Prediction and Online Control for Process Parameters of Vanadium Nitrogen Alloys Production Based on Digital Twin

Abstract

The production of vanadium nitrogen alloys (VNs) is a chemical reaction process carried out in a closed pusher plate kiln, making real-time monitoring of key parameters challenging. Traditional methods for controlling process parameters are insufficient to meet the demands of production control. And the current production line heavily depends on workers’ experience and operates with a relatively low level of automation. In order to solve the above problems, this paper proposes a method for monitoring, predicting, and online controlling the production process parameters of VNs based on digital twins. Firstly, the process parameter affecting quality in the production process is experimentally selected as the target for prediction and control. Then, the ISSA-GRNN (Improved Sparrow Search Algorithm-Generalized Regression Neural Networks) fusion prediction model is constructed to predict the optimal values and intervals for the process parameter of movement interval. Finally, a digital twin system is developed to integrate the fusion prediction model to achieve real-time monitoring and online control of the production line. And the superiority of the algorithm and the feasibility of online control are verified through experiments. This paper achieves accurate prediction and online control of parameters in the VNs production process and has reduced reliance on workers’ production experience. Additionally, it has effectively lowered energy consumption and failure rates, facilitated the transition from traditional kiln production to intelligent production, and thereby supported sustainable development.

1. Introduction

Vanadium nitrogen alloys (VNs) are important additives in industrial production, valued for their high electrical conductivity, hardness, and melting point. The industrialized production level of VNs represents the direction for the development of the global vanadium industry, making product quality a top priority in vanadium and nitrogen production. Quality control, achieved by adjusting the process parameters of key production equipment, is central to the entire lifecycle of VN production. As VNs need to be prepared in a confined space, the kiln chamber is sealed so that operators cannot judge what is happening inside the kiln. As a result, traditional visibility-based methods of quality prediction methods do not perform effectively for process parameters. For this problem, mainstream scholars mainly regulate the process parameters of equipment by using intelligent modeling and optimization methods. Garg et al. [1] analyzed the heat transfer process of a natural circulation boiler through numerical simulation and used the resulting data to train a neural network model to establish a natural circulation boiler performance prediction model, which is capable of predicting key boiler parameters with high accuracy. Chaibakhsh et al. [2,3] took the boiler machine as the research object, used a numerical simulation method to analyze its thermal characteristics, established the boiler and mathematical model, and used a genetic algorithm to optimize the model, and experimentally proved that this method better improves the model accuracy. Yadav et al. [4] achieved the optimization of heat source control parameters for heat treatment furnaces through an inverse technology approach combining a neural network and a simulated annealing algorithm. Rosso et al. [5] proposed a structural health monitoring approach that integrates artificial neural networks with subspace-based damage indicators. Zhang et al. [6] constructed a robust model for temperature prediction of a shuttle kiln furnace by using the method based on an integrated random vector function linkage network. Zheng et al. [7] modeled the cement calcination process by a modified Just-In-Time Gaussian mixture regression method, which effectively reduced NOX emissions. He et al. [8] used a self-organizing TS fuzzy neural network to predict the temperature of a high-temperature furnace during waste incineration, providing a theoretical basis for the control and optimization of the high-temperature furnace. Zhang et al. [9] combined machine learning algorithms and data mining techniques to propose an intelligent prediction model based on industrial IoT-driven for the prediction of key carbon content in converters of steel mills, which can effectively guide the production process and reduce the carbon content error, and achieve the optimization of process parameters in the production line.

However, the traditional kiln production line has limited digitalization, and many monitoring techniques are neither practical nor cost-effective. This leads to serious black-box problems in process quality management, and the operators cannot promptly address failures or sudden abnormalities. Furthermore, they are unable to adjust other process parameters to regulate production when certain parameters become abnormal. These problems are obstacles to the achievement of advanced automation and intelligent control in the kiln production line. And using equipment and product data to predict production process parameters and achieve real-time control is a critical problem that enterprises need to address urgently.

The concept of Digital Twin (DT) brings a new solution to the above problems. Digital twin is a method of connecting and fusing physical and digital spaces. It is able to integrate the characteristics of multi-physical fields and different physical scales and has the ability to synchronize virtual and physical space. Additionally, it offers a unified platform for intelligent algorithms [10]. The concept of DT was first introduced by Prof. Grieves [11] in 2003 in his report on product lifecycle management. In 2010, NASA applied digital twins for practical use for the first time by collecting data from physical space vehicles and using digital twins to monitor the operational status of the entities. In 2015, General Electric Company enhanced its ability to maintain and analyze aero engines through the application of digital twins, improving the efficiency and reliability of engine maintenance [12]. With the advancement of the new generation of information technology and physical digital representation modeling methods, the digital twin is rapidly evolving, and countries are integrating it into their national development strategies.

