Internet of Things system reliability evaluation method based on modular Petri network

Abstract

The invention discloses an Internet of Things system reliability evaluation method based on a modular Petri network, and the method comprises the following steps: 1, initializing the states of a production unit and an information node in an Internet of Things system, and building a corresponding Petri network model; step 2, constructing a connectivity check subnet, and detecting the connection condition of each node in the information network; step 3, implementing information load distribution modeling, and simulating data flow and overload state between nodes; 4, constructing a system monitoring subnet, and evaluating the state observation accuracy in the information transmission process; 5, constructing a production decision subnet, and simulating a production instruction issuing process based on monitoring information; 6, evaluating the actual production capacity and reliability of the system; and step 7, repeating the above steps, performing Petri network simulation operation for multiple times, observing output performance and fault behaviors of the system in the time evolution process, and further evaluating the overall reliability index of the system. According to the invention, the interactive degradation process of information and a physical system in the Internet of Things can be simulated efficiently, the reliability evaluation precision of the intelligent manufacturing system is improved, and a basis is provided for production decision making.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent manufacturing and industrial Internet of Things technology, and specifically relates to a reliability evaluation method for Internet of Things systems based on modular Petri nets, which is particularly suitable for evaluating system operation reliability under consideration of physical device degradation, information network transmission performance fluctuations and their coupling effects. Background Art

[0002] With the development of intelligent manufacturing, Internet of Things technology has been widely used in modern industrial production processes. By networking and integrating multiple devices such as sensors, actuators, edge computing nodes and cloud platforms, real-time perception, precise control and intelligent decision-making of production status are achieved, which significantly improves the automation and collaboration capabilities of manufacturing systems. Especially in typical scenarios such as high-end equipment, automobile manufacturing, and electronic assembly, the Internet of Things has become the basic support system for the efficient operation of smart factories.

[0003] However, the high complexity and dynamic nature of Industrial Internet of Things (IIoT) systems also introduce significant operational risks. On the one hand, physical production units can experience performance degradation under long-term high-load operation, manifesting as reduced production capacity and increased failure probability, impacting the system's overall output capacity. On the other hand, node overload, link interruptions, or cascading failures in information networks can lead to data transmission delays, increased observation errors, and, in severe cases, even control signal errors or interruptions, compromising the accuracy of production instructions. The interactive relationship between physical and cyber systems creates a chain reaction of degradation effects, easily inducing unexpected system-level failures and production disruptions. Existing industrial system reliability assessment methods mostly focus on single-level modeling, analyzing only equipment degradation behavior or network reliability, lacking a systematic characterization of the coupled relationship between the two. Furthermore, at the production scheduling level, traditional methods often assume accurate and predictable system states. However, in real-world conditions, due to perception errors and command distortion, scheduling strategies often deviate from the actual system state, further exacerbating degradation and failure risks.

[0004] Therefore, it is urgent to build a system-level modeling method that integrates physical degradation modeling, information network dynamic behavior and perception error propagation mechanism, and combine it with production control strategy optimization to achieve a comprehensive evaluation of the operational reliability of the Internet of Things system and dynamic optimization of production scheduling. Summary of the Invention

[0005] To solve the above technical problems, the purpose of the present invention is to provide an Internet of Things system reliability modeling and evaluation method based on modular Petri nets, which is used to solve the problem in existing intelligent manufacturing systems that it is difficult to consider the impact of physical device degradation, information network load changes and their interactions on system reliability.

[0006] The technical solution adopted by the present invention is: a method for reliability assessment and system decision optimization of the Internet of Things system based on modular Petri nets, the specific steps of which are as follows:

[0007] Step 1: Construct the initial system state of the Internet of Things in the intelligent manufacturing system. Based on the performance level of the production unit and the functional state of the information node, a Petri net model is established to define the state, transfer relationship and initial identification of each unit.

[0008] Step 2: Establish an information network connectivity check module to determine the connectivity and isolation status of each node based on the network topology and node fault status, and simulate the network disconnection propagation mechanism through the inhibition arc mechanism in the Petri net;

[0009] Step 3: Build an information load distribution and overload detection module to distribute data load based on node connectivity and routing path traffic, and determine whether a node enters an overload range or triggers a failover.

