Industrial wireless network resource scheduling method based on multi-dimensional conflict graph

Abstract

The invention belongs to the technical field of industrial wireless networks, and particularly relates to an industrial wireless network resource scheduling method based on a multi-dimensional conflict graph. The method comprises the following steps: modeling each controlled object into a discrete time linear time-invariant system, and deriving an evolution rule of a remote estimation error covariance along with the growth of information age; constructing a minimization system long-term average estimation error trace optimization problem according to an evolution law, and converting the minimization system long-term average estimation error trace optimization problem into a time slot-by-slot optimization problem; a multi-dimensional conflict graph is constructed, and the time slot-by-slot optimization problem is mapped to the multi-dimensional conflict graph; solving a maximum weight independent set of the multi-dimensional conflict graph to obtain a network resource scheduling scheme; according to the invention, the dynamic distribution of network resources is realized, the long-term average estimation error and information age of the system are effectively reduced, and the overall stability of the system under the condition that the resources are limited is enhanced.

Description

Technical Field

[0001] This invention belongs to the field of industrial wireless network technology, specifically relating to an industrial wireless network resource scheduling method based on a multi-dimensional conflict graph. Background Technology

[0002] Industrial wireless networks are a key infrastructure for realizing the Industrial Internet of Things (IIoT) and "smart factories." One of their core tasks is to reliably and promptly transmit measurement data (such as temperature, pressure, and vibration) collected by sensors to remote controllers or state estimators. This data is used to monitor and control physical processes in real time, and its timeliness and accuracy are directly related to production safety, efficiency, and product quality.

[0003] In the field of state estimation, Kalman filtering is widely used due to its optimal estimation characteristics. However, in resource-constrained industrial wireless multi-hop networks, limited communication resources (time slots, channels) prevent remote estimators from continuously obtaining the latest data updates from all sensors. Information age (AoI) is an important indicator of data freshness. In state estimation scenarios, information age determines the magnitude of the estimation error: when new data is successfully received, the estimator performs a Kalman filter update, and the estimation error converges; conversely, the estimator can only perform time prediction, leading to "inflation" of the estimation error. Existing scheduling methods have the following shortcomings in multi-hop networks:

[0004] 1) Most studies focus on optimizing the information age itself, rather than directly relating it to the system's state estimation error;

[0005] 2) There is a lack of a joint optimization framework that combines communication scheduling with the evolution of estimation errors;

[0006] 3) Complex conflict constraints exist in multi-hop networks, and existing methods struggle to achieve efficient scheduling with limited computing resources.

[0007] Therefore, there is an urgent need for an efficient scheduling method that can directly optimize the accuracy of remote state estimation and is applicable to multi-hop networks. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention proposes a resource scheduling method for industrial wireless networks based on a multi-dimensional conflict graph. This method includes:

[0009] S1: Model each controlled object as a discrete-time linear time-invariant system and derive the evolution law of the long-range estimation error covariance as the information age increases;

[0010] S2: Based on the evolution law, construct the optimization problem of minimizing the long-term average estimation error trace of the system and transform it into a time-slot-by-time optimization problem;

[0011] S3: Construct a multidimensional conflict graph and map the time-slot optimization problem onto the multidimensional conflict graph;

[0012] S4: Solve for the maximum weighted independent set in the multidimensional conflict graph to obtain the network resource scheduling scheme.

[0013] Preferably, the state-space equation of a discrete-time linear time-invariant system is expressed as:

[0014]

[0015] in, This represents the system state vector of data stream f in time slot t+1. Represents the system state transition matrix. This represents the system state vector of data stream f in time slot t. This represents the process noise of data stream f in time slot t. This represents the sensor's observation vector of the data stream f. Represents the observation matrix. This represents the measurement noise of the data stream f in time slot t.

[0016] Preferably, the evolution of the long-range estimation error covariance with the age of the information is expressed as follows:

[0017]

[0018] in, This represents the long-range estimation error covariance matrix of data stream f in time slot t. This represents the number of time slots since the estimator last successfully received a data packet from data stream f. The system state transition matrix represents the data flow f. Represents the steady-state covariance matrix. Let f be the process noise covariance matrix of the data stream f.

[0019] Preferably, the optimization problem of minimizing the long-run average estimation error trace of the system is expressed as:

[0020]

[0021] in, Indicates a time period. Indicates the current information age Below, the additional error caused by a single transmission failure relative to a successful transmission. This represents the information age of data stream f in time slot t. It expresses expectation.

