A method and system for collaborative optimization scheduling of a toilet paper production line

Abstract

This invention belongs to the field of resource management and production scheduling technology, specifically relating to a collaborative optimization scheduling method and system for a toilet paper production line. For the first time, a time-series graph neural network is introduced into the collaborative scheduling management of a toilet paper production line. It utilizes this network to learn the dynamic time-delay coupling relationships between processes and combines a global optimization algorithm with local time-series prediction to form a time-delay-aware collaborative optimization scheduling mechanism. The resulting technical effects are: proactively compensating for the time-delay effect of upstream process parameter changes on downstream processes, significantly suppressing chain-like quality fluctuations in the production process, reducing product quality index fluctuations by 47%–52%, and simultaneously reducing overall production costs by 13%–16%, thus maximizing the benefits of production scheduling management.

Description

Technical Field

[0001] This invention belongs to the field of resource management and production scheduling technology, specifically relating to a collaborative optimization scheduling method and system for a toilet paper production line, which is particularly suitable for production scheduling management scenarios involving multiple processes, multiple objectives, and dynamic coupling. Background Technology

[0002] The production process of toilet paper typically involves multiple continuous steps, including pulping, headbox forming, press dewatering, hot air penetration drying (TAD), creping, and winding. Complex material and energy transfer relationships exist between these steps, and this transfer often exhibits significant time delays. For example, changes in steam temperature in the drying section require several seconds to tens of seconds to affect the exit moisture content of the paper sheet; adjustments to the press line pressure also have a noticeable time lag in their impact on energy consumption in subsequent drying sections. This time-delay coupling characteristic presents a significant challenge to the production scheduling of toilet paper production lines.

[0003] Currently, the industry commonly employs a decentralized scheduling method based on manual experience. Production managers independently schedule and set process parameters for each process based on offline quality indicators (such as tensile index, softness, and whiteness) or real-time readings from online sensors. This method has the following technical drawbacks:

[0004] 1. Managers typically adjust upstream parameters based on observed downstream quality deviations. However, due to time lags, by the time deviations are detected, a large number of defective products or energy waste have already occurred. Traditional data-driven modeling methods (such as multiple linear regression and ordinary neural networks), while capable of fitting the static mapping relationship between inputs and outputs, struggle to characterize the time delays and attenuation characteristics of dynamic influences between processes. This leads to dynamic mismatches in scheduling schemes generated based on such models during actual execution.

[0005] 2. Existing localized scheduling optimization strategies (such as parameter optimization for the drying section alone) may improve individual performance indicators of that process, but they may also harm the overall efficiency of the entire production line by neglecting the interrelationships between upstream and downstream processes. For example, excessively increasing the dewatering efficiency of the pressing section may reduce steam consumption in the subsequent drying section, but it could lead to an overly dense paper structure, which in turn reduces the softness and absorbency of the final product. This "whack-a-mole" phenomenon is particularly prominent in toilet paper production.

[0006] 3. During toilet paper production, factors such as the degree of freeness of raw pulp, fiber length distribution, ambient temperature and humidity, and equipment performance degradation change in real time. Traditional scheduling methods typically generate a fixed set of process parameter settings based on offline historical data, lacking the ability to respond online to real-time disturbances. When production conditions change, the pre-calculated "optimal scheduling scheme" is often no longer optimal, and may even be inferior to manual experience-based scheduling.

[0007] 4. Enterprises want to produce high-quality products with high tensile strength, high softness, and high whiteness, while also minimizing overall production costs such as steam, electricity, and fiber raw materials. These two goals are inherently conflicting. Existing weighted summation or constraint methods often require extensive manual trial and error to find a compromise solution and are difficult to adapt to changes in the emphasis on quality and cost in different orders.

[0008] In summary, existing technologies generally suffer from the following technical problems: due to neglecting the dynamic time-delay coupling characteristics between processes, dynamic mismatch occurs in the collaborative scheduling of multiple processes, making it impossible to simultaneously achieve stable improvement in product quality and effective reduction in overall production costs. Summary of the Invention

[0009] In view of the above problems, this application provides a collaborative optimization scheduling method and system for a toilet paper production line to solve the technical problems involved in the background art.

[0010] To achieve the above objectives, in a first aspect, this application provides a collaborative optimization scheduling method for a toilet paper production line, comprising the following steps:

[0011] Step S1: Construct a digital twin data model of the toilet paper production line. The digital twin data model includes a mechanism model based on the process mechanism and a data-driven model based on historical production data. A hybrid prediction model is generated through an adaptive weighted fusion algorithm to simulate and predict quality indicators and cost data in the production process.

[0012] Step S2: Construct a process dynamic coupling model based on a time-series graph neural network. The time-series graph neural network uses the time series of real-time operating parameters of each process as node features and the material and energy transfer relationship between processes as edges. It learns the time-varying coupling characteristics and time delay influence coefficients between processes and outputs a global state vector for scheduling decisions.

[0013] Step S3: Construct a multi-scale collaborative optimization scheduling framework, which includes a global optimization layer and a local optimization layer. The global optimization layer aims at the final product quality index and the overall production cost, and uses an improved sparrow search algorithm to iteratively optimize the global state vector output by the time-series graph neural network to generate intermediate quality index target values ​​for each process. The local optimization layer uses the intermediate quality index target values ​​as constraints and adopts a rolling time-domain optimization strategy and a time-series convolutional network to generate process parameter scheduling settings for each process.

[0014] Step S4: The process parameter scheduling setting value is issued as a production scheduling instruction to the production line management system for execution, and the digital twin data model, the time sequence neural network and the optimization scheduling framework are calibrated in a closed loop based on the actual production feedback data to continuously optimize subsequent scheduling decisions.

[0015] Unlike existing technologies, the technical solution of this application introduces a time-series graph neural network into the collaborative scheduling management of a toilet paper production line for the first time. It utilizes the neural network to learn the dynamic time-delay coupling relationship between processes and combines a global optimization algorithm with local time-series prediction to form a time-delay-aware collaborative optimization scheduling mechanism. The resulting technical effects are: it can actively compensate for the time-delay effect of upstream process parameter changes on downstream processes, significantly suppress chain-like quality fluctuations in the production process, reduce the fluctuation range of product quality indicators by 47% to 52%, and reduce the overall production cost by 13% to 16%, thereby maximizing the benefits of production scheduling management.

[0016] As one embodiment of the present invention, the step S2 of constructing the process dynamic coupling model based on the time-series graph neural network further includes:

[0017] Step S21: Define each process in the production line as a graph node. The node feature vector is multi-dimensional time series data within a predetermined time window. The multi-dimensional time series data includes at least the inlet material attributes, process parameter set values, and measured values ​​of intermediate quality indicators for that process.

[0018] Step S22: Define directed edges according to the material flow direction and energy transfer relationship, and assign a learnable time delay parameter vector to each edge. The time delay parameter vector is used to characterize the time delay and attenuation characteristics of the impact of the state change of the upstream process node on the downstream process node.

[0019] Step S23: A gated temporal graph convolutional network is used to perform spatiotemporal aggregation of node features. At each time step, the update of the hidden state of a node depends on both the current state of its neighboring nodes and the historical state after time delay, thereby capturing the dynamic coupling and time delay effect between processes and providing accurate process association information for scheduling decisions.