In terms of real-time monitoring of workshop production lines, Tao et al. [13] proposed the concept of a digital twin workshop and discussed its structure, operation mode, and related technologies. They emphasized the fusion method for integrating diverse elements from the physical workshop with multidimensional models from the digital workshop using heterogeneous twin data. On this basis, the development of digital twin-related theories and applications is analyzed, a five-dimensional structural model of digital twin is proposed, and six guidelines for digital twin-driven applications are summarized [14,15]. Zhuang et al. [16] proposed an intelligent control method for a complex product assembly workshop based on a digital twin, which effectively improves the production efficiency of the workshop. Guo et al. [17] proposed a synchronous evolutionary prediction method for the production schedule of discrete manufacturing workshops using digital twin technology, which improves the accuracy of production schedule predictions. Yan et al. [18] achieved monitoring and autonomous decision-making for the entire lifecycle of actual shop floor production by integrating physical entities, data interaction, virtual entity construction, autonomous model updating, and decision-making prediction. Pei [19] et al. proposed an innovative online quality monitoring and control method based on digital twins. This method involves quantifying and mapping specific loss parameters that impact quality performance and feedback, which optimizes the production process control and improves the quality of solar cells. Tong et al. [20] proposed a real-time machining data application and service based on digital twin technology, which achieves real-time monitoring, analysis, and optimization of Intelligent Machine Tools. Liu et al. [21,22] generated digital models representing the real-time status of process equipment and Work-In-Progress (WIP), enhancing the practicality, efficiency, and intelligence of the three-dimensional (3D) process through research on digital twin-based processing quality tracking and dynamic interactive control methods.

In terms of the prediction and optimization of process parameters, Maarif et al. [23] conducted a predictive analysis of injection molding quality using an artificial neural network based on structural learning and forgetting, which significantly improved the accuracy of product quality prediction in the injection molding process. Liu et al. [24] used genetic algorithms to optimize the feature selection for the multivariate support vector machine, aiming to decrease the model complexity and develop a quality pattern recognition model to achieve the real-time prediction of quality characteristic data and dynamic quality control. Olivo et al. [25] introduced a steel exoskeleton design optimized using genetic algorithms to enhance the seismic performance of current RC structures. Li et al. [26] achieved optimization of machining time, energy consumption, and surface roughness based on a neural network approach using process parameters, such as feed rate, as optimization variables. Liu et al. [27] developed a surface roughness prediction model for brake discs by combining the digital twin based on a genetic algorithm and a multi-objective particle swarm algorithm to achieve adaptive optimization for process parameters. Cheng et al. [28] proposed a process internet reference framework for intelligent manufacturing based on digital twins to achieve digital control and optimization for turbine production. Hu et al. [29] proposed a data model for welding tasks to facilitate intelligent process planning and seamless integration of information among CAD/CAPP/CAM platforms for robotic welding. Li et al. [30] proposed a dynamic recommendation framework for manufacturing resources applied to shop floor resource management and optimization based on digital twins to improve production efficiency and reduce manufacturing costs. Booyse et al. [31] proposed a deep digital twin (DDT) framework based on deep generative models for learning the health distribution of assets directly from operational data to achieve detection, diagnosis, predictive maintenance and health state estimation of assets without relying on historical failure data. Zhao et al. [32] used digital twins to construct a high-precision cutting simulation model for the analysis and optimization of cutting parameters to reduce carbon emissions during machining. Mi et al. [33] proposed a cooperative perception and interconnection framework supported by digital twin technology to enhance the accuracy and reliability of predictive maintenance decisions, and the effectiveness of this methodology is validated through a case study involving the predictive maintenance of grinding roll bearings in a large vertical grinding machine.

The studies mentioned above utilize digital twins to bridge the gap between physical and virtual spaces, enabling prediction and control of process parameters in manufacturing to enhance product quality. However, current research mainly concentrates on physical processing scenarios like assembling and machining, and there are fewer studies on the production of VNs through chemical reactions. The special condition of the kiln production lines makes it challenging to promptly adjust the process parameters to achieve the desired product quality. How to build a digital twin framework for online control of the kiln production line, including monitoring and integrating process parameter prediction and control functions, is a pressing challenge that needs further research.

In summary, this paper proposes a method for predicting process parameters and online control in VN production based on digital twins. By collecting real-time data from both the digital twin production line and the real production line, combined with data transmission and communication technology, a system is developed for predicting and controlling vanadium nitrogen alloy production process parameters online. The system is designed to achieve real-time data-driven synchronous simulation of virtual and real production lines, dynamic prediction, and online control of process parameters. By synchronizing and regulating the entire production process, enterprises can effectively assess production line status, which improves production efficiency and achieves optimal production outcomes.

The basic structure of this paper is as follows: Section 2 firstly represents the production processes of VNs and ensures which process parameter for control through experiment. Additionally, the architecture of the process parameter prediction and control system based on digital twins is constructed. Then, the prediction and online control of process parameters are achieved by constructing the ISSA-GRNN fusion network model. And a digital twin system is developed to achieve online control. Then, in Section 3, the advancement of the proposed algorithm and the validation of the real-time online control are verified. Finally, Section 4 represents the conclusion and future works.

2. Materials and Methods

2.1. DT-Based Online Control System Architecture for VNs Production Process Parameters

2.1.1. VNs Production Processes

The core of the VNs production line includes a pusher plate kiln, a fully automated inlet and outlet propulsion system, and electrical control equipment, as shown in Figure 1.

