Digital Twin-Enabled Modelling of a Multivariable Temperature Uniformity Control System

Round 1

Reviewer 1 Report

The work is very well written. There are few errors, such as variable indexes, for example in T21, which is different from T11. Another problem is that you used "presented below", but the correct option would be to indicate the figure number, or the table number. In figure 15 it would be better to have reported the percentage error (%).

However, the problem with this paper is that it skims the surface of creating and using a DT. If I were looking for a work on DT and read this, I would be annoyed that I wasted my time. In fact, I was only interested in reviewing it because it was about DT.

I would recommend two works for authors to consult, but I noticed that you already cited both: references 21 and 22. They are very important to say what a DT is. And you described it in just 3 lines. In fact, what the authors did was create a model and adjusted and validated it with real data. The method could be something original, but the authors based themselves on the method developed in their own previous references (Viola and Chen). It's not something original. It's not DT. It is an example of application.

Author Response

The work is very well written. There are few errors, such as variable indexes, for example in T21, which is different from T11. Another problem is that you used "presented below", but the correct option would be to indicate the figure number, or the table number. In figure 15 it would be better to have reported the percentage error (%).

Thanks for your observations, the indices along the manuscript has been reviewed and the error percentages has been included on Figure 15 for clarity using the normalized root mean square error as performance index.

However, the problem with this paper is that it skims the surface of creating and using a DT. If I were looking for a work on DT and read this, I would be annoyed that I wasted my time. In fact, I was only interested in reviewing it because it was about DT. I would recommend two works for authors to consult, but I noticed that you already cited both: references 21 and 22. They are very important to say what a DT is. And you described it in just 3 lines. In fact, what the authors did was create a model and adjusted and validated it with real data. The method could be something original, but the authors based themselves on the method developed in their own previous references (Viola and Chen). It's not something original. It's not DT. It is an example of an application.

Thanks for sharing your concerns regarding our manuscript. We agree the main contribution of this paper is not on the Digital Twin design methodology but on its application to the modeling of multivariable temperature uniformity control systems and the use of sensitivity analysis to determine the most influential parameters affecting the behavioral matching process.

Regarding the digital twin concept and applications, the manuscripts from Michael Grieves and Fei Tao were fundamental part of the digital twin definition proposed in our book Viola, J., & Chen, Y. (2023). Digital-Twin-Enabled Smart Control Engineering: A Framework and Case Studies. Springer Nature.

In the mentioned references, the notion of digital twin is inspired by the replication of bigger physical assets. Some examples include electric vehicles fleets, social behavior, climate change or large manufacturing facilities, being this one the most relevant for several industries on the path of DT adoption for digital transformation. In that sense, from an industrial manufacturing point of view, Digital Twin can be analyzed on several levels, starting from subsystems and components, process replication, equipment modeling, shop floor simulation, manufacturing facility, and multi-factory simulation.

We agree most of the digital twin references and frameworks available on the literature are designed for its use at shopfloor level and above and the benefits of this approach are valuable from an enterprise point of view. These approaches require more intensive utilization of breaking technologies like data analytics, artificial intelligence, or cloud computing.

However, the same ideas used for complex systems can be translated into the subsystem, process and equipment modeling levels, which are the main target of this paper. According to Wright, L., Davidson, S.: How to tell the difference between a model and a digital twin. Advanced Modeling and Simulation in Engineering Sciences 7(1) (2020). https://doi.org/10.1186/s40323-020-00147-4, a digital twin can be differentiated from a pure simulation model in the sense that a physical asset must exist to be replicated into a virtual domain. Thus, we can say that the DT built for the uniformity temperature control system portraits the basics of Digital Twin.

Indeed, the obtained DT model will be the starting point for the implementation of enabling technologies like fault detection, prognosis, or self-optimizing control methods. Likewise, the DT will be leveraged as a reduced-order model for its execution in embedded configurations, bringing the mentioned capabilities closer to the asset without the need of additional hardware and communication infrastructure.

The following paragraph has been added to section 2.1 to cover the arguments presented above:

“It is important to notice that in \cite{Grieves2014} and \cite{Tao2019Nature}, the replication of big physical assets inspires the target of digital twin applications and their conceptualization. Some examples include electric vehicle fleets, social behaviour, climate change and large manufacturing facilities. This is one of the most relevant for several industries on the path of DT adoption for digital transformation.

Therefore, from an industrial manufacturing point of view, digital twins can be analyzed on several levels, starting from subsystems and components, process replication, equipment modelling, shop floor simulation, manufacturing facility, and multi-factory simulation. Notice that most of the digital twin references and frameworks available in the literature are designed for their application at the shop floor level and above, the benefits of which are valuable from an enterprise and operational point of view. Due to the system size and complexity, these approaches require more intensive utilization of breaking technologies like data analytics, artificial intelligence, or cloud computing.

