addition enables us to discuss and analyze the calculation results both with and without the random perturbation force. Thank you again for your valuable feedback.

Comments 2:No comparative benchmark with alternative models such as Kriging and Recurrent Neural Networks. The authors should provide a benchmark table comparing accuracy, time, memory, and complexity of various surrogate techniques. 

Response 2:Dear Professor, Your question is highly insightful. Please accept my apologies for not articulating my thoughts clearly enough initially. Allow me to reiterate the core concept of this study. Our research focuses on proposing a novel paradigm: utilizing artificial neural networks (ANNs) for surrogate modeling of active motion-compensated hydraulic cranes. This provides a new approach for surrogate modeling in this domain—one that leverages ANNs and is anticipated to effectively handle the high nonlinearity inherent in hydraulic circuits. This constitutes the primary innovation of our work.

The advantage of our approach over traditional first-principles modeling in terms of computational speed enhancement is already demonstrated in the paper. Whether this study offers improvements in computational efficiency, robustness, or adaptability compared to traditional surrogate modeling techniques—such as the RNN and Kriging methods you mentioned, or other well-established approaches like response surface models—are indeed excellent research questions. These warrant substantial time and effort for future investigation. Thank you again for your suggestions.

Comments 3:The surrogate is validated only on a single-axis actuator. Authors could extend to multi-axis cranes with joint-coupled hydraulic subsystems and test under coupled dynamics from experimental data.

Response 3:Dear Professor, Your question remains highly pertinent. Allow me to supplement some research rationale not fully elaborated in the manuscript. The single-axis system already incorporates critical characteristics present in multi-axis systems, including the strong nonlinearity, saturation, and hysteresis of high-order valve-controlled hydraulic circuits. Furthermore, the load force applied to the hydraulic cylinder is variable, which mirrors operational conditions in multi-axis systems. Crucially, neither the model nor the training procedure makes any assumptions regarding the number of degrees of freedom. Therefore, the proposed method can be directly extended to multi-axis systems. Thank you once again for your valuable comments.

Comments 4:No quantification of confidence intervals or robustness under sensor noise or model mismatch. Authors could add Monte Carlo robustness analysis under uncertain input conditions.

Response 4:Dear Professor, Your expert and valuable comments have provided us with precious insights and allowed our research to delve deeper. Quantifying confidence intervals and model robustness is a crucial aspect of surrogate modeling, significantly impacting model stability and applicability. Monte Carlo robustness analysis is a classical method for assessing surrogate model robustness, ensuring the resulting model possesses sufficient robustness.

Allow me to reiterate the core concept of this study. The current application focuses on function interpolation for a specific set of deterministic system parameters. Accuracy within the interpolation range and simulation fidelity are our primary concerns. While the load force can indeed exhibit randomness, we designed an experiment (lines 298-311 in the revised manuscript) where a random perturbation was introduced into the load. The system response under this perturbed load was then solved separately using both the traditional first-principles modeling method and the proposed neural network surrogate model. Comparing the differences in their calculation results also allows for a meaningful assessment of the model's robustness and provides an indication of the confidence interval.

Thank you for your patience and suggestions. Best regards.

Reviewer 2 Report

Comments and Suggestions for Authors

Based on the review of this paper on surrogate modeling for hydraulic actuators in active motion compensation cranes, here are some suggestions that the author need to revise it in the modified manuscript:

W1: Limited novelty in surrogate modeling approach - the three-hidden-layer neural network with tanh activation functions represents a conventional architecture without innovative design elements for this specific hydraulic application domain.

W2: Insufficient comparison with state-of-the-art surrogate modeling techniques - the paper lacks comprehensive comparison with modern methods like Gaussian Process Regression, Support Vector Machines, or ensemble methods that may offer superior performance.

W3: Oversimplified model validation methodology - testing only under "typical constant gravity load conditions" (Section 4.1) fails to demonstrate robustness across diverse operational scenarios including variable loads, different sea states, and emergency conditions.

W4: Inadequate discussion of model generalization capabilities - the surrogate model training uses a specific parameter range (Table 2) but provides no analysis of extrapolation performance beyond these bounds or sensitivity to parameter variations.

W5: Lack of real-time implementation verification - while claiming 95.33% computational speedup, the paper provides no evidence of actual real-time performance in hardware-in-the-loop simulation or digital twin applications as mentioned in the abstract.

W6: Insufficient theoretical justification for network architecture - the choice of [25, 10, 20] neuron configuration (Section 4.2.1) appears arbitrary without systematic architecture optimization or comparison with alternative configurations.

