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State Key Laboratory of Pulp and Paper Engineering, South China University of Technology, Guangzhou 510640, China

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Received: 13 December 2023 Accepted: 23 January 2024 Published: 27 February 2024

© 2024 The authors. This is an open access article under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).

ABSTRACT:
The structure of the drying section in papermaking process is complex and too compacted to install sensors. In order to monitor the parameters in dynamic and manage the process practically with virtual simulations instead of physical experiments, a digital twin-based process parameter visualization model is constructed in this study. Regarding to the possible missing data in the modeling framework, it is proposed to combine industrial data, and knowledge of mechanism with intelligent algorithms to fill in the missing parameters. Upon which, a digital twin-based data visualization model is established using CADSIM Plus simulation software. Both of the knowledge -based mechanism solution model and the random forest-based parametric prediction model perform well, and the predicted parameters can support the digital twin visualization model in CADSIM Plus. Visual modeling of surface condenser in the paper drying section was realized for example, and results show that the model is capable of monitoring the dynamic changes of parameters in real time, so as to support the optimization and decision making of papermaking process such as formation, drying, et al.

Keywords:
Digital twin; Model; Papermaking; Parameter prediction; Simulation

The papermaking process involves a large number of complex physical and chemical reactions [1], accompanied with characteristics of multi-variable, strong coupling and non-linear etc., hindering the intelligent development process of the papermaking industry [2]. At present, the process models and control systems, established by paper-making enterprises based on a new generation of information technology, have not yet solved the problem of “data silos” and cannot integrate material flow and energy flow information to achieve real-time monitoring and control of paper production, which affects the sustainability of the process dramatically.
With the development of Industry 4.0 era [3,4], digital twin is gradually being studied and applied in the process industry [5]. In the steel industry, with the applications of technologies such as intelligent data sensing, multi-source heterogeneous data integration, efficient data transmission, digital twin creation, enhanced interaction, and conversion applications, a production line that combines reality with virtuality can be established to realize the optimization of the production process [6]. In the machine building industry, simulation and optimization based on the digital twin’s dynamic perception of the physical machine tool, it can be effectively optimized machining conditions such as cutting parameters and reduce carbon emissions [7]. It is worth noting that, the establishment of a digital twin model of the process industry, can facilitate the simulation, analysis, monitoring and optimization of manufacturing processes in real time, turns out the dynamic management without physical efforts [8,9,10,11].
The papermaking industry is a typical process-oriented industry [12,13], and the information technologies such as big data and machine learning have been widely used in its energy-saving renovation [14,15], modeling [16], scheduling [17,18], fault prediction [19], decision-making support [20], and process optimization [21,22,23] sectors. However, most of the previous studies only focus on a single process or a single equipment of it, without considering the modeling and control of the whole process systematically, which tends to achieve local optimizations. Therefore, there is an urgent need to develop the digital twin model for papermaking process that can perform online sensing, analysis, simulation, optimization, and decision-making of the process. The emerging of digital twin in the industrial domain provides feasible solution ideas [24,25,26]. As aforementioned, although a large number of scholars have conducted modeling studies on digital twins and achieved some results in related fields [27,28,29], it remains empty of a robotic general digital twin frameworks for the chemical industry, especially for the papermaking industry. Therefore, this paper proposes a digital twin-based data visualization model based on CADSIM Plus simulation software for the papermaking industry to promote the process performance.

The constraints are the upper and lower limits of the range of each parameter in the actual case. To obtain better results, the limits of the error function are added to the constraints, as in Equation (9):

Table 4 shows a comparison table of the errors in solving the parameters under different methods with the number of known parameters of 5, 4, 3, 2 and 1. The errors of the values in the table are in the form of percentages. From the table it can be seen that the solution result of nonlinear programming is better than that of NSGA-II. Nonlinear programming needs to be assigned reasonable initial values before running the model, so it is already closer to reasonable values in the first run. But it is difficult to provide feasible initial solutions to determine upper and lower limits of parameters or when there are more parameters. So nonlinear programming is assumed already closer to the reasonable values in the first run.
When the upper and lower limits of parameters are not easy to determine or when there are more parameters to assign, it will not be possible to determine a suitable initial value. NSGA-II, on the other hand, uses random assignment of values in the first run, which can be applied to all cases. Normally, the more parameters are known, the more accurate the solution will be, whereas if there are only two or one known parameter values, the solution will no longer be credible. In this paper only five of these cases are listed, the rest are similar.
It can be concluded that the method can, to some extent, solve the problem of missing parameter values in the process of model calculation. Moreover, it is a relatively general method that can be used to solve the missing parameters in any process where the mechanistic equations can be established. When the range of parameters is known, the nonlinear programming solution is used; when the range of parameters is unknown and initial values are difficult to assign, NSAG-II is used to solve.

where

At present, the papermaking industry lacks efficient means of whole life-cycle control. Therefore, this paper proposed a digital twin modelling framework for the paper manufacturing process, and developed two data completion methods for addressing the possible missing data in the modeling framework, including parameter solving based on mass and heat transfer mechanisms, and parameter prediction based on random forest.
The following conclusions are obtained: the mechanism-based parameter solution can be used as a general method to solve a variety of parameter missing problems and usually obtains better results; the random forest-based parameter prediction model is robust and has high accuracy, with the average value of R^{2} above 0.9. Base on which, this paper implemented a visual modelling of the surface condenser in the dry section of papermaking process based on CADSIM Plus and the digital twin framework. The model runs well and is able to monitor the dynamic change of parameters in real time.
The digital twin-based visualization model proposed in this paper can reduce the coupling complexity of the physical entity modules, and has good scalability and generality, and can be subsequently extended to the whole process of paper production.
However, there are certain limitations of the model should be further considered in the future study. Current studies mostly focused on the drying section, pay scarce attention to other sections, which is hard to integrate the processes as a whole. Meanwhile, certain simplified assumption is too ideal to be applied in the industry, which should be studied deeper in the future. In addition, artificial intelligence and big data analysis technology can be furthermore to be explored by online analysis on the basis of interaction with the production site thorough data. And applying the established models to implement management of production process for optimization and decision making, and so on. The integration of these techniques could significantly improve the production efficiency and reduce production costs, and ultimately achieve sustainable development of the process.

Made substantial contributions to conception and design of the study and performed data analysis and interpretation: Z.L.; Performed data acquisition, as well as provided administrative, technical, and material support: J.L. and M.H.

Not applicable.

Not applicable.

This research received no external funding.

All authors declared that there are no conflicts of interest.

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