However, similar ideas can be applied to the subsystem, process and equipment modelling levels, which are the main target of this paper. According to \cite{Wright2020}, a digital twin can be differentiated from a pure simulation model in the sense that a physical asset must exist to be replicated into a virtual domain. Thus, the DT built for the uniformity temperature control system portrays the fundamentals of Digital Twin.

Thus, the obtained DT model will be the starting point for the implementation of enabling technologies like fault detection, prognosis, or self-optimizing control methods. Likewise, the DT will be leveraged as a reduced-order model for its execution in embedded configurations, bringing the mentioned capabilities closer to the asset without additional hardware and communication infrastructure. A more detailed discussion regarding the digital twin concept and applications can be found in \cite{viola2023SCE,IAIViola}.”

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript explains the development of a digital twin framework for a multivariable uniformity temperature control system. The paper is well-written and suitable for the publication after addressing some of the minor comments mentioned below. 

1. Sentence incomplete - line 39 
2. Figure 1 - taken with permission or adapted from reference? 
3. Important to include full form of abbreviations in the manuscript.
4. Figure 6 description not included in the text. Text moves to Figure 7 description.
5. Figure 13 - Here, the T profile does not closely represent that captured experimentally? Especially with the left being less than the right side. How do the authors address this part? 
6. The novelty or uniqueness of the work can be emphasized more clearly along with the need for a digital twin framework and its applications. It would also be interesting to showcase the implementation for a specific case study with the developed digital framework.

Author Response

The manuscript explains the development of a digital twin framework for a multivariable uniformity temperature control system. The paper is well-written and suitable for the publication after addressing some of the minor comments mentioned below.

1.       Sentence incomplete - line 39

Sentence completed on the manuscript, thanks for the observation.

2.       Figure 1 - taken with permission or adapted from reference?

Thanks for your comment. The figure was adapted from the reference. Additional modifications were made to the figure to fit better with the case study proposed in this paper.

3.       Important to include full form of abbreviations in the manuscript.

Table A5 was added on Appendix A with a list of acronyms used along this paper.

4.       Figure 6 description not included in the text. Text moves to Figure 7 description.

Thanks for your observation. Figure 6 has been referred properly and the following paragraph has been added to describe the figure.

“The temperature response of each thermal zone $T_{11}$ to $T_{26}$ for 50\% and 75\% duty cycle inputs applied to the Peltier cells is shown in Fig.~\ref{PhysicalTwinData}. It can be observed that there is a difference on the maximum and minimum temperatures as shown in the thermal image.”

5.       Figure 13 - Here, the T profile does not closely represent that captured experimentally? Especially with the left being less than the right side. How do the authors address this part?

Thank you so much for your observation. The thermal profile reflected in Figure 13 shows the behavior of the thermal plate for one of the first behavioral matching attempts done for the system. In the revised manuscript, the plot has been updated to reflect the correct behavior of the heat distribution of the DT.

We realized that the root cause for the heat difference between the right and left side is due to a weak coupling of the left Peltier module with the copper plate, producing a higher thermal conductive and convection resistance that affects the overall heat distribution. Although this effect is quantified on the behavioral matching reported on the manuscript, Figure 13 was not updated on the initial submission. Now it is corrected, apologies for the confusion.

6.       The novelty or uniqueness of the work can be emphasized more clearly along with the need for a digital twin framework and its applications. It would also be interesting to showcase the implementation for a specific case study with the developed digital framework.

Thanks for your comment, the main contribution of this paper is not on the Digital Twin design methodology but its application to the modeling of multivariable thermoelectric heating systems for temperature uniformity control system and the sensitivity analysis to determine the most influential parameters on the system behavioral matching process. In that sense, the paper itself is a case study for the design and implementation of a digital twin for thermal systems based on the development framework.

Author Response File: Author Response.pdf

Reviewer 3 Report

The article utilizes digital twin technology to simulate and control temperature distribution, detailing the process of model behavioral matching using an infrared thermal imager, as well as how to perform sensitivity analysis through Monte Carlo simulation. These details are valuable for understanding the construction and validation of the digital twin model. Here are some suggestions for the article:

1. The content of the article is substantial, showing that the authors have done a lot of work in this area. However, in the five-step process of constructing the digital twin, most methods are directly adopted from existing ones, lacking innovation. It is hoped that the authors can further refine and highlight innovative points.
2. The article summarizes the advantages of constructing a digital twin as: “In that sense, a digital twin can be built based on some of the temperature modeling methods presented for temperature uniformity control applications with lower computational capability and reasonable accuracy.” However, the primary objective of utilizing digital twin technology is to achieve a deep replication of physical entities. The computational load associated with this process depends on the specific model employed and does not necessarily require lower computational capability. Therefore, the article needs to further elaborate on why digital twin technology is used for temperature uniformity modeling and, compared to high-precision temperature uniformity models, what its outstanding advantages are.
3. The article mentions that digital twins can reduce computational load requirements, but does not analyze in detail the difference in computational load required between the digital twin model and other existing models.
4. The article points out that the digital twin model can accurately match specific datasets, but does not specify the model’s adaptability under different operating conditions or system changes.

