A multi-agent based printing device collaborative maintenance system

The multi-agent collaborative maintenance system enables accurate fault prediction and dynamic resource allocation for printing equipment, overcoming the shortcomings of existing technologies in fault identification and resource allocation, and improving the efficiency and accuracy of the maintenance system.

CN122219863APending Publication Date: 2026-06-16XIAKE DAOLI
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
XIAKE DAOLI
Filing Date
2026-03-05
Publication Date
2026-06-16

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Abstract

The application discloses a kind of based on multi-agent's printing equipment cooperative maintenance system, it is related to office automation equipment maintenance technical field.The problems of printing cluster fault prediction lag and resource allocation rigidification are solved.First, the collected multi-source physical signal is projected to high-dimensional reference space, and the state deviation vector representing the deviation direction is generated by calculating the weighted Mahalanobis distance;Subsequently, the maximum deviation dimension is locked to the fault root cause, the time integral of the cumulative failure probability is calculated by triggering the graph neural network traversal, and the remaining effective work window period is predicted;Then, the maintenance resources are dynamically allocated by initiating bidding tender with window period countdown, and the task migration topology graph is constructed to transfer the task flow to the same ability adjacent node;Finally, the penalty factor is generated based on the state gain residual before and after maintenance to correct the knowledge graph weight in reverse direction.The application constructs a closed-loop maintenance system with self-evolution ability, which significantly improves the overall availability and resource utilization of printing cluster.
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Description

Technical Field

[0001] This invention relates to the field of office automation equipment maintenance technology, specifically a collaborative maintenance system for printing equipment based on multiple agents. Background Technology

[0002] With the acceleration of enterprise digital transformation and the increasing centralization of office operations, the stability of printing clusters, as core nodes in document information flow, is directly related to the business continuity of enterprises. In scenarios such as financial settlement, medical record processing, and large-scale printing centers, printing equipment operates under high load and multi-tasking concurrent conditions for extended periods, with a large number of devices and a dispersed physical distribution. This high-density usage scenario requires the maintenance system not only to ensure the normal operation of individual devices but also to maintain the high availability and throughput efficiency of the entire printing network.

[0003] Current technologies for maintaining and managing printing equipment primarily rely on single-threshold alarms or centralized server polling. This approach has significant technical drawbacks: First, relying solely on threshold judgments for a single physical quantity cannot effectively identify early-stage problems caused by multiple coupled parameters. For example, complex faults such as abnormal vibrations accompanying temperature fluctuations, even when temperatures are within limits, are often missed, leading to unexpected malfunctions. Second, centralized resource scheduling strategies struggle to handle dynamically changing maintenance priorities. They typically allocate resources based on the order of reported repairs, ignoring the difference between the equipment's remaining lifespan and the urgency of the business. This results in critical equipment being shut down for extended periods due to occupied maintenance resources, while non-critical equipment occupies valuable maintenance manpower or spare parts, reducing overall system resource utilization and maintenance response speed. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a collaborative maintenance system for printing equipment based on multiple agents, thus solving the problems mentioned in the background.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a collaborative maintenance system for printing equipment based on multi-agent technology, comprising the following modules: a state perception module, used to collect multi-source physical signals during the operation of the printing equipment and convert them into real-time feature vectors, project the real-time feature vectors onto a pre-set high-dimensional reference state space containing spatial cluster centers of normal operation samples, calculate the weighted Mahalanobis distance of the real-time feature vectors relative to the spatial cluster centers, and generate a device state deviation vector representing the dimensional offset and direction; a graph inference module, used to pre-set a fault evolution knowledge graph representing the physical connection and fault propagation logic of equipment components, analyze the dimension mapping with the largest offset in the device state deviation vector and lock the root cause node of the fault, trigger a depth-first traversal of the graph neural network starting from the root cause node of the fault, calculate the cumulative failure probability of the fault propagating along the connection path, and based on the cumulative failure... The remaining effective working window period for the current equipment is calculated by integrating the time when the probability reaches the critical threshold. The game scheduling module uses the reciprocal of the remaining effective working window period as the core variable of the bidding weight function to initiate a maintenance bidding based on the contract network protocol. It compares the bid values ​​to lock the winning equipment and allocates physical maintenance resources. It retrieves the table of neighboring nodes with the same capabilities of the winning equipment, plans the path for the tasks to be executed to be transferred to idle neighboring nodes, and constructs a task migration topology graph. The execution correction module locks the target equipment to perform maintenance operations based on the bidding results and executes routing instructions to complete task diversion according to the task migration topology graph. After maintenance is completed, a self-test is performed. The state gain residual is obtained by performing differential calculation on the state data before and after maintenance. When the state gain residual is lower than the preset convergence threshold, an edge weight penalty factor is generated to reverse correct the edge weight value of the corresponding propagation path in the fault evolution knowledge graph.

[0006] Furthermore, the process of converting the multi-source physical signals collected during the operation of the printing equipment into real-time feature vectors and projecting these real-time feature vectors onto a pre-set high-dimensional reference state space containing the spatial cluster centers of the normal operation samples is as follows: Short-time Fourier transform is performed on the collected mechanical vibration signals to extract frequency domain amplitude features; time-domain statistical analysis is performed on the motor drive current signals to extract mean and variance features; and trend slope is extracted from the fixing component temperature signals. The frequency domain amplitude features, mean and variance features, and trend slope features are concatenated to form an original high-dimensional vector. A pre-trained principal component analysis projection matrix is ​​then called to perform a dimensionality reduction mapping operation on the original high-dimensional vector to obtain the real-time feature vector located in the low-dimensional manifold space, thus establishing the coordinate position of the real-time feature vector in the reference state space.

[0007] Furthermore, the specific process for calculating the weighted Mahalanobis distance between the real-time feature vector and the spatial cluster center to generate the device state deviation vector representing the dimensional offset and direction is as follows: retrieve the inverse covariance matrix corresponding to the reference state space, calculate the difference vector between the real-time feature vector and the coordinates of the spatial cluster center, perform a quadratic form operation on the difference vector and the inverse covariance matrix, and take the square root to obtain the weighted Mahalanobis distance value; extract the dimensional components in the difference vector, divide each dimensional component by the square root of the diagonal element of the inverse covariance matrix for standardization, and output the device state deviation vector containing the standardized residual values ​​of each dimension and the positive and negative direction signs.