W7: Limited error analysis scope - absolute pressure errors are only reported for chambers p1 and p2 (Table 4) without comprehensive analysis of displacement, velocity, or other critical system outputs throughout the operational envelope.

W8: Weak experimental validation framework - the validation relies entirely on simulation data without physical experiments or comparison with actual crane performance data to verify model fidelity.

W9: Poor figure quality and presentation - Figure 7 and Figure 8 lack sufficient detail and resolution to properly assess model performance, with overlapping curves that obscure important differences between methods.

W10: Incomplete discussion of computational requirements - while training duration is mentioned (20h 11min in Table 3), the paper lacks analysis of memory requirements, scalability to larger systems, or computational complexity compared to alternative approaches.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

Comments 1:Limited novelty in surrogate modeling approach - the three-hidden-layer neural network with tanh activation functions represents a conventional architecture without innovative design elements for this specific hydraulic application domain.

Response 1:Dear Professor, Your question is highly professional and very constructive for our research. Please accept my apologies for not clearly articulating some aspects of the research rationale in the manuscript. Allow me to elaborate here, and thank you for your attention.

This study focuses on proposing a research paradigm: utilizing artificial neural networks (ANNs) for surrogate modeling of active motion-compensated hydraulic cranes. This provides a novel approach to surrogate modeling in this domain—one that relies on ANNs and is anticipated to effectively handle the high nonlinearity inherent in hydraulic circuits. This constitutes the primary innovation of this work. While the ANN architecture itself may be considered conventional, its application to the study of active motion-compensated hydraulic cranes is rarely explored, making this study a novel attempt. Research into novel neural network architectures is indeed a highly valuable research direction, which we continuously monitor. In the near future, we plan to conduct more in-depth studies focused on this specific research direction. Thank you again for your valuable question.

Comments 2:Insufficient comparison with state-of-the-art surrogate modeling techniques - the paper lacks comprehensive comparison with modern methods like Gaussian Process Regression, Support Vector Machines, or ensemble methods that may offer superior performance.

Response 2:Dear Professor, Your question remains highly insightful and demonstrates a unique perspective. Gaussian Process Regression (GPR), Support Vector Machines (SVMs), and ensemble methods are all well-established and effective state-of-the-art surrogate modeling techniques that significantly contribute to building surrogate models. Allow me to further elaborate on the rationale of this study, and thank you for your patient attention.

This study focuses on a novel research paradigm: utilizing ANNs for surrogate modeling of active motion-compensated hydraulic cranes. The advantage of our approach over traditional first-principles modeling in terms of computational speed enhancement is already demonstrated in the paper. Whether this study offers superior performance compared to state-of-the-art surrogate modeling techniques—such as the GPR, SVMs, and ensemble methods you mentioned—along with comprehensive comparisons of adaptability, robustness, and other technical metrics across different techniques, are indeed excellent research ideas. These warrant substantial time and effort for future investigation. Thank you again for your suggestions.

Comments 3:Oversimplified model validation methodology - testing only under "typical constant gravity load conditions" (Section 4.1) fails to demonstrate robustness across diverse operational scenarios including variable loads, different sea states, and emergency conditions.

Response 3:Dear Professor, Allow me to elaborate further on some details of this study. Although the gravitational load is constant, the actual load applied to the hydraulic cylinder is variable; that is, the force experienced by the hydraulic cylinder is constantly changing. Robustness across diverse operational scenarios, including different sea states and emergency conditions, is a highly valuable aspect worthy of investigation. This warrants substantial time and effort for future research. Thank you again for your suggestion.

Comments 4:Inadequate discussion of model generalization capabilities - the surrogate model training uses a specific parameter range (Table 2) but provides no analysis of extrapolation performance beyond these bounds or sensitivity to parameter variations.

Response 4:Dear Professor, Your question is again highly professional and provides us with new insights. Our previously submitted manuscript indeed lacked sufficient discussion on the model's generalization ability. To address this, we have added an experiment (lines 298-311 in the revised manuscript) where a random perturbation force was introduced into the load to simulate the system response under disturbance. Comparative analysis of the simulation results was then performed. This addition helps deepen the discussion on the model's generalization capability. Thank you again for your suggestion.

Comments 5:Lack of real-time implementation verification - while claiming 95.33% computational speedup, the paper provides no evidence of actual real-time performance in hardware-in-the-loop simulation or digital twin applications as mentioned in the abstract.