[0022] The preferred time-slot optimization problem is expressed as:

[0023]

[0024] in, Represents data stream At the current scheduled hop count h, the link transmission success rate is... Indicates the current information age The following is the additional error caused by a single transmission failure relative to a successful one.

[0025] Preferably, step S3 specifically includes:

[0026] Defined as a four-dimensional tuple For nodes in a multidimensional conflict graph, This indicates that the h-th hop link of the scheduled data stream f is transmitted on time slot t and channel c;

[0027] The edges of a multidimensional conflict graph are constructed according to at least one conflict rule, where an edge indicates that there is a conflict between two scheduling tuples.

[0028] Assign weights to each node in the multidimensional conflict graph based on the time-slot optimization problem.

[0029] Furthermore, the conflict rules include:

[0030] Co-channel interference conflict: If two links are within each other's interference range and are allocated the same time slot and the same channel, then there is an edge between their corresponding nodes;

[0031] Radio frequency conflict: If two scheduled tasks share the same network node (as a transmitter or receiver) and are assigned the same time slot, then there is an edge between their corresponding nodes;

[0032] Link duplication scheduling conflict: If two nodes correspond to the same hop link of the same data flow, then there is an edge between these two nodes;

[0033] Link scheduling order conflict: For the same data flow, if the hop count of a node i is... Greater than the number of hops corresponding to another node j However, the time slot allocated to node i However, it is less than or equal to the time slot allocated to node j. If there is an edge between these two nodes, then there is an edge between them.

[0034] Furthermore, the formula for assigning weights to each node in the multidimensional conflict graph is as follows:

[0035]

[0036] in, This represents the weight of node v. Represents data stream At the current scheduled hop count h, the link transmission success rate is... Indicates the current information age Below, the additional error caused by a single transmission failure relative to a successful transmission. This represents the information age of data stream f in time slot t.

[0037] Preferably, the process of finding the maximum weighted independent set of a multidimensional conflict graph includes:

[0038] S41: Initialize the independent set S to be empty; current multidimensional conflict graph. This is the original conflict diagram;

[0039] S42: If If the node set is empty, output the independent set S; otherwise, execute S43.

[0040] S43: Calculate a multidimensional conflict graph The degree of each node is determined, and a node is selected based on its degree and weight. And add it to the independent set S;

[0041] S44: From Remove node Update and all its neighboring nodes For the next iteration, the current multidimensional conflict graph Then return to step S42.

[0042] Further, select nodes The formula is:

[0043]

[0044] in, This represents the node selected during the i-th iteration. Representing nodes in a multidimensional conflict graph The weight value, Represents the multidimensional conflict graph of the i-th iteration. The set of nodes, Represents a node Multidimensional conflict graph in the i-th iteration The degree of.

[0045] The beneficial effects of this invention are as follows:

[0046] 1. This invention directly combines communication scheduling with the evolution law of Kalman filter estimation error, and directly suppresses the growth of estimation error by optimizing the scheduling strategy, thereby realizing deterministic scheduling of industrial wireless networks.

[0047] 2. This invention proposes a weight design based on error increment, which enables scheduling decisions to prioritize serving the controlled objects whose estimation errors grow the fastest, thereby achieving optimal allocation of communication resources, effectively reducing the long-term average estimation error and information age of the system, and enhancing the overall stability of the system under resource-constrained conditions.

[0048] 3. The multidimensional conflict graph model and greedy scheduling algorithm designed in this invention can effectively solve complex conflict constraint problems in multi-hop networks within polynomial time complexity, and are suitable for large-scale industrial wireless networks. Attached Figure Description

[0049] Figure 1 This is a flowchart of the industrial wireless network resource scheduling method based on a multidimensional conflict graph in this invention;

[0050] Figure 2 This is a network topology diagram of a preferred embodiment of the present invention;

[0051] Figure 3 This is a schematic diagram illustrating the evolution of the estimation error over time in a preferred embodiment of the present invention. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] This invention proposes a resource scheduling method for industrial wireless networks based on a multi-dimensional conflict graph, such as... Figure 1 As shown, the method includes the following:

[0054] S1: Model each controlled object as a discrete-time linear time-invariant system and derive the evolution law of the long-range estimation error covariance as the information age increases.

[0055] For each controlled object, it is modeled as a discrete-time linear time-invariant system, and its state-space equation is expressed as:

[0056]

[0057] in, This represents the system state vector of data stream f in time slot t+1. Represents the system state transition matrix. This represents the system state vector of data stream f in time slot t. This represents the process noise of data stream f in time slot t. This represents the sensor's observation vector of the data stream f. Represents the observation matrix. This represents the measurement noise of the data stream f in time slot t.

