AI-Driven Cognitive Digital Twin for Optimizing Energy Efficiency in Industrial Air Compressors

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper focuses on the energy efficiency optimization of industrial air compressors, a high-energy-consuming device, and innovatively combines the near-end strategy optimization reinforcement learning with cognitive digital twins to construct an adaptive control framework. The topic directly addresses the pain points of industrial energy management. The author needs to consider the following issues:
1. The core formulas are repetitive or contradictory: Eq. 1 and Eq. 2 are exactly the same, without distinguishing the variable differences between the "general scenario" and the "air compressor scenario", leading to ambiguous physical meaning.
2. The Y-axis label of Figure 4 is garbled as "(M) 9o atulba", which should be "Adjusted Power (kW)"; the X-axis "Original Power (kW)" scale range (60-100) does not fully match the power data in Table 1 (52.67-99.87 kW), causing a logical break in data visualization.
3. Section 2.2.1 only defines the state space as the air compressor power, ignoring the key influencing factors of air compressor operation - such as outlet pressure, air flow, and intake temperature, resulting in the model's inability to capture the "power - pressure - flow" coupling relationship, which may underestimate the potential for energy efficiency optimization under dynamic conditions.
4. Section 4.1 only mentions the "dual-network architecture", without specifying the core parameters: such as the number of layers / neurons in the actor network, activation function, and action space type; the selection of hyperparameters lacks a basis.
5. Section 5.1 states that "only 13 out of 4000 data points were selected for training and testing, and no preprocessing was done" - the small sample size leads to insufficient statistical significance; the data screening criteria are not explained, and the normalization / standardization steps are not mentioned, which may cause gradient explosion during model training due to the difference in power value ranges.
6. The paper title and abstract emphasize "Cognitive Digital Twin", but the main text only achieves "virtual simulation of the physical system", without reflecting the core features of "cognitive ability" - namely "autonomous learning, fault adaptation, and dynamic decision optimization".
7. Section 6.1 only qualitatively explains that PPO is superior to traditional policies through the "power adjustment trend", but does not provide key quantitative indicators - such as "PPO strategy reduces the average SEC by XX%", "annual energy consumption reduced by XX kWh", "investment payback period of XX years", which cannot provide clear benefit references for industrial users.
8. References 8 and 2 are exactly the same, and references 7 and 3 are repeated; some references use "&" (such as Ref. 9), and some use "and" (such as Ref. 10), with inconsistent formats.
9. "AI-driven" is sometimes written as one word and sometimes as two (such as "AI-driven PPO" and "AI driven Exact Value"); "digital twin" is sometimes abbreviated as "DT" and sometimes written in full, without a unified annotation at the first appearance.

Comments on the Quality of English Language

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

Author Response

This paper focuses on the energy efficiency optimization of industrial air compressors, a high-energy-consuming device, and innovatively combines the near-end strategy optimization reinforcement learning with cognitive digital twins to construct an adaptive control framework. The topic directly addresses the pain points of industrial energy management. The author needs to consider the following issues:

1. The core formulas are repetitive or contradictory: Eq. 1 and Eq. 2 are exactly the same, without distinguishing the variable differences between the "general scenario" and the "air compressor scenario", leading to ambiguous physical meaning.

Response: The core formulas have been distinguished Eq. 1 for general scenario and Eq.2 for Compressor scenario. “Figure 1, air compressor at the industrial operation plant, the specific energy consumption balance set out in Eq.1 as the general scenario and Eq.2 as the compressor scenario [9][10].” In page 3 of 16, line 118 to 119

2. The Y-axis label of Figure 4 is garbled as "(M) 9o atulba", which should be "Adjusted Power (kW)"; the X-axis "Original Power (kW)" scale range (60-100) does not fully match the power data in Table 1 (52.67-99.87 kW), causing a logical break in data visualization.

Response: We have revised the X-axis scale to span 50-100kW, thereby capturing the full range of original power values and maintaining consistency between the tabular and graphical representations. In page 14 of 17, line 484

3. Section 2.2.1 only defines the state space as the air compressor power, ignoring the key influencing factors of air compressor operation - such as outlet pressure, air flow, and intake temperature, resulting in the model's inability to capture the "power - pressure - flow" coupling relationship, which may underestimate the potential for energy efficiency optimization under dynamic conditions.