Response 5:Dear Professor, Your question remains highly insightful and prompts valuable reflection. Real-time experimental validation, such as actual real-time verification in hardware-in-the-loop (HIL) simulations or digital twin applications, is indeed a highly valuable research direction. It holds significant importance for validating the proposed surrogate model under realistic experimental conditions. Please accept my apologies for not clearly articulating our research rationale in the manuscript. Allow me to elaborate further here, and thank you for your patient attention.

The statement in the abstract claiming that this study "can be applied" to HIL simulation or real-time applications like digital twins did not accurately convey our intended meaning. It should be revised to state that this study has the application potential for scenarios with high real-time demands, such as HIL simulation and digital twins (lines 16-19 in the revised manuscript). Applying this study to actual equipment for experimental validation holds significant research value and warrants substantial time and effort for future investigation. Thank you again for your suggestion.

Comments 6:Insufficient theoretical justification for network architecture - the choice of [25, 10, 20] neuron configuration (Section 4.2.1) appears arbitrary without systematic architecture optimization or comparison with alternative configurations.

Response 6:Dear Professor, Your question remains highly professional and provides us with new research avenues. The theory and optimization of network architecture constitute a highly valuable research topic, as different network configurations can significantly impact training and performance.

In our previously submitted manuscript, we acknowledge that the theoretical basis for the chosen network architecture was not provided. In practice, the selection of tanh as the activation function and the [25 10 20] neuron configuration emerged as a feasible solution through extensive trial-and-error experimentation. More in-depth theoretical studies on this aspect will be conducted in the near future. Thank you again for your suggestion.

Comments 7:Limited error analysis scope - absolute pressure errors are only reported for chambers p1 and p2 (Table 4) without comprehensive analysis of displacement, velocity, or other critical system outputs throughout the operational envelope.

Response 7:Dear Professor, Your question is again highly pertinent and directly addresses a core aspect of the research. Displacement, velocity, and other key system outputs across the entire operational range are indeed crucial components. Please accept my apologies for not clearly articulating our research rationale in the manuscript. Allow me to elaborate further here, and thank you for your patient attention.

Regarding our prior work (WEI Qi, etc. Surrogate Model Based Fast Solution Method for Dynamics of Mechanisms with Friction, 2025,61(04):323-332.), we investigated surrogate modeling for displacement and velocity in mechanism dynamics. We found that ANN surrogate models can achieve very high accuracy for displacement fitting (maximum error of 0.0234 mm). Consequently, this current study focuses more intensely on fitting parameters of the highly nonlinear hydraulic subsystem (e.g., p1, p2). Therefore, we adopted the premise that "the mechanism's displacement and velocity are accurate values." Developing a surrogate model capable of coupled simulation of both hydraulic parameters and mechanism parameters remains a key focus for our future research, which we plan to pursue extensively. Thank you again for your question.

Comments 8:Weak experimental validation framework - the validation relies entirely on simulation data without physical experiments or comparison with actual crane performance data to verify model fidelity.

Response 8:Dear Professor, Your question is consistently insightful and always provides valuable inspiration. Physical experiments or comparisons with actual crane performance data would indeed be highly effective for validating model fidelity and hold significant research value.

To address this, we designed an experiment (lines 298-311 in the revised manuscript) where a random perturbation was introduced into the load to simulate real-world conditions. The system response under this perturbed load was computed using both the traditional first-principles model and the proposed surrogate model. The errors between the two sets of results were then compared. The results demonstrate that the proposed model maintains high accuracy even under perturbed load conditions. Thank you again for your suggestion.

Comments 9:Poor figure quality and presentation - Figure 7 and Figure 8 lack sufficient detail and resolution to properly assess model performance, with overlapping curves that obscure important differences between methods.

Response 9:Dear Professor, Your question is, as always, highly astute and precisely identifies key issues. We acknowledge that the overlapping curves in Figures 7 and 8 could cause readability problems. We have modified these figures by separating the overlapping curves into distinct subplots and have added inset zoomed-in views for clarity (above line 286 in the revised manuscript). Thank you again for highlighting this point.

Comments 10:Incomplete discussion of computational requirements - while training duration is mentioned (20h 11min in Table 3), the paper lacks analysis of memory requirements, scalability to larger systems, or computational complexity compared to alternative approaches.

Response 10:Dear Professor, Your question remains highly comprehensive, consistently considering the broader perspective. Analyzing memory requirements, the potential for scaling to larger systems, or performing computational complexity comparisons with alternative methods would undoubtedly strengthen our research.

In response, we have measured and compared the memory usage of the traditional method and the proposed method, presenting the results in a table (lines 318-319 in the revised manuscript). Thank you once again for your patience and valuable suggestions. Best regards.