[0058] The remote estimator alternately performs Kalman filtering updates or time predictions based on whether sensor measurement data is successfully received, and derives the evolution law of the remote estimation error covariance with the age of the information, specifically:

[0059] Define two operating modes for the remote estimator based on packet reception status: when observation data is successfully received. When no data is received, the estimator performs a Kalman filter update to obtain the posterior estimation error covariance; when no data is received, the estimator only makes time predictions based on the system model.

[0060] The steady-state error covariance matrix of the long-range Kalman filter is calculated by solving the discrete-time algebraic Riccati equation, denoted as . When an update is successfully received, its remote error covariance matrix will be reset to... The definition is as follows:

[0061]

[0062] in, This represents the long-range estimation error covariance matrix of data stream f in time slot t+1. Indicates the data packet reception status in time slot t ( This indicates successful reception. (Indicates reception failure); Let f be the system state transition matrix for data flow f. Let f be the process noise covariance matrix of the data stream f.

[0063] Define the information age of data stream f in time slot t as: That is, the number of time slots since the remote estimator last successfully received the data packets of this stream. Then the recursive relationship of AoI is:

[0064]

[0065] in, This indicates whether the data stream f was successfully transmitted; 1 indicates success and 0 indicates failure.

[0066] Establish information age With the remote estimation error covariance matrix The evolutionary relationship, assuming data flow The most recent successful update occurred at [time]. From time Initially, there are no observation updates, and predictions continue until time t. The evolution of the long-range estimation error covariance with the age of the information can be expressed by the following formula:

[0067]

[0068] in, Let represent the long-range estimation error covariance matrix of data stream f in time slot t. Let f denote the steady-state error covariance matrix of the data stream f.

[0069] S2: Based on the evolution law, construct the optimization problem of minimizing the long-term average estimation error trace of the system and transform it into a time-slot optimization problem.

[0070] Define the error trace function Then the expected error trace for time slot t+1 is:

[0071]

[0072] in, For end-to-end transmission success rate, Let f be the maximum number of hops in the data stream. It expresses expectation.

[0073] Define the estimation error increment as Its physical meaning is the amount of additional error that will result from the failure of the current time slot scheduling compared to its success.

[0074] Based on this, the long-term optimization objective of the system is to minimize the average error of all data streams, that is:

[0075]

[0076] in, Indicates a time period. This indicates that the average performance is considered over an infinite time period.

[0077] By approximating the problem in each time slot and ignoring constant terms irrelevant to the current decision, the optimization problem of minimizing the long-term average estimation error trace of the system is transformed into an instantaneous optimization problem that maximizes the "expected error reduction" of all data streams in each time slot, i.e., a time-slot optimization problem, expressed as:

[0078]

[0079] in, Represents data stream At the current scheduled hop count h, the link transmission success rate is... Let be the error increment function, representing the time slot t, i.e., the current information age. The objective function is defined as the increase in estimation error (scalar) caused by a single transmission failure relative to a successful transmission. The physical meaning of this objective function is to prioritize data streams that would result in the largest increase in estimation error if a transmission failure occurs, thereby avoiding the most severe performance loss through scheduling decisions.

[0080] S3: Construct a multidimensional conflict graph and map the time-slot optimization problem onto the multidimensional conflict graph.

[0081] Based on network topology, data flow routing, and resource constraints, a multidimensional conflict graph is constructed, and then the time-slot optimization problem is mapped onto the multidimensional conflict graph; specifically:

[0082] Step 1: Define as a four-dimensional tuple For nodes in a multidimensional conflict graph, This indicates that the h-th hop link of the scheduled data stream f is transmitted on time slot t and channel c.

[0083] Step 2: Construct the edges of a multidimensional conflict graph based on at least one conflict rule. An edge represents a conflict between two scheduling tuples. Conflict rules include:

[0084] Co-channel interference conflict: If two links are within each other's interference range and are allocated the same time slot and the same channel, then there is an edge between their corresponding nodes;

[0085] Radio frequency conflict: If two scheduled tasks share the same network node (as a transmitter or receiver) and are assigned the same time slot, then there is an edge between their corresponding nodes;

[0086] Link duplication scheduling conflict: If two nodes correspond to the same hop link of the same data flow, then there is an edge between these two nodes;

[0087] Link scheduling order conflict: For the same data flow, if the hop count of a node i is... Greater than the number of hops corresponding to another node j However, the time slot allocated to node i However, it is less than or equal to the time slot allocated to node j. If there is an edge between these two nodes, then there is an edge between them.