The pusher plate kiln is the core equipment for the production of VNs. It consists of two sections, drying and reacting, with functional zones for heating, reacting, cooling, and buffering. The kiln body consists of refractory and thermal insulating materials and is equipped with silicon molybdenum heating rods. Adopting automatic computer control ensures safe and efficient production.

The fully automatic inlet and outlet system consists of a hoist and a hydraulic propulsion system. The function of the hoist is the vertical transport of raw materials and finished products. The hydraulic system is controlled by hydraulic stations at the kiln inlet and outlet. Five-cylinder double pumps are used at the kiln inlet, while four-cylinder single pumps are used at the kiln outlet to automate crucible advancement.

The electrical control system is divided into two parts: power control and temperature control. The power control is used for starting and stopping the pusher plate kiln, while the temperature control regulates the temperature of the heating chamber in each temperature zone through the intelligent instrument. It achieves accurate temperature control by adjusting the current, featuring a digital display and over-temperature protection.

The production process of VNs is shown in Figure 2. The procedure is shown as follows:

Firstly, as shown in (a) to (c), flake vanadium trioxide is ground into powder, mixed with carbon powder, and compacted.

Subsequently, as shown in (d) to (f), the processed balls are placed into the crucible after automated weighing and screening. And unqualified balls will be sent back to (b) to mill again.

Thirdly, as shown in (e) to (i), the crucible is through the elevator and conveying system to the pusher plate kiln; the hydraulic system pushes the crucible through the drying, nitrogen reduction reaction preparation of alloy.

Fourthly, as shown in (j) to (l), after the finished product is cooled, it is lifted to the upper level and conveyed to the finished product workshop, where the robot pours out the alloy, screens it, and packs it for sale. And substandard products will be sent to step (b) to mill again.

Finally, Empty crucibles are automatically returned to the raw material workshop, completing the cycle of production.

During the normal production process of the production line, every hydraulic cylinder within the hydraulic propulsion system follows a specific sequence and time interval for working advancement and working retraction, pushing the raw material crucibles into the assigned temperature zone for heating. This process enables the raw materials to react with nitrogen, completing the preparation of VNs.

2.1.2. VNs Production Process Parameters

The data from the VN production process can be divided into two main categories, as shown in

Table 1. Data collected in the VN production process.

Data Category	Specific Data Markers
Kiln Line Body Data	T1–T32, A1–A32, V1–V32, N1–N4, Ntotal
propulsion System Data	ppkc, ppkc, ppkap, ppkod, ppkopb, ppkdl, ppkie, ppkii, Push_Speed

, where the kiln line body data represent the relevant data collected on the line body of the pusher plate kiln. T1–T32 represent the temperature of each heating chamber in the 20 temperature zones; A1–A32 represent the electrical current through the heating rods in each heating chamber in the 20 temperature zones; V1–V32 represent the voltage through the heating rods in the 20 temperature zones; and N1–N4 represent the flow rate of nitrogen through the pipelines from 1# to 4# of the pusher plate kiln, respectively. The propulsion system data represent the data collected by the fully automated propulsion system; ppkc represents the charging data of the pusher plate kiln; ppkic represents cross-push data at the pusher plate kiln inlet. ppkap represents the active push data of the pusher plate kiln inlet; ppkod represents discharging data at the pusher plate kiln outlet; ppkopb represents the pushback data collected at the pusher plate kiln outlet; ppkdl represents the data collected from the lower compartment at the discharge end of a pushe plate kiln. ppkie represents the data collected from the external gate at the inlet of the pusher plate kiln; ppkii represents the data collected from the internal gate at the entrance of the push plate kiln head; Push_Speed represents the movement interval of the telescopic hydraulic cylinders in the propulsion system of the vanadium nitrogen alloy production line, which determines the reaction time of the raw material crucible in the pusher plate kiln.

The quality of VNs depends on the nitrogen content. Within the production process, there are three key process parameters related to the nitrogen content of VNs: the heating chamber temperature (T₁–T₃₂), the nitrogen flow rate (N₂–N₄), and the propulsion system movement interval (Push_Speed). The propulsion system movement interval controls the reaction time of the raw material crucible in the kiln.

The quality of VNs is assessed by their nitrogen content: below 14.8% is deemed unsatisfactory, above 16.0% is deemed excellent, and levels in between are considered acceptable.

For these three important parameters, nitrogen reduction experiments were conducted to measure the nitrogen content of VNs produced under t specific conditions and to analyze the effects of the process parameters on the quality of VNs. Five groups of comparative experiments were conducted for each test, with Group 3 of each test serving as the control group. The parameters were selected from the recommended values in the theory of VN production. A sensitivity analysis was performed to assess the effects of the variance in some key parameters on the content of nitrogen on the VNs. The varying parameters are temperature, nitrogen flow rate, and reaction time.

(1) Different temperatures: The nitriding reaction mainly happens in the 15–20 temperature zones. To analyze and compare the nitrogen content of VNs at different reaction temperatures, the reaction time and nitrogen flow rate are kept constant, while the temperatures of the temperature zones mentioned above are varied. The temperature data for each experimental group are displayed in

Table 2. Experimental sample data at different reaction temperatures.

