# Machining Phenomenon Twin Construction for Industry 4.0: A Case of Surface Roughness

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Phenomenon Twin Construction System

## 4. PTCS for Surface Roughness

_{ij}∈ $\mathcal{R}$ | o = 1,…,O, i = 0,1,…,N, j = 1,…,J}. These time series datasets (collected from the work described in [51]) are shown in Figure A1 in Appendix A. However, as seen in Figure 3, SD becomes the main concern of IC of the PTCS. PC recognizes the outcomes of IC and, thereby, digitizes the surface heights using its three subcomponents: MC, SC, and VC. In this respect, MC uses two modelling approaches, namely Markov chain and semantic modeling, to encapsulate the dynamics underlying SD (time series of surface heights). SC uses a discrete event Monte Carlo simulation approach to recreate the surface heights. VC uses three approaches, namely arithmetic mean height roughness (Ra), possibility distribution, and DNA-based computing, for the sake of validation. The goal is to find the efficacy of these approaches in constructing the phenomenon twin.

_{ij}

_{= 1}, as seen in Figure 4; this time series is the real or expected one. The return map is also shown to understand the variability associated with the time series.

## 5. Modeling, Simulation, and Validation Components—Option 1

_{ij}

_{=1}(can also be seen from Figure 4) in terms of a Markov chain, as seen in Figure 6. SC simulates the surface heights by using a Monte Carlo simulation of discrete states associated with the Markov chain. In this respect, Figure 7 shows the simulated time series of surface heights denoted as zs

_{ij}

_{=1}and its return map. As seen in Figure 4 and Figure 7, zs

_{ij}

_{= 1}is more stochastic compared to z

_{ij}

_{=1}. In particular, the returns from one point to another are non-identical. This means that zs

_{ij}

_{=1}is not similar to z

_{ij}

_{=1}. This also means that the Markov chain-based modeling approach is not effective for modeling surface roughness.

_{ij}

_{=1}(expected roughness) and zs

_{ij}

_{=1}(simulated roughness) are 1.979261025 and 2.014569035, respectively. This means that the values of Ra of two dissimilar roughness profiles (expected and simulated) resemble each other, which should not be the case. On the other hand, the possibility distributions of the expected and simulated surface roughness are not the same, as seen in Figure 8a. This means that the possibility distribution-driven validation approach is comparatively effective. A similar result is obtained for the other validation approach, that is DNA-based computing. The frequencies of the amino acids (generated by applying DNA-based computing) of the expected and simulated roughness profiles exhibit dissimilar patterns, as seen in Figure 8b.

## 6. Modeling, Simulation, and Validation Components—Option 2

_{ij}

_{=1}(can also be seen from Figure 4), as seen in Figure 10. The stochastic features contain four trends associated with noise and sudden burst. MC models these features using certain mathematical formulations. SC simulates the surface heights by using a Monte Carlo simulation associated with the models. In this respect, Figure 11 shows the simulated time series of surface heights denoted as zsf

_{ij}

_{=1}and its return map. As seen in Figure 4 and Figure 11, zsf

_{ij}

_{=1}resembles z

_{ij}

_{=1}. In particular, the returns from one point to another are identical. This means that zsf

_{ij}

_{=1}is similar to z

_{ij}

_{=1}. This also means that the semantic modeling approach is effective for modeling surface roughness.

_{ij}

_{=1}(expected roughness) and zsf

_{ij}

_{=1}(simulated roughness) are 1.979261025 and 2.053738039, respectively. This means that the values of Ra of two similar roughness profiles (expected and simulated) resemble each other. Similar results are obtained for the other validation approaches (possibility distribution and DNA-based computing). The possibility distributions of the expected and simulated surface roughness are the same, as seen in Figure 12a. In the case of DNA-based computing, the frequencies of the amino acids (generated by applying DNA-based computing) of the expected and simulated roughness profiles exhibit similar patterns, as seen in Figure 12b. This means the possibility distribution and DNA-based computing-driven validation approaches are effective. However, the above-mentioned approaches (semantic modeling, possibility distribution, and DNA-based computing) have also been applied to the rest of the real time series datasets of surface heights (see Figure A1b–d in Appendix A), for understanding their (the approaches) efficacy to a vast extent. In this respect, Figure A2, Figure A3 and Figure A4 (in Appendices B–D) show the results corresponding to Figure A1b–d, respectively.