Author Response

The article utilizes digital twin technology to simulate and control temperature distribution, detailing the process of model behavioral matching using an infrared thermal imager, as well as how to perform sensitivity analysis through Monte Carlo simulation. These details are valuable for understanding the construction and validation of the digital twin model. Here are some suggestions for the article:

1.   The content of the article is substantial, showing that the authors have done a lot of work in this area. However, in the five-step process of constructing the digital twin, most methods are directly adopted from existing ones, lacking innovation. It is hoped that the authors can further refine and highlight innovative points.

Thanks for your comment, the main contribution of this paper is not on the Digital Twin design methodology but its application to the modeling of multivariable thermoelectric heating systems and the sensitivity analysis to determine the most influential parameters on the system behavioral matching process. In that sense, the paper itself is a case study for the design and implementation of a digital twin for thermal systems based on the proposed five steps development framework. This is highlighted on the introduction section as follows:

• Developing a digital twin for multivariable temperature uniformity control systems based on Peltier thermoelectric heating elements using a discrete lumped elements approach and multiphysics behavior based on the DT development framework which can be used for developing reduced-order models of the physical assets for its real-time execution on embedded devices. 
• Use the Digital Twin development framework to perform a series of behavioral matching algorithms to find the real values of the digital twin system parameters using optimization tools.
• Performing a sensitivity analysis to determine the most influential parameters on the digital twin model based on its real behavior.

2.       The article summarizes the advantages of constructing a digital twin as: “In that sense, a digital twin can be built based on some of the temperature modeling methods presented for temperature uniformity control applications with lower computational capability and reasonable accuracy.” However, the primary objective of utilizing digital twin technology is to achieve a deep replication of physical entities. The computational load associated with this process depends on the specific model employed and does not necessarily require lower computational capability. Therefore, the article needs to further elaborate on why digital twin technology is used for temperature uniformity modeling and, compared to high-precision temperature uniformity models, what its outstanding advantages are.

This is a valid appreciation, thanks for your comment. The following section was added on the introduction to elaborate more on the advantages of a reduced-order digital twin model:

 "Notice that the computational load of a digital twin virtual depends on the computational approach employed to represent the system (lumped elements, finite element analysis, partial differential equations, deep learning).  As we emphasize in \cite{viola2023SCE}, a Digital Twin can be used as an enabling technology to provide awareness capabilities to a physical asset to develop smart control systems able to self-optimize with minimal user intervention to achieve a set of desired performance objectives based on analytics derived from the use of digital twin like health prognosis, fault detection or model-predictive control.  However, the perspective about using digital twin shown in \cite{viola2023SCE} is focused on its implementation under an edge/embedded/hardware approach instead of a cloud solution. It means bringing the digital twin closer to the source of information to provide awareness capabilities to the system, leveraging the existing computational capabilities of processing systems installed on the physical assets without relying on additional cloud/enterprise solutions that could make the system sensitive to intellectual property violations or external attacks.  In that sense, a digital twin should look to develop a physical asset representation that can be used as a reduced-order models (ROM) executable on embedded processors or register transfer level (FPGA) to enabling the development of smart controllers, bringing the process knowledge to the edge/embedded domain"

3.   The article mentions that digital twins can reduce computational load requirements, but does not analyze in detail the difference in computational load required between the digital twin model and other existing models.

Thanks for your comment. Comparing the digital twin approach proposed in this paper for temperature uniformity control applications against more complex computational models is part of our next research directions. Although, evidence can be found on the literature regarding how digital twins designed with the proposed framework are able to execute on real-time (in the millisecond/microsecond execution rate) based on FPGA hardware-based implementations:

1.   J. Nwoke, M. Milanesi, J. Viola and Y. Q. Chen, "FPGA-Based Digital Twin Implementation for Mechatronic System Monitoring," 2023 5th International Conference on Industrial Artificial Intelligence (IAI), Shenyang, China, 2023, pp. 1-6, doi: 10.1109/IAI59504.2023.10327502.
2.   J. Nwoke, M. Milanesi, J. Viola and Y. Chen, "FPGA-Based Digital Twin Implementation for Power Converter System Monitoring," 2023 IEEE 3rd International Conference on Digital Twins and Parallel Intelligence (DTPI), Orlando, FL, USA, 2023, pp. 1-6, doi: 10.1109/DTPI59677.2023.10365466.
3.   M. Ruba, R. O. Nemes, S. M. Ciornei, C. Martis, A. Bouscayrol and H. Hedesiu, "Digital Twin Real-Time FPGA Implementation for Light Electric Vehicle Propulsion System Using EMR Organization," 2019 IEEE Vehicle Power and Propulsion Conference (VPPC), Hanoi, Vietnam, 2019, pp. 1-6, doi: 10.1109/VPPC46532.2019.8952428.