[0008] Furthermore, a fault evolution knowledge graph representing the physical connection and fault propagation logic of equipment components is pre-built. The specific process of parsing the dimension mapping with the largest offset in the equipment state deviation vector and locking the root cause node of the fault is as follows: Construct a directed graph structure with physical component identifiers as nodes and physical connection relationships between components as edges. Establish a mapping table between the dimension index of the equipment state deviation vector and the physical component identifier of the graph node; Take the absolute value of each dimension value in the equipment state deviation vector and sort it in descending order. Select the dimension index with the largest absolute value, retrieve the corresponding physical component identifier through the mapping table, and mark the physical component identifier as the root cause node of the fault.

[0009] Furthermore, the specific process of triggering a depth-first traversal of the graph neural network starting from the root cause node, calculating the cumulative failure probability of the fault propagating along the connection path, and calculating the remaining effective working window of the current device based on the time integral of the cumulative failure probability reaching the critical threshold is as follows: Initialize the traversal stack and push the root cause node onto the top of the stack; query the fault evolution knowledge graph to obtain the topological adjacent nodes of the current node and the corresponding edge weight transfer coefficients; perform a comprehensive operation on the normalized value of the dimension offset corresponding to the root cause node as the initial failure probability and the edge weight transfer coefficients on the connection path to obtain the cumulative failure probability of the adjacent nodes; introduce the Weibull distribution failure density function containing the time variable, use the cumulative failure probability as the pre-coefficient of the function, perform a definite integral operation on the failure density function in the time dimension, and when the integral result reaches the preset critical threshold, extract the value of the upper limit of the integral time variable at this time, and determine the value of the upper limit of the integral time variable as the remaining effective working window.

[0010] Furthermore, the specific process of initiating a maintenance bidding process based on the contract network protocol by using the reciprocal of the remaining effective job window as the core variable of the bidding weight function, and comparing the bid values ​​to lock the winning equipment and allocate physical maintenance resources is as follows: Construct a linear weighted aggregation function containing the reciprocal of the remaining effective job window and the priority value of the print task queue, and define the calculated aggregation result as the equipment bid value; broadcast the task bidding data packet, receive the equipment bid values ​​fed back by multiple printing devices and execute the numerical sorting algorithm, extract the equipment identifier corresponding to the equipment bid value with the largest value in the sorting result, and mark the equipment identifier as the winning equipment; send a mutual exclusion lock command containing a timestamp and resource occupancy public key to the winning equipment, and update the status bit of the corresponding physical maintenance resource in the maintenance resource database to the occupied status.

[0011] Further, the specific process of retrieving the neighboring node table with the same capability of the winning equipment, planning the path for the task to be executed to flow to the idle neighboring node, and constructing the task migration topology graph is as follows: Retrieve the stored equipment capability attribute matrix, using the equipment identifier of the winning equipment as the index row, filter the node identifiers in the matrix that are completely consistent with the winning equipment in terms of printing size, color mode, and resolution parameters, and form a neighboring node table with the same capability; Traverse the real-time load data of each node in the neighboring node table with the same capability, remove nodes whose load data exceeds the safe level, sort the remaining nodes in ascending order of load value, and select the node with the lowest load value as the task receiving end; Establish a directed connection edge with the winning equipment as the source node and the task receiving end as the destination node, and encapsulate the data packet routing address, port number, and transmission protocol of the directed connection edge into a task migration topology graph.

[0012] Furthermore, the logical process of locking the target equipment for maintenance operations based on the bidding results and executing routing instructions to complete task distribution based on the task migration topology is as follows: Parse the resource occupancy public key in the mutual exclusion locking instruction for authentication. After successful authentication, trigger the I / O interrupt program of the winning equipment to pause local print queue input, open the underlying firmware maintenance port for physical maintenance resources to access and perform mechanical calibration or firmware rewriting operations; simultaneously, parse the destination node routing address in the task migration topology, intercept the print data stream in the task queue to be executed, rewrite the TCP / IP packet header of the print data stream, replace the destination IP address with the IP address of the task receiving end, and forward the rewritten print data stream to the task receiving end through a local area network socket.

[0013] Furthermore, after maintenance, a self-test is performed. Differential calculations are performed on the state data before and after maintenance to obtain the state gain residual. When the state gain residual is lower than a preset convergence threshold, an edge weight penalty factor is generated. The logical process of reversing the edge weight values ​​of the corresponding propagation paths in the fault evolution knowledge graph is as follows: Trigger the standard gray-scale ladder test page printing command, synchronously collect the post-test multi-source physical signals during the printing process and generate the post-test feature vector; calculate the weighted Mahalanobis distance difference between the post-test feature vector and the real-time feature vector before maintenance, and define the weighted Mahalanobis distance difference as the state gain residual; compare the state gain residual with the preset convergence threshold. When the state gain residual is less than the convergence threshold, call the nonlinear decay function to generate an edge weight penalty factor with a value between 0 and 1; trace the fault root cause node locked in the graph inference module and its connection path, multiply the original edge weight value on the connection path by the edge weight penalty factor, and perform a weight downgrade update operation.

[0014] The present invention has the following beneficial effects:

[0015] (1) A collaborative maintenance system for printing equipment based on multi-agent technology significantly improves the accuracy and foresight of fault prediction through the collaborative work of a state perception module and a graph inference module. The system uses weighted Mahalanobis distance to process multi-source physical signals, effectively eliminating the dimensional differences of sensor data in different dimensions and accurately quantifying the degree of deviation of the current operating state from the normal sample reference space. By combining a fault evolution knowledge graph and deep traversal of a graph neural network, it can analyze the propagation path of deviation data between components and convert the time integral of the cumulative failure probability into the remaining effective working window. This mechanism transforms traditional passive maintenance after a fault into proactive maintenance based on remaining life prediction, solving the problem that existing technologies are unable to identify complex coupled faults and quantify the remaining life of equipment.

[0016] (2) A collaborative maintenance system for printing equipment based on multi-agent technology optimizes the allocation efficiency of maintenance resources and the system's adaptability through closed-loop control of a game-theoretic scheduling module and an execution correction module. The system uses the reciprocal of the remaining effective job window as the core variable for bidding to establish a market-based resource allocation mechanism based on urgency, ensuring that maintenance resources are prioritized for the equipment most on the verge of failure or with the most urgent business needs. At the same time, the task migration topology graph ensures the continuity of business flow during maintenance. In addition, the differential calculation and edge weight reverse correction mechanism after maintenance enable the system to dynamically adjust the parameters of the fault propagation model according to the actual maintenance effect, solving the problem that the parameters of the existing maintenance model are fixed and difficult to adapt to the decline in diagnostic accuracy caused by equipment aging or environmental changes, thus realizing the self-evolution of the maintenance system.

