Knowledge-data Collaborated Digital Twin Model of Papermaking Process

2.1. A Digital Twin Framework for the Papermaking Process The papermaking process has the following characteristics: diverse raw materials with different nature and complex interrelationships in the process, and there are a large number of parameters that are difficult to be detected along the process; various complicated physical and chemical reactions occur in its process [30]. The core of designing a digital twin of a papermaking process is to perform mechanistic or data-driven modeling of the process to rationally describe the production process [31,32,33]. Industrial data are first collected, pre-processed, and stored in a database. Then data-driven methods are used to infer parameters that cannot be directly measured, find relationships in the production process, and simulate the process to enable assessment of the current state, diagnosis of past problems, prediction of future trends, provide more reasonable and reliable process parameters and optimize the process g process [34,35]. Figure 1 illustrates the digital twin framework for the papermaking process, and the individual modules are described correspondingly.The physical layer mainly includes materials, equipment, production lines, environment and personnel, etc. It mainly provides data on all production factors and production elements such as materials, equipment and processes in the papermaking process. Materials such as fibers, fillers, retention aids, dry strength agents, etc., equipment such as pulper, headbox, white part, core winder and cutter etc., production lines are also divided into different production lines such as newsprint, household paper, boxboard, etc., as well as the temperature and humidity of the environment, personnel operation, etc. The sensing layer is mainly responsible for data collection and transmission. The original data in the process is collected by the sensors on site to the distributed control system, and then uploaded to the enterprise’s cloud service platform through the net gate, and the data can be downloaded directly through the cloud service platform when used. The data collection also includes the data of offline inspection such as the quality index of raw paper, etc. The data layer is responsible for receiving the original data. Due to the different frequency of data collection, spatial location of sensors, etc., as well as the fact that some of the data are obtained by offline laboratory tests, and there are many uncertainties in the process, such as process abnormalities, equipment failures, or irregularities in operation, there are time differences and delays in the collected data. Therefore, after operations such as data 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.2.2.1. Data Processing The raw data required for this paper is collected from the mill’s distributed control system, which collects process data such as Vehicle speed, steam pressure, temperature, and humidity for four quantifications, as shown in Table 1. The data collected had null values, missing values or data redundancy, and some of the data were collected at different frequencies, making modeling more complex [39]. To address the above characteristics, the originally collected data were matched in time series, with most of the data being sampled in 60 s, 10 min and 20 min sets, and the collected data were matched in 5 min sets to take the average value within the sampling interval. Missing values are filled by averaging and interpolation. Outliers are removed using box plots. Paper production can be divided into working conditions based on basic weight, as shown in Table 2. In this paper, four basic weights are considered as four working conditions are modeled separately to compare the predictive effect of the model under different working conditions.2.2.2. Parametric Solver Model Based on Digital Twin For processes where the mechanistic equations have been constructed, the solve function of the math module in Python is used to calculate the unknown solution. If only a partial solution can be found, the found parameters can be used together with the known parameters as known parameters, and the other parameters can be assigned values until the error in each mechanistic equation is minimized, and when the solution is stable, the value at this point can be considered to be the value of the sought parameter. Since there are multiple equations in which the computational error needs to be minimized simultaneously, this problem can be transformed into a multi-objective, multi-constraint optimization problem. Classical nonlinear programming (Sequential Least Squares Programming, SLSQP) and NSGA-II are used in this paper [16]. SLSQP [23] is one of the nonlinear planning algorithms for constrained problems, which can solve iterative methods for nonlinear optimization problems with constraints, such as boundary constraints, equation constraints, and inequality constraints [40]. Its method has the following characteristics: it can handle any degree of nonlinearity, including nonlinearity in constraints, and it must choose appropriate parameters such as initial solution, shift acceptance criterion, and step control strategy to ensure convergence and efficiency. NSGA-II is an improvement on the first generation of non-dominated sorting genetic algorithm: it proposes a fast non-dominated sorting algorithm [41,42,43], which reduces the computational complexity on the one hand, and merges the parent population with the offspring population on the other hand, retaining all the best individuals; it introduces an elite 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.