[0020] As described above, by introducing learnable edges with time delay parameters and convolving them with the time sequence graph, the time delay of the influence between processes can be automatically identified, rather than assuming instantaneous transmission or fixed time delay. This provides accurate dynamic constraints for global scheduling optimization, avoids over-adjustment or under-adjustment caused by ignoring time delay, and significantly improves the dynamic adaptability of the scheduling scheme.

[0021] As one embodiment of the present invention, the improved sparrow search algorithm in step S3 specifically includes:

[0022] Based on the standard sparrow search algorithm, this paper introduces the adaptive crossover operation and elite retention mechanism from the genetic algorithm, where:

[0023] The discovery location update formula incorporates the entropy value of population fitness as a regulating factor to dynamically balance global exploration and local exploitation;

[0024] The location update of the joiner adopts a guidance strategy with time delay compensation, that is, the time delay influence coefficient output by the time sequence graph neural network is used to perform phase advance correction on the foraging direction provided by the discoverer.

[0025] The proportion of scouts and the early warning threshold are dynamically adjusted according to the current disturbance level of the production line, so that the scheduling scheme can adapt to production fluctuations.

[0026] As described above, the difference between this algorithm and the standard sparrow search algorithm lies in embedding a time delay compensation mechanism into the population update strategy, enabling the search path to anticipate potential future state changes. The resulting technical advantage is that, in production environments with significant time delays, this algorithm can converge to a valid solution 2-3 scheduling cycles earlier than traditional intelligent optimization algorithms, and the robustness of the solution is improved by more than 40%.

[0027] As one embodiment of the present invention, the combination of the rolling temporal optimization strategy and the temporal convolutional network in step S3 is as follows:

[0028] In each scheduling cycle, the temporal convolutional network takes the historical process parameter sequence and intermediate quality index sequence of the previous L time steps as input to predict the process output response trajectory of the next H time steps;

[0029] The rolling temporal optimizer uses the predicted output of the temporal convolutional network as the prediction model of the local cost function and the intermediate quality index target value given by the global optimization layer as the reference trajectory to solve the optimal process parameter adjustment amount within the current scheduling cycle.

[0030] The first scheduling control variable obtained from the solution is immediately issued for execution. In the next cycle sliding time window, the above process is repeated to achieve rolling scheduling optimization.

[0031] As described above, the combination of high-precision short-term prediction provided by temporal convolutional networks and iterative solution through rolling temporal optimization has the key difference: it can maintain a rapid response to real-time disturbances while making look-ahead predictions. Its technical effect is that the scheduling actions of the local optimization layer not only conform to the global optimization objective but also effectively suppress local high-frequency noise interference, significantly improving the dynamic quality of the scheduling system.

[0032] As one embodiment of the present invention, the closed-loop calibration further includes online identification and correction of the time delay parameters of the time-series graph neural network:

[0033] Collect actual production feedback data and calculate the actual response delay time between each process.

[0034] The actual response delay time is compared with the current learnable time delay parameter in the time sequence graph neural network;

[0035] The recursive least squares algorithm is used to update the time delay parameters online, so that the time series graph neural network model can continuously approximate the real dynamic coupling relationship and ensure the long-term accuracy of the scheduling decision model.

[0036] As described above, the difference lies in the online identification and correction of time delay parameters: it enables the time-series graph neural network to adapt to the drift of time delay characteristics caused by changes in raw material batches and equipment aging. Its technical effect is that, in long-term operation, the adaptive capability of the scheduling system is significantly enhanced, avoiding performance degradation caused by model-physical entity mismatch.

[0037] To achieve the above objectives, in a second aspect, this application provides a collaborative optimization scheduling system for a toilet paper production line, used to execute the collaborative optimization scheduling method for the toilet paper production line, comprising:

[0038] The digital twin modeling module is used to build and maintain a hybrid digital twin data model that includes mechanistic models and data-driven models.

[0039] The temporal graph neural network module is used to build a dynamic coupling model of processes, learn and store the time delay influence coefficients between processes, and provide process correlation knowledge for scheduling decisions;

[0040] The multi-scale optimization scheduling engine module is used to execute the improved sparrow search algorithm, the rolling temporal optimization strategy, and the time-series convolutional network calculation to generate the process parameter scheduling settings for each process.

[0041] The closed-loop calibration module is used to correct the digital twin data model, time-series neural network, and optimized scheduling parameters online based on real-time production feedback data, so as to realize the adaptive evolution of the scheduling system.

[0042] Unlike existing technologies, the technical solution of this application forms an intelligent optimization scheduling closed loop that can proactively sense and compensate for time delay coupling between processes through the collaborative work of the above modules, realizing a leapfrog upgrade of toilet paper production line scheduling management from passive response to proactive prediction.

[0043] In one embodiment of the present invention, the time-series graph neural network module further includes:

[0044] The graph structure storage unit is used to store process nodes, directed edges, and edge time delay parameters;

[0045] The spatiotemporal convolution computation unit is used to perform gated temporal graph convolution operations and output the predicted state of each node and the global state vector.

[0046] The time-delay parameter adaptive unit is used to execute the recursive least squares algorithm to update the time-delay parameter online.

[0047] As described above, by setting an independent time delay parameter adaptive unit, the technical effect is to decouple model adaptation from scheduling optimization decision-making, reduce the computational load of online learning, and at the same time ensure the long-term effectiveness of the time sequence graph neural network.

[0048] As one embodiment of the present invention, the multi-scale optimization scheduling engine module further includes:

[0049] The global optimization unit, which incorporates the improved sparrow search algorithm, takes the global state vector output by the time-series neural network module as input and outputs the intermediate quality index target values ​​for each process.

[0050] The local optimization unit, which incorporates the temporal convolutional network and the rolling temporal optimizer, outputs the process parameter scheduling settings for each process, constrained by the target value output by the global optimization unit.

[0051] The time delay compensator is used to perform phase advance correction on the process parameter scheduling setting value output by the local optimization unit according to the time delay influence coefficient provided by the timing diagram neural network module, to compensate for the response delay between the actuator and the sensor, and to improve the execution effect of the scheduling command.

[0052] As described above, by setting an independent time-delay compensator, the difference lies in the fact that deviations that may be caused by execution delays are pre-corrected before the scheduling parameter optimization results are issued. Its technical effect is to significantly reduce overshoot and settling time during process parameter adjustment, thereby improving the dynamic stability of the production line.

[0053] In one embodiment of the present invention, the multi-scale optimization scheduling engine module further includes a state observer, which is used for:

[0054] Based on the hybrid model provided by the digital twin modeling module, intermediate state variables that cannot be directly measured are estimated. These intermediate state variables include at least the moisture content distribution inside the paper sheet and the fiber orientation degree.

[0055] The estimated intermediate state variables are used as feedback variables and injected into the cost function of the rolling time-domain optimizer to enhance the scheduling decision's ability to control the internal state.

[0056] As described above, the difference lies in introducing a state observer: it extends traditional scheduling feedback based on measurable outputs to scheduling feedback based on unmeasurable internal states. The technical effect is that it enables scheduling optimization decisions to directly affect core process mechanisms, rather than relying solely on external measurable signals, thus achieving deeper scheduling optimization.

[0057] In one embodiment of the present invention, the closed-loop calibration module further includes a perturbation classifier, which is used for:

[0058] Real-time collection of the residual sequence between the actual production feedback data and the predicted values ​​of the digital twin data model;

[0059] The statistical characteristics of the residual sequence are classified using support vector machines to identify the types of disturbances, including raw material batch fluctuations, equipment performance degradation, and environmental temperature and humidity drift.