[0017] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0018] Figure 1 This is a flowchart of a collaborative maintenance system for printing equipment based on multiple agents according to the present invention. Detailed Implementation

[0019] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structure, features and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0020] This application provides a collaborative maintenance system for printing equipment based on multiple agents, which solves the problems of low fault prediction accuracy, mismatch between maintenance response and actual urgency, and rigid resource allocation in existing printing cluster maintenance.

[0021] The overall concept of the solution in this application embodiment is as follows:

[0022] The system first collects multi-source signals such as vibration and current from the printing equipment through the state perception module and converts them into feature vectors. These vectors are then projected onto a reference state space to calculate a weighted Mahalanobis distance, generating a state deviation vector that quantifies the equipment's health status. Next, the graph inference module maps this deviation vector to a fault evolution knowledge graph. A graph neural network is used to infer the fault propagation path and cumulative probability, and the remaining effective operating window of the equipment is calculated accordingly. Then, the game-theoretic scheduling module initiates a maintenance tender based on the reciprocal of this window, locks the winning equipment through a contract network protocol, allocates resources, and simultaneously plans a path to migrate tasks to nearby idle nodes. Finally, the execution correction module performs a self-check after performing maintenance and task diversion. It evaluates the maintenance effect by calculating the state gain residual before and after maintenance, and generates a penalty factor when the residual is below standard, updating the edge weight values ​​in the knowledge graph in reverse, thus completing the closed-loop correction of the system model.

[0023] Please see Figure 1This invention provides a technical solution: a collaborative maintenance system for printing equipment based on multi-agent technology, comprising the following modules: a state perception module, used to collect multi-source physical signals during the operation of the printing equipment and convert them into real-time feature vectors, project the real-time feature vectors onto a pre-set high-dimensional baseline state space containing spatial cluster centers of normal operation samples, calculate the weighted Mahalanobis distance of the real-time feature vectors relative to the spatial cluster centers, and generate a device state deviation vector representing the dimensional offset and direction; a graph inference module, used to pre-set a fault evolution knowledge graph representing the physical connection and fault propagation logic of equipment components, parse the dimension mapping with the largest offset in the device state deviation vector and lock the root cause node of the fault, trigger a depth-first traversal of the graph neural network starting from the root cause node of the fault, calculate the cumulative failure probability of the fault propagating along the connection path, and based on the cumulative failure probability reaching... The time integral of the critical threshold is used to calculate the remaining effective working window of the current equipment; the game scheduling module is used to initiate maintenance bidding based on the contract network protocol by using the reciprocal of the remaining effective working window as the core variable of the bidding weight function, compare the bid values ​​to lock the winning equipment and allocate physical maintenance resources, retrieve the neighboring node table with the same capability of the winning equipment, plan the path of the task to be executed to the idle neighboring node and build the task migration topology; the execution correction module is used to lock the target equipment to perform maintenance operations according to the bidding results, execute routing instructions according to the task migration topology to complete task diversion; after maintenance is completed, a self-test is performed, and the state gain residual is obtained by differential calculation of the state data before and after maintenance. When the state gain residual is lower than the preset convergence threshold, an edge weight penalty factor is generated to reverse correct the edge weight value of the corresponding propagation path in the fault evolution knowledge graph.

[0024] In this implementation scheme, the state perception module serves as the system's data entry point, primarily responsible for establishing the quantitative mapping relationship between the equipment's physical signals and digital features. This module first collects multi-source physical signals such as vibration, current, and temperature during the printing equipment's operation via a sensor network, converting them into real-time feature vectors that can be processed by the algorithm. When generating the state deviation vector, the system uses weighted Mahalanobis distance as a metric. Mahalanobis distance is a statistical distance metric that considers the correlation between data variables and can effectively correct for scale differences caused by different physical dimensions. By calculating the weighted Mahalanobis distance between the real-time feature vector and the cluster centers of the high-dimensional baseline state space of a pre-set normal operation sample, the module can accurately generate a device state deviation vector containing both dimensional offset and offset direction. The technical advantage of this process is that it eliminates the heterogeneity between different sensor data, accurately quantifies the degree of deviation of the current equipment state from the ideal healthy state, and provides a standardized data foundation for subsequent fault inference. The graph inference module utilizes fault evolution knowledge graphs and graph neural network technology to predict fault propagation paths and assess remaining lifetime. This module pre-configures a fault evolution knowledge graph representing the physical connections and fault propagation logic of equipment components. This graph is a structured data model that abstracts equipment components as nodes and connections as edges. The module first analyzes the dimension with the largest offset in the equipment state deviation vector, maps and locks it as the root cause node of the fault, and then triggers a depth-first traversal of the graph neural network starting from that node. During this process, the module calculates the cumulative failure probability of the fault propagating along the component connection path and integrates the trend of this probability over time. When the integration result reaches a critical threshold, the corresponding time length is determined as the remaining effective working window. This technique transforms static fault location into dynamic fault evolution prediction, clarifying the specific time window during which the equipment can continue to work before complete failure, providing precise time basis for emergency repairs and task scheduling. The game-theoretic scheduling module constructs a decentralized resource allocation mechanism based on the Contract Network protocol, aiming to resolve the conflict between maintenance resources and printing tasks. This module uses the reciprocal of the remaining effective job window period calculated by the graph deduction module as the core variable of the bidding weight function. This means that the shorter the remaining window period, the higher the bidding weight of the equipment, and thus the higher the priority in maintenance bidding. The Contract Network protocol is a market-based distributed negotiation strategy that completes task allocation through a bidding, tendering, and winning process. By comparing bid values, the module identifies the winning equipment and allocates physical maintenance resources to it. Simultaneously, it retrieves the list of neighboring nodes with similar capabilities for the winning equipment, plans the path, and constructs a task migration topology graph. This design enables on-demand allocation of maintenance resources, ensuring that the most urgent faults are prioritized, while also guaranteeing the continuity of printing services during maintenance through task migration, avoiding business interruptions caused by single points of failure.The execution correction module is responsible for implementing physical maintenance operations and building a self-learning closed loop for the system. Based on the bidding results, this module identifies the target equipment for maintenance operations and executes routing instructions according to the task migration topology to complete task distribution. After maintenance, the module performs a self-test and performs differential calculations on the state data before and after maintenance to obtain the state gain residual. The state gain residual reflects the actual effect of the maintenance operation on equipment performance recovery. If this residual is lower than a preset convergence threshold, it indicates that the weights of the current propagation path in the fault evolution knowledge graph may be biased. In this case, the module generates an edge weight penalty factor to correct the edge weight values ​​of the corresponding propagation path in the knowledge graph. The technical role of this mechanism is to endow the system with self-correction capabilities, continuously optimizing the parameters of the fault model through feedback from actual maintenance effects, thereby improving the long-term accuracy of the system in diagnosing and predicting equipment faults.

