A coating distributed closed-loop control method and system based on multi-agent cooperation

Abstract

The application discloses a coating distributed closed-loop control method and system based on multi-agent cooperation, relates to the technical field of multi-agent cooperative control and causal reasoning control, and comprises the following steps: constructing a multi-agent, collecting a local observation state of the multi-agent; establishing a directed acyclic causal graph of a state variable based on a PC algorithm, calculating a causal strength coefficient, extracting a strong causal link, forming a cross-unit state conduction chain; when a state is abnormal, a root cause agent is located reversely along the conduction chain, a pre-compensation adjustment amount based on a causal strength and a state deviation is generated, and the pre-compensation adjustment amount is issued to downstream agents to superimpose local control instructions, and meanwhile, a state update causal relationship is returned in real time, so that distributed closed-loop regulation and control are realized. The application can realize causal tracing and cooperative control of a multivariable coupling process, and improves system response speed and control precision.

Description

Technical Field

[0001] This invention relates to the field of multi-agent cooperative control and causal reasoning control technology, and in particular to a coating distributed closed-loop control method and system based on multi-agent cooperation. Background Technology

[0002] With the rapid development of industries such as lithium battery electrode manufacturing, functional thin film processing, and high-end coating material preparation, coating production lines are evolving towards higher speed, continuous operation, and higher consistency. In this process, coating quality is not only affected by single process parameters but also by the coupled effects of multiple factors, including slurry supply stability, coating head output uniformity, drying heat field distribution, tension control accuracy, and correction response capability, exhibiting significant multivariate strong coupling and time-varying nonlinear characteristics. Traditional coating control methods are mostly based on centralized control architectures or local closed-loop adjustment strategies, achieving local optimal control by independently regulating key variables such as tension, speed, or temperature. However, these methods often ignore the cross-process influence mechanisms between different process units and lack the ability to model the inherent causal relationships between multi-source state variables. This makes it difficult to identify the source of anomalies and perform feedforward compensation adjustments in a timely manner during complex operating conditions or disturbance propagation. Furthermore, with the expansion of production line scale and the increase in equipment heterogeneity, centralized control methods are gradually showing bottlenecks in terms of real-time performance, robustness, and scalability, making it difficult to meet the requirements of high-end coating processes for refined and adaptive control.

[0003] CN120507997B discloses a sludge drying process control system based on coating backmixing. This system acquires material state information through a multi-source sensor array and combines a multi-agent decision-making mechanism with a Nash equilibrium arbitration strategy to achieve closed-loop control during the drying process. While this method incorporates multi-agent collaboration to some extent and achieves multi-objective coordinated control through Pareto optimization, its core focus is on optimization allocation at the risk analysis and strategy generation levels. It lacks explicit modeling of the causal structure between state variables, particularly failing to construct interpretable cross-unit state transmission paths. This makes it difficult to achieve accurate source tracing and pre-compensation control based on causal links when system states become abnormal. The control strategy relies more on global optimization than structured causal reasoning, limiting its applicability in highly dynamically coupled coating scenarios.

[0004] CN119644925A proposes a precise control method for transmission tension in a printing film coating production line. This method combines a DCS and PLC system to implement PID closed-loop control at each transmission point. It also constructs a dual closed-loop system for speed and tension using a frequency converter and encoder, achieving synchronous control and tension stability among multiple drive points. While this method demonstrates high maturity in engineering applications, its control mechanism primarily relies on preset models and feedback adjustment, lacking in-depth analysis of the dynamic relationships between multiple variables within the system. In particular, it fails to consider the coupling and propagation effects between variables such as coating speed, slurry viscosity, and oven load, making it difficult to achieve cross-unit coordinated response in the early stages of disturbances and unable to achieve predictive adjustment based on global state evolution trends. Consequently, it still suffers from response lag and limited adjustment accuracy under complex operating conditions. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section, as well as in the abstract and title of the present application, to avoid obscuring the purpose of this section, the abstract and title of the invention. Such simplifications or omissions shall not be used to limit the scope of the present invention.

[0006] In view of the problems in existing coating production line control technology, such as insufficient coordination among multiple process units, unclear causal relationships between state variables, and difficulty in accurately tracing the source of disturbance, this invention is proposed.

[0007] Therefore, the problem to be solved by this invention is how to construct a collaborative control mechanism with causal reasoning ability in a multivariate strongly coupled coating process, so as to realize cross-unit state transmission path identification and root cause-based pre-compensation adjustment.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, embodiments of the present invention provide a coating distributed closed-loop control method based on multi-agent cooperation, comprising, Construct a multi-agent system for the coating production line and collect local observation data of the multi-agent system. The multi-agent system includes a slurry supply agent, a coating head agent, an oven agent, a tension agent, a deviation correction agent, and a line inspection agent. The PC algorithm is used to construct a directed acyclic causal graph for the state variables of each agent, and the local observation state is used as the node variable of the causal graph to calculate the causal strength coefficient between the node variables. Based on the causal strength coefficient, a causal strength threshold is set. Directed edges in the directed acyclic causal graph with a causal strength coefficient greater than or equal to the causal strength threshold are marked as strong causal links. The state transmission paths between agents are extracted along the strong causal links to form cross-unit state transmission chains. When the local observation state of any agent deviates from the preset normal range, it is traced back to the root agent along the cross-unit state transmission chain, and the root agent sends the pre-compensation adjustment amount to the downstream agents. After receiving the pre-compensation adjustment amount, each downstream agent adds the pre-compensation adjustment amount to the local closed-loop control command, and transmits the adjusted local observation state back to the directed acyclic causal graph in real time to update the causal strength coefficient, thus completing the distributed closed-loop control of the coating production line.

[0009] Secondly, embodiments of the present invention provide a coating distributed closed-loop control system based on multi-agent cooperation, comprising: The multi-agent construction and status acquisition module is used to construct multi-agents in the coating production line and acquire the local observation status of the multi-agents. The multi-agents include a slurry supply agent, a coating head agent, an oven agent, a tension agent, a deviation correction agent, and a line inspection agent. The causal graph construction and strength calculation module is used to construct a directed acyclic causal graph for the state variables of each agent using the PC algorithm, and to calculate the causal strength coefficient between each node variable using the local observation state as the node variable of the causal graph. The strong causal link extraction module is used to set a causal strength threshold based on the causal strength coefficient, mark the directed edges in the directed acyclic causal graph with a causal strength coefficient greater than or equal to the causal strength threshold as strong causal links, and extract the state transmission path between each agent along the strong causal link to form a cross-unit state transmission chain. The root cause tracing and pre-compensation generation module is used to trace back to the root cause agent along the cross-unit state transmission chain when the local observation state of any agent deviates from the preset normal range, and the root cause agent sends the pre-compensation adjustment amount to the downstream agents. The distributed closed-loop control and dynamic update module is used by each downstream agent to receive the pre-compensation adjustment amount, add the pre-compensation adjustment amount to the local closed-loop control command, and transmit the adjusted local observation state back to the directed acyclic causal graph in real time to update the causal strength coefficient, thereby completing the distributed closed-loop control of the coating production line.