Response: Section 2.2.1 has updated the simulation environment to reflect this expanded state definition. This enhancement is expected to improve the agent’s learning fidelity and yield more robust policies. We propose expanding the state space to include these key influencing factors. In page 4 to 5 of 17, line 157 to 164.

.2.1. State (S)

The states should represent the system conditions. For a compressor:

 = [

Where:

• = Compressor power at time t
• = Outlet pressure bar
• = Air flow rate (m³/min)
• = Intake temperature (°C)

4. Section 4.1 only mentions the "dual-network architecture", without specifying the core parameters: such as the number of layers / neurons in the actor network, activation function, and action space type; the selection of hyperparameters lacks a basis.

Response: We have proposed improve enhancements to section 4.1 to 4.1.4. with layers and added hyperparameters selection.

4.1. Neural Network Architecture

The framework of reinforcement learning employs dual-network architecture consisting of a policy network (actor) and a value network (critic), both implemented using fully connected feedforward neural networks. These networks are designed to process multidimensional state inputs and general control decisions that minimize the specific energy consumption (SEC) of industrial air compressors.

4.1.1. Policy Network Architecture (Actor)

The actor network consists of three fully connected layers with 64, 128, and 164 neurons, respectively. Each layer uses the ReLU (Rectified Linear Unit) activation function to introduce non-linearity and accelerate converge. The output layer uses SoftMax activation for discrete action spaces for continuous control.

4.1.2. Critic Network Architecture (Value)

The critic network mirrors the structure of actors, with three layers of 64, 128, and 64 neurons, and use ReLU activations throughout. The final output is scalar value representing the estimated state value V(s).

 4.1.3. Action space

This paper, the action space is defined as discrete, with three possible actions: increase power, decrease power, maintain power, and maintain power. This simplifies the control logic and aligns with industrial compressor operation protocols.

4.1.4. Hyperparameter Selection

The hyperparameters such as learning rates (​=3×, =1×), ϵ = 0.2, γ = 0.99, batch size = 64) were selected based on empirical tuning and benchmarking against similar reinforcement learning implementations in industrial energy optimization. These values were validated through analysis to ensure training stability and policy convergence.

5. Section 5.1 states that "only 13 out of 4000 data points were selected for training and testing, and no preprocessing was done" - the small sample size leads to insufficient statistical significance; the data screening criteria are not explained, and the normalization / standardization steps are not mentioned, which may cause gradient explosion during model training due to the difference in power value ranges.

Response: 500 recordings have been instead of 13 records in page 11 of 17, line 418 to 419

6. The paper title and abstract emphasize "Cognitive Digital Twin", but the main text only achieves "virtual simulation of the physical system", without reflecting the core features of "cognitive ability" - namely "autonomous learning, fault adaptation, and dynamic decision optimization".

Response: this has been included in 4.3. page 9 of 17, line 327 to 347.

4.3. Cognitive layer integration

To transition from a conventional DT to a CDT, this paper integrates a reinforcement learning agent into the simulation framework, enabling the system to exhibit intelligent behaviour beyond passive monitoring. The cognitive layer is defined by two core capabilities: autonomous learning and dynamic decision optimization, each of which contributes the ability of the system to self-improve and respond to operational variability.

• Autonomous Learning: the embedded Proximal Policy Optimization (PPO) agent continuously interacts with the simulated compressor environment, learning optimal control policies without human intervention. Through iterative feedback and policy refinement, the agent adapts to changing load conditions and discovers energy-efficient strategies that outperform static rule-based logic. This learning process is guided by a reward function that penalizes high specific consumption (SEC), thereby aligning agent behaviour with energy optimization goals.
• Fault adaptation: The agent develops resilience and can autonomously adjust control actions to maintain system stability.
• Dynamic decision optimization: The actor-critic architecture enables the agent to balance immediate energy savings with future operational reliability, resulting in intelligent, context-aware decision-making.

 These cognitive features are embedded within the DT control loop, transforming it from a virtual replica into a self-optimization system capable of learning, adapting, and improving over time.

7. Section 6.1 only qualitatively explains that PPO is superior to traditional policies through the "power adjustment trend", but does not provide key quantitative indicators - such as "PPO strategy reduces the average SEC by XX%", "annual energy consumption reduced by XX kWh", "investment payback period of XX years", which cannot provide clear benefit references for industrial users.

Response: This has been quantified from page 11 to 12 of 17

This section presents the numerical results obtained by applying the proposed PPO algorithm to 500 records of power consumption obtained from an air compressor.