[0088] Based on the above conflict rules, a multi-dimensional conflict diagram can be constructed. ,in It is a set of scheduling nodes, containing all possible scheduling tasks. It is a set of edges, representing which scheduled tasks conflict and cannot be executed in the same time slot. Each node in the graph represents a scheduling tuple, and an edge indicates a conflict between two scheduling tuples.

[0089]

[0090] From the global conflict diagram In this context, select all scheduled tasks v=(f,h,t,c) in the current time slot t. These tasks include all scheduled tasks for all data streams in the current time slot t.

[0091] Step 3: Assign weights to each node in the multidimensional conflict graph based on the time-slot optimization problem.

[0092] The formula for assigning weights to each node in a multidimensional conflict graph is:

[0093]

[0094] in, This represents the weight of node v. Represents data stream The link transmission success rate at the current scheduled hop count h.

[0095] S4: Solve for the maximum weighted independent set in the multidimensional conflict graph to obtain the network resource scheduling scheme.

[0096] In order to give the set Allocating a collision-free time slot and channel to all data stream links in the (data stream set) requires analyzing the collision graph. Find the largest independent set. For ease of subsequent representation, a binary variable is introduced. To represent the conflict diagram The Middle Nodes Is it in the conflict diagram? The largest independent set, The definition of is:

[0097]

[0098] In practical industrial wireless networks, the number of available channels within a time slot is limited, denoted as 𝑀. To ensure resource finiteness, each time slot can schedule at most M flows. Therefore, the elements in the largest independent set found in the conflict graph correspond to the time slot and channel allocation results of the data flow links. The conflict graph... The number of elements in the maximally independent set equals the number of available channels. The constraint is defined by the following formula:

[0099]

[0100] Based on the preceding analysis, the model for the optimization scheduling problem can be obtained as follows:

[0101]

[0102] For any node The corresponding node weight is .

[0103] Solving the above optimization scheduling problem is equivalent to solving the maximum weighted independent set of a multidimensional conflict graph. The solution process includes:

[0104] S41: Initialize the independent set S to be empty; current multidimensional conflict graph. This is the original conflict diagram;

[0105] S42: If If the node set is empty, output the independent set S; otherwise, execute S43.

[0106] S43: Calculate a multidimensional conflict graph The degree of each node is determined, and a node is selected based on its degree and weight. And add it to the independent set S, that is, update the independent set. ;

[0107] Select node The formula is:

[0108]

[0109] in, This represents the node selected during the i-th iteration. Representing nodes in a multidimensional conflict graph The weight value, Represents the multidimensional conflict graph of the i-th iteration. The set of nodes, Represents a node Multidimensional conflict graph in the i-th iteration The degree of.

[0110] S44: From Remove node Update and all its neighboring nodes For the next iteration, the current multidimensional conflict graph Then return to step S42.

[0111] The pseudocode for finding the maximum weighted independent set is as follows:

[0112] The final output is the largest weighted independent set S, which is the network resource scheduling scheme.

[0113] Simulation verification of the present invention:

[0114] A specific preferred embodiment of the present invention was verified. Figure 2 The network topology of this embodiment is shown. Figure 3This demonstrates how the estimation error trace of a typical data stream changes over time after applying the method of this invention. From Figure 3 As can be seen, when the estimation error increases, the scheduler will prioritize allocating resources to the data stream so that it can successfully transmit data, thereby performing Kalman filter updates and significantly reducing the estimation error, proving the effectiveness of the present invention.

[0115] In summary, this invention establishes a mathematical relationship between the long-range estimation error covariance and information age; it models the scheduling problem of minimizing the long-term average estimation error as an integer programming model of time slot and channel allocation; and it constructs a four-dimensional conflict graph composed of four-dimensional tuples of data flow-link-time slot-channel, transforming the time slot scheduling and channel allocation problem into a maximum independent set problem and solving it, thereby obtaining the data flow scheduling scheme in the network. This invention realizes the dynamic allocation of network resources, effectively reduces the long-term average estimation error and information age of the system, and enhances the overall stability of the system under resource-constrained conditions.

[0116] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A resource scheduling method for industrial wireless networks based on a multi-dimensional conflict graph, characterized in that, Includes the following steps: S1: Model each controlled object as a discrete-time linear time-invariant system and derive the evolution law of the long-range estimation error covariance as the information age increases; S2: Based on the evolution law, construct the optimization problem of minimizing the long-term average estimation error trace of the system and transform it into a time-slot-by-time optimization problem; S3: Construct a multidimensional conflict graph and map the time-slot optimization problem onto the multidimensional conflict graph; S4: Solve for the maximum weighted independent set in the multidimensional conflict graph to obtain the network resource scheduling scheme.