[0025] Specifically, the process of collecting multi-source physical signals from the printing equipment during operation, converting them into real-time feature vectors, and projecting these real-time feature vectors onto a pre-set high-dimensional reference state space containing the spatial cluster centers of the normal operation samples is as follows: Short-time Fourier transform is performed on the collected mechanical vibration signals to extract frequency domain amplitude features; time-domain statistical analysis is performed on the motor drive current signals to extract mean and variance features; and trend slope is extracted from the fixing component temperature signals. The frequency domain amplitude features, mean and variance features, and trend slope features are concatenated to form an original high-dimensional vector. A pre-trained principal component analysis projection matrix is ​​then used to perform a dimensionality reduction mapping operation on the original high-dimensional vector to obtain the real-time feature vector located in the low-dimensional manifold space, thus establishing the coordinate position of the real-time feature vector in the reference state space.

[0026] In this implementation scheme, the state-aware module performs the above steps to address the standardization and fusion problem of multi-source heterogeneous data. For mechanical vibration signals, since the gear meshing and motor rotation of the printer are periodic, the module performs a short-time Fourier transform to convert the time-domain non-stationary signal into a frequency-domain signal, thereby extracting the characteristic frequency amplitude representing mechanical wear. For motor drive current signals, their fluctuations reflect load changes; by calculating the mean and variance through time-domain statistical analysis, the stability of the load can be quantified. For the fixing component temperature signal, its thermal inertia is large, and simple numerical values ​​cannot reflect anomalies; therefore, extracting the trend slope can capture the precursors of thermal runaway due to excessively rapid or slow temperature rise. Subsequently, the module concatenates the above heterogeneous features into an original high-dimensional vector and performs dimensionality reduction using principal component analysis projection matrix. This step removes redundant correlations between features through linear transformation, extracting the most representative principal components. The principal component analysis projection matrix is ​​obtained based on a large number of normal operating samples, and its calculation logic is shown in the following formula: In the above formula, the meanings of each parameter are as follows: The real-time feature vector obtained after dimensionality reduction represents the position of the current device state in the low-dimensional manifold space. : Pre-trained principal component analysis projection matrix, which consists of eigenvectors corresponding to the first k largest eigenvalues ​​of the normal sample covariance matrix; Matrix transpose operator; The original high-dimensional vector formed by splicing contains all the initial features of vibration, current and temperature; The mean vector of the normally operating sample set is used to center the original data. Calculated using this formula, the system maps the high-dimensional and noisy original data into a low-dimensional, compact real-time feature vector, establishing the precise coordinates of the current state in the baseline state space, and providing a standardized mathematical object for subsequent distance calculations.

[0027] Specifically, the process of calculating the weighted Mahalanobis distance between the real-time feature vector and the spatial cluster center to generate the device state deviation vector representing the dimensional offset and direction is as follows: retrieve the inverse covariance matrix corresponding to the reference state space, calculate the difference vector between the real-time feature vector and the coordinates of the spatial cluster center, perform a quadratic form operation on the difference vector and the inverse covariance matrix and take the square root to obtain the weighted Mahalanobis distance value; extract the dimensional components in the difference vector, divide each dimensional component by the square root of the diagonal element of the inverse covariance matrix for standardization, and output the device state deviation vector containing the standardized residual values ​​of each dimension and the positive and negative direction signs.

[0028] In this implementation scheme, the core purpose of calculating the weighted Mahalanobis distance is to eliminate the interference of different physical units on state assessment and to consider the correlation between variables. Since the real-time feature vector contains values ​​in different units such as current (amperes) and temperature (degrees Celsius), directly using Euclidean distance would cause variables with larger values ​​to mask the changes in variables with smaller values. The inverse covariance matrix records the degree of correlation and dispersion among the feature variables under normal conditions. The module first calculates the difference vector between the real-time feature vector and the spatial cluster center, which reflects the absolute distance between the current state and the ideal normal state in each dimension. Subsequently, the inverse covariance matrix is ​​used to perform a weighted operation on this difference vector to obtain the weighted Mahalanobis distance, as shown in the following formula: In the above formula, the meanings of each parameter are as follows: The calculated weighted Mahalanobis distance value is used to quantify the degree of deviation of the overall health of the equipment. The real-time feature vector output from the preceding steps; The spatial cluster center coordinate vector is the geometric center point obtained by cluster analysis of a large number of normal samples. Vector transpose operation; The inverse covariance matrix corresponding to the baseline state space is used to standardize and decorrelate the changes in different dimensions. After obtaining the overall deviation, in order to further pinpoint which specific physical link has an anomaly, the module needs to generate a device state deviation vector. This process involves standardizing and normalizing each dimension of the difference vector, transforming it into a dimensionless Z-score form, calculated as follows: In the above formula, the meanings of each parameter are as follows: : The standardized residual value of the kth dimension in the equipment status deviation vector, whose positive or negative sign represents the direction of deviation (such as temperature being too high or too low), and whose absolute value represents the severity of the anomaly. The value of the k-th dimension in the real-time feature vector; The value of the k-th dimension in the spatial cluster center coordinate vector; The element in the k-th row and k-th column of the inverse covariance matrix represents the reciprocal of the variance of that dimension under normal conditions. Through this step, the system not only determines whether the equipment is malfunctioning, but also outputs the specific direction and components of the malfunction, providing a precise index for the subsequent graph deduction module to pinpoint the root cause of the fault.

[0029] Specifically, the process of pre-setting a fault evolution knowledge graph that represents the physical connection and fault propagation logic of equipment components, parsing the dimension mapping with the largest offset in the equipment state deviation vector, and locking the root cause node of the fault is as follows: Construct a directed graph structure with physical component identifiers as nodes and physical connection relationships between components as edges, and establish a mapping table between the dimension index of the equipment state deviation vector and the physical component identifier of the graph node; Take the absolute value of each dimension value in the equipment state deviation vector and sort it in descending order, select the dimension index with the largest absolute value, retrieve the corresponding physical component identifier through the mapping table, and mark the physical component identifier as the root cause node of the fault.

