Advanced Materials & Sustainable Manufacturing 2024 , 1, 10003 5 of 14 strategy to ensure that some good population individuals will not be discarded in the evolutionary process, and improves the accuracy of the optimization results; it adopts the crowding degree and crowding degree comparison operators as the criteria for comparison among individuals in the quasi-Pareto domain to ensure that the diversity of individuals in the quasi-Pareto domain can be evenly extended to the whole Pareto domain. Adopting crowding degree and crowding degree comparison operator as the comparison criteria among individuals in the population, so that the individuals in the quasi-Pareto domain can be evenly extended to the whole Pareto domain and ensure the diversity of the population. 2.2.3. Parametric Prediction Model Based on Digital Twins When it is difficult to construct a mechanistic model to find the relationship between these parameters, a predictive model based on machine learning is established. Taking the ventilation system of the drying department as an example, the exhaust air temperature and humidity is an important index that reflects the operational status of the drying department and the rationality of the process, and the mechanism of the process is difficult to construct, so the prediction models for its exhaust air temperature and humidity are established. In this paper, it is chosen the more classical linear regression (LR), gradient boost regression (GBR) and random forest (RF) methods [44]. The proposal of these algorithms involves the considerations of that GBR and RF are typical ensemble learning algorithms of bagging and boosting, respectively. And they good at generalization with learning from small data sets. On the other hand, LR is relatively easy to conducted with good robustness, which could be seen as a baseline in this study. LR is a type of regression analysis that models the relationship between one or more independent and dependent variables using a least square function called a linear regression equation [44]. Linear regression models are very easy to understand and the results are very interpretable, which facilitates decision analysis, but for nonlinear data or polynomial regression with correlation between data features is difficult to model and difficult to represent highly complex data well. GBR use a continuous approach to constructing trees, with each tree trying to fix the errors of the previous tree [45]. By default, gradient boosted regression trees are not randomized, but use strong prepruning, and gradient boosting usually uses trees with very small depths. Such models have a small memory footprint and faster prediction speed [46]. The main idea of gradient boosting is to merge multiple simple models, where each tree makes good predictions for only part of the data, and the more trees added, the more iterations can be made to improve performance. RF is an algorithm that integrates multiple trees through the idea of integrated learning, based on which the samples are trained and predicted [47,48]. When used as a regression algorithm, the output value of the sample prediction is weighted by the regression value of the decision trees that make up the random forest as the output. It can handle both discrete and continuous data, and operates with high efficiency and accuracy. 2.3. Visualization Model Based on Digital Twin Most of the traditional simulation models of the papermaking process have only focused on a single section, without considering the whole process, or have only calculated a relatively small number of parameters; The visualization model of the papermaking process is only based on a mechanistic model, but does not consider processes that cannot be modelled mechanistically, and does not incorporate advanced information technology. The built simulation process can only be calculated in a specific order. In view of the above problems, this paper uses the chemical simulation software CADSIM Plus to build the simulation process. CADSIM Plus is a chemical process simulation software that has built-in physical property system database and operation unit module library of papermaking. It consists of a lot of physical property methods and physical property parameters. It can be flexibly used all the arrangement and combination of these methods to develop process simulation. At the same time, based on the previous work, it can be applied the mechanism model combined with process data to build modules of various parts in the software and store them in the model library. In the future, when building different processes, it can be continued to reuse this module, which improves the simplicity of modeling and reduces the time required for modeling. 3. Results and Discussion 3.1. Solver Model This paper takes the surface condenser of the drying process as the object of study. Firstly, the mechanistic process is analyzed: the secondary steam entering the surface condenser is discharged as condensate through heat exchange, and the incoming cold water is heated and discharged as hot water. Figure 3 is a schematic diagram of the surface condenser module, and Table 3 shows the input and output parameters of the surface condenser module.
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