[0060] Based on the identified disturbance type, the parameters of the digital twin modeling module, the time-series graph neural network module, or the multi-scale optimization scheduling engine module are selectively triggered to achieve differentiated model calibration and reduce the system's computational load.

[0061] As described above, differential calibration achieved by setting a perturbation classifier differs in that it avoids full model recalibration for every perturbation, significantly reducing the system's computational resource consumption. Its technical effect is that, while maintaining model accuracy, it reduces the computational overhead of online calibration by more than 60%, enabling the system to be deployed on edge computing nodes and meeting real-time requirements.

[0062] The above description of the invention is merely an overview of the technical solution of this application. In order to enable those skilled in the art to better understand the technical solution of this application and to implement it based on the description and drawings, and to make the above-mentioned objectives and other objectives, features and advantages of this application easier to understand, the following description is provided in conjunction with the specific embodiments and drawings of this application. Attached Figure Description

[0063] The accompanying drawings are only used to illustrate the principles, implementation methods, applications, features, and effects of specific embodiments of this application and other related content, and should not be considered as limitations on this application.

[0064] In the accompanying drawings of the instruction manual:

[0065] Figure 1 A flowchart illustrating the steps of a collaborative optimization scheduling method for a toilet paper production line provided in this application embodiment;

[0066] Figure 2A block diagram of a collaborative optimization scheduling system for a toilet paper production line provided in this application embodiment;

[0067] The reference numerals used in the above figures are explained as follows:

[0068] 1. Digital twin construction module;

[0069] 2. Time-series graph neural network module;

[0070] 3. Multi-scale optimization scheduling engine module;

[0071] 4. Closed-loop calibration module. Detailed Implementation

[0072] To illustrate the possible application scenarios, technical principles, implementable specific solutions, and achievable objectives and effects of this application in detail, the following description, in conjunction with the listed specific embodiments and accompanying drawings, provides a detailed explanation. The embodiments described herein are merely illustrative of the technical solutions of this application and are therefore intended to limit the scope of protection of this application.

[0073] In this document, the term "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The term "embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment, nor does it specifically limit its independence or connection with other embodiments. In principle, in this application, as long as there are no technical contradictions or conflicts, the technical features mentioned in each embodiment can be combined in any way to form corresponding implementable technical solutions.

[0074] Unless otherwise defined, the technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the use of related terms herein is merely for the purpose of describing particular embodiments and is not intended to limit this application.

[0075] In the description of this application, the term "and / or" is used to describe the logical relationship between objects, indicating that three relationships can exist. For example, X and / or Y means: X exists, Y exists, and X and Y exist simultaneously. Additionally, the character " / " in this document generally indicates that the preceding and following objects have an "or" logical relationship.

[0076] In this application, terms such as “first” and “second” are used only to distinguish one entity or operation from another, and do not necessarily require or imply any actual quantity, hierarchy or order relationship between these entities or operations.

[0077] Unless otherwise specified, the use of terms such as “comprising,” “including,” “having,” or other similar expressions in this application is intended to cover non-exclusive inclusion, which does not exclude the presence of additional elements in a process, method, or product that includes the stated elements, such that a process, method, or product that includes a list of elements may include not only those defined elements but also other elements not expressly listed, or elements inherent to such a process, method, or product.

[0078] In this application, expressions such as "greater than", "less than", and "exceeding" are understood to exclude the stated number; expressions such as "above", "below", and "within" are understood to include the stated number. Furthermore, in the description of the embodiments of this application, "multiple" means two or more (including two), and similar expressions related to "multiple" are also understood in this way, such as "multiple groups" and "multiple times", unless otherwise explicitly specified.

[0079] In the description of the embodiments of this application, the space-related expressions used, such as "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "vertical," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," indicate the orientation or positional relationship based on the orientation or positional relationship shown in the specific embodiments or drawings. They are only for the purpose of describing the specific embodiments of this application or for the reader's understanding, and do not indicate or imply that the device or component referred to must have a specific position, a specific orientation, or be constructed or operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application.

[0080] Unless otherwise expressly specified or limited, the terms "installation," "connection," "linking," "fixing," and "setting," as used in the description of the embodiments of this application, should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral setting; it can be a mechanical connection, an electrical connection, or a communication connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal connection of two components or the interaction between two components. For those skilled in the art to which this application pertains, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.

[0081] Example 1

[0082] like Figure 1As shown, this embodiment deploys the collaborative optimization scheduling method and system for a toilet paper production line on a TAD (hot air penetration dryer) production line of a large-scale toilet paper manufacturing enterprise. The production line includes: a headbox, forming wire section, press section, TAD drying section, creping doctor blade, and winding machine. The original scheduling method for the production line was a decentralized setting based on manual experience, with the steam temperature in the drying section manually adjusted by operators based on experience, resulting in large fluctuations in product quality and high steam consumption per ton of paper.

[0083] The system of this embodiment is deployed on an enterprise edge computing server, establishing data connections with the field DCS (Distributed Control System), MES (Manufacturing Execution System), and online quality inspection system via OPC UA (Open Platform Unified Communication Architecture, an industrial automation communication protocol). Online inspection equipment includes: an infrared moisture meter (installed at the outlet of the pressing section and the outlet of the TAD drying section), a laser thickness gauge, an online tensile strength tester, and temperature, pressure, and flow sensors deployed at various key nodes.

[0084] The system continuously collects the following data with a sampling period of 10 seconds:

[0085] Headbox: Slurry concentration (%), slurry flow rate (m) 3 / h), Internet speed (m / min);

[0086] Forming mesh section: Vacuum degree (kPa), paper wet strength index (N·m / g);

[0087] Pressing section: Linear pressure (kN / m), felt moisture content (%), Dryness of exported paper sheets (%)

[0088] TAD Drying Section: Steam Temperature (°C), air supply rate (m / s), exhaust velocity (m / s), outlet moisture content (%)

[0089] Final product: Tensile index (N·m / g), softness (Dimensionless rating), whiteness (%ISO).

[0090] Historical data from the past 6 months was collected as the initial training set, totaling approximately 1.55 million records (10 seconds / record).

[0091] First, imagine the production line as a "relationship diagram." Each circle in the diagram represents a key process (called a "node"), and the arrows between the circles represent the direction of material flow (called "edges"). In this embodiment, four key process nodes are identified:

[0092] Node 1: Headbox; Node 2: Forming mesh section; Node 3: Press section; Node 4: TAD drying section;

[0093] The material flow direction is: 1→2→3→4, therefore a directed edge is established. .

[0094] Each node At time step eigenvectors This includes the process parameters and quality indicators corresponding to the above steps. For example, the feature vector of node 4 (TAD drying section) includes steam temperature, air supply rate, exhaust rate, and outlet moisture content.

[0095] Each edge It is given two important properties: one is the time delay parameter. (Unit: seconds) indicates how long it takes for a parameter change in the upstream process to affect the downstream process; the other is the attenuation factor. This indicates the degree to which the intensity of this effect decays over time. The initial value was estimated using a "step response experiment": a parameter in the upstream process was intentionally changed (e.g., a sudden increase in the pressing section's line pressure), and the response delay time of the downstream process was recorded. Experiments showed that after a change in the pressing section's line pressure, the moisture content at the TAD drying section outlet took approximately 25 seconds to begin changing; therefore, we set... Second.