[0010] Step 4: Establish a system status monitoring module. According to the load path and node performance, calculate the information transmission accuracy v to construct the state observation probability matrix, and map the error between the actual state and the observed state in the form of probability transition;

[0011] Step 5: Build a production decision module. Based on the current state observation results, set the production rate of each production unit through the optimization model and map the control instructions to the production instruction path that may fail.

[0012] Step 6: Build a capacity assessment module to match the instruction execution results with the current unit capacity, calculate the actual output of the system, determine whether it meets the set capacity requirements, and decide whether to record a system failure;

[0013] Step 7: Repeat the above process and run multiple Petri net simulations to observe the output performance and failure behavior of the system during time evolution, and then evaluate the overall reliability indicators of the system.

[0014] 2. To accurately describe the interaction between production units and information nodes in the IoT environment, this step uses a modular Petri net formal modeling method to construct a two-layer topology structure of the physical layer and information layer in the manufacturing system, and completes the modeling of the system's initial state. By hierarchically dividing and mapping multiple functional units and perception networks in the production system, static configuration and state initialization of the system structure are achieved, ensuring a unified data foundation and structural semantics for subsequent degradation modeling, perception error simulation, and reliability assessment processes. The specific steps are as follows:

[0015] Step 11: System hierarchical structure modeling: Divide the system into two main levels:

[0016] Physical layer network G P =(V P , E P ): It consists of multiple production units with production capacity, each node l∈V P Corresponding to a production device, it has state evolution capability and control input;

[0017] Information Layer Network G I =(V I , E I ): It consists of multiple information collection and transmission nodes, node k∈V I Including roles such as terminal nodes, routing nodes, and gateway nodes, responsible for data collection, transmission, and reporting;

[0018] Binding mapping matrix A = [a lk ]: used to indicate the connection between production unit l and information node k. If there is a connection, then a lk =1, otherwise 0.

[0019] Step 12, modular Petri net construction method: According to the above system structure, a modular Petri net model N = (P, T, F, W, M0) is constructed, where P corresponds to the status bit of the physical unit, the function bit of the information node, and the communication connectivity bit respectively; T represents event-driven state changes, including device degradation, communication interruption, perception error, instruction triggering, etc.; F represents the causal relationship between position and change; W represents the number of tokens used in the change; M0 is the initial identification distribution, which is used to define the initial state configuration of the system operation.

[0020] In order to ensure the scalability and reusability of the model, the present invention adopts the following modular modeling strategy to establish three module structures, namely, physical unit subnet module, information node subnet module, and cross-domain interaction interface.

[0021] Physical unit subnet module: Each production unit is modeled separately, including multiple status bits (for example: healthy, slightly degraded, severely degraded, and failed) and their corresponding migration paths, supporting process modeling such as degradation, maintenance, and recovery;

[0022] Information node subnet module: constructs different functional subnets according to node types, including: terminal node: mainly contains data generation bit and sending bit; routing node: contains cache bit, forwarding bit and congestion status bit; gateway node: contains reporting bit and relay control bit.

[0023] Cross-domain interaction interface: Connects the physical unit status bit with the information node binding bit through special "shared location" or "synchronous transition", representing coupling mechanisms such as state perception and control signal input.

[0024] Step 13. Initial state definition: Based on the system's initial deployment and operating condition configuration, assign a number of tokens to each position in M0: for the physical unit status bit, only set one token at its initial health state position to indicate normal operation; for the information node function bit, set tokens based on its initial health status to indicate whether it is invalid; for the cross-domain interaction position, the initialization token indicates whether the perception link and control channel are established.

[0025] 3. To simulate the performance degradation of production units during long-term operation due to load or instruction influence, this step establishes a degradation modeling framework based on state transitions. Each production unit is divided into multiple health levels, and degradation paths and state transition intensity functions are constructed to reflect the dynamic coupling mechanism between production unit capacity control and lifespan evolution.