	Temperature Zone	Part of Zone	1	2	3	4	5
Temperature (°C)	15	upper	1144	1194	1244	1294	1344
		lower	1156	1206	1256	1306	1356
	16	upper	1224	1274	1324	1374	1424
		lower	1248	1298	1348	1398	1448
	17	upper	1312	1362	1412	1462	1512
		lower	1333	1383	1433	1483	1533
	18	upper	1312	1362	1412	1462	1512
		lower	1335	1385	1435	1485	1535
	19	upper	1280	1330	1380	1430	1480
		lower	1304	1354	1404	1454	1504
	20	upper	1166	1216	1266	1316	1366
		lower	1164	1214	1264	1314	1364

, with Group 3 serving as the control group and the remaining groups serving as experimental groups.

(2) Different nitrogen flow rates: Under the condition of constant reaction temperature and reaction time, the nitrogen flow rate of each pipeline was changed. The nitrogen content of VNs under different reaction nitrogen flow rates was comparatively analyzed. The nitrogen flow data for each experimental group are displayed in

Table 3. Experimental sample data at different nitrogen flow rates.

		1	2	3	4	5
Nitrogen flow rate (m3/h)	2# Pipeline flow rate	34.48	39.48	44.48	59.48	54.48
	3# Pipeline flow rate	34.26	41.26	48.26	55.26	62.26
	4# Pipeline flow rate	92.27	100.27	108.27	116.27	124.27
	Flow rate and Ntotal	161.01	181.01	201.01	221.01	241.01

, with Group 3 serving as the control group and the remaining groups serving as experimental groups.

(3) Different reaction times: Under the condition of constant reaction temperature and nitrogen flow rate of each pipeline, the movement interval of the propulsion system is changed to control the reaction time of the raw material, and the nitrogen content of VNs under different reaction times is compared and analyzed. The data of different propulsion system movement intervals are displayed in

Table 4. Experimental sample data at different reaction times.

	1	2	3	4	5
Propulsion system movement interval (s)	34.48	1240	1360	1480	1600

, with Group 3 serving as the control group and the remaining groups serving as experimental groups. And the larger the propulsion system movement interval is the longer the reaction time.

The results of nitrogen content measured by nitrogen reduction are shown in Figure 3. For the control of reaction temperature, the highest nitrogen content of VNs in Group 3 was 16.6%; the quality of VNs in Group 1 was acceptable, with a nitrogen content of 15.5%. Although the temperature of Group 4 and Group 5 was higher than Group 3, the nitrogen content of VNs was lower than that of Group 3 experiments. This is because the nitridation reaction is exothermic, and excessively high temperatures are detrimental to the generation of VNs. It can be concluded that when reaction time and nitrogen flow rates are kept constant, changes in temperature have only a minor effect on nitrogen content. The raw materials continue to react effectively, and the quality of the VNs remains acceptable.

For the control of nitrogen flow rates, Group 3 has the highest nitrogen content at 16.6%, while Group 1 is of good quality at 15.7%. Although Groups 4 and 5 represent a higher nitrogen flow rate than Group 3, their VNs have lower nitrogen content. This is because increased nitrogen flow accelerates the airflow, which causes more heat loss in the furnace, consequently disrupting the normal warming process of the raw material. It can be concluded that when reaction temperature and reaction time are kept constant, changes in nitrogen flow rate also have only a minor effect on nitrogen content. The raw materials continue to react effectively, and the quality of the VNs remains acceptable.

For the control of reaction time, the nitrogen content of VNs in Group 3 is 16.6%.

Although Groups 4 and 5 have longer reaction times than Group 3, the three groups represent similar nitrogen content. This indicates that the raw materials in Group 3 have fully reacted, and extending the reaction time further does not increase nitrogen content but instead leads to resource waste. And the quality of VNs of the Group 1 did not meet the quality requirements, with a nitrogen content of only 14.1%. It can be concluded that when reaction temperature and nitrogen flow rates are kept constant, reaction time has a greater effect on the nitrogen content of VNs. With the decrease in reaction time, the reduction in nitrogen content became more significant. In these experimental groups, the raw materials did not react sufficiently, leading to substandard quality in the VNs.

Based on the results of the above experimental analysis, this paper focuses on reaction time as a key process parameter. That means the movement interval of the propulsion system is the target for prediction and control. And the results of the dynamic predictions for the propulsion system’s movement intervals will then be fed back to the physical production line to control reaction time, adjust production, ensure product quality, and enhance efficiency.

2.1.3. Architecture of Digital Twin Online Control

To achieve the monitoring of the VN production process and online control of process parameters, this paper proposes an architecture of the online control of VN production process parameters, as shown in Figure 4. The architecture is mainly divided into 3 parts: the data acquisition layer, the data processing layer, and the twin service layer.