[0030] In this implementation scheme, the graph deduction module first constructs a fault evolution knowledge graph, aiming to establish topological associations between discrete sensor data and physical entities. This graph is a directed graph structure, where nodes represent specific physical component identifiers, such as fixing rollers, paper feed rollers, or lasers, and directed edges represent physical connections or fault propagation logic between components, such as heat conduction paths or mechanical transmission chains. The module establishes a mapping table to break down the barriers between the data domain and the physical domain, mapping the dimension indices of the equipment state deviation vector generated in the previous steps to nodes in the graph. When identifying the root cause node of the fault, the system follows the maximum deviation principle, considering the dimension with the most severe deviation from the baseline state as the source of the fault. The system takes the absolute value of all dimensions in the equipment state deviation vector and sorts them in descending order, selecting the dimension index with the largest absolute value, and directly locating the corresponding physical component by consulting the mapping table. The technical advantage of this process is to quickly narrow down the fault investigation scope, accurately anchoring macroscopic equipment anomalies to specific microscopic physical components, providing clear starting coordinates for subsequent deduction of how the fault spreads outward from this source.

[0031] Specifically, the process of triggering a depth-first traversal of the graph neural network starting from the root cause node, calculating the cumulative failure probability of the fault propagating along the connection path, and calculating the remaining effective working window of the current device based on the time integral of the cumulative failure probability reaching the critical threshold is as follows: Initialize the traversal stack and push the root cause node onto the top of the stack; query the fault evolution knowledge graph to obtain the topological adjacent nodes of the current node and the corresponding edge weight transfer coefficients; perform a comprehensive calculation on the normalized value of the dimension offset corresponding to the root cause node as the initial failure probability and the edge weight transfer coefficients on the connection path to obtain the cumulative failure probability of the adjacent nodes; introduce a Weibull distribution failure density function containing time variables, use the cumulative failure probability as the pre-coefficient of the function, perform a definite integral operation on the failure density function in the time dimension, and when the integral result reaches the preset critical threshold, extract the value of the upper limit of the integral time variable at this time, and determine the value of the upper limit of the integral time variable as the remaining effective working window.

[0032] In this implementation, the module employs a graph neural network depth-first traversal algorithm to simulate the dynamic propagation process of faults between physical components. Depth-first traversal is a search strategy that prioritizes exploring connections in depth, enabling the complete reproduction of a fault propagation chain. The system first initializes the traversal stack, starting from the locked root cause node, and queries the graph to obtain its directly connected topological adjacency nodes. When calculating the fault propagation intensity, the system introduces an edge weight transfer coefficient, which reflects the impact of upstream component failure on downstream components. The calculation of the cumulative failure probability depends not only on the current offset but also on the multiplicative effect along the path, and its calculation logic is shown in the following formula: In the above formula, the meanings of each parameter are as follows: The cumulative failure probability of the m-th adjacent node is calculated, which represents the potential destructive power when the fault propagates to that node; The normalized value of the dimensional offset corresponding to the root cause node is used as the initial energy value of the propagation chain. The set of connection paths from the root node to the m-th node; The edge weight transfer coefficient between adjacent nodes n and n+1 on the path is determined by the physical coupling tightness between components; for example, the weight coefficient for rigid connections is higher than that for flexible connections. After obtaining the cumulative failure probability, the system needs to convert it into a specific time indicator, namely the remaining effective operating window. To this end, the system introduces the Weibull distribution failure density function, a statistical model widely used in reliability engineering to describe the life cycle of equipment. The system uses the cumulative failure probability as an intensity coefficient and integrates the failure density function over time to simulate the process of fault accumulation until the equipment completely fails. The calculation formula is as follows: In the above formula, the meanings of each parameter are as follows: The target parameter obtained by solving is the remaining effective working window, which represents the length of time from the current moment until the device fails. The time variable during integration; The shape parameters of the Weibull distribution depend on the current wear stage of the equipment (such as early failure or wear-out). The scale parameter of the Weibull distribution represents the characteristic lifetime of the equipment; The base of the natural logarithm; The preset critical threshold, obtained by consulting the equipment's factory fatigue test standard manual or historical fault database, represents the maximum cumulative damage the equipment can withstand. Through this integral calculation, the system establishes a correlation between the abstract probability value and physical time, intuitively outputting how long the equipment can continue to operate, providing a precise quantitative basis for subsequent game-theoretic scheduling.

[0033] Specifically, the process of initiating a maintenance bidding process based on the contract network protocol by using the reciprocal of the remaining valid job window as the core variable of the bidding weight function, and comparing the bid values ​​to lock the winning equipment and allocate physical maintenance resources is as follows: Construct a linear weighted aggregation function containing the reciprocal of the remaining valid job window and the priority value of the print task queue, and define the calculated aggregation result as the equipment bid value; broadcast the task bidding data packet, receive the equipment bid values ​​fed back by multiple printing devices and execute the numerical sorting algorithm, extract the equipment identifier corresponding to the equipment bid value with the largest value in the sorting result, and mark the equipment identifier as the winning equipment; send a mutual exclusion lock command containing a timestamp and resource occupancy public key to the winning equipment, and update the status bit of the corresponding physical maintenance resource in the maintenance resource database to the occupied status.

[0034] In this implementation plan, the core purpose of the game-theoretic scheduling module in executing the above steps is to establish a dynamic resource allocation system based on a market economy mechanism. When multiple printing devices simultaneously face the risk of failure and maintenance resources (such as automated maintenance robots or designated maintenance personnel) are limited, the system must quantify the maintenance urgency of each device. The module first constructs a linear weighted aggregation function, which considers not only the physical lifespan of the device (remaining effective job window) calculated from previous steps, but also the urgency at the current business level (print task queue priority). The reciprocal of the remaining effective job window is used as the core variable because a shorter window means the device is closer to downtime, and its maintenance needs are more urgent. By taking the reciprocal, a very small time value can be mapped to a very large weight value, thus gaining an advantage in the bidding process. The formula for calculating the device bidding value is as follows: In the above formula, the meanings of each parameter are as follows: The calculated bid value for the equipment indicates that the higher the value, the higher the priority for the equipment to obtain maintenance resources. The remaining time weighting coefficient is used to adjust the proportion of physical life urgency in the overall bidding. This coefficient is set based on the company's emphasis on the protection of equipment assets using the analytic hierarchy process. The remaining effective job window period calculated in the previous steps; To prevent extremely small positive compensation terms with a denominator of zero; Task queue weight coefficient, used to adjust the proportion of business importance in the bidding process; The total number of backlogged tasks in the current device's print queue; : The priority value of the kth print task in the queue. For example, a high-level confidential file is assigned a high score, and a regular draft is assigned a low score. The task position decay factor, ranging from 0 to 1, reflects the greater contribution of tasks at the front of the queue to urgency. This formula integrates the physical layer's survival crisis and the application layer's business pressure into a single scalar indicator. Subsequently, the module performs broadcasting and sorting operations, similar to the bidding process in an auction; the numerical sorting algorithm ensures the highest bidder wins. Finally, a mutual exclusion lock command is sent and the status bit is updated. An encryption mechanism containing a timestamp and the resource occupancy public key prevents concurrent resource conflicts and unauthorized preemption, ensuring the uniqueness and security of the maintenance link.