[0026] By introducing the transition structure of modular Petri nets, the degradation path is explicitly modeled and dynamically associated with the instruction type received by the production unit, realizing the modeling of the chain process of "overload-degradation-output reduction". The specific steps are as follows:

[0027] Aiming at the state evolution of production units in intelligent manufacturing systems, a Petri net structure with probabilistic transition is constructed. l states, numbered from 1 to m l , where state i=1 indicates a good state, state i=m l Indicates a complete failure state. According to the production rate γ of the production unit l (t), the transition probability of its state from i to a worse state j (j>i) (normal production instruction) is defined as follows:

[0028]

[0029]

[0030] Among them, α l (γ l (t))∈[0,1] is the weighted coefficient related to productivity, which increases with γ l (t) monotonically increasing; represents the nominal degradation rate of the production unit at maximum production rate;

[0031] If the production unit is in the state of executing abnormal production instructions, its state transition probability is affected by the abnormal acceleration coefficient ζ l The abnormal state activates the corresponding abnormal degradation transition through the identification site in the Petri net. The probability calculation method of transferring from state i to j (j>i) is specifically expressed as:

[0032]

[0033] 4. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1 is characterized in that the specific implementation method of step 3 is as follows: by treating information nodes as binary components, describing their lifespans with probability density functions, and expressing data processing capabilities with normalization coefficients and throughput, calculating loads based on the characteristics of different types of nodes and considering information load distribution, and analyzing the impact of node loads on data transmission accuracy; for different types of information nodes, the load calculation method is different, specifically expressed as follows:

[0034]

[0035] k represents the information node index; ω k (t) represents the load of information node k at time t; normalization coefficient z k Indicates the data flow density between information nodes; Represents a collection of terminal nodes in an information network. Terminal nodes are responsible for collecting production unit data and transmitting it to routing nodes. Represents a collection of routing nodes in an information network. Routing nodes must not only forward their own data but also process data from other nodes. Represents the collection of gateway nodes in the information network. Gateway nodes are responsible for uploading the data of routing nodes to the cloud. l，k (t) indicates whether the routing path from node l to the gateway passes through node k at time t. If it passes through h l,k (t)=1, otherwise h l，k (t)=0.

[0036] 5. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein the state perception modeling module in step 4 uses a probability matrix to characterize the perception error to reflect the impact of the information node load on the perception accuracy; in this step, a multi-hop path is used to upload data. The higher the path node load, the greater the perception error, which is specifically expressed as:

[0037]

[0038] ω k (t) represents the information node load; Q k Indicates link capacity; The accuracy of data transmission when the load of information nodes does not exceed the capacity; b k represents the minimum transmission accuracy of the information node in the tolerable overload phase; ε k Indicates the tolerable load factor of the information node.

[0039] The overall perception probability matrix B corresponding to the perception pathl The details are as follows:

[0040]

[0041] Among them, B l，k is the error probability matrix of the observation signal of the production unit when it passes through node k; H l (t) represents the set of all information nodes passed through on the observation path of production unit l; the (i, o)th element in the matrix represents the probability of observing o when the actual state is i.

[0042] 6. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein the decision control module in step 5 determines the production rate of a production unit based on its observed value, constructs a productivity control model, and slows down equipment degradation while meeting system production requirements; the control model is expressed as follows:

[0043]

[0044] The constraints are as follows:

[0045]

[0046] in, represents the actual output function of the system; D represents the minimum output demand threshold set by the system; γ l (t) represents the production rate of production unit 1 at time t; l (t) represents the current observed state of production unit l; represents the maximum capacity of the production unit under observation; if the observation error causes the production rate to exceed the capacity of the production unit, a penalty coefficient ζ is applied l >1, accelerating its degradation.

[0047] 7. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein the capacity evaluation module in step 6 compares the current output with the preset capacity requirement to determine whether the system meets the operating target; if not, the system is deemed to be faulty; and the system reliability is defined as follows:

[0048]

[0049] Among them, R s (t) represents the reliability of the system at time t; The actual output capacity of the system is determined by the production capacity of all production units; D represents the minimum output demand threshold set by the system. Then the system is considered to have failed at time t.