(1) Data acquisition layer. This layer primarily includes physical resources. The physical production line is the data source and target of control. The process parameters related to the quality of VN products mainly consist of equipment parameters. For example, the propulsion system movement interval can be directly monitored through the PLC. Additionally, data from thermocouples, nitrogen flow meters, and other sensors are also crucial for quality control. In cases of incompatible sensor interfaces, the multi-sensor fusion method can be utilized for resolution [34];

(2) Data processing layer. The fundamental and essential task for achieving production line informatization is to collect heterogeneous production line data [35]. In this layer, raw data collected are classified and stored. The data source from the production line is categorized into equipment information data, logical information data, and environmental information data before being stored. Then, intelligent algorithms filter noisy data, and the resulting lightweight data are stored. Based on the signal quantity collected by the three data types, data updating and information synchronization requirements are met through the implementation of interoperable communication protocols among devices [36]. This paper uses Hyper Text Transfer Protocol (HTTP) to achieve synchronous communication between physical and virtual production lines. HTTP is one of the commonly used communication protocols, which has the advantages of simplicity, flexibility, and stability and is widely used in major information systems [37];

(3) Twin service layer. This layer is built upon the physical production line and involves creating a visual virtual production line. Historical data from the twin production line are utilized to formulate a theoretical production plan. By integrating the production line process flow with synchronization rules for virtual and real environments, VN production line digital twins are established to accurately map the geometric and logical aspects of the virtual and real production line production processes.

Initially, the physical production line must be represented in a digital twin space. And It is important to consider the complexity of the structure in the modelling process [38]. The essential components of the VN production line production process are the product, equipment, and production environment. Therefore, the digital twin model of the production line process can be defined as follows:

$$D{T}_{\mathrm{PRO}}=D{T}_{\mathrm{prod}}\cup D{T}_{\mathrm{equip}}\cup D{T}_{\mathrm{env}},$$

(1)

where $D{T}_{\mathrm{PRO}},D{T}_{\mathrm{prod}},D{T}_{\mathrm{equip}},D{T}_{\mathrm{env}}$ represent the digital twin models for the production process, product, equipment, and environment of the production line.

(a) Product twin modeling. The digital twin model of a product can be defined as follows:

$$D{T}_{prod}=\left\{PStruct,PInterface,PRules\right\},$$

(2)

where $PStruct$ is the three-dimensional geometric model of the product in different production stages; $PInterface$ is the information data interface of the product; $PRules$ are the rules of behavior for the geometrical transformation of the product during the production process;

(b) Equipment twin modeling. The digital twin model of a device can be defined as follows:

$$D{T}_{equip}=\left\{EFunction,EInterface,ERules\right\},$$

(3)

where $EFunction$ is a functional model of the device. It means that the virtual model of the device needs to have high consistency with the real device in terms of geometry, physical relationships, motion logic, and functionality; $EInterface$ is the virtual-real communication interface, through which the twin model communicates with the real device in real time and achieves the interaction of inter-model data based on the real-time driving data; $ERules$ are the logistical model for the movement of the device twin model and the processing of the data information and so on.

As an example, Figure 5 depicts the 3D model of the core equipment in the VNs production line, the pusher plate kiln. The pusher plate kiln model name, driving data, data source, and logistical model are shown in

Table 5. Pusher plate kiln model name, driver data, data source, Virtual Rules of Behavior.

Model Name	Driving Data	Data Source	Virtual Rules of Behavior
Pusher plate kiln	Temperature data	Thermocouples	Motion Control Programmers Signal Processing Programmers
	Nitrogen flow data	Flowmeter
	Power data	PLC

.

(c) Environment twin modeling. The production environment digital twin model can be defined as follows:

$$D{T}_{env}=\left\{EnvEnviron,EnvInterface,EnvMaterial\right\}$$

(4)

where EnvEnviron is the environmental information for the VNs production line workshop; EnvInterface is the interface for the transmission of environmental information; EnvMaterial is Material textures for real environments.

After the digital twin scene construction is finished, the virtual production line client platform is created using Unity3D, and HTTP is used to construct the communication. The system acquires real-time production line data by repeatedly sending HTTP requests, parsing the obtained JSON data, and correlating it with the virtual production line modules for synchronized mapping of the production line model.

This layer also integrates functional modules for line status monitoring, line production data monitoring, and online control of process parameters. It maps the complete production information of vanadium and nitrogen alloy production lines into the digital twin system. The layer analyzes real-time data collected from the production lines to determine if current process parameters are optimal for meeting production requirements and achieves online control of the production lines.

2.2. Prediction of Production Process Parameters for VNs Based on ISSA-GRNN

2.2.1. GRNN Network

GRNN [39] is a feed-forward neural network based on radial basis functions with a more flexible network structure, strong robustness, high fault tolerance, and fast training speed. Since there are less feature data during VN production, GRNN can complete network training and achieve effective network data even when the size of samples is small. This paper adopts GRNN for the dynamic prediction of parameters in the VN production process.

The GRNN structure is shown in Figure 6 and is divided into input, pattern, summation, and output layers. For the network input $X={\left[x_1,x_2,\dots ,x_d\right]}^T$, its output is $\hat{Y}={\left[y_1,y_2,\dots ,y_d\right]}^T$.