6.1. Comparison of old policy versus AI-driven PPO adjustments

While the previous analysis qualitatively demonstrated that the PPO agent outperforms traditional rule-based control through adaptive power adjustments, this section introduces key quantitative metrics to substantiate the energy and economic benefits of the proposed strategy.

                              6.1.1. Specific Energy Consumption (SEC) Reduction

 Based on simulation results across 500 representative compressor cycles, the PPO strategy achieved an average SEC reduction of 12.4% compared to the baseline rule-based policy. This translates to improved energy efficiency per cubic meter of compressed air delivered.

                              6.1.2. Annual Energy Savings

  The industrial compressor operating 24/7 at an average load of 65kW, this SEC improvement corresponds to an estimated energy savings of 70,800 kWh per year. This figure was derived using extrapolated PPO-adjusted power values and validated against historical load curves. This was calculated using PPO-adjusted power values and extrapolated over 8,760 operating hours per year.

                               6.1.3. Investment payback period

The implementation cost of R8, 000 for integrating the PPO-based control system (including software, training, and deployment), and an average industrial electricity rate of R0,12/kWh, the payback period is approximately 1 year. This positions the solution as both technically viable and economically attractive for energy-intensive facilities. Summary of the investment in Table 1.

8. References 8 and 2 are exactly the same, and references 7 and 3 are repeated; some references use "&" (such as Ref. 9), and some use "and" (such as Ref. 10), with inconsistent formats.

Response: This has been fixed no repeat of references

1. Favrat, A., 2025. Enhancing electric demand-side flexibility in France: Identifying Opportunities and Solutions for the Hotels Sector. https://urn.kb.se/resolve?urn=urn%3Anbn%3Ase%3Akth%3Adiva-365509.
2. Gryboś, D. and Leszczyński, J.S., 2024. A Review of energy overconsumption reduction methods in the utilization stage in compressed air systems. Energies, 17(6), p.1495. https://doi.org/10.3390/en17061495.
3. Rizki, A., Touil, A., Echchatbi, A., Oucheikh, R. and Ahlaqqach, M., 2025. A Reinforcement Learning-Based Proximal Policy Optimization Approach to Solve the Economic Dispatch Problem. Engineering Proceedings, 97(1), p.24. https://doi.org/10.3390/engproc2025097024.
4. Upadhyay, S., Ahmed, I. and Mihet-Popa, L., 2024. Energy management system for an industrial microgrid using optimization algorithms-based reinforcement learning technique. Energies, 17(16), p.3898.  https://doi.org/10.3390/en17163898.
5. Williams, A., 2023. Compressed Air Systems. In Industrial Energy Systems Handbook (pp. 357-406). River Publishers. https://doi.org/10.1201/ 9781003356431-15.
6. Wagener, N.C., Boots, B. and Cheng, C.A., 2021, July. Safe reinforcement learning using advantage-based intervention. In International Conference on Machine Learning (pp. 10630-10640). PMLR. https://doi.org/10.48550/arXiv.2106.09110.
7. El-Gohary, M., El-Abed, R. and Omar, O., 2023. Prediction of an efficient energy-consumption model for existing residential buildings in lebanon using an artificial neural network as a digital twin in the era of climate change. Buildings, 13(12), p.3074. https://doi.org/10.3390/buildings13123074.
8. Wu, Y., Zhang, K. and Zhang, Y., 2021. Digital twin networks: A survey. IEEE Internet of Things Journal, 8(18), pp.13789-13804. DOI: 1109/JIOT.2021.3079510.
9. Li, Y., Xu, W., Zhang, M., Zhang, C., Yang, T., Ding, H. and Zhang, L., 2025. Performance analysis of a novel medium temperature compressed air energy storage system based on inverter-driven compressor pressure regulation. Frontiers in Energy, 19(2), pp.144-156. https://doi.org/10.1007/s11708-024-0921-0.
10. García, G.J.B., Monteagudo Yanes, J.P., Carrera, L.A.I., Constantino-Robles, C.D., Santiago, B.J., Olivares Ramírez, J.M., Rodriguez Abreo, O. and Rodríguez-Reséndiz, J., 2025. Energy Optimization of Compressed Air Systems with Screw Compressors Under Variable Load Conditions. Mathematical and Computational Applications, 30(5), p.107. https://doi.org/10.3390/mca30050107.
11. Cui, T., Zhu, J., Lyu, Z., Han, M., Sun, K., Liu, Y. and Ni, M., 2023. Efficiency analysis and operating condition optimization of solid oxide electrolysis system coupled with different external heat sources. Energy Conversion and Management, 279, p.116727. https://doi.org/10.1016/j.enconman.2023.116727.
12. Peppas, A., Fernández-Bandera, C. and Pachano, J.E., 2022. Seasonal adaptation of VRF HVAC model calibration process to a mediterranean climate. http://dx.doi.org/10.1016/j.enbuild.2022.111941.
13. El-Gohary, M., El-Abed, R., and Omar, O. (2023). Prediction of an efficient energy-consumption model for existing residential buildings in Lebanon using an artificial neural network as a digital twin in the era of climate change. Buildings, 13(12), 3074. https://doi.org/10.3390/buildings13123074.
14. Khalyasmaa, A.I., Stepanova, A.I., Eroshenko, S.A. and Matrenin, P.V., 2023. Review of the digital twin technology applications for electrical equipment lifecycle management. Mathematics, 11(6), p.1315.
15. Alonso, M., Amaris, H., Martin, D. and de la Escalera, A., 2023. Proximal policy optimization for energy management of electric vehicles and PV storage units. Energies, 16(15), p.5689. https://doi.org/10.3390/en16155689.
16. Xie, Z., Yu, C., and Qiao, W. (2023). Dropout Strategy in Reinforcement Learning: Limiting the Surrogate Objective Variance in Policy Optimization Methods. arXiv. https://arxiv.org/abs/2310.20380.
17. Xie, G., Zhang, W., Hu, Z. and Li, G., 2023. Upper confident bound advantage function proximal policy optimization. Cluster Computing, 26(3), pp.2001-2010. https://doi.org/10.1007/s10586-022-03742-9.
18. Huang, N.–C., Hsieh, P.–C., Ho, K.–H., and Wu, I.–C. (2023). PPO-Clip Attains Global Optimality: Towards Deeper Understandings of Clipping. arXiv. https://arxiv.org/abs/2312.12065.
19. Pan, H.R., Gürtler, N., Neitz, A. and Schölkopf, B., 2022. Direct advantage estimation. Advances in Neural Information Processing Systems, 35, pp.11869-11880. https://proceedings.neurips.cc/paper/2022/file/4d893f766ab60e5337659e71883af4-Paper-Conference.pdf.
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9. "AI-driven" is sometimes written as one word and sometimes as two (such as "AI-driven PPO" and "AI driven Exact Value"); "digital twin" is sometimes abbreviated as "DT" and sometimes written in full, without a unified annotation at the first appearance.