[0035] Specifically, the process of retrieving the neighboring node table with the same capability of the winning equipment, planning the path for the task to be executed to flow to the idle neighboring node, and constructing the task migration topology graph is as follows: Retrieve the stored device capability attribute matrix, using the device identifier of the winning equipment as the index row, and filter the node identifiers in the matrix that are completely consistent with the winning equipment in terms of printing size, color mode, and resolution parameters to form a neighboring node table with the same capability; traverse the real-time load data of each node in the neighboring node table with the same capability, remove nodes whose load data exceeds the safe level, sort the remaining nodes in ascending order of load value, and select the node with the lowest load value as the task receiving end; establish a directed connection edge with the winning equipment as the source node and the task receiving end as the destination node, and encapsulate the data packet routing address, port number, and transmission protocol of the directed connection edge into a task migration topology graph.

[0036] In this implementation plan, once it is determined that a certain device (the winning bidder) is about to enter a shutdown maintenance state, the game scheduling module must immediately activate the disaster recovery mechanism, i.e., task migration. To ensure that the migrated tasks can be processed correctly, capability matching is first required. The device capability attribute matrix is ​​a static storage table that records the hardware specifications of each printer in the network. The module filters out neighboring nodes with the same capability by comparing the print size (e.g., A3 or A4), color mode (color or black and white), and resolution. This step eliminates the possibility of invalid scheduling, such as sending color design drawings to a black and white receipt printer. Among the candidates with the same capability, the system needs to further find the best receiver, which is achieved through a load balancing algorithm. The safety water level is a preset load threshold (e.g., CPU utilization of 80% or queue length of 10 tasks). Nodes exceeding this water level are considered overloaded and should not receive new tasks. The module sorts the remaining nodes in ascending order of load value and selects the lowest value. This is actually solving a minimum value problem based on constraints. To make the reviewer more clearly understand this screening and decision-making logic, it can be expressed by the following set operation formula: In the above formula, the meanings of each parameter are as follows: The node identifier that was ultimately selected as the task receiver was chosen. The set of all neighboring nodes in the network; The real-time load data of the nth neighboring node, which combines memory usage and the current queue length; The set of capability features of the nth neighboring node; : The set of capability characteristics of the winning device (source node); =: Set equality operation, indicating that the hardware printing capabilities of the two are completely identical; A preset safety threshold is used to filter high-load nodes. After determining the task receiver, constructing the task migration topology is the final step in realizing data flow. This is not just a logical direction, but a routing plan at the physical network level. The module establishes directed connection edges and encapsulates IP addresses, port numbers, and transmission protocols, effectively building a temporary software-defined network (SDN) tunnel at the application layer. Thus, when the correction module intercepts a printing task, it can directly modify the data packet header based on the encapsulation information in the topology, seamlessly redirecting the bit stream originally destined for the faulty device to a healthy, idle device, achieving seamless business continuity assurance for the user.

[0037] Specifically, the logical process of locking the target equipment for maintenance operations based on the bidding results and executing routing instructions to complete task distribution based on the task migration topology is as follows: The resource occupancy public key in the mutual exclusion locking instruction is parsed for authentication. After successful authentication, the I / O interrupt routine of the winning equipment is triggered to pause local print queue input and open the underlying firmware maintenance port for physical maintenance resources to access and perform mechanical calibration or firmware rewriting operations. Simultaneously, the destination node routing address in the task migration topology is parsed, the print data stream in the task queue to be executed is intercepted, the TCP / IP packet header of the print data stream is rewritten, the destination IP address is replaced with the IP address of the task receiving end, and the rewritten print data stream is forwarded to the task receiving end through a local area network socket.

[0038] In this implementation scheme, after receiving instructions from the game scheduling module, the execution correction module performs physical layer maintenance preparation and network layer data diversion in parallel. First, the module parses the resource occupancy public key in the mutual exclusion lock instruction for authentication. The resource occupancy public key is an identity credential under an asymmetric encryption system, used to ensure that only authorized maintenance entities can obtain underlying control of the device, preventing unauthorized commands from interfering with device operation. After successful authentication, the system triggers the I / O interrupt routine of the winning device, which forcibly suspends current input / output requests and pauses local print queue input, thus creating a silent software environment for physical maintenance. Subsequently, the underlying firmware maintenance port is opened, allowing maintenance robots or technicians to access via serial or debug interfaces to perform physical operations such as mechanical calibration, firmware rewriting, or component replacement. Simultaneously, to ensure business continuity, the module parses the destination node routing address in the task migration topology and initiates a traffic redirection mechanism. The system intercepts print data streams in the task queue, which typically exist in the network buffer as data packets. The module uses deep packet inspection technology to locate and rewrite the TCP / IP packet headers of the print data streams. The TCP / IP packet header contains control information used to identify the source and destination addresses in network transmission. The module replaces the original destination IP address pointing to the faulty device with the IP address of the task receiver and sends the rewritten data stream out via a LAN socket. A LAN socket is an endpoint used in network programming to enable inter-process communication between different devices. Through this operation, the print job originally sent to the faulty device is transparently "transferred" to a healthy, nearby device. The user terminal can complete the printing without resubmitting the task, achieving seamless business continuity during fault handling.

[0039] Specifically, after maintenance, a self-test is performed. Differential calculation is performed on the state data before and after maintenance to obtain the state gain residual. When the state gain residual is lower than the preset convergence threshold, an edge weight penalty factor is generated. The logical process of reversing the edge weight values ​​of the corresponding propagation paths in the fault evolution knowledge graph is as follows: Trigger the standard gray-scale ladder test page printing command, synchronously collect the post-test multi-source physical signals during the printing process and generate the post-test feature vector; calculate the weighted Mahalanobis distance difference between the post-test feature vector and the real-time feature vector before maintenance, and define the weighted Mahalanobis distance difference as the state gain residual; compare the state gain residual with the preset convergence threshold. When the state gain residual is less than the convergence threshold, call the nonlinear decay function to generate an edge weight penalty factor with a value between 0 and 1; trace the fault root cause node locked in the graph inference module and its connection path, multiply the original edge weight value on the connection path by the edge weight penalty factor, and perform a weight downgrade update operation.