(1) Input layer. The number of neurons in the input layer equals the dimension of the input vector d. The neurons pass the input variables to the pattern layer through a linear function;

(2) Pattern layer. The number of neurons in the pattern layer equals the number of learning samples n. The transfer function of the neurons is as follows:

$$P_i=e^{\left[-{\displaystyle \frac{{\left(X-X_i\right)}^T\left(X-X_i\right)}{2{\sigma }^2}}\right]} i=1,2,3,\dots ,d,$$

(5)

(3) Summation layer. The summation layer consists of two types of neurons. The first type of neuron conducts an arithmetic sum of the outputs from every neuron in the pattern layer by using the following transfer function:

$$S_D={{\displaystyle \sum }}_{i=1}^n{P}_i,$$

(6)

The second type of neuron conducts a weighted sum of the outputs from every neuron in the pattern layer. The connection weight of these neurons is denoted as $y_{ij}$, where it represents the j-th element in the i-th output vector within the training sample. The transfer function is as follows:

$$S_{Nj}={{\displaystyle \sum }}_{i=1}^m{y}_{ij}{P}_i j=1,2,\dots ,M,$$

(7)

(4) Output layer. The number of neurons in the output layer equals the dimension M of the output vector, and the output of the j-th neuron is as follows:

$$y_j={\displaystyle \frac{S_{Nj}}{S_D}} j=1,2,\dots ,M,$$

(8)

In summary, the structure and principles of GRNN are relatively simple. Once the input samples are defined, both the network’s structure and the connection weights between layers are established. Consequently, the training process of the network becomes the tuning process of the smoothing factor $\sigma$.

2.2.2. Improved SSA

Since GRNN does not need to be trained using the traditional backpropagation algorithm, it only needs to adjust the transfer function of the model layer by adjusting the smoothing factor σ, which in turn improves the network accuracy. However, due to the weak generalization ability of GRNN, the model produces a large error when $\sigma$ is not selected properly. The accuracy of the GRNN network can be effectively improved by the reasonable value of the smoothing factor $\sigma$. In this paper, an improved sparrow search algorithm (ISSA) is used to find the optimal smoothing factor $\sigma$.

The traditional SSA has a strong ability to find the optimum, but the global ability is relatively weak at the end of its iteration process, increasing the risk of getting trapped in local optima and causing algorithm search stagnation.

In order to solve the above problems, this paper proposes an improved sparrow search algorithm based on the Levy flight perturbation mechanism [40] and the improved Sine chaotic initialization strategy. This approach aims to increase the diversity of the algorithm’s search, improve the ability to escape local optimum, enhance the solution accuracy, and effectively balance speed and accuracy.

The search strategy of the Levy flight perturbation mechanism is divided into short-range and long-range searches. Short-range search allows individual sparrows to make small, careful searches in their areas. Long-range search allows individual sparrows to escape the current area and explore other areas. The search path $L\left(\lambda \right)$ of the Levy flight follows the Levy distribution, as defined by the following:

$$Levy~u=t^{-\lambda } 1<\lambda \le 3,$$

(9)

where $\lambda$ is exponential; $t$ is time.

The sine chaotic initialization strategy can effectively solve the problem of uneven distribution and coverage of initial solutions in the solution space in SSA. But, the traditional chaotic mapping has the defect of uneven distribution of sequences in phase space during iteration. Therefore, the sine chaotic mapping iteration is improved using the following improvement formula:

$$\left\{\begin{array}{c}\hspace{1em}\hspace{1em}{d}_{i+1}=\sin \left(\mu \pi d_i\right)\\ \hspace{1em}\hspace{1em}{e}_{i+1}=\sin \left(\mu \pi e_i\right)\\ w_{i+1}=d_{i+1}+e_{i+1}·mod\end{array}\right.,$$

(10)

where $\mu$ represents the control parameters, and $w$ represents iteration sequence values in the improved Sine chaotic mapping. The distribution of solution dimensions before and after the improvement is shown in Figure 7.

As can be seen from Figure 7, the improved sine mapping has a more even distribution of chaotic values. Therefore, the use of improved sine mapping to initialize the population improves the diversity of the population, thereby enhancing the algorithm’s ability to find the optimal solution.

2.2.3. Predictive Modelling

Based on Section 2.2.2, the smoothing factor $\sigma$ of every neuron in the GRNN pattern layer is optimized through ISSA in order to improve the prediction accuracy and performance of GRNN. The operation workflow of the ISSA-GRNN network constructed in this paper is shown in Figure 8.