[0050] 8. The modular Petri net-based IoT system reliability assessment method according to claim 1, characterized in that step 7 is specifically represented as follows: by repeating steps 2 to 6, in order to quantitatively assess the reliability performance of the constructed model under different structural configurations and operating conditions, this step, based on the modeling completed in steps 1 to 6, performs multiple Petri net simulation runs to observe the output performance and failure behavior of the system during time evolution, and then evaluates the overall reliability index of the system. The specific operation process includes the following:

[0051] Repeat steps 2 to 6, recording the system failure moment in each simulation;

[0052] The proportion of the system that has not failed before time t under all simulation samples is counted, which is the reliability at that moment;

[0053] Get the system reliability-time evolution curve R s (t), used to guide equipment maintenance and production scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The present invention provides a method for reliability assessment and system decision optimization of an Internet of Things system based on modular Petri nets.

[0055] Figure 2 Schematic diagram of the cyber-physical network connection of the system in an embodiment of the present invention Figure 1

[0056] Figure 3 Schematic diagram of the PN model for production unit state transition.

[0057] Figure 4 Schematic diagram of the PN model for information node state transfer.

[0058] Figure 5 Schematic diagram of the PN model for information network connectivity verification.

[0059] Figure 6 Schematic diagram of the PN model for information network load distribution.

[0060] Figure 7 Schematic diagram of the PN model for system status monitoring.

[0061] Figure 8 Schematic diagram of the PN subnet used for production decision-making.

[0062] Figure 9 is the productivity distribution of the manufacturing system.

[0063] Figure 10 The system reliability at different production rates. DETAILED DESCRIPTION

[0064] The technical solution of the invention is further described below with reference to the accompanying drawings and embodiments.

[0065] Step 1: Construct the initial system state of the Internet of Things in the intelligent manufacturing system. Based on the performance level of the production unit and the functional state of the information node, a Petri net model is established to define the state, transfer relationship and initial identification of each unit.

[0066] Step 2: Establish an information network connectivity check module to determine the connectivity and isolation status of each node based on the network topology and node fault status, and simulate the network disconnection propagation mechanism through the inhibition arc mechanism in the Petri net;

[0067] Step 3: Build an information load distribution and overload detection module to distribute data load according to node connectivity and routing path traffic, and determine whether a node enters an overload range or triggers a failover.

[0068] Step 4: Establish a system status monitoring module, calculate the information transmission accuracy based on the load path and node performance, construct a state observation probability matrix, and map the error between the actual state and the observed state in the form of probability transition;

[0069] Step 5: Build a production decision module. Based on the current state observation results, set the production rate of each production unit through the optimization model and map the control instructions to the production instruction path that may fail.

[0070] Step 6: Build a capacity assessment module to match the instruction execution results with the current unit capacity, calculate the actual output of the system, determine whether it meets the set capacity requirements, and decide whether to record a system failure;

[0071] Step 7: Repeat the above process and run multiple Petri net simulations to observe the output performance and failure behavior of the system during time evolution, and then evaluate the overall reliability index of the system.

[0072] This step is based on the modular Petri net method to formally model the structural hierarchy of the Internet of Things system, focusing on the dual dynamic process of the physical production system and the information transmission network, and constructing its initial operating state, laying a unified modeling foundation for subsequent degradation analysis, load calculation and control optimization. In this embodiment, an intelligent manufacturing system model consisting of 8 production units and 12 information nodes is used as the Internet of Things system object, such as Figure 2 As shown in Figure 1. The production unit includes multiple physical functional modules such as machining, welding, transportation, and assembly; the information nodes include terminal collection nodes, relay routing nodes, and cloud gateway nodes. The system topology is represented by the binding matrix A∈{0,1} 8×12 , each element ωk Indicates whether there is a connection between production unit l and information node k. The system parameters are shown in Tables 1 to 3:

[0073] Table 1 Production capacity of each production unit (10 work-in-progress / hour)

[0074] Table 2 Transfer intensity of production unit (0.01 times / month)

[0075] Table 3 Information node parameters

[0076] This case sets three production scenarios:

[0077] Scenario 1: Production scenario with degraded cyber-physical system coupling

[0078] Scenario 2: Assume the information network always operates perfectly, with only production units deteriorating during operation. In this scenario, the true state of the production units is fully accessible, allowing optimal production instructions to be executed. This scenario is indeed a common reliability assessment model for manufacturing systems without an information network.