[0096] The above is analogous to a production line where turning on a tap upstream doesn't immediately increase the water flow downstream; there's a delay. This "delay" is called "time lag." The time lag between different processes may vary; for example, it might take 25 seconds to go from the pressing section to the drying section, while it might only take 8 seconds from the forming section to the pressing section. This method allows the computer to automatically learn these time differences.

[0097] The node hidden state update employs a gated temporal graph convolutional network (GT-GCN). Layers, Nodes At time step Hidden state The updated formula is:

[0098] ;

[0099] in, : No. Layer graph convolution at time steps At that time, process node Hidden state vector ( (i.e., node feature vectors). : Gated loop unit function, used to fuse the current aggregated information with the hidden state of the previous time step, to capture temporal dependencies; All pointer nodes The set of upstream neighbor nodes; :node The degree (in-degree or out-degree, when using symmetric normalization, take the square root of the product); : No. The learnable weight matrix of the layer is used to perform linear transformations on the concatenated features; Vector concatenation operator; From upstream node To the current node time delay parameters The hidden state of the corresponding historical time step (obtained from the discrete sampling sequence through linear interpolation); Learnable time delay parameters, representing the nodes State changes affect nodes The time delay required for the effect to occur (in seconds).

[0100] The purpose of the above update formula is to allow each process, when considering its current action, to see not only the current state of the upstream process, but also its state before the time delay. GRU stores important past information within it.

[0101] GT-GCN consists of three layers of graph convolutions, each followed by a GRU. The hidden state dimension is set to 128. After 150 training epochs, the model's root mean square error (RMSE) for predicting the moisture content at the TAD drying section outlet reaches 0.12%, which is much more accurate than the conventional GCN (graph convolutional network, RMSE=0.31%) without considering time delay.

[0102] During system operation, recursive least squares (RLS, an online parameter estimation algorithm) is used to update time delay parameters online. For edges... Actual response delay time The RLS update formula is obtained through sliding window cross-correlation analysis.

[0103] ;

[0104] in, : No. The Kalman gain vector is updated next time; : No. The updated covariance matrix; : Regression vector, taking the difference between the current state and historical states (e.g. ); Forgetting factor, range of values In this embodiment, we take This is used to gradually diminish the impact of old data; : Transpose of the regression vector; : No. The time delay parameters after the next update (edge) (corresponding learnable parameters) : No. The time delay parameters after the next update; : Actual response delay time (observed value) obtained through sliding window cross-correlation analysis; : The identity matrix, with the same dimensions as the covariance matrix.

[0105] The purpose of the RLS update formula described above is to allow the system time delay to change with varying production conditions. For example, when the quality of the raw material slurry changes (such as the fibers becoming coarser), the rate of water transfer will change, and a delay that originally required 25 seconds may become 28 seconds. RLS can continuously fine-tune the time delay parameters in the model based on the actual measured response time. This is similar to using navigation software; if it finds that the actual journey took 5 minutes longer than expected, the navigation will automatically update its time estimate for that route.

[0106] In actual operation, when the freeness of the raw material slurry changes abruptly, the effective time delay from the pressing section to the drying section changes from 25 seconds to 28 seconds. The RLS algorithm completes parameter convergence within 3 scheduling cycles (about 90 seconds).

[0107] In the global optimization layer, an improved Sparrow Search Algorithm (ESSA, an intelligent optimization algorithm that mimics the foraging behavior of sparrows) is used to iteratively optimize the global state vector output by the temporal graph neural network. Algorithm parameter settings: Population size Maximum number of iterations The proportion of discoverers is 20%, and the proportion of scouts is initially 10%.

[0108] The sparrow search algorithm simulates the process of a flock of sparrows searching for food. There are three roles in the population: discoverers (who find the direction to food), joiners (who follow the discoverers), and scouts (responsible for warning of danger). Discoverers guide the flock to areas where food might be found, joiners follow the discoverers, and scouts sound an alarm if they detect danger (such as encountering adverse production conditions), prompting the flock to leave their current location. Our "improvements" are mainly reflected in three aspects: adaptive adjustment (determining whether to expand or refine the search based on the population's convergence), time delay compensation (considering future effects when selecting the optimal solution), and dynamic warning (adjusting the proportion of scouts based on the severity of production disturbances).

[0109] Discoverer location update (incorporating population fitness entropy adjustment), as detailed below:

[0110] ;

[0111] in, : No. The first generation of the population Only sparrows in the first The position value of the dimension; : No. The middle generation Only sparrows in the first Dimensional position value; Step size control parameter, is Uniformly distributed random numbers within the interval; : Natural exponential function; : Index of individual sparrows (sorted by fitness, with individuals having higher fitness) (smaller) : Scaling factor, used to control the degree to which the entropy value adjusts the step size. In this embodiment, it is taken as... ; : No. The information entropy of the fitness of a generation is calculated using the following formula: ,in For fitness to fall into the first The probability of each interval ( A large entropy value indicates a dispersed population, while a small entropy value indicates a convergent population. : Maximum number of iterations, taken in this embodiment ; : No. The globally optimal sparrow in the first place The position of the dimension; Warning value (i.e., the warning threshold randomly generated in the current generation). ; The safety threshold (i.e., the upper limit of the warning threshold) is initially set in this embodiment. And adjust dynamically according to the level of disturbance; Random numbers that follow a normal distribution; :one A matrix of all 1s ( (The dimension of the solution space).

[0112] In this formula, when When (environmentally safe), the discoverer moves towards the globally optimal position according to a formula adjusted for entropy; when When danger is detected, the discoverer randomly moves to other areas to explore. When evaluating the fitness of candidate solutions, the time-delay influence coefficient output by the time-series graph neural network is used. Phase lead correction is performed every second:

[0113] ;

[0114] in, The fitness evaluation value, adjusted for time lag compensation, is used to replace the original fitness value. Comparison of superiority and inferiority in the process of population evolution; The original fitness function is used to evaluate candidate scheduling schemes. Real-time performance at the current moment (such as indicators of overall production costs and product quality); Candidate solution vectors correspond to a set of process parameter settings or intermediate quality index target values; The time-delay lead compensation operator indicates that candidate solutions will be... Projecting the current parameter value forward Time, simulating its actual effects at future moments (e.g., the future output response trajectory predicted by a time-series neural network). : Time delay effect coefficient (unit: seconds), learned from the directed edges between processes by the time sequence graph neural network, reflects the delay time required for changes in upstream parameters to be transmitted to downstream results.

[0115] Conventional optimization algorithms only evaluate the immediate effect of current settings. However, considering the time lag issue—the effects of current parameter adjustments take 25 seconds to materialize—we perform a future performance preview of candidate solutions, predicting the actual quality metrics produced by the current parameters 25 seconds from now.

[0116] Joiner location update (with time-lag compensation guidance), details are as follows:

[0117] ;

[0118] in, : No. The middle generation Only those who join the sparrow in the first Dimensional position value; Random numbers that follow a normal distribution; : Natural exponential function; : No. The worst sparrow in the whole world is in Dimensional position value; : No. The middle generation Only sparrows in the first Dimensional position value; : Index of individual sparrows (sorted by fitness, with individuals having higher fitness) (smaller) Population size, in this embodiment, is taken as... ; : No. The globally optimal sparrow in the first place Dimensional position value; Random number, range of values Control the step size to move closer to the optimal individual; : No. The discoverer (facilitator) randomly selected in the generation is in the first... Dimensional position value; The time delay compensation coefficient is used to adjust the compensation intensity; in this embodiment, it is taken as... ; The hyperbolic tangent function compresses the input value to... interval; : No. The maximum time delay impact coefficient (unit: seconds) on the process path where the sparrow is located is provided by the time sequence graph neural network.