[0010] Thirdly, embodiments of the present invention provide a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement any step of the above-described coating distributed closed-loop control method based on multi-agent cooperation.

[0011] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the above-described coating distributed closed-loop control method based on multi-agent cooperation.

[0012] Compared with existing technologies, the beneficial effects of this invention are as follows: By constructing a multi-agent system including agents for slurry supply, coating head, oven, tension, correction, and line inspection, and collecting the local observation states of each agent, distributed perception and modular modeling of key process links in the coating production line are achieved. This solves the problem that traditional centralized control cannot simultaneously handle multi-variable coupling and real-time response, thereby improving the system's adaptability and scalability to complex working conditions. Furthermore, a PC algorithm is used to construct a directed acyclic causal graph for the state variables of each agent, and the nonlinear time-delay causal weights are calculated based on transfer entropy and then normalized. The causal strength coefficient step enables the quantitative identification and structured expression of dynamic causal relationships among multiple variables in a nonlinear, long-time-delay coating process. It makes implicit process coupling relationships explicit into a computable graphical model, avoiding misadjustments and oscillations caused by empirical judgments. By setting a causal strength threshold to extract strong causal links and then extracting state transmission paths along these links to form cross-unit state transmission chains, the step achieves reduction and focusing from the global causal graph to key influence paths. This preserves the dominant causal backbone in the process, eliminates weak correlations and noise interference, and thus constructs a high-confidence model. The disturbance propagation channel significantly reduces the computational redundancy and communication load of the control system. When the state of any agent deviates from the preset range, the process traces back to the root agent along the cross-unit state transmission chain, and the root agent sends the pre-compensation adjustment amount downstream. This achieves rapid location of the disturbance source and feedforward collaborative adjustment, transforming the passive response in traditional feedback control into active prediction based on causal paths. This effectively shortens the disturbance propagation path and suppresses chain fluctuations between multiple agents. At the same time, the pre-compensation adjustment amount is calculated based on the product of the causal strength coefficient and the local observed state deviation value, realizing adaptive matching of the causal weight of the adjustment amplitude and avoiding over-adjustment or under-adjustment. Each downstream agent adds the pre-compensation adjustment amount to the local closed-loop control command and sends back the adjusted local observed state in real time to update the causal strength coefficient. This ensures the stability of each execution unit while completing global collaborative optimization. Through the dynamic update of the causal strength coefficient, the causal model can adaptively track process drift and operating condition changes, ensuring the long-term effectiveness and robustness of the control strategy. Overall, this achieves high-precision and high-stability distributed closed-loop control of the coating production line under multivariable coupling and nonlinear time delay conditions. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of a coating distributed closed-loop control method based on multi-agent collaboration. Detailed Implementation

[0014] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0015] Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort should fall within the scope of protection of this invention.

[0016] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0017] As mentioned in the background section, existing methods mostly rely on local closed-loop or empirical models, lacking modeling and utilization of global state evolution relationships, making it difficult to meet the high-precision control requirements under complex operating conditions. To address these issues, this invention provides a coating distributed closed-loop control method based on multi-agent cooperation.