[0079] Scenario 3: Assume that the production unit always operates perfectly, and only the information nodes deteriorate during operation. In this scenario, the decline in production performance of the manufacturing system is entirely due to the degradation of the information network. Although this scenario does not exist in practice, it is intended to illustrate the impact of information network degradation on the production performance of the manufacturing system.

[0080] Step 11: System hierarchical structure modeling: Divide the system into two main levels:

[0081] Physical layer network G P =(V P , E P ): It consists of multiple production units with production capacity, each node l∈V P Corresponding to a production device, it has state evolution capability and control input;

[0082] Information Layer Network G I =(V I , E I ): It consists of multiple information collection and transmission nodes, node k∈V I Including roles such as terminal nodes, routing nodes, and gateway nodes, responsible for data collection, transmission, and reporting;

[0083] Binding mapping matrix A = [a lk ]: used to indicate the connection between production unit l and information node k. If there is a connection, then alk =, otherwise it is 0.

[0084] Step 12, modular Petri net construction method: According to the above system structure, a modular Petri net model N = (User, T, F, W, M0) is constructed, where P corresponds to the status bit of the physical unit, the function bit of the information node and the communication connectivity bit respectively; T represents event-driven state changes, including device degradation, communication interruption, perception error, instruction triggering, etc.; F represents the causal relationship between position and change; W represents the number of tokens used in the change; M0 is the initial identification distribution, which is used to define the initial state configuration of the system operation.

[0085] In order to ensure the scalability and reusability of the model, the present invention adopts the following modular modeling strategy to establish three module structures, namely, physical unit subnet module, information node subnet module, and cross-domain interaction interface.

[0086] Physical unit subnet module: Each production unit is modeled separately, including multiple status bits (for example: healthy, slightly degraded, severely degraded, and failed) and their corresponding migration paths, supporting process modeling such as degradation, maintenance, and recovery. Figure 3 As shown;

[0087] Information node subnet module: Construct different functional subnets according to the node type, including: terminal node: mainly contains data generation bit and sending bit; routing node: contains cache bit, forwarding bit and congestion status bit; gateway node: contains reporting bit and relay control bit, such as Figure 4 shown.

[0088] Cross-domain interaction interface: The physical unit status bit is connected to the information node binding bit through a special "shared location" or "synchronous transition", representing coupling mechanisms such as state perception and control signal input.

[0089] Step 13. Initial state definition: Based on the system's initial deployment and operating condition configuration, assign a number of tokens to each position in M0: for the physical unit status bit, only set one token at its initial health state position to indicate normal operation; for the information node function bit, set tokens based on its initial health status to indicate whether it is invalid; for the cross-domain interaction position, the initialization token indicates whether the perception link and control channel are established.

[0090] 3. Establish an information network connectivity check module to determine the connectivity and isolation status of each node based on the network topology and node fault status, and simulate the network disconnection propagation mechanism through the inhibition arc mechanism in the Petri net, as follows:

[0091] Aiming at the state evolution of production units in intelligent manufacturing systems, a Petri net structure with probability transition is constructed. l states, numbered from 1 to m t , where state i=1 indicates a good state, state i=m l Indicates a complete failure state. According to the production rate γ of the production unit l (t), the transition probability of its state from i to a worse state j (j>i) (normal production instruction) is defined as follows:

[0092]

[0093]

[0094] Among them, α l (γ l (t))∈[0,1] is the weighted coefficient related to productivity, which increases with γ l (t) monotonically increasing; represents the nominal degradation rate of the production unit at maximum production rate;

[0095] If the production unit is in the state of executing abnormal production instructions, its state transition probability is affected by the abnormal acceleration coefficient ζ l > 1, the abnormal state activates the corresponding abnormal degradation transition through the identification site in the Petri net, and the probability calculation method of transferring from state i to j (j > i) is specifically expressed as:

[0096]

[0097] 4. Build an information load distribution and overload detection module to distribute data load based on node connectivity and routing path traffic, and determine whether a node enters an overload range or triggers a failover.