## 7. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Measured Time Series Datasets Used in this Study

## Appendix B. Results Corresponding to Figure A1b

**Figure A2.**Outcomes of SC and VC corresponding to the semantic modeling-based MC for z

_{ij}

_{=2}: (

**a**) real surface heights; (

**b**) return map of (

**a**); (

**c**) simulated surface heights; (

**d**) return map of (

**c**); (

**e**) possibility distribution; (

**f**) DNA-based computing.

## Appendix C. Results Corresponding to Figure A1c

**Figure A3.**Outcomes of SC and VC corresponding to the semantic modeling-based MC for z

_{ij}

_{=3}: (

**a**) real surface heights; (

**b**) return map of (

**a**); (

**c**) simulated surface heights; (

**d**) return map of (

**c**); (

**e**) possibility distribution; (

**f**) DNA-based computing.

## Appendix D. Results corresponding to Figure A1d

**Figure A4.**Outcomes of SC and VC corresponding to the semantic modeling-based MC for z

_{ij}

_{=4}: (

**a**) real surface heights; (

**b**) return map of (

**a**); (

**c**) simulated surface heights; (

**d**) return map of (

**c**); (

**e**) possibility distribution; (

**f**) DNA-based computing.

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**Figure 5.**Outlining phenomenon twin construction of surface roughness using the Markov chain-based modeling approach [17].

**Figure 7.**Outcomes of discrete event Monte Carlo simulation-based SC associated with Markov chain-based MC: (

**a**) simulated surface heights; (

**b**) return map of (

**a**).

**Figure 8.**Outcomes of VC corresponding to Markov chain-based MC and discrete event Monte Carlo simulation-based SC: (

**a**) possibility distribution; (

**b**) DNA-based computing.

**Figure 9.**Outlining phenomenon twin construction of surface roughness using the semantic modeling approach [16].

**Figure 11.**Outcomes of the Monte Carlo simulation-based SC associated with the semantic modeling-based MC: (

**a**) simulated surface heights; (

**b**) return map of (

**a**).

**Figure 12.**Outcomes of VC corresponding to the semantic modeling-based MC and Monte Carlo simulation-based SC: (

**a**) possibility distribution; (

**b**) DNA-based computing.

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## Share and Cite

**MDPI and ACS Style**

Ghosh, A.K.; Ullah, A.S.; Kubo, A.; Akamatsu, T.; D’Addona, D.M.
Machining Phenomenon Twin Construction for Industry 4.0: A Case of Surface Roughness. *J. Manuf. Mater. Process.* **2020**, *4*, 11.
https://doi.org/10.3390/jmmp4010011

**AMA Style**

Ghosh AK, Ullah AS, Kubo A, Akamatsu T, D’Addona DM.
Machining Phenomenon Twin Construction for Industry 4.0: A Case of Surface Roughness. *Journal of Manufacturing and Materials Processing*. 2020; 4(1):11.
https://doi.org/10.3390/jmmp4010011

**Chicago/Turabian Style**

Ghosh, Angkush Kumar, AMM Sharif Ullah, Akihiko Kubo, Takeshi Akamatsu, and Doriana Marilena D’Addona.
2020. "Machining Phenomenon Twin Construction for Industry 4.0: A Case of Surface Roughness" *Journal of Manufacturing and Materials Processing* 4, no. 1: 11.
https://doi.org/10.3390/jmmp4010011