[0018] Reference Figure 1 , Figure 1 This is a flowchart of a coating distributed closed-loop control method based on multi-agent cooperation according to an embodiment of the present invention. Figure 1 As shown, a coating distributed closed-loop control method based on multi-agent cooperation includes: S1: Construct a multi-agent system for the coating production line and collect the local observation status of the multi-agent system, including coating speed, slurry viscosity, oven load rate and tension deviation value. S1.1: Based on the process flow of the coating production line, the production line is divided into a slurry supply station, a coating head station, an oven station, a tension station, a deviation correction station, and a line inspection station. Corresponding control nodes are deployed at each station, and each control node is configured as an independent decision-making unit to obtain a multi-agent system. The multi-agent system includes a slurry supply agent, a coating head agent, an oven agent, a tension agent, a deviation correction agent, and a line inspection agent. Specifically, the slurry supply intelligence is deployed at the slurry pump and slurry delivery pipeline nodes, responsible for local sensing of slurry flow rate and pressure; the coating head intelligence is deployed at the coating die head, responsible for local sensing of coating gap and coating speed; the oven intelligence is deployed at each oven temperature zone controller, responsible for local sensing of heating power and oven load rate for each temperature zone; the tension intelligence is deployed at each tension roller sensor node, responsible for local sensing of tension deviation; the correction intelligence is deployed at the correction actuator, responsible for local sensing of substrate lateral offset; and the online inspection intelligence is deployed at the online inspection instrument, responsible for local sensing of coating thickness and appearance defect data. S1.2: Configure a local data acquisition module on the multi-agent to synchronously collect process variables of each station according to a unified sampling period to form a local observation status; Furthermore, the sampling period is set to 100ms; the coating speed is calculated from the encoder signal at the coating head station, in m / min; the slurry viscosity is measured in real time by the online viscometer at the slurry supply station, in mPa·s; the oven load rate is calculated from the ratio of the actual heating power to the rated heating power of each temperature zone at the oven station, with a value range of 0 to 1; the tension deviation value is obtained by subtracting the tension sensor measurement value from the tension set value at the tension station, in N. S1.3: Perform timestamp alignment and outlier removal on the local observation states, and arrange the local observation states of each agent according to the acquisition timestamp to construct a multi-dimensional time-series state matrix; Furthermore, timestamp alignment employs a linear interpolation method to uniformly interpolate the local observation states of different agents that are inconsistent in their collection times to the whole sampling period. Outlier removal uses the 3σ criterion, calculating the mean and standard deviation within a sliding window for coating speed, slurry viscosity, oven load rate, and tension deviation values. Sampling points that deviate from the mean by more than 3 times the standard deviation are replaced with the window mean. The sliding window length is set to 30 sampling points. After timestamp alignment and outlier removal, the coating speed, slurry viscosity, oven load rate, and tension deviation values ​​are concatenated column by column to form a multidimensional time-series state matrix. The row index of the multidimensional time-series state matrix represents the sampling time, and the column indices correspond to the state variables of the slurry supply agent, coating head agent, oven agent, tension agent, correction agent, and line inspection agent, respectively. S2: The PC algorithm is used to construct a directed acyclic causal graph for the state variables of each agent, and the local observation state is used as the node variable of the causal graph to calculate the causal strength coefficient between the node variables. S2.1: Using coating speed, slurry viscosity, oven load rate and tension deviation value in the multidimensional time-series state matrix as node variables, construct a set of node variables, and initialize a completely undirected graph with the set of node variables; It should be noted that there is an undirected edge between every two node variables in a completely undirected graph; the number of nodes in a completely undirected graph is the same as the number of columns in the multidimensional temporal state matrix, and the nodes correspond to the state variables of the slurry supply agent, coating head agent, oven agent, tension agent, correction agent, and line inspection agent in sequence; the edge set of a completely undirected graph is initialized to the undirected edges between all node variables, and the total number of edges is the number of nodes multiplied by the number of nodes minus one and then divided by two; S2.2: For each undirected edge in a completely undirected graph, the kernel conditional independence test algorithm is used to calculate the nonlinear unconditional partial correlation statistic of the two node variables connected at both ends of the undirected edge under the zero-order condition set. The nonlinear unconditional partial correlation statistic is compared with the preset independence test threshold. If the nonlinear unconditional partial correlation statistic is less than the preset independence test threshold, the two node variables are determined to be independent, and the corresponding undirected edge is deleted from the completely undirected graph. Specifically, the kernel conditional independence test algorithm is based on the regenerating kernel Hilbert space theory. It measures the nonlinear statistical dependence between node variables through the inner product operation of the kernel matrix. Compared with the limitation of the traditional Fisher Z-transform, which is only applicable to the linear Gaussian assumption, the kernel conditional independence test algorithm can identify the nonlinear conditional independence relationship between coating speed and tension deviation value. It should be noted that the preset independence test threshold is set to 0.05. This value is determined based on the significance level of hypothesis testing in statistics. In the kernel conditional independence test, this threshold corresponds to the critical probability of rejecting the null hypothesis (i.e., the two node variables are independent under a given condition set). By calculating the p-value corresponding to the kernel conditional independence test statistic, if the p-value is less than 0.05, it is considered that there is a statistical dependence between the two variables at a 95% confidence level. S2.3: After deleting some undirected edges in the completely undirected graph, the order of the condition set is increased by the breadth-first search algorithm. The kernel conditional independence test algorithm is then used to calculate the nonlinear conditional partial correlation metric of the two node variables corresponding to the remaining undirected edges under the higher-order condition set. The nonlinear conditional partial correlation metric is compared with the preset independence test threshold. If the nonlinear conditional partial correlation metric is less than the preset independence test threshold, the corresponding undirected edge is deleted, and the current higher-order condition set is recorded as a separation set. The higher-order condition set test is iteratively performed until there is no neighbor node set that meets the order requirement, and the skeleton undirected graph is obtained. Preferably, the order of the condition set is gradually increased from zero, with each increment being one step; the separation set is stored in dictionary form with node variable pairs as index keys and the corresponding condition set content as values; the sample size of the multidimensional time-series state matrix is ​​no less than 300 sampling points to ensure the statistical test power of the kernel conditional independence test algorithm. S2.4: Traverse the non-closed triplet structure in the skeleton undirected graph, find the separation set, and if the center node variable does not belong to the corresponding separation set, convert the two undirected edges in the non-closed triplet structure into first-class directed edges that both point to the center node variable, and generate a partially directed graph. In an optional embodiment, for any three node variables A, B, and C in the skeleton undirected graph, if there is an undirected edge between A and B, an undirected edge between B and C, and no undirected edge between A and C, then A, B, and C constitute a non-closed triplet structure with B as the central node variable; when the central node variable B does not belong to the separating set corresponding to A and C, then the first type of directed edges pointing from A to B and from C to B are written into the partially directed graph; when the automatic orientation result conflicts with the physical causal prior knowledge of the coating production line process, the physical causal prior knowledge is used to cover the automatic orientation result. It should be noted that the non-closed triplet structure contains three node variables, two of which are not adjacent but have a common central node variable; the physical causal prior knowledge includes changes in slurry pressure preceding the coating gap response and changes in coating speed preceding the oven load rate response. S2.5: Based on the Meck direction deduction rule sequence, the remaining undirected edges in a partially directed graph are oriented, the remaining undirected edges are converted into second-type directed edges, and the first-type directed edges and the second-type directed edges are collectively referred to as topological directed edges, thus obtaining a directed acyclic causal graph. Furthermore, the Makek direction deduction rule sequence includes the directed collision structure principle and the directed closed-loop principle. The directed collision structure principle states that if orienting an undirected edge to a certain direction would introduce a new collision structure in a part of the directed graph, then it should be oriented to the opposite direction. The directed closed-loop principle states that if orienting an undirected edge to a certain direction would form a directed loop in a part of the directed graph, then it should be oriented to the opposite direction. For undirected edges whose direction cannot be determined after orienting by the Makek direction deduction rule sequence, manual orientation is performed based on prior knowledge of physical causality. S2.6: Extract the source node variable data sequence and target node variable data sequence corresponding to each topological directed edge in the directed acyclic causal graph, and calculate the transfer entropy values ​​of the source node variable data sequence and target node variable data sequence. Record the time delay step corresponding to the maximum transfer entropy value as the nonlinear time delay causal weight of the topological directed edge. Furthermore, both the source node variable data sequences and the target node variable data sequences are extracted from the corresponding columns of the multidimensional time-series state matrix; the time delay step size of the time delay sliding window set is set to range from one sampling period to thirty sampling periods, with a step size interval of one sampling period; the calculation of the transfer entropy value adopts a non-parametric method based on kernel density estimation to eliminate the influence of the non-Gaussian distribution characteristics between slurry viscosity and oven load rate on the numerical estimation of transfer entropy; the physical conduction delay time is obtained by multiplying the time delay step size in the nonlinear time delay causality weight by the sampling period. In an optional embodiment, when the transfer entropy values ​​at each time delay step within the time delay sliding window set are all lower than the transfer entropy significance threshold, the nonlinear time delay causal weight of the corresponding topological directed edge is recorded as zero. The transfer entropy significance threshold is determined by calculating the 95th percentile of the transfer entropy value after performing a time-series random permutation on the multidimensional time-series state matrix. S2.7: Obtain the nonlinear time-delay causal weights of all topological directed edges in the directed acyclic causal graph, use the minimax normalization function to perform linear mapping calculation on all nonlinear time-delay causal weights to obtain the causal strength coefficient, and bind the causal strength coefficient as a weight attribute to the corresponding topological directed edge. Store the directed acyclic causal graph and the corresponding causal strength coefficient in the form of an adjacency matrix. Specifically, the minimax normalization function is calculated as follows: subtract the minimum value among all nonlinear time delay causality weights of all topological directed edges from the nonlinear time delay causality weight of a certain topological directed edge, and then divide by the difference between the maximum and minimum values ​​among all nonlinear time delay causality weights of all topological directed edges to obtain the corresponding causality strength coefficient; the row and column indices of the adjacency matrix correspond to the column indices of the multidimensional temporal state matrix, and the value at the intersection of the row and column is the causality strength coefficient of the corresponding topological directed edge. Node variables without topological directed edges are recorded as zero for their corresponding adjacency matrix elements; the causality strength coefficient ranges from [0, 1]. S3: Set the causal strength threshold based on the causal strength coefficient, mark the directed edges in the directed acyclic causal graph with a causal strength coefficient greater than or equal to the causal strength threshold as strong causal links, and extract the state transmission path between agents along the strong causal links to form a cross-unit state transmission chain. S3.1: Extract all non-zero causal strength coefficients from the adjacency matrix, calculate the mean and standard deviation of all non-zero causal strength coefficients, and set the value obtained by adding one standard deviation to the mean as the causal strength threshold. Furthermore, when all non-zero causal strength coefficients in the adjacency matrix are less than the causal strength threshold, the topological directed edge corresponding to the largest causal strength coefficient among all non-zero causal strength coefficients is retained as a strong causal link to prevent the situation where no strong causal link can be extracted from the directed acyclic causal graph; if all non-zero causal strength coefficients are greater than or equal to the causal strength threshold, the upper quartile of all non-zero causal strength coefficients is taken as the new causal strength threshold, and the strong causal link screening is re-executed to ensure that the extracted set of strong causal links has sufficient sparsity and representativeness, and to avoid affecting the physical interpretability of the state propagation path due to excessive link density; the causal strength threshold is periodically recalculated with the update of the multidimensional temporal state matrix, and the triggering condition for recalculation is consistent with the update period of the adjacency matrix in step S2.7; S3.2: Traverse all topological directed edges in the adjacency matrix, mark topological directed edges with causal strength coefficients greater than or equal to the causal strength threshold as strong causal links, and mark topological directed edges with causal strength coefficients less than the causal strength threshold as weak causal links, thus obtaining the set of strong causal links and the set of weak causal links. Preferably, the set of strong causal links is stored in the form of ordered node variable pairs. Each ordered node variable pair consists of a start node variable and a stop node variable, and is accompanied by the corresponding causal strength coefficient value and the time delay step recorded in the nonlinear time delay causal weight. The set of strong causal links and the set of weak causal links together cover all non-zero topological directed edges in the adjacency matrix. S3.3: Using the slurry supply agent, coating head agent, oven agent, tension agent, correction agent, and line inspection agent as graph nodes, and the ordered node variable pairs in the strong causal link set as directed edges, a strong causal subgraph is constructed, where the weight of the directed edge is assigned the corresponding causal strength coefficient. Furthermore, the construction method of strong causal subgraph is as follows: initialize an empty graph, add the start node variable and the end node variable of each ordered node variable pair in the strong causal link set as graph nodes to the empty graph, and add directed edges between the corresponding graph nodes; if the node variable corresponding to an agent in the strong causal link set does not appear in any ordered node variable pair, then this agent is retained in the strong causal subgraph as an isolated node and does not participate in the extraction of subsequent state propagation paths; S3.4: For strong causal subgraphs, a depth-first traversal algorithm is used. Starting from each graph node in the strong causal subgraph, the downstream graph nodes that can be reached are traversed level by level along the direction of the directed edges. All directed paths from the starting graph node to each downstream graph node are extracted. Directed paths with fewer directed edges than the preset number of directed edges are retained to obtain the set of state propagation paths. It should be noted that the depth-first traversal algorithm records the list of visited graph nodes during the traversal process. When a graph node is already present in the list of visited graph nodes, the current traversal branch is terminated. The number of directed edges in the directed path is preset to six, corresponding to the total number of the slurry supply agent, coating head agent, oven agent, tension agent, correction agent, and line inspection agent. Each directed path in the state transmission path set is stored in the form of an ordered graph node sequence, along with a list of causal strength coefficients and time delay steps for each directed edge in the path. S3.5: Calculate the path causality strength product for each directed path in the state transmission path set, and filter and retain directed paths whose path causality strength product is greater than or equal to the path strength threshold to form a cross-unit state transmission chain; Specifically, the path causality strength product is calculated as follows: the causality strength coefficients of each directed edge in the directed path are multiplied sequentially, and the resulting product is the path causality strength product; the path strength threshold is set to the square of the causality strength threshold to maintain dimensional consistency with the causality strength threshold of a single topological directed edge; the cross-unit state transmission chain is stored in the form of an ordered graph node sequence list, where each ordered graph node sequence corresponds to a cross-unit state transmission path, and includes the path causality strength product value and a list of time delay steps for each directed edge in the path; the cross-unit state transmission chains are