[0098]

[0099] k represents the information node index; ω k (t) represents the load of information node k at time t; normalization coefficient z k Indicates the data flow density between information nodes; Represents a collection of terminal nodes in an information network. Terminal nodes are responsible for collecting production unit data and transmitting it to routing nodes. Represents a collection of routing nodes in an information network. Routing nodes must not only forward their own data but also process data from other nodes. Represents the collection of gateway nodes in the information network. Gateway nodes are responsible for uploading the data of routing nodes to the cloud. l,k(t) indicates whether the routing path from node l to the gateway passes through node k at time t. If it passes through h l，k (t)=1, otherwise h l,k (t)=0.

[0100] 5. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein the state perception modeling module in step 4 uses a probability matrix to characterize the perception error to reflect the impact of information node load on perception accuracy; in this step, a multi-hop path is used to upload data. The higher the path node load, the greater the perception error, which is specifically expressed as:

[0101]

[0102] ω k (t) represents the information node load; Q k Indicates link capacity; The accuracy of data transmission when the load of information nodes does not exceed the capacity; b k represents the minimum transmission accuracy of the information node in the tolerable overload phase; ε k Indicates the tolerable load factor of the information node.

[0103] The overall perception probability matrix B corresponding to the perception path l The details are as follows:

[0104]

[0105] Among them, B l，k is the error probability matrix of the observation signal of production unit l when passing through node k; H l (t) represents the set of all information nodes passed through on the observation path of production unit l; the (i, o)th element in the matrix represents the probability of observing o when the actual state is i.

[0106] 6. The method for evaluating the reliability of an Internet of Things system based on a modular Peri-net according to claim 1, wherein the decision control module in step 5 determines the production rate of a production unit based on its observed value and constructs a productivity control model to slow down equipment degradation while meeting system production requirements; the control model is expressed as follows:

[0107]

[0108] The constraints are as follows:

[0109]

[0110] in, represents the actual output function of the system; D represents the minimum output demand threshold set by the system; γl (t) represents the production rate of production unit 1 at time t; l (t) represents the current observed state of production unit l; represents the maximum capacity of the production unit under observation; if the observation error causes the production rate to exceed the capacity of the production unit, a penalty coefficient ζ is applied l >1, accelerating its degradation.

[0111] 7. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein the capacity evaluation module in step 6 compares the current output with the preset capacity requirement to determine whether the system meets the operating target; if not, the system is deemed to be faulty; and the system reliability is defined as follows:

[0112]

[0113] Among them, R s (t) represents the reliability of the system at time t; Represents the actual output capacity of the system, which is determined by the production capacity of all production units; D represents the minimum output demand threshold set by the system. Then the system is considered to have failed at time t.

[0114] 8. The reliability assessment method of the Internet of Things system based on modular Petri nets according to claim 1 is to quantitatively assess the reliability performance of the system in long-term operation. This step completes the modeling of steps 1 to 6, performs multiple Petri net simulations, and records whether the system's production capacity at different time points meets the production demand D. Based on this, a reliability time evolution curve is constructed, such as Figure 10 As shown in the figure, the reliability performance of the system is different under different production targets. In the period from 0 to 5 months, the difference in system reliability is small, indicating that the system degradation in the short term is not significant. When the operation time is greater than 20 months, the system reliability decreases significantly with the increase of production targets.