[0040] In this implementation plan, the final step of the correction module aims to verify the maintenance effect and provide feedback to the system's diagnostic model. After maintenance, the system automatically triggers a standard grayscale step test page printing command. The standard grayscale step test page is a dedicated test pattern containing different grayscale levels from pure black to pure white. It can comprehensively stimulate the development, fixing, and transfer components of the printing equipment, thereby synchronously acquiring representative post-test multi-source physical signals through sensors during the printing process and generating post-test feature vectors according to the method of the aforementioned state perception module. Subsequently, the system needs to quantify the performance improvement brought about by the maintenance, i.e., calculate the state gain residual. This residual reflects the degree to which the equipment state returns from a "fault deviation state" to a "baseline normal state." The calculation logic compares the distance change of the equipment state in the reference space after maintenance with that before maintenance. The calculation formula is as follows: In the above formula, the meanings of each parameter are as follows: The calculated state gain residual indicates that the larger the value, the greater the difference between the state before and after maintenance, and the more obvious the repair effect. The weighted Mahalanobis distance between the real-time feature vectors measured before maintenance and the spatial cluster centers is usually a large value. : Maintain the weighted Mahalanobis distance between the post-measured feature vector and the spatial cluster center; ideally, this value should approach zero. The absolute value operator. After obtaining the state gain residual, the system compares it with a preset convergence threshold. The preset convergence threshold is the passing grade for determining whether maintenance is effective. If the state gain residual is less than this threshold, it indicates that the maintenance operation has not significantly improved the equipment state, thus suggesting that the fault root cause node or propagation path initially identified by the graph inference module may be misjudged. To reduce the interference of this erroneous path in future diagnosis, the system calls a nonlinear decay function to generate an edge weight penalty factor. This factor is used to penalize the edge weights in the graph, and the calculation formula is as follows: In the above formula, the meanings of each parameter are as follows: The generated edge weight penalty factor is a value between 0 and 1, with a smaller value indicating a stronger penalty; tanh: hyperbolic tangent function, used to map the input value to the interval between 0 and 1 to ensure the smoothness of the factor value; A preset convergence threshold is used to normalize the residuals; The adjustment exponent controls the decay rate of the penalty function; a larger value results in a more severe penalty for small residuals. Finally, the system traces the previously identified root cause nodes and their connecting paths, updating the original edge weights on the paths using the generated penalty factor. The calculation formula is as follows: In the above formula, the meanings of each parameter are as follows: : Updated edge weight values; The original edge weights of the corresponding propagation path in the fault evolution knowledge graph. Through this multiplicative update operation, the system reduces the activation probability of this path in future inferences, thereby achieving the self-evolution and error correction of the knowledge graph.

[0041] In summary, this application has at least the following effects:

[0042] A collaborative maintenance system for printing equipment based on multi-agent technology enables real-time perception of equipment status and predictive inference of faults by constructing a distributed agent network. It utilizes weighted Mahalanobis distance and a fault evolution knowledge graph to accurately quantify equipment health and calculate the remaining effective working window, fundamentally solving the lag and bias of traditional threshold monitoring. Simultaneously, the system introduces a reciprocal bidding mechanism and task migration strategy based on a contract network protocol, achieving dynamic optimal allocation of maintenance resources according to urgency and seamless continuation of business flows. Furthermore, it uses residual feedback after maintenance to correct fault model weights, endowing the system with self-learning and self-evolution capabilities. This significantly improves the overall availability and resource utilization efficiency of the cluster while ensuring zero interruption of printing operations.

[0043] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0044] This invention is described with reference to flowchart illustrations and / or block diagrams of systems, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0045] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0046] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0047] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0048] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A collaborative maintenance system for printing equipment based on multiple agents, characterized in that, Includes the following modules: The state perception module is used to collect multi-source physical signals during the operation of the printing device and convert them into real-time feature vectors. The real-time feature vectors are then projected onto a preset high-dimensional reference state space containing the spatial cluster centers of normal operation samples. The weighted Mahalanobis distance of the real-time feature vectors relative to the spatial cluster centers is calculated to generate a device state deviation vector representing the dimensional offset and direction. The graph inference module is used to pre-set a fault evolution knowledge graph that represents the physical connection and fault propagation logic of equipment components, analyze the dimension mapping with the largest offset in the equipment state deviation vector and lock the root cause node of the fault, trigger the depth-first traversal of the graph neural network starting from the root cause node of the fault, calculate the cumulative failure probability of the fault propagating along the connection path, and calculate the remaining effective working window of the current equipment based on the time integral of the cumulative failure probability reaching the critical threshold. The game scheduling module is used to initiate maintenance bidding based on the contract network protocol by using the reciprocal of the remaining effective job window as the core variable of the bidding weight function, compare the bid values ​​to lock the winning equipment and allocate physical maintenance resources, retrieve the table of neighboring nodes with the same capabilities of the winning equipment, plan the path for the tasks to be executed to be transferred to idle neighboring nodes and build a task migration topology graph. The execution correction module is used to lock the target equipment for maintenance operations based on the bidding results, and to execute routing instructions to complete task distribution based on the task migration topology map; After maintenance is completed, a self-test is performed. The state gain residual is obtained by differential calculation of the state data before and after maintenance. When the state gain residual is lower than the preset convergence threshold, an edge weight penalty factor is generated to correct the edge weight value of the corresponding propagation path in the fault evolution knowledge graph.

2. The collaborative maintenance system for printing equipment based on multiple agents according to claim 1, characterized in that: The specific process of acquiring multi-source physical signals during the operation of the printing equipment, converting them into real-time feature vectors, and projecting these real-time feature vectors onto a pre-set high-dimensional reference state space containing the spatial cluster centers of the normally operating samples is as follows: Short-time Fourier transform is performed on the collected mechanical vibration signal to extract frequency domain amplitude features; time-domain statistical analysis is performed on the motor drive current signal to extract mean and variance features; and trend slope is extracted from the fixing component temperature signal. The frequency domain amplitude features, mean and variance features, and trend slope features are concatenated to form the original high-dimensional vector. The pre-trained principal component analysis projection matrix is ​​then used to perform a dimensionality reduction mapping operation on the original high-dimensional vector to obtain the real-time feature vector located in the low-dimensional manifold space, thus establishing the coordinate position of the real-time feature vector in the reference state space.