arranged in descending order of path causality strength product, and the cross-unit state transmission path with the largest path causality strength product is taken as the main transmission chain; S4: When the local observation state of any agent deviates from the preset normal range, it is traced back to the root agent along the cross-unit state transmission chain, and the root agent sends the pre-compensation adjustment amount to the downstream agents. S4.1: Continuously monitor the local observation status of each agent according to the sampling period, and compare the local observation status of each agent at the current sampling time with the corresponding preset normal range to determine whether there are any agents whose local observation status deviates from the preset normal range; It should be noted that the pre-compensation adjustment amount is calculated based on the product of the causality strength coefficient and the deviation value of the local observation state; the preset normal range is obtained from the statistical analysis of historical operating data of the coating production line, and upper and lower limits are set for coating speed, slurry viscosity, oven load rate, and tension deviation value respectively; the preset normal range of coating speed is calculated by adding or subtracting 10% from the process set speed; the preset normal range of slurry viscosity is calculated by adding or subtracting 15% from the process set viscosity; the preset normal range of oven load rate is [0.6, 0.9]; the preset normal range of tension deviation value is set to [-5N, 5N]; the local observation state deviation value is the absolute value of the difference between the current sampled value and the upper or lower limit of the preset normal range that has been exceeded. Furthermore, when the current sampled value of any state variable in the local observation state of an agent is greater than or equal to the upper limit of the corresponding preset normal range or lower than the lower limit of the corresponding preset normal range, it is determined that the local observation state of this agent deviates from the preset normal range, and this agent is marked as a deviation-triggered agent, and the deviation value of the local observation state of the deviation-triggered agent is calculated. In an optional embodiment, when the local observation state of any agent deviates from the preset normal range, the subsequent tracing and compensation process is triggered. However, there are two special cases in actual operation: First, the local observation state of all agents does not deviate from the preset normal range. In this case, there is no need to trigger compensation. The system continues to monitor according to the sampling period and continuously writes the local observation state of each agent into the multi-dimensional time-series state matrix for subsequent periodic updates of the causal intensity coefficient. Second, the local observation state of all agents is outside the preset normal range (i.e., all deviate). In this case, the system will have multiple deviation trigger agents at the same time. The system will sort the deviation values ​​of the local observation states of each deviation trigger agent from large to small and execute the root cause tracing and pre-compensation adjustment sending process of steps S4.2 to S4.5 for each deviation trigger agent in turn. This ensures that the most serious process deviation is responded to first, while avoiding the superposition of multiple compensation commands in the same control cycle, which may cause the actuator to saturate. S4.2: Using the node variable corresponding to the deviation-triggered agent as the termination node, search all cross-unit state transmission paths in the cross-unit state transmission chain with the node variable corresponding to the deviation-triggered agent as the termination node. Backtrack the upstream node variable level by level along the cross-unit state transmission path and mark the agent corresponding to the starting node variable in the cross-unit state transmission path that has no upstream node variable as the root cause candidate agent. Furthermore, the reverse tracing method is as follows: starting from the node variable corresponding to the deviation trigger agent, traverse the upstream node variables in the opposite direction of the topological directed edge in the cross-unit state transmission chain until the node variable with no in-degree topological directed edge in the cross-unit state transmission chain is reached; if the number of cross-unit state transmission paths retrieved is greater than one, then the agents corresponding to the starting node variables of all cross-unit state transmission paths are included in the root cause candidate agent set, and the deviation of each candidate agent's local observation state from the preset normal range median value is calculated, and the agent with the largest deviation is selected as the root cause agent; If the number of cross-unit state propagation paths retrieved is equal to one, then the agent corresponding to the starting node variable of this unique path is directly identified as the root agent. If the number of cross-unit state propagation paths retrieved is zero, that is, there is no cross-unit state propagation path with the node variable corresponding to the deviation trigger agent as the terminating node, then it indicates that this deviation trigger agent itself is the root agent, and its local observed state deviation is caused by local disturbance or unmodeled factors. In this case, the agent itself directly corrects the local closed-loop control command based on the local observed state deviation value, without sending pre-compensation adjustment amounts to other agents. Preferably, if there is only one root cause candidate agent in the root cause candidate agent set, then the root cause candidate agent is directly determined as the root cause agent; if the root cause candidate agent set is empty, then the deviation trigger agent itself is determined as the root cause agent, and there is no need to trace upstream. The deviation trigger agent directly performs local closed-loop control command superposition correction based on its local observation state deviation value; if there are multiple root cause candidate agents in the root cause candidate agent set, then the deviation of the local observation state of each candidate agent from the corresponding preset normal range median value is calculated, and the root cause candidate agent with the largest deviation is selected as the final root cause agent; if the deviation of multiple candidate agents is equal, then the agent that is more upstream in the topological level of the strong causal subgraph (i.e., has an in-degree of zero or a longer path length) is preferentially selected as the root cause agent to reflect the source priority principle of the causal relationship chain. S4.3: Based on the position of the root cause agent in the cross-unit state transmission chain, extract the cross-unit state transmission path with the root cause agent's corresponding node variable as the starting node and the deviation trigger agent's corresponding node variable as the ending node. When there are multiple cross-unit state transmission paths, select the cross-unit state transmission path with the largest path causal strength product, and arrange each downstream agent along the cross-unit state transmission path in the order of the ordered graph node sequence to obtain the downstream agent transmission sequence. Specifically, the downstream agent transmission sequence starts with the root agent and extracts the agents corresponding to each node variable downstream of the root agent in the order of the ordered graph node sequence in the selected cross-unit state transmission path to form an ordered list. The list of causal strength coefficients and time delay step size of the topological directed edges corresponding to each downstream agent in the downstream agent transmission sequence are extracted synchronously from the storage structure of the cross-unit state transmission chain. S4.4: Calculate the pre-compensation adjustment amount sent by the root agent to each downstream agent based on the product of the local observation state deviation value of the root agent and the causal strength coefficient of the topological directed edge corresponding to each downstream agent in the downstream agent transmission sequence. Furthermore, for the first-level downstream agent in the downstream agent transmission sequence, the pre-compensation adjustment amount is the local observation state deviation value of the root agent multiplied by the causal strength coefficient of the topological directed edge from the root agent to the first-level downstream agent; for the second-level and above downstream agents in the downstream agent transmission sequence, the pre-compensation adjustment amount is the local observation state deviation value of the root agent multiplied by the product of the causal strength coefficients of all topological directed edges in the cross-unit state transmission path from the root agent to the downstream agent of that level. It should be noted that the sign of the pre-compensation adjustment amount is determined by the positive or negative sign of the product of the corresponding causal strength coefficients. A positive value indicates that the local closed-loop control commands of the corresponding downstream intelligent agent need to be superimposed in the positive direction, and a negative value indicates that the local closed-loop control commands of the corresponding downstream intelligent agent need to be superimposed in the negative direction. The unit of the pre-compensation adjustment amount is consistent with the unit of the local closed-loop control command of the corresponding downstream intelligent agent and is converted according to the physical dimensions of the state variables of each intelligent agent. S4.5: The root cause agent, based on the physical transmission delay time obtained by multiplying the time delay step of each downstream agent in the downstream agent transmission sequence by the sampling period, sends a pre-compensation adjustment amount to the corresponding downstream agent in advance according to the physical transmission delay time. After receiving the pre-compensation adjustment amount, each downstream agent adds the pre-compensation adjustment amount to the local closed-loop control command to obtain the pre-compensated control command, and outputs it to the actuator of the corresponding workstation. Furthermore, the physical conduction delay time is calculated as follows: the time delay step is multiplied by the sampling period, where the time delay step is extracted from the time delay step list attached to the ordered node variable pairs in the strong causal link set. Specifically, when a downstream agent in the downstream agent transmission sequence still deviates from the preset normal range in the local observation state within three sampling periods after receiving the pre-compensation adjustment amount, the local observation state deviation value of the downstream agent is fed back to the root agent. The root agent then adds the product of the local observation state deviation value and the correction gain coefficient to the original pre-compensation adjustment amount to obtain the corrected pre-compensation adjustment amount. Preferably, the pre-compensated control command is output to the actuator after upper and lower limit processing. The upper and lower limit ranges are determined based on the upper and lower limits of the physical stroke of the actuator at each workstation. The correction gain coefficient is set to 0.5, which is determined based on the response characteristics and stability requirements of the closed-loop control of the coating production line. In industrial control, if the local observation state of a downstream agent still deviates from the preset normal range within three sampling cycles (i.e., 300ms) after receiving the pre-compensation adjustment, it indicates that the original pre-compensation adjustment is undercompensated. The correction gain coefficient is set to 0.5, which means that half of the currently observed residual deviation value is added to the original pre-compensation adjustment value. This can achieve rapid iterative approximation of the compensation value while avoiding... This avoids overshoot or system oscillation caused by excessively large single corrections. The coefficient has been verified through step response tests under actual coating production line conditions. In typical scenarios such as slurry viscosity disturbances and coating speed fluctuations, it can converge the deviation to within the preset normal range within 3 to 5 control cycles, with overshoot not exceeding 15% of the deviation value, balancing the speed of compensation with the robustness of the system. For workstations with large response time constants (such as oven temperature zones), the coefficient can be configured differently for each workstation based on the actual temperature rise rate, but 0.5 as a general default value can cover the dynamic characteristics of most coating production line workstations. After correction, the pre-compensation adjustment amount replaces the original pre-compensation adjustment amount and is resent to the corresponding downstream agent. S5: After receiving the pre-compensation adjustment amount, each downstream intelligent agent adds the pre-compensation adjustment amount to the local closed-loop control command, and sends the adjusted local observation state back to the directed acyclic causal graph in real time to update the causal strength coefficient and complete the distributed closed-loop control of the coating production line. S5.1: In the downstream agent transmission sequence, each downstream agent will superimpose the received pre-compensation adjustment amount with the local closed-loop control command to obtain the pre-compensation control command, and output the pre-compensation control command to the corresponding work station's actuator. Then, according to the sampling period, the local observation state after executing the pre-compensation control command will be continuously collected to obtain the adjusted local observation state. Preferably, the local closed-loop control command is independently calculated by the local PID controller of each downstream intelligent agent based on the deviation between the current local observation state and the process set value; the superposition method of the control command after pre-compensation is to directly add the value of the pre-compensation adjustment amount and the local closed-loop control command, and the superposition result is output to the actuator after upper and lower limit processing. The upper and lower limit ranges are determined based on the upper and lower limits of the physical stroke of the actuator at each station; the local observation state after adjustment includes the coating speed, slurry viscosity, oven load rate and tension deviation value at each sampling time after superimposing the pre-compensation adjustment amount; S5.2: Each downstream agent will timestamp the adjusted local observation state according to the sampling period and send it back to the data aggregation node. The data aggregation node will then concatenate the adjusted local observation states of each agent by column to update the multidimensional time-series state matrix and obtain the updated multidimensional time-series state matrix. Furthermore, when the number of adjusted local observation states accumulated in the queue reaches the sliding window length, the adjusted local observation state corresponding to the latest sliding window length sampling point in the queue replaces the data row of the corresponding time period in the multidimensional time series state matrix to obtain the updated multidimensional time series state matrix. It should be noted that the data aggregation node uses a first-in-first-out queue to cache the adjusted local observation status, and the queue length is set to 600 sampling points; the row index and column index format of the updated multidimensional time series state matrix are consistent with those of the multidimensional time series state matrix. S5.3: Based on the updated multidimensional temporal state matrix, following the kernel conditional independence test algorithm, skeleton undirected graph construction process, collision structure orientation process, Meck direction inference rule sequence and transfer entropy numerical calculation process in step S2, recalculate the causal strength coefficient between each node variable to obtain the updated causal strength coefficient, and write the updated causal strength coefficient into the adjacency matrix to obtain the updated adjacency matrix. Furthermore, the triggering condition for calculating the updated causal strength coefficient is as follows: the cumulative number of newly added sampling points in the updated multidimensional time-series state matrix reaches 300; during the recalculation process, the preset independence test threshold, the range of the time delay sliding window set, and the application rules of physical causal prior knowledge are consistent with those in step S2; the row and column indexes and storage format of the updated adjacency matrix are consistent with those of the adjacency matrix. S5.4: Based on the updated adjacency matrix, recalculate the causal strength threshold according to the causal strength threshold setting method in step S3, re-label the strong causal link set according to the updated causal strength coefficient, and re-extract the cross-unit state transmission chain to obtain the updated cross-unit state transmission chain. Specifically, when the ordered graph node sequence of the main transmission chain in the updated cross-unit state transmission chain changes, the change information is pushed synchronously to each intelligence. Each intelligence updates the transmission path information stored locally according to the updated cross-unit state transmission chain, and the time delay step list attached to each cross-unit state transmission path in the updated cross-unit state transmission chain is updated synchronously. S5.5: Replace the cross-unit state transmission chain with the updated cross-unit state transmission chain, replace the adjacency matrix with the updated adjacency matrix, return to step S4 to perform the detection of the deviation trigger agent and the reverse tracing of the root cause agent, recalculate the pre-compensation adjustment amount based on the updated causal strength coefficient, and form a distributed closed-loop control loop for the coating production line with the core of continuous updating of the updated multi-dimensional temporal state matrix, periodic iteration of the updated causal strength coefficient, and dynamic correction of the updated cross-unit state transmission chain; Preferably, the control period of the distributed closed-loop control loop is consistent with the sampling period, which is 100 milliseconds; the iterative update period of the updated causal strength coefficient is the time length corresponding to 300 sampling points, i.e., 30 seconds; the dynamic correction of the updated cross-unit state transmission chain and the iterative update of the updated causal strength coefficient are triggered synchronously. Furthermore, when the coating production line experiences a product change or speed change, the historical adjusted local observation status in the FIFO queue is cleared, and the FIFO queue is refilled with the latest collected local observation status after the product change or speed change. Once the number of accumulated sampling points in the FIFO queue reaches the sliding window length again, the first recalculation of the updated causal strength coefficient is triggered to adapt to the changes in the causal relationship structure between node variables caused by the changes in the coating production line operating conditions after the product change or speed change.

