Advanced Materials & Sustainable Manufacturing 2024 , 1, 10003 3 of 14 matching, data filling, and outlier deletion, various information needs to be stored in the database, which can later be used as input for the construction of the digital twin model in virtual space. The model layer is the digital modeling of physical entities. The model layer includes a solver model for the process parameters, a prediction model, and a simulation model of the physical entity [36]. Based on the principle of mass and heat transfer, a parameter prediction model is built by analyzing the data generated in the process and simulating and calculating the production process to visualize the process parameters and process monitoring. The application layer includes functions such as process optimization, parameter optimization, operation guidance, testing and diagnosis, and inventory calculation [37,38]. Finally, it is fed back to the physical entity to realize the control management and closed-loop optimization of the whole process. Based on the massive data, it can be provided more reasonable and reliable process parameters and optimize the process through prediction and optimization models to achieve the evaluation of the current state, or the prediction of future trends. 2.2. Research on Digital Twin-based Modeling Techniques The above research provides a method for constructing a digital twin framework for the papermaking process, but due to the complexity and variety of variables in the papermaking process, cost, and technical constraints that prevent access to certain key information on process variables, there is still a need to find suitable methods to address the problem that certain variables in the process are difficult to measure or cannot be measured directly by sensors. Therefore, it is proposed a method for parameter solution and parameter prediction in which, when the process mechanism can be constructed, constraints are set on the unknown parameters, and the missing parameters are solved by combining the mechanism equation with a multi-objective optimization algorithm; in the case where the process mechanism is difficult to construct, the parameters are predicted by using a data-driven model by screening the characteristic variables through correlation analysis. Figure 2 shows the technical route of the method. It starts from the preprocessing treatment of the raw data with data matching, outlier deletion, and data filling. The derived data could be used for parameter prediction and solution obtaining. When there are not mechanistic equations about the process, LR, GBR, and RF models would be used to present the unclear interrelationships of variables, and turning the output with data. Whereas, when there are equations, the outputs would be calculated in different scenarios based on the availabilities of parameters. Specifically, NLP and NSGA-II were used to find the optimal parameter setting when it is not fully available.
Figure 2. Technical route of the constructed digital twin papermaking model.
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