[0115] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A reliability assessment method for IoT systems based on modular Petri nets, with the following specific steps: Step 1: Construct the initial system state of the Internet of Things in the intelligent manufacturing system. Based on the performance level of the production unit and the functional state of the information node, a Petri net model is established to define the state, transfer relationship and initial identification of each unit. Step 2: Establish an information network connectivity check module to determine the connectivity and isolation status of each node based on the network topology and node fault status, and simulate the network disconnection propagation mechanism through the inhibition arc mechanism in the Petri net; Step 3: Build an information load distribution and overload detection module to distribute data load based on node connectivity and routing path traffic, and determine whether a node enters an overload range or triggers a failover. Step 4: Establish a system status monitoring module, calculate the information transmission accuracy based on the load path and node performance, construct a state observation probability matrix, and map the error between the actual state and the observed state in the form of probability transition; Step 5: Build a production decision module. Based on the current state observation results, set the production rate of each production unit through the optimization model and map the control instructions to the production instruction path that may fail. Step 6: Build a capacity assessment module to match the instruction execution results with the current unit capacity, calculate the actual output of the system, determine whether it meets the set capacity requirements, and decide whether to record a system failure; Step 7: Repeat the above process and run multiple Petri net simulations to observe the output performance and failure behavior of the system during time evolution, and then evaluate the overall reliability indicators of the system.

2. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, characterized in that: The step 1 is specifically as follows: This step uses a modular Petri net approach to formally model the structural hierarchy of the IoT system, focusing on representing the dual dynamic processes of the physical production system and the information transmission network. It also constructs its initial operating state, laying a unified modeling foundation for subsequent degradation analysis, load calculation, and control optimization. Step 11: System hierarchical structure modeling: Divide the system into two main layers: physical layer network G P =(V P , E P ): It consists of multiple production units with production capacity, each node l∈V P Corresponding to a production device, it has state evolution capability and control input; information layer network G I =(V I , E I ): It consists of multiple information collection and transmission nodes, node k∈V I Including terminal nodes, routing nodes, gateway nodes and other roles, responsible for data collection, transmission and reporting tasks; the mapping matrix A = [a lk ]: used to indicate the connection relationship between production unit l and information node k. If there is a connection, then a lk =1, otherwise 0; Step 12: Modular Petri net model construction: Based on the above system structure, a modular Petri net model N = (P, T, F, W, M0) is constructed, where P represents the state bit corresponding to the physical unit, the function bit of the information node, and the communication connectivity bit; T represents event-driven state changes, including device degradation, communication interruption, perception error, instruction triggering, etc.; F represents the causal relationship between position and transition; W represents the number of tokens used in the transition; M0 is the initial identifier distribution, which is used to define the initial state configuration of the system operation. To ensure the scalability and reusability of the model, the present invention adopts the following modular modeling strategy to establish three modular structures: physical unit subnet module, information node subnet module, and cross-domain interaction interface. Physical unit subnet module: Each production unit is individually modeled, including multiple status bits (for example, healthy, slightly degraded, severely degraded, and failed) and their corresponding transition paths, supporting process modeling for degradation, maintenance, and recovery. Information node subnet module: Different functional subnets are constructed based on node type, including: terminal nodes: mainly including data generation bits and transmission bits; routing nodes: including cache bits, forwarding bits, and congestion status bits; gateway nodes: including reporting bits and relay control bits. Cross-domain interaction interface: The physical unit status bits are connected to the information node binding bits through special "shared locations" or "synchronous transitions", representing coupling mechanisms such as state perception and control signal input. Step 13. Initial state definition: Based on the system's initial deployment and operating condition configuration, assign a number of tokens to each position in M0: for the physical unit status bit, only set one token at its initial health state position to indicate normal operation; for the information node function bit, set tokens based on its initial health status to indicate whether it is invalid; for the cross-domain interaction position, the initialization token indicates whether the perception link and control channel are established.

3. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein: The step 2 is specifically as follows: Aiming at the state evolution of production units in intelligent manufacturing systems, a Petri net structure with probabilistic transition is constructed. l states, numbered from 1 to m l , where state i=1 indicates a good state, state i=m l Indicates a complete failure state. According to the production rate γ of the production unit l (t), the transition probability of its state from i to a worse state j (j>i) (normal production instruction) is defined as follows, where α l (γ l (t))∈[0,1] is the weighted coefficient related to productivity, which increases with γ l (t) monotonically increasing; Shows the nominal degradation rate of the production unit at maximum production rate:

4. If the production unit is in the state of executing abnormal production instructions, its state transition probability is affected by the abnormal acceleration coefficient ζ l The abnormal state activates the corresponding abnormal degradation transition through the identification site in the Petri net. The probability calculation method of transferring from state i to j (j>i) is specifically expressed as:

5. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1 is characterized in that the specific implementation method of step 3 is: By considering information nodes as binary components, describing their lifetimes with probability density functions, and expressing data processing capabilities with normalization coefficients and throughput, the load is calculated based on the characteristics of different types of nodes and information load distribution is considered to analyze the impact of node load on data transmission accuracy. For different types of information nodes, the load calculation method is different, specifically expressed as, where, k represents the information node index; ω k (t) represents the load of information node k at time t; normalization coefficient z k Indicates the data flow density between information nodes; Represents a collection of terminal nodes in an information network. Terminal nodes are responsible for collecting production unit data and transmitting it to routing nodes. Represents a collection of routing nodes in an information network. Routing nodes must not only forward their own data but also process data from other nodes. Represents the collection of gateway nodes in the information network. Gateway nodes are responsible for uploading the data of routing nodes to the cloud. l，k (t) indicates whether the routing path from node l to the gateway passes through node k at time t. If it passes through h l，k (t)=1, otherwise h l，k (t) = 0:

6. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein: The state perception modeling module in step 4 uses a probability matrix to characterize the perception error to reflect the impact of the information node load on the perception accuracy. In this step, a multi-hop path is used to upload data. The higher the path node load, the greater the perception error. Specifically, it is expressed as follows: k (t) represents the information node load; Q k Indicates link capacity; The accuracy of data transmission when the load of the information node does not exceed the capacity; b. k represents the minimum transmission accuracy of the information node in the tolerable overload phase; ε k Indicates the tolerable load factor of the information node:

7. Overall perception probability matrix B corresponding to the perception path l The details are as follows, among which, B l，k is the error probability matrix of the observation signal of unit l when passing through node k; H l (t) represents the set of all information nodes passed through on the observation path of unit l; the (i, o)th element in the matrix represents the probability of observing o when the true state is i:

8. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein: The decision control module in step 5 determines the production rate of the production unit based on the observed value, and constructs a productivity control model to slow down equipment degradation while meeting the production requirements of the system. The control model is expressed as follows, where: represents the actual output function of the system; D represents the minimum output demand threshold set by the system; γ l (t) represents the production rate of unit 1 at time t; l (t) represents the current observation state of unit l; represents the maximum bearable production rate of the production unit under the observation state; if the observation error causes the production rate to exceed the production capacity, a penalty coefficient ζ is applied l >1, accelerating its degradation: The constraints are as follows:

9. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein: The capacity assessment module in step 6 determines whether the system meets the operation target by comparing the current output with the preset capacity demand; if not, the system is considered to be faulty. The system reliability is defined as follows, where R s (t) represents the reliability of the system at time t; Represents the actual output capacity of the system, which is determined by the production capacity of all production units; D represents the minimum output demand threshold set by the system. Then the system is considered to have failed at time t:

10. The method for evaluating the reliability of an Internet of Things system based on a modular Petri net according to claim 1, wherein: The specific representation of step 7 is as follows: by repeating steps 2 to 6, in order to quantitatively evaluate the reliability performance of the constructed model under different structural configurations and operating conditions, this step, based on the modeling completed in steps 1 to 6, performs multiple Petri net simulations to observe the output performance and failure behavior of the system during time evolution, and then evaluates the overall reliability index of the system. The specific operation process includes the following: repeating steps 2 to 6, recording the time of system failure in each simulation; counting the proportion of systems that have not failed before time t under all simulation samples, which is the reliability at that time; obtaining the system reliability-time evolution curve R s (t), used to guide equipment maintenance and production scheduling.

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