[0019] In summary, this invention achieves distributed perception and modular modeling of key process steps in the coating production line by constructing a multi-agent system comprising agents for slurry supply, coating head, oven, tension, web correction, and line inspection, and collecting the local observation states of each agent. This solves the problem that traditional centralized control struggles to balance multi-variable coupling and real-time response, thereby improving the system's adaptability and scalability to complex operating conditions. Furthermore, the invention employs a PC algorithm to construct a directed acyclic causal graph of the state variables of each agent, and calculates nonlinear time-delay causal weights based on transfer entropy, then normalizes them to causal strength coefficients. This method achieves quantitative identification and structured expression of dynamic causal relationships among multiple variables in a nonlinear, long-time-delay coating process, making implicit process coupling relationships explicit into a computable graphical model, thus avoiding misadjustments and oscillations caused by empirical judgments. By setting a causal strength threshold to extract strong causal links and extracting state transmission paths along these links to form cross-unit state transmission chains, it achieves reduction and focusing from the global causal graph to key influence paths, retaining the dominant causal backbone in the process and eliminating weak correlations and noise interference, thereby constructing a high-confidence disturbance propagation path. This approach significantly reduces computational redundancy and communication load in the control system. When any agent's state deviates from the preset range, the process traces back along the cross-unit state transmission chain to the root agent, which then sends a pre-compensation adjustment to the downstream. This enables rapid location of the disturbance source and feedforward collaborative adjustment, transforming the passive response in traditional feedback control into proactive prediction based on causal paths. This effectively shortens the disturbance propagation path and suppresses chain fluctuations between multiple agents. Simultaneously, the pre-compensation adjustment is calculated based on the product of the causal strength coefficient and the local observed state deviation, achieving adaptive matching of the causal weight of the adjustment amplitude and avoiding over-adjustment or under-adjustment. Each downstream agent adds the pre-compensation adjustment to the local closed-loop control command and sends back the adjusted local observed state in real time to update the causal strength coefficient. This ensures the stability of each execution unit while achieving global collaborative optimization. The dynamic update of the causal strength coefficient enables the causal model to adaptively track process drift and operating condition changes, ensuring the long-term effectiveness and robustness of the control strategy. Overall, this achieves high-precision, high-stability distributed closed-loop control of the coating production line under multivariable coupling and nonlinear time delay conditions.