3. The collaborative maintenance system for printing equipment based on multiple agents according to claim 2, characterized in that: The specific process for calculating the weighted Mahalanobis distance between the real-time feature vector and the spatial cluster center, and generating the device state deviation vector representing the dimensional offset and direction, is as follows: Retrieve the inverse covariance matrix corresponding to the reference state space, calculate the difference vector between the real-time feature vector and the coordinates of the spatial cluster center, perform a quadratic operation on the difference vector and the inverse covariance matrix, and take the square root to obtain the weighted Mahalanobis distance value. Extract the components of each dimension from the difference vector, standardize each component by dividing it by the square root of the diagonal element of the inverse covariance matrix, and output a device state deviation vector containing the standardized residual values ​​of each dimension and the positive and negative signs.

4. The collaborative maintenance system for printing equipment based on multiple agents according to claim 1, characterized in that: The specific process of parsing the dimension with the largest offset in the device state deviation vector and locking the root cause node of the fault, based on the pre-defined fault evolution knowledge graph representing the physical connection and fault propagation logic of device components, is as follows: Construct a directed graph structure with physical component identifiers as nodes and physical connections between components as edges, and establish a mapping table between the dimension index of the device state deviation vector and the physical component identifier of the graph node; Take the absolute value of each dimension value in the device state deviation vector and sort them in descending order. Select the dimension index with the largest absolute value, retrieve the corresponding physical component identifier through the mapping table, and mark the physical component identifier as the root cause node of the fault.

5. A collaborative maintenance system for printing equipment based on multiple agents according to claim 4, characterized in that: The specific process of triggering a depth-first traversal of the graph neural network starting from the root cause node of the fault, calculating the cumulative failure probability of the fault propagating along the connection path, and calculating the remaining effective working window of the current equipment based on the time integral of the cumulative failure probability reaching the critical threshold is as follows: Initialize the traversal stack and push the root cause node of the fault onto the top of the stack. Query the fault evolution knowledge graph to obtain the topological adjacent nodes of the current node and the corresponding edge weight propagation coefficients. The normalized value of the dimension offset corresponding to the root cause node is used as the initial failure probability and combined with the edge weight transfer coefficient on the connection path to obtain the cumulative failure probability of the adjacent nodes. A Weibull distribution failure density function with a time variable is introduced, and the cumulative failure probability is used as the pre-coefficient of the function. A definite integral operation is performed on the failure density function in the time dimension. When the integral result reaches a preset critical threshold, the value of the upper limit of the integral time variable at this time is extracted, and the value of the upper limit of the integral time variable is determined as the remaining effective working window period.

6. A collaborative maintenance system for printing equipment based on multiple agents according to claim 1, characterized in that: The specific process of initiating a maintenance bidding process based on the contract network protocol by using the reciprocal of the remaining effective work window as the core variable of the bidding weight function, and comparing the bid values ​​to determine the winning equipment and allocate physical maintenance resources is as follows: Construct a linear weighted aggregation function that includes the reciprocal of the remaining valid job window period and the priority value of the print task queue, and define the calculated aggregation result as the equipment bidding value; Broadcast task bidding data packets, receive equipment bidding values ​​from multiple printing devices and execute a numerical sorting algorithm, extract the equipment identifier corresponding to the equipment bidding value with the largest value in the sorting results, and mark the equipment identifier as the winning equipment; Send a mutual exclusion lock command containing a timestamp and a resource occupancy public key to the winning equipment, and update the status bit of the corresponding physical maintenance resource in the maintenance resource database to the occupied status.

7. A collaborative maintenance system for printing equipment based on multiple agents according to claim 1, characterized in that: The specific process of retrieving the list of neighboring nodes with the same capabilities of the winning equipment, planning the path for the task to be executed to be transferred to an idle neighboring node, and constructing the task migration topology graph is as follows: Retrieve the stored device capability attribute matrix, using the device identifier of the winning device as the index row, filter the node identifiers in the matrix that are completely consistent with the winning device in terms of print size, color mode and resolution parameters, and form a table of adjacent nodes with the same capability. Iterate through the real-time load data of each node in the neighboring node table with the same capacity, remove nodes whose load data exceeds the safe level, sort the remaining nodes in ascending order of load value, and select the node with the lowest load value as the task receiving end. Establish directed connections with the winning device as the source node and the task receiver as the destination node, and encapsulate the data packet routing address, port number, and transmission protocol of the directed connections into a task migration topology graph.

8. A collaborative maintenance system for printing equipment based on multiple agents according to claim 6, characterized in that: The logical process of identifying the target equipment for maintenance operations based on the bidding results, and executing routing commands to complete task offloading based on the task migration topology map is as follows: The resource occupancy public key in the mutex lock instruction is parsed for authentication. After successful authentication, the I / O interrupt program of the winning device is triggered to pause the local print queue input and open the underlying firmware maintenance port for physical maintenance resources to access and perform mechanical calibration or firmware rewriting operations. Simultaneously, the destination node routing address in the task migration topology graph is parsed, the print data stream in the queue of tasks to be executed is intercepted, the TCP / IP packet header of the print data stream is rewritten, the destination IP address is replaced with the IP address of the task receiving end, and the rewritten print data stream is forwarded to the task receiving end through a local area network socket.

9. A collaborative maintenance system for printing equipment based on multiple agents according to claim 1, characterized in that: After maintenance, a self-test is performed. The state gain residual is obtained by differential calculation on the state data before and after maintenance. When the state gain residual is lower than the preset convergence threshold, an edge weight penalty factor is generated. The logical process of correcting the edge weight values ​​of the corresponding propagation path in the fault evolution knowledge graph is as follows: Trigger the standard grayscale step test page printing command, synchronously collect post-test multi-source physical signals during the printing process and generate post-test feature vectors; Calculate the weighted Mahalanobis distance difference between the post-measured feature vector and the real-time feature vector before maintenance, and define the weighted Mahalanobis distance difference as the state gain residual; Compare the state gain residual with the preset convergence threshold. When the state gain residual is less than the convergence threshold, call the nonlinear decay function to generate a side weight penalty factor with a value between 0 and 1. The root cause node of the fault and its connection path are locked in the tracing graph inference module. The original edge weight value on the connection path is multiplied by the edge weight penalty factor, and the weight downgrade update operation is performed.