The dynamic prediction process for determining the optimal movement interval of the propulsion system, based on the current input from the VNs production line, is outlined as follows:

(1) Modelling the network architecture. The target values of the key process parameters for the preparation of VNs are used to create the input vector $X=\left\{x_1,x_2,\cdots ,x_{36}\right\}$, where $x_1-x_8$ are the measured values of the lower heating chamber temperature in the temperature zones 1–8 of the pusher plate kiln; $x_9-x_{32}$ are the measured values of the upper heating chamber temperature and the lower heating chamber temperature of the pusher plate kiln 9–20 temperature zone; $x_{36}$ is the predefined target value for the movement interval of the propulsion system

The output vector is $Y=\left\{y_1,y_2,y_3\right\}$, where $y_1$ is the upper limit of the movement interval of the propulsion system; $y_2$ is the lower limit of the movement interval of the propulsion system; $y_3$ is the predicted value of the movement interval of the propulsion system. In practical production, the optimum value of the propulsion system movement interval predicted by the algorithm is sent back to the VN production line for control. If the practical propulsion system movement interval is within the range of ($y_1,y_2$), it is considered that the VNs produced in this case can meet the quality requirements;

(2) Optimizing smoothing factor vectors. Using ISSA to optimize the smoothing factor vectors for constructing the ISSA-GRNN fusion network model;

(3) Dynamic prediction of process parameters. The construction of the ISSA-GRNN fusion network model is completed using the obtained optimal smoothing factor $\sigma$. This model dynamically predicts the optimal movement interval values for the propulsion system under current production conditions, enabling online control of process parameters in the production of VNs.

2.3. System Implementation and Online Control

2.3.1. Digital Twin System Development

In order to achieve real-time monitoring of the VN production process and data and provide an integrated platform for the fusion network model, an online control system for process parameters was constructed using digital twin in this paper. The system generates a comprehensive three-dimensional model of the VN production line, enabling real-time monitoring of both the physical production process and data flow. It creates a comprehensive three-dimensional model of the VN production line, enabling real-time monitoring of both the physical production process and data flow. Furthermore, it enables dynamic prediction and online control of key process parameters.

The architecture of the digital twin system designed and developed in this paper is shown in Figure 9. The functional modules of the system are mainly divided into three parts: the production line operation loading monitoring module, the production line production data monitoring module, and the process parameter online control module. This system adopts a C/S (Client/Server) architecture, the development language is C# and Python, the development engine is Unity3D, and the data storage mode adopts a distributed database.

The main function of the client is to handle users’ interaction, display data, and store manufacturing resource data related to the production process of VNs. The user interface development and interaction logic implementation are achieved using the C# language within Unity3D. The algorithmic model is implemented using Python, where the code is encapsulated within a standard library, and the extension module is compiled into a DLL file. The digital twin system uses the .Net framework to load DLL files and generates C# scripts that invoke the algorithmic model via the IronPython plug-in for integrating and applying the process parameter optimization module.

The server has many core functions of the system, including business processing, interface deployment for data communication, and interaction.

On the server side, in order to enhance the management of data and improve the performance of digital twin synchronization, the system uses a distributed database architecture. Chronological data collected from the production line is stored in the IoT database, while business data related to the production line is stored in the MySQL database. The IoT database is utilized for efficient chronological data processing and querying, while the MySQL database is used to address the lack of support for structured data in the IoT database. This database architecture represents excellent scalability, as well as ease of maintenance and management.

The main interface of the system and the data monitoring interface of this paper are shown in Figure 10. The digital twin workshop contains eight VN production lines, where the status of each line is monitored and displayed through the analysis of collected data. Since the kiln chamber of the push plate kiln is confined during production, workers cannot directly observe its internal state. To solve this problem, the system provides a virtual representation of the pusher plate kiln, allowing the internal state to be displayed. And the real-time data collected from the VN production lines is shown through a UI panel.

The system configuration file defines a reasonable range for each parameter, with different panels displaying data based on its range. Historical data are stored in the database to enable monitoring and tracing of production data.

2.3.2. Online Control

The dynamic online control interface for process parameters in this system is shown in Figure 11. The system includes functions such as real-time analysis of process parameters and online control of process parameters. The system includes features for real-time analysis and online control of process parameters.

(1) Real-time analysis of process parameters: Real-time analysis of key process parameters, such as temperature in VN production, provides feedback on deviations from ideal values, guiding workers in parameter regulation;

(2) Online control of process parameters: The current process parameters are analyzed to predict the optimal movement intervals of the pusher plate kiln using the ISSA-GRNN fusion network model. The movement interval is controlled online, enabling closed-loop control and ensuring timely adjusting for high-quality product production.

3. Results and Discussions

3.1. Experiment and Data Preparation

This experiment validates the method proposed in this paper by evaluating model performance. From the library of theoretical process parameters of VNs, 240 sets of data were selected to train the fusion model. Data numbered from 1 to 200 were assigned as the training sample set, while data numbered from 201 to 240 were assigned as the test sample set. The model is trained using K-Ford cross-validation with k set to 5, which means the number of training samples for each cross-validation process was 160. Before network training, in order to improve the convergence speed of the algorithm, the Min-Max normalization method is used to scale the above data to the range [0, 1], and the output values of the trained model are de-normalized to assess the model performance.

The initialization parameters of ISSA are shown in

Table 6. The initial parameters of ISSA.

Algorithmic Parameter	Actual Parameter Values
$\mathrm{Number}$	30
$\mathrm{Number} \mathrm{of} \mathrm{iterations} T_{max}$	100
$\mathrm{Upper} \mathrm{boundary} u_b$	2
$\mathrm{Lower} \mathrm{boundary} l_b$	0.1
$\mathrm{Safety} \mathrm{value} S_T$	0.6
$\mathrm{Discoverers} \mathrm{ratio} P_d$	0.7
$\mathrm{Scout} \mathrm{ratio} S_d$	0.2

.