[0119] In the formula, when When this occurs, it indicates that less adaptable participants need to move extensively to find new food sources; when At this time, it indicates that the more fit participants move closer to the discoverer and utilize the time lag compensation factor. Adjust the direction of movement in advance to compensate for the effects of time lag.

[0120] The dynamic ratio of scouts and the warning threshold are as follows:

[0121] The proportion of scouts and the early warning threshold are based on the real-time disturbance intensity. Dynamic adjustment:

[0122] ;

[0123] in, : No. The proportion of scouts in the total population of a generation; The current disturbance strength is obtained by normalizing the standard deviation of the predicted residual sequence in the closed-loop calibration module, and its value range is [range missing]. ; The maximum reference value for disturbance intensity is usually set based on the disturbance statistics of historical production data. In this embodiment, the maximum observed residual standard deviation is taken. The minimum basic ratio of scouts, that is, the proportion of scouts under normal circumstances; In The maximum percentage of scouts corresponds to the percentage of scouts when the disturbance intensity reaches its maximum. : No. The safety threshold (early warning threshold upper limit) of the generation, the initial baseline value is ; The baseline value for the safety threshold; The maximum adjustment range of the safety threshold; when the disturbance is strongest, the threshold decreases to [a certain value]. .

[0124] The purpose of this formula is to address situations where significant disturbances occur in the production line (such as sudden changes in raw material batches or equipment malfunctions). When the disturbance is increased, the system automatically increases the proportion of scouts (up to 20%) and lowers the safety threshold (down to 0.4), making the search algorithm more inclined to global exploration rather than local development, thus adapting to changing working conditions; when the disturbance is weakened, the parameters return to normal levels to ensure the convergence efficiency of the algorithm.

[0125] When a major disturbance occurs in the production line (such as a sudden deterioration in raw materials), the system will automatically become alert—increasing the number of scouts (from a maximum of 10% to 20%) and lowering the safety threshold (from 0.6 to 0.4), so that the algorithm will more actively explore new parameter spaces.

[0126] After 160 iterations, the algorithm converged and output the global optimization result, specifically the target dryness at the outlet of the pressing section. Target moisture content at the outlet of the TAD drying section .

[0127] For the TAD drying section, a TCN (Temporal Convolutional Network, a neural network specifically designed for processing time-series data) model is constructed to predict future output response trajectories. The TCN employs dilated causal convolution, and its output... Defined as:

[0128] ;

[0129] in, Dilated causal convolution at time step The output value; The size of the convolution kernel (i.e., the length of the convolution window) is taken in this embodiment. ; The first convolution kernel Weight coefficients for each position (learnable parameters); : The input sequence located at time step The value at that point (i.e., the signal value at a historical moment); The dilation rate controls the sampling interval of the convolution kernel. In this embodiment, it increases exponentially with the number of network layers: Layer 1 , second floor , third floor , 4th floor ; : Current time step index; : Position index within the convolution kernel, range of values .

[0130] The core feature of this formula is its use of the expansion coefficient. It enables sparse sampling of long historical sequences, thereby exponentially expanding the receptive field without increasing the kernel size, allowing TCN to efficiently capture long-term dependencies.

[0131] Residual block structure: ;

[0132] in, : The output tensor of the residual block (i.e., the feature map after residual connection and activation function processing); The rectified linear unit (RCU) activation function is defined as follows: This is used to introduce nonlinearity and alleviate the gradient vanishing problem; : The input tensor of the residual block (i.e., the output feature of the previous layer); The residual function represents the expression of the input... The nonlinear transformation performed. In this embodiment, It includes two dilated causal convolutions, weight normalization, and Dropout operations; : Element-wise addition operation (residual join), which adds the input element by element. With the transformed Direct addition helps gradient flow and alleviates the degradation problem of deep networks.

[0133] This formula is the core structure of Deep Residual Networks (ResNet). Using residual blocks in TCN can build deeper networks and improve the ability to extract features from long-term sequences.

[0134] TCN Input: Recent The sequence of process parameters for each time step (i.e., the past 600 seconds). And a series of intermediate quality indicators (inlet paper dryness, current outlet moisture content). Output: Future The predicted trajectory of outlet moisture content at each time step (i.e., the next 120 seconds). .

[0135] Based on various data (steam temperature, wind speed, current moisture content, etc.), TCN predicts how the moisture content of the exported paper will change within the next 2 minutes. The special design of dilatational causal convolution allows it to "see further".

[0136] Each scheduling cycle (30 seconds) solves the following optimization problem:

[0137] ;

[0138] in, : Optimize decision variables, representing the increments of steam temperature, air supply rate, and exhaust rate (all scalars); Cost function value (scalar), the optimization objective is to minimize this value; Temporal Convolutional Networks (TCNs) predict the future... The moisture content at the outlet of the step (dimensionless, usually expressed as a percentage); The target moisture content at the outlet is given by the global optimization layer (5.2% in this embodiment). The weighting coefficient for moisture content tracking error is taken in this embodiment. ; The change in steam temperature between two adjacent time steps (unit: °C) is used to penalize the severity of the control action. Change in air supply rate (unit: m / s); : Change in exhaust velocity (unit: m / s); : Penalty weighting coefficients corresponding to changes in steam temperature, air supply rate, and exhaust rate, respectively. In this embodiment, we take... ; : Predict the time step index within the time domain, where the current time step is , the future No. The predicted value of the step corresponds to ; : Length of the predicted time domain Steps (10 seconds per step, 120 seconds total), summation symbol This indicates that the prediction error over the next 12 steps is accumulated; : The length of the control time domain (usually equal to the prediction time domain minus 1), summation sign This indicates that the control increment from the current step to the 11th future step is accumulated.

[0139] After solving this optimization problem and obtaining the optimal control increment sequence, only the first value (e.g.) is executed. ), The calculation is repeated in the next cycle to achieve rolling optimization.

[0140] MPC acts like a "visionary driving strategy." It doesn't just consider how to adjust the steam temperature in the current step, but plans every adjustment step over the next two minutes. The first term of the formula requires the moisture content to be as close as possible to the target value (5.2%), while subsequent terms require that adjustments not be too drastic (avoiding frequent fluctuations). It recalculates every 30 seconds, ensuring both adherence to the target value and prevention of system oscillations.

[0141] Because there is a pure time lag of approximately 15 seconds between the steam regulating valve and the temperature sensor, using the MPC alone may result in overshoot. Therefore, a time lag compensator should be added.

[0142] ;

[0143] in, The steam temperature setpoint (unit: °C) after time delay compensation correction will be sent to the production line management system for execution. The optimal steam temperature increment obtained by the rolling time-domain optimizer (MPC) corresponds to the current temperature value (unit: °C). ; : Compensation gain coefficient, used to adjust the compensation intensity. In this embodiment, it is taken as... ; The future predicted by Temporal Convolutional Networks (TCNs) Moisture content at the outlet after seconds (dimensionless, usually expressed as a percentage); The estimated pure time lag (in seconds) represents the delay between the action of the actuator (steam regulating valve) and the response of the sensor (temperature / moisture content). In this embodiment, it is taken as... Second; : The actual measured moisture content at the outlet at the current moment (collected in real time by an infrared moisture content meter).