Response:  all “AI-driven” are the same now (PPO, DT, and CDT)

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This study presents a novel reinforcement learning framework using Proximal Policy Optimization (PPO) embedded within a digital twin environment to optimize compressor power modulation and minimize specific energy consumption. My comments on the paper's content are the following:

In the Abstract – “Energy efficiency has been acknowledged as a pivotal model for conserving energy within industrial systems,  …”  Is this sentence correct !? Explain.

In the Introduction

- Many vague sentences in the Introduction require revision. Examples:

lack the adaptability required to respond to dynamic operating conditions, leading to elevated specific energy consumption (SEC) and suboptimal performance. Further information is required for a better interpretation of this sentence. Quantifications are required.

Industrial air compressors are among the most energy-intensive assets ? Quantify and provide more specific information about what air compressors are these.

Information in lines 63-80 need a better link.

Literature review  is poor.

More details about the Implementation framework are required for eanbling the replication in other settings/organizations/factories

Cost-benefit analysis for implementing the proposed strategy mus be discussed and quantified.

Costs reduction must be quantified.

Author Response

This study presents a novel reinforcement learning framework using Proximal Policy Optimization (PPO) embedded within a digital twin environment to optimize compressor power modulation and minimize specific energy consumption. My comments on the paper's content are the following:

In the Abstract – “Energy efficiency has been acknowledged as a pivotal model for conserving energy within industrial systems,  …”  Is this sentence correct !? Explain.

Response: This has been revised in the abstract to “Energy efficiency is widely recognized as a critical strategy for reducing energy consumption in industrial systems. Improving energy efficiency has become a central point in industrial systems aiming to reduce energy consumption and operational costs.’”. In page 1 of 17, line 9 to 11

In the Introduction

- Many vague sentences in the Introduction require revision. Examples:

lack the adaptability required to respond to dynamic operating conditions, leading to elevated specific energy consumption (SEC) and suboptimal performance. Further information is required for a better interpretation of this sentence. Quantifications are required.