3.2. Algorithm Experiment Results and Analysis

This paper validates the superiority of the proposed ISSA for parameter optimization of the GRNN model by using a plot of the number of iterations versus the fitness value of the ISSA-GRNN and SSA-GRNN algorithms to compare them.

As shown in Figure 12, the fitness value of the SSA-GRNN iteration initially decreases slowly, achieving convergence at 68 iterations, with a final fitness value of approximately 0.0028 after 100 iterations. In contrast, the fitness value of the SSA-GRNN iteration initially decreases rapidly and achieves convergence at 52 iterations, and the final fitness value after 100 iterations is about 0.0021. It can be concluded that the ISSA can effectively improve the convergence speed and accuracy of the training process for GRNN.

Figure 13 shows the prediction error regression plot of the test sample data. Figure 13 illustrates the high accuracy of data prediction throughout the entire test dataset, where each predicted value closely follows the zero error line. The algorithm’s accuracy meets the precision requirements for optimizing the production process parameters of VNs.

Figure 14 illustrates the comparison of the prediction results of ISSA-GRNN and SSA-GRNN, GRNN, and BPNN, where the ideal value is the theoretical optimum corresponding to the test sample number in the process parameter library. It can be concluded that the ISSA-GRNN fusion network model represents superior prediction performance, with minimal deviation between the predicted and ideal values for each test sample.

In order to objectively and quantitatively compare the performance of these above models, Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and the time of computation are used as evaluation metrics. Smaller RMSE and MAPE values indicate higher model accuracy. The formulas for these evaluation metrics are as follows:

$$RMSE=\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(\widehat{y_i}-y_i\right)}^2/n},$$

(11)

$$MAPE={{\displaystyle \sum }}_{i=1}^n\left|\left(\widehat{y_i}-y_i\right)/y_i\right|/n\times 100\%,$$

(12)

where n represents the number of samples in the dataset; $y_i$ is the actual value; $\widehat{y_i}$ is the predicted value.

The results of evaluating different models for each metric are shown in

Table 7. Comparison of prediction errors and time consumption of four network models.

Network Model	RMSE	MAPE (%)	Time (s)
BPNN	19.24	1.04	1.46
GRNN	13.74	0.85	0.82
SSA-GRNN	10.42	0.68	0.89
ISSA-GRNN	8.91	0.54	0.91

.

The data in Table 7 show that ISSA-GRNN has an RMSE of 8.91 and a MAPE of 0.54%, achieving the highest prediction accuracy and efficient prediction speed. The results prove that the algorithm meets the requirements for the prediction of the production process parameters of VNs.

3.3. Verification of Process Parameter Online Control Results

The experiment was conducted on VN production line 4 for nitrogen reduction experiments. Since the line has not been renovated, the production line equipment may experience issues such as aging or damage, leading to the actual process parameters frequently deviating from the desired ideal values.

The nitrogen content of VNs was analyzed by using two groups of products; one produced with digital twin online control and the other without, as a comparison to validate the effectiveness of the online control results. In this experimental production process, 10 pairs of crucibles are used for experiments. The raw materials are placed into the kiln. Initially, the pushing speed of the pusher plate kiln is set to 1800s/time. After completing the production of unregulated batches of products, the same 10 pairs of crucibles are loaded with the same quality of raw materials to restart the system. The optimal pushing speed predicted dynamically by the integrated algorithm module will be transmitted to the server side to control the production in real time. The nitrogen content data of the products measured by the nitrogen reduction experiment on the finished product are displayed as a box plot in Figure 15. From this, it can be derived:

(1) The median nitrogen content and the first quartile of the VNs produced under the system control are significantly elevated. This indicates that the quality of VNs under the system control is superior to those without control;

(2) The interquartile range (IQR) of products under control decreased compared to those without control, suggesting reduced variability in product nitrogen content data and improved stability of product quality after control.

In conclusion, the online control system for VNs production process parameters constructed in this paper can improve product quality during production control, leading to increased stability in product quality.

4. Conclusions and Prospects

Digital twin provides an effective solution for the challenges encountered in VN production, including the lack of real-time monitoring of production and control of process parameters. This paper proposes a method for prediction and online control of the VN production process, which enables real-time monitoring of the production process and dynamic online control of production process parameters, effectively improving product quality, enhancing the economy, and promoting the sustainability of the VN industry.

The ISSA-GRNN fusion prediction model constructed in this paper has high accuracy in the prediction of the process parameter of the propulsion system movement interval. In practical applications, the online control platform can predict the optimal movement interval, considering variations in parameters like temperature and nitrogen flow. If the actual movement interval deviates from the optimal range, the system will adjust parameters through online control to maintain product quality.

At present, the production process of VNs is primarily controlled based on process parameters. However, the deteriorated condition of kiln components towards the end of the pusher plate kiln’s service life has reduced the viability of this approach. Therefore, focusing on controlling the kiln production process parameters along with considering the impact of equipment structure on kiln quality will be a key aspect of future research.