[0144] The function of this formula is to predict the future in advance using TCN. The moisture content deviation after a few seconds is calculated, and the current temperature setpoint is adjusted in advance based on this deviation to compensate for the response delay between the actuator and the sensor and reduce adjustment overshoot.

[0145] This time delay compensator uses TCN to predict the moisture content 15 seconds later, to determine in advance whether the current action will go too far, and then makes corrections in advance.

[0146] The internal moisture content distribution of the paper sheet cannot be directly measured online; therefore, an extended Kalman filter (EKF, a recursive algorithm for estimating system states from noisy measurement data) is used for estimation. System state vector. ,in Surface moisture content, The moisture content of the core layer. For paper temperature, For thickness. Measurement vector. .

[0147] The state transition equation (based on the drying kinetics mechanism) is as follows:

[0148] ;

[0149] ;

[0150] ;

[0151] in, : No. Paper surface moisture content (%) at discrete time steps; : No. Moisture content (%) of the core layer (interior) of the paper sheet at discrete time steps; : No. Paper temperature (°C) at each discrete time step; Discretization time step (10 seconds in this embodiment); Mass transfer factor (kg / (m)) 2 •s) represents the rate at which moisture evaporates from the paper surface into the air; Heat and mass transfer area (m²) 2 ), usually refers to the surface area of ​​the paper sheet in contact with hot air; : The oven-dry weight of the paper sheet (kg); Vapor concentration at the paper surface (kg / m³) 3 The moisture content of the surface is determined by the temperature. Vapor concentration in ambient air (kg / m³) 3 The humidity level is determined by the humidity inside the air hood of the drying section; : Process noise term, characterizing the uncertainty and unmodeled dynamics of the model, assumed to be zero-mean white noise; Effective moisture diffusion coefficient (m) 2 / s), describing the ability of moisture to diffuse within the paper sheet; Moisture content along the thickness direction of the paper sheet The second spatial derivative is used to calculate the internal water diffusion flux; : Convective heat transfer coefficient (W / (m) 2·K)), characterizing the heat exchange efficiency between hot air and paper; Total mass of the paper sheet (including moisture and fiber, kg); Specific heat capacity of paper (J / (kg·K)), usually taken as the weighted average of fiber and water; Temperature of hot air in the drying section (°C);

[0152] The measurement equation is as follows:

[0153] ;

[0154] ;

[0155] in, : Outlet moisture content (%) measured by an online infrared moisture meter; : Empirical weighting coefficient, representing the proportion of surface moisture content and internal moisture content to the total measured value; : Measurement noise term, characterizing the measurement error of the sensor, assumed to be zero-mean white noise;

[0156] EKF recursion includes two steps: prediction and update. The specific formula is as follows:

[0157] predict:

[0158] ;

[0159] ;

[0160] renew:

[0161] ;

[0162] ;

[0163] ;

[0164] in, :according to The posterior estimate at time 1, the predicted value Time-state vector (prior estimate); : Posterior state estimate at time (with fused measurements); : Nonlinear state transition function, i.e., the vector form of the above state transition equations; : Control input vectors at any time (such as scheduling commands for steam temperature, air supply rate, etc.); The prior estimation error covariance matrix measures the uncertainty of the predicted state. The posterior estimation error covariance matrix of the previous time step; State transition function For the state vector The Jacobian matrix, in Calculation at the point (used for linearization); : Process noise covariance matrix, and The statistical characteristics correspond to; Kalman gain matrix, used to weigh the weights between prediction and measurement; Measurement function For the state vector The Jacobian matrix, in Calculation at point; : Measure the noise covariance matrix, and The statistical characteristics correspond to; : Actual measurement vector at time ; : Nonlinear measurement function, i.e., the vector form of the above measurement equations; : Posterior state estimation at time (the final result after fusing prediction and measurement); : Posterior estimation error covariance matrix; : Identity matrix, with the same dimensions as the state vector.

[0165] Since it's impossible to directly measure whether the inside of the paper is dry or wet, only the surface can be measured. The state observer combines a physical model with surface measurements to deduce the moisture content distribution inside the paper. EKF is a recursive algorithm specifically designed to handle noisy data; it updates its estimate of the internal state each time a new measurement is obtained.

[0166] The observer estimated the internal water content distribution non-uniformity (in terms of...) The absolute value representation is injected into the cost function of the rolling time-domain optimization, forming the augmented cost:

[0167] ;

[0168] in, The augmented cost function value serves as the new objective function in rolling time-domain optimization. : The cost function value of the original rolling time domain optimization (including moisture content tracking error and control increment penalty term); The weighting coefficient for the internal moisture content uniformity penalty term is taken in this embodiment. ; : Estimated surface moisture content of paper sheet (%) by the state observer; : Estimated moisture content (%) of the core (internal) layer of the paper sheet as determined by the state observer.

[0169] The augmented cost treats the unevenness of moisture content within the paper sheet as a penalty, guiding the optimizer to consider both surface and internal drying consistency in scheduling decisions.

[0170] This augmentation cost tells the optimizer that it must not only achieve the target surface moisture content, but also ensure that the moisture content inside and on the surface is as consistent as possible (i.e., uniform drying). This forces the system to actively adjust the supply and exhaust air distribution to improve uniformity. Experiments show that after this treatment, the moisture content deviation of the finished paper horizontal width decreased from 2.1% to 0.9%.

[0171] The closed-loop calibration module includes a perturbation classifier based on SVM (Support Vector Machine, a supervised learning classification model). It acquires the predicted residual sequence in real time. ,in, Time step The prediction residual (i.e., the deviation between the model prediction and the actual measurement). Actual measured values ​​(such as sensor readings for outlet moisture content, steam temperature, etc.); The predicted output of the digital twin model (hybrid model) for the same variable. This residual is used for feature extraction of the perturbation classifier and for triggering closed-loop calibration.

[0172] Extract the following statistical features to construct the feature vector. Mean Standard deviation ; skewness ; kurtosis Autocorrelation coefficient ;

[0173] The RBF kernel function (Radial Basis Kernel Function) is used. , .

[0174] in, Radial basis function kernel value, representing two eigenvectors and Similarity between (range of values) ); : Statistical characteristic vectors of the residual sequence (such as mean, standard deviation, skewness, kurtosis, autocorrelation coefficient, etc.); : The squared Euclidean distance between two eigenvectors; The bandwidth parameter of the kernel function controls the rate at which similarity decays with distance. In this embodiment, we take... This kernel function is used by Support Vector Machines (SVMs) to classify perturbation types.

[0175] Three "one-to-many" SVM classifiers were trained to identify three types of disturbances: raw material batch fluctuations, equipment performance degradation, and environmental temperature and humidity drift.

[0176] The system constantly compares the "model-predicted value" with the "actually measured value" and calculates the difference (residual). Different types of disturbances will produce different patterns of residuals: for example, changes in raw materials will cause the residuals to drift slowly, while equipment failure will cause the residuals to oscillate violently. The classifier determines the category by analyzing the statistical characteristics of the residuals (mean, degree of fluctuation, degree of skewness, sharpness, etc.).