2. The industrial wireless network resource scheduling method based on a multi-dimensional conflict graph according to claim 1, characterized in that, The state-space equation of a discrete-time linear time-invariant system is expressed as: ； in, This represents the system state vector of data stream f in time slot t+1. Represents the system state transition matrix. This represents the system state vector of data stream f in time slot t. This represents the process noise of data stream f in time slot t. This represents the sensor's observation vector of the data stream f. Represents the observation matrix. This represents the measurement noise of the data stream f in time slot t.

3. The industrial wireless network resource scheduling method based on a multi-dimensional conflict graph according to claim 1, characterized in that, The evolution of the long-range estimation error covariance with the age of the information is expressed as follows: ； in, This represents the long-range estimation error covariance matrix of data stream f in time slot t. This represents the number of time slots since the estimator last successfully received a data packet from data stream f. The system state transition matrix represents the data flow f. Represents the steady-state covariance matrix. Let f be the process noise covariance matrix of the data stream f.

4. The industrial wireless network resource scheduling method based on a multi-dimensional conflict graph according to claim 1, characterized in that, The optimization problem of minimizing the long-run average estimation error trace of the system is expressed as: ； in, Indicates a time period. Indicates the current information age Below, the additional error caused by a single transmission failure relative to a successful transmission. This represents the information age of data stream f in time slot t. It expresses expectation.

5. The industrial wireless network resource scheduling method based on a multi-dimensional conflict graph according to claim 1, characterized in that, The time-slot optimization problem is expressed as: ； in, Represents data stream At the current scheduled hop count h, the link transmission success rate is... Indicates the current information age The following is the additional error caused by a single transmission failure relative to a successful one.

6. The industrial wireless network resource scheduling method based on a multi-dimensional conflict graph according to claim 1, characterized in that, Step S3 specifically includes: Defined as a four-dimensional tuple For nodes in a multidimensional conflict graph, This indicates that the h-th hop link of the scheduled data stream f is transmitted on time slot t and channel c; The edges of a multidimensional conflict graph are constructed according to at least one conflict rule, where an edge indicates that there is a conflict between two scheduling tuples. Assign weights to each node in the multidimensional conflict graph based on the time-slot optimization problem.

7. The industrial wireless network resource scheduling method based on a multi-dimensional conflict graph according to claim 6, characterized in that, Conflict rules include: Co-channel interference conflict: If two links are within each other's interference range and are allocated the same time slot and the same channel, then there is an edge between their corresponding nodes; Radio frequency conflict: If two scheduled tasks share the same network node (as a transmitter or receiver) and are assigned the same time slot, then there is an edge between their corresponding nodes; Link duplication scheduling conflict: If two nodes correspond to the same hop link of the same data flow, then there is an edge between these two nodes; Link scheduling order conflict: For the same data flow, if the hop count of a node i is... Greater than the number of hops corresponding to another node j However, the time slot allocated to node i However, it is less than or equal to the time slot allocated to node j. If there is an edge between these two nodes, then there is an edge between them.

8. A resource scheduling method for industrial wireless networks based on a multi-dimensional conflict graph according to claim 6, characterized in that, The formula for assigning weights to each node in a multidimensional conflict graph is: ； in, This represents the weight of node v. Represents data stream At the current scheduled hop count h, the link transmission success rate is... Indicates the current information age Below, the additional error caused by a single transmission failure relative to a successful transmission. This represents the information age of data stream f in time slot t.

9. The industrial wireless network resource scheduling method based on a multi-dimensional conflict graph according to claim 1, characterized in that, The process of finding the maximum weighted independent set in a multidimensional conflict graph includes: S41: Initialize the independent set S to be empty; current multidimensional conflict graph. This is the original conflict diagram; S42: If If the node set is empty, output the independent set S; otherwise, execute S43. S43: Calculate a multidimensional conflict graph The degree of each node is determined, and a node is selected based on its degree and weight. And add it to the independent set S; S44: From Remove node Update and all its neighboring nodes For the next iteration, the current multidimensional conflict graph Then return to step S42.

10. A resource scheduling method for industrial wireless networks based on a multi-dimensional conflict graph according to claim 9, characterized in that, Select node The formula is: ； in, This represents the node selected during the i-th iteration. Representing nodes in a multidimensional conflict graph The weight value, Represents the multidimensional conflict graph of the i-th iteration. The set of nodes, Represents a node Multidimensional conflict graph in the i-th iteration The degree of.

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