[0020] Based on the teachings of the above embodiments, other aspects of the present invention also propose a coating distributed closed-loop control system based on multi-agent cooperation, comprising: The multi-agent construction and status acquisition module is used to construct multi-agents in the coating production line and acquire the local observation status of the multi-agents. The multi-agents include a slurry supply agent, a coating head agent, an oven agent, a tension agent, a deviation correction agent, and a line inspection agent. The causal graph construction and strength calculation module is used to construct a directed acyclic causal graph for the state variables of each agent using the PC algorithm, and to calculate the causal strength coefficient between each node variable using the local observation state as the node variable of the causal graph. The strong causal link extraction module is used to set a causal strength threshold based on the causal strength coefficient, mark the directed edges in the directed acyclic causal graph with a causal strength coefficient greater than or equal to the causal strength threshold as strong causal links, and extract the state transmission path between each agent along the strong causal link to form a cross-unit state transmission chain. The root cause tracing and pre-compensation generation module is used to trace back to the root cause agent along the cross-unit state transmission chain when the local observation state of any agent deviates from the preset normal range, and the root cause agent sends the pre-compensation adjustment amount to the downstream agents. The distributed closed-loop control and dynamic update module is used by each downstream agent to receive the pre-compensation adjustment amount, add the pre-compensation adjustment amount to the local closed-loop control command, and transmit the adjusted local observation state back to the directed acyclic causal graph in real time to update the causal strength coefficient, thereby completing the distributed closed-loop control of the coating production line.