Likewise, other digital twin models rely on high speed RT execution hardware like RT-OPAL, System on a Chip, or dSpace platforms, which were developed using different methodologies are also executable on real-time hardware in the loop platforms:

1.   Bouzid, S.; Viarouge, P.; Cros, J. Real-Time Digital Twin of a Wound Rotor Induction Machine Based on Finite Element Method. Energies 2020, 13, 5413. https://doi.org/10.3390/en13205413
2.   S. Zhang, T. Liang and V. Dinavahi, "Hybrid ML-EMT-Based Digital Twin for Device-Level HIL Real-Time Emulation of Ship-Board Microgrid on FPGA," in IEEE Journal of Emerging and Selected Topics in Industrial Electronics, vol. 4, no. 4, pp. 1265-1277, Oct. 2023, doi: 10.1109/JESTIE.2023.3282776.
3.   C. Dufour, Z. Soghomonian and W. Li, "Hardware-in-the-Loop Testing of Modern On-Board Power Systems Using Digital Twins," 2018 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Amalfi, Italy, 2018, pp. 118-123, doi: 10.1109/SPEEDAM.2018.8445302

The following paragraph on section 3.5 has been added to address this concern:

“On the other hand, the concept of smart control engineering shown in [19] uses Digital Twin as an enabling technology to create smart systems. It means using a DT next to the source of information running on embedded hardware, requiring a reduced-order model digital twin compatible with the available hardware. So, the digital twin model developed in this paper serves as a starting point for deriving reduced-order models compatible with embedded hardware whose execution speed is parallel and real-time with the physical asset emulated. Although the execution speed of the digital twin built in this paper needs to be assessed in depth, there are applications where Digital Twins developed with the proposed framework can be deployed for its real-time execution. For example [46, 47] shows a FPGA real-time DT implementation of a mechatronic system executed on the millisecond time scale and a power electronics converter with dynamical response on the microseconds range respectively. Other applications like [48, 49]includes DT for micro-grids and power boards with more powerful real-time hardware-in-the loop platforms like Opal RT or Texas instruments System on a Chip.”

4.   The article points out that the digital twin model can accurately match specific datasets, but does not specify the model’s adaptability under different operating conditions or system changes.

Thanks for your observation. This is one of the most important features to be considered on a Digital Twin towards its use on industrial systems. As we discussed on some of our previous works listed below, a Digital Twin can be combined with a self-optimizing control, which adds a supervisory awareness layer on the system physical condition, allowing the Digital Twin to adapt to the system changes by performing an online optimization to keep updated the DT parameters. This method has been tested to update closed loop controller parameters and make the system aware of changes on its dynamics like larger delays or variable time constants. Our next research directions include the implementation of DT and self-optimizing control for multivariable systems as the case study presented on this manuscript.

•  Viola, J., & Chen, Y. (2023). Digital-Twin-Enabled Smart Control Engineering: A Framework and Case Studies. Springer Nature.
• Villamizar, V., & Bernardo, J. (2022). Self-Optimizing Smart Control Engineering Enabled by Digital Twins (Doctoral dissertation, UC Merced).
• Viola, J., & Chen, Y. (2021, November). A self optimizing control framework and a benchmark for smart process control. In 2021 3rd International Conference on Industrial Artificial Intelligence (IAI) (pp. 1-6). IEEE.
• Viola, J., Chen, Y., & Wang, J. (2020, October). Information-based model discrimination for digital twin behavioral matching. In 2020 2nd International Conference on Industrial Artificial Intelligence (IAI) (pp. 1-6). IEEE.
• Viola, J., & Chen, Y. (2020, October). Digital twin enabled smart control engineering as an industrial ai: A new framework and case study. In 2020 2nd International Conference on Industrial Artificial Intelligence (IAI) (pp. 1-6). IEEE.

The following paragraph on section 3.5 has been added to address this concern:

Initially, how often the execution rate of the behavioral matching needs to be executed to determine the most updated parameters of the model? It requires an awareness and monitoring mechanism that detects any significant change in the system response. In that sense, using a self-optimizing control layer enables system awareness by performing online optimization of the system parameters along with the system execution and parallel instances of the system digital twin to accelerate its convergence and ensure that unsafe or unstable conditions are tested on the virtual environment before a final update of the DT model. In [44 , 45] some applications of self-optimizing control are employed for control systems parametric updating, which could be used also for the digital twin behavioral matching.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report