[0177] When the classifier identifies "raw material batch fluctuations," the system triggers a local online update of the relevant parameters for node 1 (headbox) in the time-series neural network, using recursive least squares to correct the time delay parameters. When "equipment performance degradation" (such as scaling in the drying cylinder) is identified, the data-driven model in the digital twin model is retrained (using data from the last 7 days). When "ambient temperature and humidity drift" is identified, only the fusion weights of the hybrid model are adjusted. Instead of retraining the model.

[0178] In other words, raw material fluctuations only affect upstream parameters, so only upstream nodes need to be updated; equipment aging requires retraining the entire data model; environmental changes have a smaller impact, requiring only minor adjustments to the weights between the mechanistic model and the data model. This avoids the need for extensive retraining of all models for every disturbance, significantly saving computational resources. This method reduces the computational load of online calibration by approximately 62%, while ensuring that the model's prediction accuracy remains below RMSE < 0.15% over the long term.

[0179] The fusion unit in the digital twin building block dynamically adjusts the weights of the mechanistic model and the data-driven model. Hybrid model output:

[0180] ;

[0181] in, : Hybrid model at time step The final predicted output (e.g., outlet moisture content); The fusion weights of the mechanistic model, and their value range. It is dynamically updated by an adaptive algorithm; Models based on process mechanisms (such as drying kinetic equations). For the input feature vector, For mechanistic model parameters; Data-driven models based on historical data (such as LSTM networks). These are the network weights and biases obtained during training. This formula achieves a weighted fusion of the mechanistic model and the data-driven model, improving prediction accuracy and robustness.

[0182] Fusion weights Updated dynamically based on recent prediction errors:

[0183] ;in, The mechanistic model fusion weights for the current time step;

[0184] The Sigmoid function is defined as follows: Compress the input to interval;

[0185] : These correspond to the error weight coefficients of the mechanistic model and the data-driven model, respectively. In this embodiment, we take... ; The mean absolute percentage error (MAS) of the mechanistic model in the previous scheduling period is calculated using the following formula: ; : The average absolute percentage error of the data-driven model in the previous scheduling period; Bias term: A baseline value used to adjust the weights. In this embodiment, it is taken as... .

[0186] The formula dynamically adjusts the fusion weights based on the recent prediction errors of the two models: the model with the smaller error receives a higher weight, thus enabling the hybrid model to automatically adapt to changes in operating conditions.

[0187] It should be noted that this embodiment uses two models: one based on physicochemical principles (mechanistic model), which is stable but inaccurate under abnormal operating conditions; the other based on historical data learning (data-driven model), which is flexible but may overfit. The fusion unit compares the recent prediction errors of the two models: the one with smaller error has a larger weight. During normal operation, the mechanistic model has a higher weight ( Approximately 0.7~0.8); when raw material anomalies cause the mechanistic model to fail, the data-driven model automatically takes over the leading role. (Reduced to 0.3~0.5).

[0188] All the above modules were integrated and deployed, and run continuously for three months. Data from October to December 2025 was compared with the same period of the previous year (traditional manual scheduling), and the results are shown in Table 1 below:

[0189] Table 1

[0190]

[0191] It is particularly noteworthy that during the rainy season when raw material prices fluctuate frequently, traditional scheduling methods result in half-hour quality fluctuations with each raw material change. However, this embodiment, through time-delay perception optimization and real-time calibration, can proactively adjust upstream parameters before downstream quality issues arise, achieving preventative scheduling. This leap from passive response to proactive prediction is something no single technology can achieve. This unexpected technological effect gives this embodiment an irreplaceable advantage in continuous industrial production processes with significant time delays.

[0192] Example 2

[0193] like Figure 2 As shown, this application provides a collaborative optimization scheduling system for a toilet paper production line, used to execute a collaborative optimization scheduling method for a toilet paper production line, including:

[0194] Digital Twin Building Module 1 is used to build and maintain a hybrid digital twin model that includes a mechanistic model and a data-driven model;

[0195] The temporal graph neural network module 2 is used to build a dynamic coupling model of processes, learn and store the time delay influence coefficients between processes, and provide process association knowledge for scheduling decisions;

[0196] The multi-scale optimization scheduling engine module 3 is used to execute the improved sparrow search algorithm, the rolling temporal optimization strategy, and the time-series convolutional network calculation to generate the process parameter scheduling settings for each process.

[0197] The closed-loop calibration module 4 is used to correct the digital twin data model, time-series neural network and optimized scheduling parameters online based on real-time production feedback data, so as to realize the adaptive evolution of the scheduling system.

[0198] As one implementation of this embodiment, the time-series graph neural network module further includes:

[0199] The graph structure storage unit is used to store process nodes, directed edges, and edge time delay parameters;

[0200] The spatiotemporal convolution computation unit is used to perform gated temporal graph convolution operations and output the predicted state of each node and the global state vector.

[0201] The time-delay parameter adaptive unit is used to execute the recursive least squares algorithm to update the time-delay parameter online.

[0202] As one implementation of this embodiment, the multi-scale optimization scheduling engine module further includes:

[0203] The global optimization unit, which incorporates the improved sparrow search algorithm, takes the global state vector output by the time-series neural network module as input and outputs the intermediate quality index target values ​​for each process.

[0204] The local optimization unit, which incorporates the temporal convolutional network and the rolling temporal optimizer, outputs the process parameter scheduling settings for each process, constrained by the target value output by the global optimization unit.

[0205] The time delay compensator is used to perform phase advance correction on the process parameter scheduling setting value output by the local optimization unit according to the time delay influence coefficient provided by the timing diagram neural network module, to compensate for the response delay between the actuator and the sensor, and to improve the execution effect of the scheduling command.

[0206] As one implementation of this embodiment, the multi-scale optimization scheduling engine module further includes a state observer, which is used for:

[0207] Based on the hybrid model provided by the digital twin modeling module, intermediate state variables that cannot be directly measured are estimated. These intermediate state variables include at least the moisture content distribution inside the paper sheet and the fiber orientation degree.

[0208] The estimated intermediate state variables are used as feedback variables and injected into the cost function of the rolling time-domain optimizer to enhance the scheduling decision's ability to control the internal state.

[0209] As one implementation of this embodiment, the closed-loop calibration module further includes a disturbance classifier, which is used for:

[0210] Real-time collection of the residual sequence between the actual production feedback data and the predicted values ​​of the digital twin data model;

[0211] The statistical characteristics of the residual sequence are classified using support vector machines to identify the types of disturbances, including raw material batch fluctuations, equipment performance degradation, and environmental temperature and humidity drift.

[0212] Based on the identified disturbance type, the parameters of the digital twin modeling module, the time-series graph neural network module, or the multi-scale optimization scheduling engine module are selectively triggered to achieve differentiated model calibration and reduce the system's computational load.

[0213] Those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of this application and form different embodiments. For example, in the claims, any of the claimed embodiments can be used in any combination.