[0021] This embodiment also provides a computer device applicable to the coating distributed closed-loop control method based on multi-agent cooperation, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the coating distributed closed-loop control method based on multi-agent cooperation as proposed in the above embodiment.

[0022] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0023] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the coating distributed closed-loop control method based on multi-agent cooperation as proposed in the above embodiments.

[0024] The storage medium proposed in this embodiment and the data storage method proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0025] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A coating distributed closed-loop control method based on multi-agent cooperation, characterized in that, include: Construct a multi-agent system for the coating production line and collect the local observation status of the multi-agent system, wherein the multi-agent system includes a slurry supply agent, a coating head agent, an oven agent, a tension agent, a deviation correction agent, and a line inspection agent; The PC algorithm is used to construct a directed acyclic causal graph for the state variables of each agent, and the local observation state is used as the node variable of the causal graph to calculate the causal strength coefficient between the node variables. Based on the causal strength coefficient, a causal strength threshold is set, and directed edges in the directed acyclic causal graph with a causal strength coefficient greater than or equal to the causal strength threshold are marked as strong causal links. The state transmission paths between agents are extracted along the strong causal links to form cross-unit state transmission chains. When the local observation state of any agent deviates from the preset normal range, it is traced back to the root agent along the cross-unit state transmission chain, and the root agent sends a pre-compensation adjustment amount to the downstream agents. After receiving the pre-compensation adjustment amount, each downstream agent adds the pre-compensation adjustment amount to the local closed-loop control command and sends the adjusted local observation state back to the directed acyclic causal graph in real time to update the causal strength coefficient, thereby completing the distributed closed-loop control of the coating production line.

2. The coating distributed closed-loop control method based on multi-agent cooperation as described in claim 1, characterized in that, The cross-unit state transmission chain includes: Extract all non-zero causality strength coefficients from the adjacency matrix, calculate the mean and standard deviation of all non-zero causality strength coefficients, and set the value obtained by adding one time the standard deviation to the mean as the causality strength threshold. Traverse all topological directed edges in the adjacency matrix, mark topological directed edges with causal strength coefficients greater than or equal to the causal strength threshold as strong causal links, and mark topological directed edges with causal strength coefficients less than the causal strength threshold as weak causal links, thus obtaining a set of strong causal links and a set of weak causal links. Using the slurry supply agent, the coating head agent, the oven agent, the tension agent, the correction agent, and the line inspection agent as graph nodes, and the ordered node variable pairs in the strong causal link set as directed edges, a strong causal subgraph is constructed, wherein the weight of the directed edge is assigned the corresponding causal strength coefficient. A depth-first traversal algorithm is used for the strong causal subgraph. Starting from each graph node in the strong causal subgraph, the downstream graph nodes that can be reached are traversed level by level along the direction of the directed edges. All directed paths from the starting graph node to each downstream graph node are extracted. Directed paths with fewer directed edges than the preset number of directed edges are retained to obtain the set of state propagation paths. For each directed path in the set of state transmission paths, calculate the path causality strength product, and filter and retain directed paths whose path causality strength product is greater than or equal to the path strength threshold to form a cross-unit state transmission chain.