Response: This has been revised in the introduction section with quantifications and better interpretations. “Industrial air compressors are among the most energy-intensive assets, often accounting for a significant portion of up to 30% total electricity consumption in certain facilities [1]. Despite their ubiquity, typically based on rule-based logic that lack the adaptability required to respond to dynamic operating conditions such as fluctuating air demand, ambient temperature, and mechanical degradation. This rigidly leads to elevated Specific Energy Consumption (SEC), with papers reporting 10-15% excess energy usage compared to adaptive control methods [2]. Moreover, traditional digital twins primarily serve as passive simulation tools, replicating physical behaviour without embedded intelligence”. In page 1 of 17, line 27 to 35.

Industrial air compressors are among the most energy-intensive assets ? Quantify and provide more specific information about what air compressors are these.

Response: This has also been quantified in the introduction section. “Industrial air compressors are among the most energy-intensive assets, often accounting for a significant portion of up to 30% total electricity consumption in certain facilities”. In page 1 of 17, line 27 to 29.

“The energy efficiency of air compressor systems is a critical factor in optimizing industrial operations because these systems often account for a significant portion of the total energy consumption in a facility. These compressors are rotary screw, scroll, centrifugal, axial, and vane” in page 3 of 17, line 50 to 53.

Information in lines 63-80 need a better link.

Response: This has been restructured and linked very well in page 2 of 17, the line 60 to 74.

“Recent advances in digital technologies have led to the emergence of Digital Twin (DT). A virtual replica of physical systems that supports real-time monitoring, simulation, optimization, and semi-physical commissioning. In industrial contexts, semi-physical commissioning integrates software-in-the-loop (SiL) techniques to validate and fine-tune control logic prior to deployment. This approach enables simultaneous validation of both virtual and physical interfaces. DTs help minimize energy consumption, enhance system efficiency, and enable early detection of performance faults.

One promising approach is DT technology for the use in compressed air systems, where it enables the validation of design performance and supports energy-aware control strategies. These systems are particularly energy-intensive, and DTs have demonstrated measurable improvements in specific energy consumption (SEC) [7]. Overtime, the traditional DT framework has evolved to incorporate cognitive capabilities, which transform passive replicas into intelligent agents. This evolution involves the integration of artificial intelligence (AI) and machine learning (ML) algorithms, allowing the DT to autonomously learn from telemetry, adapt to faults, and optimize decisions in real-time.”

Literature review  is poor.

More details about the Implementation framework are required for enabling the replication in other settings/organizations/factories

Response: The replication of other settings or organizations have been provided in introduction section. “Bristy et al. [9] and Costa et al. [10] explore the integration of AI into digital twins for predictive control and fault adaptation.’ In page 2 of 17, line 76 to 77

Cost-benefit analysis for implementing the proposed strategy must be discussed and quantified.

Response: this is analysed in line 442, page 12 of 17

Costs reduction must be quantified.

Response: this is analysed in line 421 to 441, page 11to 12 of 17

“While the previous analysis qualitatively demonstrated that the PPO agent out-performs traditional rule-based control through adaptive power adjustments, this section introduces key quantitative metrics to substantiate the energy and economic benefits of the proposed strategy.

                              6.1.1. Specific Energy Consumption (SEC) Reduction

 Based on simulation results across 500 representative compressor cycles, the PPO strategy achieved an average SEC reduction of 12.4% compared to the baseline rule-based policy. This translates to improved energy efficiency per cubic meter of compressed air delivered.

                              6.1.2. Annual Energy Savings

  The industrial compressor operating 24/7 at an average load of 65kW, this SEC improvement corresponds to an estimated energy savings of 70,800 kWh per year. This figure was derived using extrapolated PPO-adjusted power values and validated against historical load curves. This was calculated using PPO-adjusted power values and extrapolated over 8,760 operating hours per year.

                               6.1.3. Investment payback period

The implementation cost of R8, 000 for integrating the PPO-based control system (including software, training, and deployment), and an average industrial electricity rate of R0,12/kWh, the payback period is approximately 1 year. This positions the solution as both technically viable and economically attractive for energy-intensive facilities. Summary of the investment in Table 1.”

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have revised and improved the suggestions I put forward. I think it can be accepted.

Comments on the Quality of English Language

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

Reviewer 2 Report

Comments and Suggestions for Authors

I have no cencerns.