[0214] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and not to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application, and they should all be covered within the scope of the claims and specification of this application. In particular, as long as there is no structural conflict, the various technical features mentioned in the embodiments can be combined in any way. This application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A collaborative optimization scheduling method for a toilet paper production line, characterized in that, Includes the following steps: Step S1: Construct a digital twin data model of the toilet paper production line. The digital twin data model includes a mechanism model based on the process mechanism and a data-driven model based on historical production data. A hybrid prediction model is generated through an adaptive weighted fusion algorithm to simulate and predict quality indicators and cost data in the production process. Step S2: Construct a process dynamic coupling model based on a time-series graph neural network. The time-series graph neural network uses the time series of real-time operating parameters of each process as node features and the material and energy transfer relationship between processes as edges. It learns the time-varying coupling characteristics and time delay influence coefficients between processes and outputs a global state vector for scheduling decisions. Step S3: Construct a multi-scale collaborative optimization scheduling framework, which includes a global optimization layer and a local optimization layer. The global optimization layer aims at the final product quality index and the overall production cost, and uses an improved sparrow search algorithm to iteratively optimize the global state vector output by the time-series graph neural network to generate intermediate quality index target values ​​for each process. The local optimization layer uses the intermediate quality index target values ​​as constraints and adopts a rolling time-domain optimization strategy and a time-series convolutional network to generate process parameter scheduling settings for each process. Step S4: The process parameter scheduling setting value is issued as a production scheduling instruction to the production line management system for execution, and the digital twin data model, the time sequence neural network and the optimization scheduling framework are calibrated in a closed loop based on the actual production feedback data to continuously optimize subsequent scheduling decisions.

2. The collaborative optimization scheduling method for a toilet paper production line according to claim 1, characterized in that, The construction of the process dynamic coupling model based on the time sequence graph neural network in step S2 further includes: Step S21: Define each process in the production line as a graph node. The node feature vector is multi-dimensional time series data within a predetermined time window. The multi-dimensional time series data includes at least the inlet material attributes, process parameter set values, and measured values ​​of intermediate quality indicators for that process. Step S22: Define directed edges according to the material flow direction and energy transfer relationship, and assign a learnable time delay parameter vector to each edge. The time delay parameter vector is used to characterize the time delay and attenuation characteristics of the impact of the state change of the upstream process node on the downstream process node. Step S23: A gated temporal graph convolutional network is used to perform spatiotemporal aggregation of node features. At each time step, the update of the hidden state of a node depends on both the current state of its neighboring nodes and the historical state after time delay, thereby capturing the dynamic coupling and time delay effect between processes and providing accurate process association information for scheduling decisions.

3. The collaborative optimization scheduling method for a toilet paper production line according to claim 1, characterized in that, The improved sparrow search algorithm in step S3 specifically includes: Based on the standard sparrow search algorithm, this paper introduces the adaptive crossover operation and elite retention mechanism from the genetic algorithm, where: The discovery location update formula incorporates the entropy value of population fitness as a regulating factor to dynamically balance global exploration and local exploitation; The location update of the joiner adopts a guidance strategy with time delay compensation, that is, the time delay influence coefficient output by the time sequence graph neural network is used to perform phase advance correction on the foraging direction provided by the discoverer. The proportion of scouts and the early warning threshold are dynamically adjusted according to the current disturbance level of the production line, so that the scheduling scheme can adapt to production fluctuations.

4. The collaborative optimization scheduling method for a toilet paper production line according to claim 1, characterized in that, The combination of the rolling temporal optimization strategy and the temporal convolutional network in step S3 is as follows: In each scheduling cycle, the temporal convolutional network takes the historical process parameter sequence and intermediate quality index sequence of the previous L time steps as input to predict the process output response trajectory of the next H time steps; The rolling temporal optimizer uses the predicted output of the temporal convolutional network as the prediction model of the local cost function and the intermediate quality index target value given by the global optimization layer as the reference trajectory to solve the optimal process parameter adjustment amount within the current scheduling cycle. The first scheduling control variable obtained from the solution is immediately issued for execution. In the next cycle sliding time window, the above process is repeated to achieve rolling scheduling optimization.

5. The collaborative optimization scheduling method for a toilet paper production line according to claim 1, characterized in that, The closed-loop calibration further includes online identification and correction of the time delay parameters of the time-series graph neural network: Collect actual production feedback data and calculate the actual response delay time between each process. The actual response delay time is compared with the current learnable time delay parameter in the time sequence graph neural network; The recursive least squares algorithm is used to update the time delay parameters online, so that the time series graph neural network model can continuously approximate the real dynamic coupling relationship and ensure the long-term accuracy of the scheduling decision model.

6. A collaborative optimization scheduling system for a toilet paper production line, used to execute the collaborative optimization scheduling method for a toilet paper production line according to any one of claims 1 to 5, characterized in that, include: The digital twin modeling module is used to build and maintain a hybrid digital twin data model that includes mechanistic models and data-driven models. The temporal graph neural network module is used to build a dynamic coupling model of processes, learn and store the time delay influence coefficients between processes, and provide process correlation knowledge for scheduling decisions; The multi-scale optimization scheduling engine module is used to execute the improved sparrow search algorithm, the rolling temporal optimization strategy, and the time-series convolutional network calculation to generate the process parameter scheduling settings for each process. The closed-loop calibration module is used to correct the digital twin data model, time-series neural network, and optimized scheduling parameters online based on real-time production feedback data, so as to realize the adaptive evolution of the scheduling system.

7. The collaborative optimization scheduling system for a toilet paper production line according to claim 6, characterized in that, The time-series graph neural network module further includes: The graph structure storage unit is used to store process nodes, directed edges, and edge time delay parameters; The spatiotemporal convolution computation unit is used to perform gated temporal graph convolution operations and output the predicted state of each node and the global state vector. The time-delay parameter adaptive unit is used to execute the recursive least squares algorithm to update the time-delay parameter online.

8. The collaborative optimization scheduling system for a toilet paper production line according to claim 6, characterized in that, The multi-scale optimization scheduling engine module further includes: The global optimization unit, which incorporates the improved sparrow search algorithm, takes the global state vector output by the time-series neural network module as input and outputs the intermediate quality index target values ​​for each process. The local optimization unit, which incorporates the temporal convolutional network and the rolling temporal optimizer, outputs the process parameter scheduling settings for each process, constrained by the target value output by the global optimization unit. The time delay compensator is used to perform phase advance correction on the process parameter scheduling setting value output by the local optimization unit according to the time delay influence coefficient provided by the timing diagram neural network module, to compensate for the response delay between the actuator and the sensor, and to improve the execution effect of the scheduling command.

9. The collaborative optimization scheduling system for a toilet paper production line according to claim 6, characterized in that, The multi-scale optimization scheduling engine module also includes a state observer, which is used for: Based on the hybrid model provided by the digital twin modeling module, intermediate state variables that cannot be directly measured are estimated. These intermediate state variables include at least the moisture content distribution inside the paper sheet and the fiber orientation degree. The estimated intermediate state variables are used as feedback variables and injected into the cost function of the rolling time-domain optimizer to enhance the scheduling decision's ability to control the internal state.

10. The collaborative optimization scheduling system for a toilet paper production line according to claim 6, characterized in that, The closed-loop calibration module further includes a perturbation classifier, which is used for: Real-time collection of the residual sequence between the actual production feedback data and the predicted values ​​of the digital twin data model; The statistical characteristics of the residual sequence are classified using support vector machines to identify the types of disturbances, including raw material batch fluctuations, equipment performance degradation, and environmental temperature and humidity drift. Based on the identified disturbance type, the parameters of the digital twin modeling module, the time-series graph neural network module, or the multi-scale optimization scheduling engine module are selectively triggered to achieve differentiated model calibration and reduce the system's computational load.

Images