3. The coating distributed closed-loop control method based on multi-agent cooperation as described in claim 2, characterized in that, The construction of the strong causal subgraph includes: Initialize an empty graph by adding the start and end node variables of each ordered node variable pair in the strong causal link set as graph nodes to the empty graph, and adding directed edges between the corresponding graph nodes. If the node variable corresponding to an agent in the set of strong causal links does not appear in any ordered pair of node variables, then the agent is retained as an isolated node in the strong causal subgraph.

4. The coating distributed closed-loop control method based on multi-agent cooperation as described in claim 2, characterized in that, The pre-compensation adjustment amount is calculated based on the product of the causal intensity coefficient and the deviation value of the local observation state, wherein the local observation state includes coating speed, slurry viscosity, oven load rate and tension deviation value.

5. The coating distributed closed-loop control method based on multi-agent cooperation as described in claim 4, characterized in that, The causality strength coefficient includes: Extract the source node variable data sequence and the target node variable data sequence corresponding to each topological directed edge in the directed acyclic causal graph, and calculate the transfer entropy values ​​of the source node variable data sequence and the target node variable data sequence. Record the time delay step corresponding to the maximum transfer entropy value among the transfer entropy values ​​as the nonlinear time delay causal weight of the topological directed edge. Obtain the nonlinear time-delay causal weights of all topological directed edges in the directed acyclic causal graph, perform linear mapping calculation on all the nonlinear time-delay causal weights using a minimax normalization function to obtain the causal strength coefficients, and bind the causal strength coefficients as weight attributes to the corresponding topological directed edges. Store the directed acyclic causal graph and the corresponding causal strength coefficients in the form of an adjacency matrix.

6. The coating distributed closed-loop control method based on multi-agent cooperation as described in claim 5, characterized in that, The directed acyclic causal graph includes: Using coating speed, slurry viscosity, oven load rate, and tension deviation value in the multidimensional time-series state matrix as node variables, a set of node variables is constructed, and a completely undirected graph is initialized with the set of node variables. For each undirected edge in the completely undirected graph, the kernel conditional independence test algorithm is used to calculate the nonlinear unconditional partial correlation statistic of the two node variables connected at both ends of the undirected edge under the zero-order condition set. The nonlinear unconditional partial correlation statistic is then compared with a preset independence test threshold. If the nonlinear unconditional partial correlation statistic is less than the preset independence test threshold, the two node variables are determined to be independent, and the corresponding undirected edge is deleted from the completely undirected graph. After deleting some undirected edges from the completely undirected graph, the order of the condition set is increased by a breadth-first search algorithm. The kernel conditional independence test algorithm is then used to calculate the nonlinear conditional partial correlation metric of the two node variables corresponding to the remaining undirected edges under the higher-order condition set. The nonlinear conditional partial correlation metric is compared with the preset independence test threshold. If the nonlinear conditional partial correlation metric is less than the preset independence test threshold, the corresponding undirected edge is deleted, and the current higher-order condition set is recorded as a separation set. The higher-order condition set test is iteratively performed until there is no neighbor node set that meets the order requirement, thus obtaining the skeleton undirected graph. Traverse the non-closed triplet structure in the skeleton undirected graph, search for the separation set. If the center node variable does not belong to the corresponding separation set, convert the two undirected edges in the non-closed triplet structure into first-type directed edges that both point to the center node variable, and generate a partially directed graph. Based on the Meck direction inference rule sequence, the remaining undirected edges in the partially directed graph are oriented, and the remaining undirected edges are converted into second-type directed edges. The first-type directed edges and the second-type directed edges are collectively referred to as topological directed edges, resulting in a directed acyclic causal graph.

7. The coating distributed closed-loop control method based on multi-agent cooperation as described in claim 6, characterized in that, The Makek direction deduction rule sequence includes the directed collision structure principle and the directed closed-loop principle. The directed collision structure principle states that if orienting an undirected edge to a certain direction would introduce a new collision structure in the directed graph, then it should be oriented to the opposite direction. The directed closed-loop principle states that if orienting an undirected edge to a certain direction would form a directed loop in the directed graph, then it should be oriented to the opposite direction. Undirected edges whose direction cannot be determined after orienting by the Makek direction deduction rule sequence are manually oriented based on prior knowledge of physical causality.

8. A coating distributed closed-loop control system based on multi-agent cooperation, based on the coating distributed closed-loop control method based on multi-agent cooperation as described in any one of claims 1 to 7, characterized in that, include: The multi-agent construction and status acquisition module is used to construct multi-agents in the coating production line and acquire the local observation status of the multi-agents, wherein the multi-agents include a slurry supply agent, a coating head agent, an oven agent, a tension agent, a deviation correction agent, and a line inspection agent; The causal graph construction and strength calculation module is used to construct a directed acyclic causal graph for the state variables of each agent using the PC algorithm, and to calculate the causal strength coefficient between each node variable using the local observation state as the node variable of the causal graph. The strong causal link extraction module is used to set a causal strength threshold according to the causal strength coefficient, mark the directed edges in the directed acyclic causal graph with a causal strength coefficient greater than or equal to the causal strength threshold as strong causal links, and extract the state transmission path between each agent along the strong causal link to form a cross-unit state transmission chain. The root cause tracing and pre-compensation generation module is used to trace back to the root cause agent along the cross-unit state transmission chain when the local observation state of any agent deviates from the preset normal range, and the root cause agent sends a pre-compensation adjustment amount to the downstream agents. The distributed closed-loop control and dynamic update module is used by each downstream agent to receive the pre-compensation adjustment amount, superimpose the pre-compensation adjustment amount onto the local closed-loop control command, and transmit the adjusted local observation state back to the directed acyclic causal graph in real time to update the causal strength coefficient, thereby completing the distributed closed-loop control of the coating production line.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the coating distributed closed-loop control method based on multi-agent cooperation as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the coating distributed closed-loop control method based on multi-agent cooperation as described in any one of claims 1 to 7.

Images