Reviewer 3 Report

Comments and Suggestions for Authors

My comments are attached.

Comments for author File: Comments.pdf

Author Response

Comments 1:Authors should present a nomenclature table in their manuscript.

Response 1:Dear Professor, Your suggestion is highly insightful. Including a glossary in the manuscript would indeed significantly enhance the readability of the article. We have followed your guidance and added a glossary (line 22, Section 1 of the revised manuscript). Thank you again for your valuable suggestion.

Comments 2:In Figure 1, please include the component names beside their numbers to enhance readability.

Response 2:Dear Professor, Your comment remains highly pertinent and consistently demonstrates thorough consideration. Including component names adjacent to the numbers in Figure 1 would indeed greatly improve the figure's readability. We have followed your guidance and added these labels (below line 105, Figure 1 in the revised manuscript). Thank you again for your suggestion.

Comments 3:The schematics of the bond graphs in Figures 1 and 2 are difficult to follow; please include a legend.

Response 3:Dear Professor, Your suggestion is highly valuable. We acknowledge that the hydraulic schematics in Figures 1 and 2 were not sufficiently clear. We have added corresponding legends (below line 105 for Figure 1 and below line 124 for Figure 2 in the revised manuscript) and provided additional explanations within the text (lines 114-120 and 126-129 in the revised manuscript). Thank you again for your suggestion.

Comments 4:In the introduction section, please include a broader literature survey on surrogate and DoE methods, such as RSM, Kriging, and factorial designs. Please refer to this paper:

-A Systematic Analysis of a Small-Scale HAWT Configuration and Aerodynamic Performance Optimization Through Kriging, Factorial, and RSM Methods

Response 4:Dear Professor, Your suggestion provides significant benefit to our research. We have carefully reviewed the literature you recommended (particularly the review sections on surrogate methods and Design of Experiments (DOE) methods, which served as highly valuable references). Accordingly, we have added a corresponding review section to the Introduction (lines 48-62 in the revised manuscript), including new citations. This addition significantly strengthens our Introduction. Thank you again for your suggestion.

Comments 5:At the end of the introduction section, it is essential to emphasize the originality of your research and highlight the advantages it offers in comparison to existing studies. Additionally, it is important to address the specific research gap that your work aims to fill.

Response 5:Dear Professor, Your suggestion demonstrates unique professional insight. It is indeed appropriate to emphasize the study's originality, highlight its advantages over existing research, and identify the specific gap it fills towards the end of the Introduction. This strengthens the section's completeness. We have followed your guidance and implemented these modifications (lines 88-92 in the revised manuscript). Thank you again for your suggestion.

Comments 6:How do the authors determine their time step size? ls a time step size study possible?

Response 6:Dear Professor, Your question is again highly relevant. Allow me to elaborate on a specific detail of this study. Hydraulic systems are typically stiff systems. The time step size is governed by the fastest dynamics in the system, namely the pressure dynamics within the hydraulic chambers. As shown in Figure 7, initial simulations required extremely small time steps to accurately capture the pressure oscillation period. Subsequently, the step size was adjusted to a more computationally efficient value. The current selection represents this optimized choice. Thank you again for your suggestion.

Comments 7:Figures 6, 7, and 8 require a more in-depth analysis.

Response 7:Dear Professor, Your question provided significant inspiration. We designed an experiment where a random perturbation was introduced into the load force. The system response was then computed separately using both the traditional method and the proposed surrogate model method, and their results were compared (lines 298-311 in the revised manuscript). This experiment facilitates the analysis of the model's robustness in the presence of random disturbances. Thank you again for your valuable insight.

Comments 8:Could the authors provide a sensitivity analysis and an ANOVA analysis based on their algorithm?

Response 8:Dear Professor, Your question remains highly comprehensive, consistently considering the broader perspective. Sensitivity analysis and variance analysis would indeed provide deeper insights into the model's robustness and help identify key influencing factors, thereby strengthening our research.

To address this, we designed an experiment—the one mentioned in the previous response involving the addition of random perturbation to the load (lines 298-311 in the revised manuscript). This experiment serves to evaluate the model's sensitivity to load variations to a certain extent.

Thank you once again for your patience and valuable suggestions. Best regards.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors answered all the proposed improvements, and the paper could be accepted in its present form.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have answered all the questions. It can be accepted in the current form.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Reviewer 3 Report

Comments and Suggestions for Authors

The reference format must be revised in accordance with the journal's guidelines. Some references are incomplete, lacking author names, volume numbers, and other relevant information. (Refs 6 and 19).